Subgroups — C₃×#40588 #10659195

Order 768.

3218 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2819	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2815	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2703	C₂	1	2	yes	maximal, complemented
6	C₃×#2696	C₂	1	2	yes	maximal, complemented
7	C₃×#2673	C₂	1	2	yes	maximal, complemented
8	C₃×#2669	C₂	1	2	yes	maximal, complemented
9	C₃×#2639	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2631	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2631	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2617	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2615	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2535	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2412	C₂	1	2	yes	maximal, complemented
18	C₃×#2410	C₂	1	2	yes	maximal, complemented
19	C₃×#2404	C₂	1	2	yes	maximal, complemented
20	C₃×#2404	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2403	C₂	1	2	yes	maximal, complemented
22	C₂×C₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
24	#40588	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂²×C₃×#41	C₂²	1	1	yes	characteristic, complemented
27	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
28	C₂³×C₃×D₄	C₂²	1	2	yes	—
29	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×#546	—	2	8	no	—
31	C₃×#546	—	2	8	no	—
32	C₂×C₃×#127	C₂²	1	2	yes	complemented
33	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×#123	C₂²	1	1	yes	characteristic
36	C₂×C₃×#123	C₂²	1	2	yes	complemented
37	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×#121	C₂²	1	2	yes	complemented
43	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×#121	C₂²	1	2	yes	complemented
46	C₂×C₃×#121	C₂²	1	2	yes	complemented
47	C₂×C₃×#120	C₂²	1	2	yes	—
48	C₂×C₃×#120	C₂²	1	1	yes	characteristic
49	C₂×C₃×#120	C₂²	1	2	yes	—
50	C₂×C₃×#120	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×#120	C₂²	1	2	yes	complemented
52	C₂×C₃×#120	C₂²	1	2	yes	complemented
53	C₂×C₃×#120	C₂²	1	2	yes	complemented
54	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
55	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
58	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
60	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
61	C₃×#400	C₂²	1	2	yes	complemented
62	C₃×#397	C₂²	1	1	yes	characteristic, complemented
63	C₃×#397	C₂²	1	1	yes	characteristic, complemented
64	C₃×#397	C₂²	1	2	yes	complemented
65	C₃×#397	C₂²	1	1	yes	characteristic, complemented
66	C₃×#397	C₂²	1	1	yes	characteristic, complemented
67	C₃×#397	C₂²	1	2	yes	complemented
68	C₃×#394	C₂²	1	2	yes	complemented
69	C₃×#394	C₂²	1	2	yes	complemented
70	C₃×#394	C₂²	1	2	yes	complemented
71	C₃×#394	C₂²	1	2	yes	complemented
72	C₃×#394	C₂²	1	2	yes	complemented
73	C₃×#393	C₂²	1	1	yes	characteristic, complemented
74	C₃×#393	C₂²	1	2	yes	complemented
75	C₃×#393	C₂²	1	1	yes	characteristic, complemented
76	C₃×#393	C₂²	1	1	yes	characteristic, complemented
77	C₃×#393	C₂²	1	2	yes	complemented
78	C₃×#393	C₂²	1	1	yes	characteristic, complemented
79	C₃×#392	C₂²	1	1	yes	characteristic
80	C₃×#392	C₂²	1	1	yes	characteristic
81	C₃×#392	C₂²	1	2	yes	—
82	C₃×#392	C₂²	1	1	yes	characteristic, complemented
83	C₃×#392	C₂²	1	1	yes	characteristic, complemented
84	C₃×#392	C₂²	1	2	yes	complemented
85	C₃×#392	C₂²	1	1	yes	characteristic, complemented
86	C₃×#392	C₂²	1	2	yes	complemented
87	C₃×#392	C₂²	1	1	yes	characteristic, complemented
88	C₃×#392	C₂²	1	2	yes	complemented
89	C₃×#392	C₂²	1	1	yes	characteristic, complemented
90	C₃×#392	C₂²	1	2	yes	complemented
91	C₃×#392	C₂²	1	2	yes	complemented
92	C₃×#392	C₂²	1	2	yes	complemented
93	C₃×#392	C₂²	1	2	yes	complemented
94	C₃×#392	C₂²	1	2	yes	complemented
95	C₃×#392	C₂²	1	2	yes	complemented
96	C₃×#392	C₂²	1	1	yes	characteristic, complemented
97	C₃×#390	C₂²	1	2	yes	complemented
98	C₃×#388	C₂²	1	2	yes	complemented
99	C₃×#388	C₂²	1	2	yes	complemented
100	C₃×#388	C₂²	1	2	yes	complemented
101	C₃×#387	C₂²	1	2	yes	complemented
102	C₃×#386	C₂²	1	2	yes	—
103	C₃×#386	C₂²	1	2	yes	—
104	C₃×#386	C₂²	1	2	yes	complemented
105	C₃×#386	C₂²	1	2	yes	complemented
106	C₃×#386	C₂²	1	2	yes	complemented
107	C₃×#386	C₂²	1	2	yes	complemented
108	C₃×#386	C₂²	1	2	yes	complemented
109	C₃×#386	C₂²	1	2	yes	complemented
110	C₃×#386	C₂²	1	2	yes	complemented
111	C₃×#386	C₂²	1	2	yes	complemented
112	C₃×#386	C₂²	1	2	yes	complemented
113	C₃×#386	C₂²	1	2	yes	complemented
114	C₃×#386	C₂²	1	2	yes	complemented
115	C₃×#385	C₂²	1	2	yes	complemented
116	C₃×#383	C₂²	1	1	yes	characteristic, complemented
117	C₃×#382	C₂²	1	1	yes	characteristic, complemented
118	C₃×#381	C₂²	1	2	yes	complemented
119	C₃×#381	C₂²	1	1	yes	characteristic, complemented
120	C₃×#380	C₂²	1	1	yes	characteristic, complemented
121	C₃×#380	C₂²	1	2	yes	complemented
122	C₃×#380	C₂²	1	2	yes	complemented
123	C₃×#379	C₂²	1	2	yes	—
124	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
126	C₂×#546	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#546	C₂×C₃	1	1	yes	characteristic, complemented
128	#2819	C₂×C₃	1	1	yes	characteristic, complemented
129	#2815	C₂×C₃	1	1	yes	characteristic, complemented
130	#2703	C₂×C₃	1	2	yes	complemented
131	#2696	C₂×C₃	1	2	yes	complemented
132	#2673	C₂×C₃	1	2	yes	complemented
133	#2669	C₂×C₃	1	2	yes	complemented
134	#2639	C₂×C₃	1	1	yes	characteristic, complemented
135	#2631	C₂×C₃	1	1	yes	characteristic, complemented
136	#2631	C₂×C₃	1	1	yes	characteristic, complemented
137	#2617	C₂×C₃	1	1	yes	characteristic, complemented
138	#2615	C₂×C₃	1	1	yes	characteristic, complemented
139	#2561	C₂×C₃	1	1	yes	characteristic, complemented
140	#2535	C₂×C₃	1	1	yes	characteristic, complemented
141	#2433	C₂×C₃	1	1	yes	characteristic, complemented
142	#2412	C₂×C₃	1	2	yes	complemented
143	#2410	C₂×C₃	1	2	yes	complemented
144	#2404	C₂×C₃	1	2	yes	complemented
145	#2404	C₂×C₃	1	1	yes	characteristic, complemented
146	#2403	C₂×C₃	1	2	yes	complemented
147	C₂×#392	C₂×C₃	1	1	yes	characteristic, complemented
148	#2318	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂⁵×C₃	C₂³	1	1	yes	characteristic
150	C₂⁵×C₃	C₂³	1	2	yes	—
151	C₂⁵×C₃	C₂³	1	1	yes	characteristic
152	C₂×C₃×#41	—	2	4	no	—
153	C₂×C₃×#41	—	2	4	no	—
154	C₂×C₃×#41	—	4	4	no	—
155	C₂×C₃×#41	—	4	4	no	—
156	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
157	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	—	2	4	no	—
159	C₂²×C₃×D₄	—	2	4	no	—
160	C₂²×C₃×D₄	—	4	4	no	—
161	C₂²×C₃×D₄	—	4	4	no	—
162	C₂²×C₃×D₄	—	4	4	no	—
163	C₂²×C₃×D₄	—	4	4	no	—
164	C₂²×C₃×D₄	—	4	4	no	—
165	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
166	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
167	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
168	C₂²×C₃×D₄	C₂³	1	2	yes	—
169	C₂²×C₃×D₄	C₂³	1	2	yes	—
170	C₂²×C₃×D₄	C₂³	1	2	yes	—
171	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
172	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
173	C₂²×C₃×D₄	C₂³	1	2	yes	—
174	C₂²×C₃×D₄	C₂³	1	2	yes	—
175	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
176	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
177	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
178	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
179	C₂²×C₃×D₄	C₂³	1	2	yes	—
180	C₂²×C₃×D₄	C₂³	1	2	yes	—
181	C₂²×C₃×D₄	C₂³	1	2	yes	—
182	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
183	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
184	C₂²×C₃×D₄	C₂³	1	2	yes	—
185	C₂²×C₃×D₄	C₂³	1	2	yes	—
186	C₂²×C₃×D₄	C₂³	1	2	yes	—
187	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
188	C₂³×C₃×C₄	C₂³	1	2	yes	—
189	C₂³×C₃×C₄	C₂³	1	2	yes	—
190	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
191	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
192	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
193	C₂³×C₃×C₄	C₂³	1	2	yes	—
194	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
195	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
196	C₃×#127	—	4	4	no	—
197	C₃×#124	—	2	4	no	—
198	C₃×#124	—	2	4	no	—
199	C₃×#123	—	2	8	no	—
200	C₃×#123	—	2	4	no	—
201	C₃×#123	—	2	4	no	—
202	C₃×C₂²⋊Q₈	—	2	4	no	—
203	C₃×C₂²⋊Q₈	—	2	4	no	—
204	C₃×#121	—	2	4	no	—
205	C₃×#121	—	2	4	no	—
206	C₃×#121	—	2	4	no	—
207	C₃×#121	—	2	4	no	—
208	C₃×#121	—	2	8	no	—
209	C₃×#121	—	4	4	no	—
210	C₃×#121	—	4	4	no	—
211	C₃×#120	—	2	8	no	—
212	C₃×#120	—	2	4	no	—
213	C₃×#120	—	2	4	no	—
214	C₃×#120	—	4	4	no	—
215	C₃×#120	—	4	4	no	—
216	C₃×#120	—	4	4	no	—
217	C₃×#120	—	4	4	no	—
218	C₃×C₄×D₄	—	2	4	no	—
219	C₃×C₄×D₄	—	2	4	no	—
220	C₃×C₄×D₄	D₄	1	8	yes	complemented
221	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
224	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
230	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
231	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
232	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
239	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
241	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
249	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
250	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
251	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
252	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
253	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
254	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
255	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
256	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
257	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
258	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
259	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
260	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
261	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
262	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
263	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
264	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
265	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
266	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
267	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₃×C₄²	C₂³	1	2	yes	—
270	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
271	C₃×#95	C₂³	1	1	yes	characteristic
272	C₃×#95	C₂³	1	1	yes	characteristic
273	C₃×#95	C₂³	1	2	yes	—
274	C₃×#95	C₂³	1	1	yes	characteristic
275	C₃×#95	C₂³	1	1	yes	characteristic
276	C₃×#95	C₂³	1	2	yes	—
277	C₃×#95	C₂³	1	2	yes	—
278	C₃×#95	C₂³	1	2	yes	—
279	C₃×#95	C₂³	1	2	yes	—
280	C₃×#95	C₂³	1	2	yes	—
281	C₃×#95	C₂³	1	2	yes	—
282	C₃×#95	C₂³	1	2	yes	—
283	C₃×#95	C₂³	1	2	yes	—
284	C₃×#95	C₂³	1	2	yes	—
285	C₃×#95	C₂³	1	2	yes	—
286	C₃×#95	C₂³	1	2	yes	—
287	C₃×#95	C₂³	1	2	yes	—
288	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
289	C₂²×#41	C₂²×C₃	1	1	yes	characteristic, complemented
290	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
291	C₂³×D₄	C₂²×C₃	1	2	yes	—
292	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
293	#546	—	2	8	no	—
294	#546	—	2	8	no	—
295	C₂×#127	C₂²×C₃	1	2	yes	complemented
296	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
297	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
298	C₂×#123	C₂²×C₃	1	1	yes	characteristic
299	C₂×#123	C₂²×C₃	1	2	yes	complemented
300	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
301	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
302	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
303	C₂×#121	C₂²×C₃	1	1	yes	characteristic
304	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
305	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
306	C₂×#121	C₂²×C₃	1	2	yes	complemented
307	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
308	C₂×#121	C₂²×C₃	1	2	yes	complemented
309	C₂×#121	C₂²×C₃	1	2	yes	complemented
310	C₂×#120	C₂²×C₃	1	2	yes	—
311	C₂×#120	C₂²×C₃	1	1	yes	characteristic
312	C₂×#120	C₂²×C₃	1	2	yes	—
313	C₂×#120	C₂²×C₃	1	1	yes	characteristic, complemented
314	C₂×#120	C₂²×C₃	1	2	yes	complemented
315	C₂×#120	C₂²×C₃	1	2	yes	complemented
316	C₂×#120	C₂²×C₃	1	2	yes	complemented
317	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
318	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
319	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
320	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
321	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
322	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
323	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
324	#400	C₂²×C₃	1	2	yes	complemented
325	#397	C₂²×C₃	1	1	yes	characteristic, complemented
326	#397	C₂²×C₃	1	1	yes	characteristic, complemented
327	#397	C₂²×C₃	1	1	yes	characteristic, complemented
328	#397	C₂²×C₃	1	2	yes	complemented
329	#397	C₂²×C₃	1	1	yes	characteristic, complemented
330	#397	C₂²×C₃	1	2	yes	complemented
331	#394	C₂²×C₃	1	2	yes	complemented
332	#394	C₂²×C₃	1	2	yes	complemented
333	#394	C₂²×C₃	1	2	yes	complemented
334	#394	C₂²×C₃	1	2	yes	complemented
335	#394	C₂²×C₃	1	2	yes	complemented
336	#393	C₂²×C₃	1	1	yes	characteristic, complemented
337	#393	C₂²×C₃	1	1	yes	characteristic, complemented
338	#393	C₂²×C₃	1	1	yes	characteristic, complemented
339	#393	C₂²×C₃	1	2	yes	complemented
340	#393	C₂²×C₃	1	1	yes	characteristic, complemented
341	#393	C₂²×C₃	1	2	yes	complemented
342	#392	C₂²×C₃	1	1	yes	characteristic
343	#392	C₂²×C₃	1	1	yes	characteristic
344	#392	C₂²×C₃	1	2	yes	—
345	#392	C₂²×C₃	1	1	yes	characteristic, complemented
346	#392	C₂²×C₃	1	1	yes	characteristic, complemented
347	#392	C₂²×C₃	1	2	yes	complemented
348	#392	C₂²×C₃	1	1	yes	characteristic, complemented
349	#392	C₂²×C₃	1	2	yes	complemented
350	#392	C₂²×C₃	1	2	yes	complemented
351	#392	C₂²×C₃	1	1	yes	characteristic, complemented
352	#392	C₂²×C₃	1	2	yes	complemented
353	#392	C₂²×C₃	1	1	yes	characteristic, complemented
354	#392	C₂²×C₃	1	2	yes	complemented
355	#392	C₂²×C₃	1	1	yes	characteristic, complemented
356	#392	C₂²×C₃	1	2	yes	complemented
357	#392	C₂²×C₃	1	2	yes	complemented
358	#392	C₂²×C₃	1	2	yes	complemented
359	#392	C₂²×C₃	1	2	yes	complemented
360	#390	C₂²×C₃	1	2	yes	complemented
361	#388	C₂²×C₃	1	2	yes	complemented
362	#388	C₂²×C₃	1	2	yes	complemented
363	#388	C₂²×C₃	1	2	yes	complemented
364	#387	C₂²×C₃	1	2	yes	complemented
365	#386	C₂²×C₃	1	2	yes	—
366	#386	C₂²×C₃	1	2	yes	—
367	#386	C₂²×C₃	1	2	yes	complemented
368	#386	C₂²×C₃	1	2	yes	complemented
369	#386	C₂²×C₃	1	2	yes	complemented
370	#386	C₂²×C₃	1	2	yes	complemented
371	#386	C₂²×C₃	1	2	yes	complemented
372	#386	C₂²×C₃	1	2	yes	complemented
373	#386	C₂²×C₃	1	2	yes	complemented
374	#386	C₂²×C₃	1	2	yes	complemented
375	#386	C₂²×C₃	1	2	yes	complemented
376	#386	C₂²×C₃	1	2	yes	complemented
377	#386	C₂²×C₃	1	2	yes	complemented
378	#385	C₂²×C₃	1	2	yes	complemented
379	#383	C₂²×C₃	1	1	yes	characteristic, complemented
380	#382	C₂²×C₃	1	1	yes	characteristic, complemented
381	#381	C₂²×C₃	1	2	yes	complemented
382	#381	C₂²×C₃	1	1	yes	characteristic, complemented
383	#380	C₂²×C₃	1	1	yes	characteristic, complemented
384	#380	C₂²×C₃	1	2	yes	complemented
385	#380	C₂²×C₃	1	2	yes	complemented
386	#379	C₂²×C₃	1	2	yes	—
387	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
388	C₂×#95	C₂²×C₃	1	1	yes	characteristic, complemented
389	C₂⁴×C₃	—	2	2	no	—
390	C₂⁴×C₃	—	2	4	no	—
391	C₂⁴×C₃	—	2	2	no	—
392	C₂⁴×C₃	—	2	2	no	—
393	C₂⁴×C₃	—	2	4	no	—
394	C₂⁴×C₃	—	2	4	no	—
395	C₂⁴×C₃	—	2	4	no	—
396	C₂⁴×C₃	—	2	4	no	—
397	C₂⁴×C₃	—	2	2	no	—
398	C₂⁴×C₃	—	4	2	no	—
399	C₂⁴×C₃	—	4	1	no	—
400	C₂⁴×C₃	—	4	1	no	—
401	C₂⁴×C₃	—	4	2	no	—
402	C₂⁴×C₃	—	4	2	no	—
403	C₂⁴×C₃	—	4	2	no	—
404	C₂⁴×C₃	—	4	2	no	—
405	C₂⁴×C₃	—	4	2	no	—
406	C₂⁴×C₃	C₂⁴	1	2	yes	—
407	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
408	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
409	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
410	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
411	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
412	C₂⁴×C₃	C₂⁴	1	2	yes	—
413	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
414	C₃×#41	—	4	16	no	—
415	C₃×#41	—	4	16	no	—
416	C₂×C₃×Q₈	—	2	2	no	—
417	C₂×C₃×Q₈	—	2	2	no	—
418	C₂×C₃×Q₈	—	4	2	no	—
419	C₂×C₃×Q₈	—	4	2	no	—
420	C₂×C₃×D₄	—	2	4	no	—
421	C₂×C₃×D₄	—	2	4	no	—
422	C₂×C₃×D₄	—	2	4	no	—
423	C₂×C₃×D₄	—	2	2	no	—
424	C₂×C₃×D₄	—	2	2	no	—
425	C₂×C₃×D₄	—	2	2	no	—
426	C₂×C₃×D₄	—	2	2	no	—
427	C₂×C₃×D₄	—	2	4	no	—
428	C₂×C₃×D₄	—	2	4	no	—
429	C₂×C₃×D₄	—	2	4	no	—
430	C₂×C₃×D₄	—	2	4	no	—
431	C₂×C₃×D₄	—	2	4	no	—
432	C₂×C₃×D₄	—	2	2	no	—
433	C₂×C₃×D₄	—	2	4	no	—
434	C₂×C₃×D₄	—	2	4	no	—
435	C₂×C₃×D₄	—	2	4	no	—
436	C₂×C₃×D₄	—	2	4	no	—
437	C₂×C₃×D₄	—	2	4	no	—
438	C₂×C₃×D₄	—	2	4	no	—
439	C₂×C₃×D₄	—	2	2	no	—
440	C₂×C₃×D₄	—	2	2	no	—
441	C₂×C₃×D₄	—	2	4	no	—
442	C₂×C₃×D₄	—	2	2	no	—
443	C₂×C₃×D₄	—	2	2	no	—
444	C₂×C₃×D₄	—	2	2	no	—
445	C₂×C₃×D₄	—	2	2	no	—
446	C₂×C₃×D₄	—	4	2	no	—
447	C₂×C₃×D₄	—	4	2	no	—
448	C₂×C₃×D₄	—	4	2	no	—
449	C₂×C₃×D₄	—	4	2	no	—
450	C₂×C₃×D₄	—	4	2	no	—
451	C₂×C₃×D₄	—	4	2	no	—
452	C₂×C₃×D₄	—	4	2	no	—
453	C₂×C₃×D₄	—	4	2	no	—
454	C₂×C₃×D₄	—	4	2	no	—
455	C₂×C₃×D₄	—	4	2	no	—
456	C₂×C₃×D₄	—	4	2	no	—
457	C₂×C₃×D₄	—	4	2	no	—
458	C₂×C₃×D₄	—	4	1	no	—
459	C₂×C₃×D₄	—	4	2	no	—
460	C₂×C₃×D₄	—	4	2	no	—
461	C₂×C₃×D₄	—	4	2	no	—
462	C₂×C₃×D₄	—	4	2	no	—
463	C₂×C₃×D₄	—	4	2	no	—
464	C₂×C₃×D₄	—	4	2	no	—
465	C₂×C₃×D₄	—	4	2	no	—
466	C₂×C₃×D₄	—	4	2	no	—
467	C₂×C₃×D₄	—	4	2	no	—
468	C₂×C₃×D₄	—	4	2	no	—
469	C₂×C₃×D₄	—	4	2	no	—
470	C₂×C₃×D₄	—	4	2	no	—
471	C₂×C₃×D₄	—	4	2	no	—
472	C₂×C₃×D₄	—	4	2	no	—
473	C₂×C₃×D₄	—	4	2	no	—
474	C₂×C₃×D₄	—	4	2	no	—
475	C₂×C₃×D₄	—	4	16	no	—
476	C₂×C₃×D₄	—	4	16	no	—
477	C₂×C₃×D₄	—	4	32	no	—
478	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
479	C₂²×C₃×C₄	—	2	2	no	—
480	C₂²×C₃×C₄	—	2	2	no	—
481	C₂²×C₃×C₄	—	2	4	no	—
482	C₂²×C₃×C₄	—	2	4	no	—
483	C₂²×C₃×C₄	—	2	4	no	—
484	C₂²×C₃×C₄	—	2	4	no	—
485	C₂²×C₃×C₄	—	2	2	no	—
486	C₂²×C₃×C₄	—	2	2	no	—
487	C₂²×C₃×C₄	—	2	4	no	—
488	C₂²×C₃×C₄	—	4	2	no	—
489	C₂²×C₃×C₄	—	4	2	no	—
490	C₂²×C₃×C₄	—	4	2	no	—
491	C₂²×C₃×C₄	—	4	2	no	—
492	C₂²×C₃×C₄	—	4	2	no	—
493	C₂²×C₃×C₄	—	4	2	no	—
494	C₂²×C₃×C₄	—	4	2	no	—
495	C₂²×C₃×C₄	—	4	2	no	—
496	C₂²×C₃×C₄	—	4	2	no	—
497	C₂²×C₃×C₄	—	4	2	no	—
498	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
499	C₂²×C₃×C₄	C₂×D₄	1	4	yes	complemented
500	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
501	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
502	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
503	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
504	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
505	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
506	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
507	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
508	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
509	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
510	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
511	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
512	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
513	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
514	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
515	C₃×C₄⋊C₄	—	2	2	no	—
516	C₃×C₄⋊C₄	—	2	2	no	—
517	C₃×C₄⋊C₄	—	2	4	no	—
518	C₃×C₄⋊C₄	—	2	2	no	—
519	C₃×C₄⋊C₄	—	2	2	no	—
520	C₃×C₄⋊C₄	—	4	2	no	—
521	C₃×C₄⋊C₄	—	4	2	no	—
522	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
523	C₃×C₂²⋊C₄	—	2	4	no	—
524	C₃×C₂²⋊C₄	—	2	4	no	—
525	C₃×C₂²⋊C₄	—	2	4	no	—
526	C₃×C₂²⋊C₄	—	2	2	no	—
527	C₃×C₂²⋊C₄	—	2	2	no	—
528	C₃×C₂²⋊C₄	—	2	2	no	—
529	C₃×C₂²⋊C₄	—	2	4	no	—
530	C₃×C₂²⋊C₄	—	2	2	no	—
531	C₃×C₂²⋊C₄	—	2	2	no	—
532	C₃×C₂²⋊C₄	—	2	4	no	—
533	C₃×C₂²⋊C₄	—	2	2	no	—
534	C₃×C₂²⋊C₄	—	2	2	no	—
535	C₃×C₂²⋊C₄	—	2	4	no	—
536	C₃×C₂²⋊C₄	—	2	2	no	—
537	C₃×C₂²⋊C₄	—	2	2	no	—
538	C₃×C₂²⋊C₄	—	2	2	no	—
539	C₃×C₂²⋊C₄	—	2	4	no	—
540	C₃×C₂²⋊C₄	—	4	2	no	—
541	C₃×C₂²⋊C₄	—	4	2	no	—
542	C₃×C₂²⋊C₄	—	4	2	no	—
543	C₃×C₂²⋊C₄	—	4	2	no	—
544	C₃×C₂²⋊C₄	—	4	2	no	—
545	C₃×C₂²⋊C₄	—	4	2	no	—
546	C₃×C₂²⋊C₄	—	4	2	no	—
547	C₃×C₂²⋊C₄	—	4	2	no	—
548	C₃×C₂²⋊C₄	—	4	2	no	—
549	C₃×C₂²⋊C₄	—	4	2	no	—
550	C₃×C₂²⋊C₄	—	4	2	no	—
551	C₃×C₂²⋊C₄	—	4	2	no	—
552	C₃×C₂²⋊C₄	—	4	2	no	—
553	C₃×C₂²⋊C₄	—	4	2	no	—
554	C₃×C₂²⋊C₄	—	4	2	no	—
555	C₃×C₂²⋊C₄	—	4	2	no	—
556	C₃×C₂²⋊C₄	—	4	2	no	—
557	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
558	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
559	C₃×C₄²	—	4	2	no	—
560	C₃×C₄²	C₂×D₄	1	4	yes	complemented
561	C₂⁵	C₂³×C₃	1	1	yes	characteristic
562	C₂⁵	C₂³×C₃	1	2	yes	—
563	C₂⁵	C₂³×C₃	1	1	yes	characteristic
564	C₂×#41	—	2	4	no	—
565	C₂×#41	—	2	4	no	—
566	C₂×#41	—	4	4	no	—
567	C₂×#41	—	4	4	no	—
568	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
569	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
570	C₂²×D₄	—	2	4	no	—
571	C₂²×D₄	—	2	4	no	—
572	C₂²×D₄	—	4	4	no	—
573	C₂²×D₄	—	4	4	no	—
574	C₂²×D₄	—	4	4	no	—
575	C₂²×D₄	—	4	4	no	—
576	C₂²×D₄	—	4	4	no	—
577	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₃	1	2	yes	—
582	C₂²×D₄	C₂³×C₃	1	2	yes	—
583	C₂²×D₄	C₂³×C₃	1	2	yes	—
584	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
585	C₂²×D₄	C₂³×C₃	1	2	yes	—
586	C₂²×D₄	C₂³×C₃	1	2	yes	—
587	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₃	1	2	yes	—
590	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
591	C₂²×D₄	C₂³×C₃	1	2	yes	—
592	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
594	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
595	C₂²×D₄	C₂³×C₃	1	2	yes	—
596	C₂²×D₄	C₂³×C₃	1	2	yes	—
597	C₂²×D₄	C₂³×C₃	1	2	yes	—
598	C₂²×D₄	C₂³×C₃	1	2	yes	—
599	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₃	1	2	yes	—
601	C₂³×C₄	C₂³×C₃	1	2	yes	—
602	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₃	1	2	yes	—
604	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
608	#127	—	4	4	no	—
609	#124	—	2	4	no	—
610	#124	—	2	4	no	—
611	#123	—	2	8	no	—
612	#123	—	2	4	no	—
613	#123	—	2	4	no	—
614	C₂²⋊Q₈	—	2	4	no	—
615	C₂²⋊Q₈	—	2	4	no	—
616	#121	—	2	4	no	—
617	#121	—	2	4	no	—
618	#121	—	2	4	no	—
619	#121	—	2	4	no	—
620	#121	—	2	8	no	—
621	#121	—	4	4	no	—
622	#121	—	4	4	no	—
623	#120	—	2	8	no	—
624	#120	—	2	4	no	—
625	#120	—	2	4	no	—
626	#120	—	4	4	no	—
627	#120	—	4	4	no	—
628	#120	—	4	4	no	—
629	#120	—	4	4	no	—
630	C₄×D₄	—	2	4	no	—
631	C₄×D₄	—	2	4	no	—
632	C₄×D₄	C₃×D₄	1	8	yes	complemented
633	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	—	2	4	no	—
642	C₂×C₂²⋊C₄	—	2	4	no	—
643	C₂×C₂²⋊C₄	—	2	8	no	—
644	C₂×C₂²⋊C₄	—	4	4	no	—
645	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
680	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₃	1	2	yes	—
682	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
683	#95	C₂³×C₃	1	1	yes	characteristic
684	#95	C₂³×C₃	1	1	yes	characteristic
685	#95	C₂³×C₃	1	2	yes	—
686	#95	C₂³×C₃	1	1	yes	characteristic
687	#95	C₂³×C₃	1	1	yes	characteristic
688	#95	C₂³×C₃	1	2	yes	—
689	#95	C₂³×C₃	1	2	yes	—
690	#95	C₂³×C₃	1	2	yes	—
691	#95	C₂³×C₃	1	2	yes	—
692	#95	C₂³×C₃	1	2	yes	—
693	#95	C₂³×C₃	1	2	yes	—
694	#95	C₂³×C₃	1	2	yes	—
695	#95	C₂³×C₃	1	2	yes	—
696	#95	C₂³×C₃	1	2	yes	—
697	#95	C₂³×C₃	1	2	yes	—
698	#95	C₂³×C₃	1	2	yes	—
699	#95	C₂³×C₃	1	2	yes	—
700	C₂³×C₃	—	2	2	no	—
701	C₂³×C₃	—	2	1	no	—
702	C₂³×C₃	—	2	1	no	—
703	C₂³×C₃	—	2	1	no	—
704	C₂³×C₃	—	2	2	no	—
705	C₂³×C₃	—	2	2	no	—
706	C₂³×C₃	—	2	1	no	—
707	C₂³×C₃	—	2	2	no	—
708	C₂³×C₃	—	2	2	no	—
709	C₂³×C₃	—	2	2	no	—
710	C₂³×C₃	—	2	2	no	—
711	C₂³×C₃	—	2	2	no	—
712	C₂³×C₃	—	2	2	no	—
713	C₂³×C₃	—	2	2	no	—
714	C₂³×C₃	—	2	2	no	—
715	C₂³×C₃	—	2	1	no	—
716	C₂³×C₃	—	2	1	no	—
717	C₂³×C₃	—	2	1	no	—
718	C₂³×C₃	—	2	1	no	—
719	C₂³×C₃	—	2	2	no	—
720	C₂³×C₃	—	2	1	no	—
721	C₂³×C₃	—	2	2	no	—
722	C₂³×C₃	—	2	1	no	—
723	C₂³×C₃	—	2	1	no	—
724	C₂³×C₃	—	2	2	no	—
725	C₂³×C₃	—	2	2	no	—
726	C₂³×C₃	—	2	2	no	—
727	C₂³×C₃	—	2	2	no	—
728	C₂³×C₃	—	2	2	no	—
729	C₂³×C₃	—	2	2	no	—
730	C₂³×C₃	—	2	2	no	—
731	C₂³×C₃	—	2	2	no	—
732	C₂³×C₃	—	2	2	no	—
733	C₂³×C₃	—	2	2	no	—
734	C₂³×C₃	—	2	1	no	—
735	C₂³×C₃	—	2	1	no	—
736	C₂³×C₃	—	2	1	no	—
737	C₂³×C₃	—	2	2	no	—
738	C₂³×C₃	—	2	1	no	—
739	C₂³×C₃	—	4	8	no	—
740	C₂³×C₃	—	4	8	no	—
741	C₂³×C₃	—	4	8	no	—
742	C₂³×C₃	—	4	4	no	—
743	C₂³×C₃	—	4	8	no	—
744	C₂³×C₃	—	4	4	no	—
745	C₂³×C₃	—	4	4	no	—
746	C₂³×C₃	—	4	4	no	—
747	C₂³×C₃	—	4	8	no	—
748	C₂³×C₃	—	8	2	no	—
749	C₂³×C₃	—	8	4	no	—
750	C₂³×C₃	—	8	4	no	—
751	C₂³×C₃	—	8	4	no	—
752	C₂³×C₃	—	8	4	no	—
753	C₂³×C₃	—	8	2	no	—
754	C₂³×C₃	—	8	4	no	—
755	C₂³×C₃	—	8	4	no	—
756	C₂³×C₃	C₂²×D₄	1	2	yes	—
757	C₂³×C₃	C₂²×D₄	1	2	yes	—
758	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
759	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
760	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
761	C₂³×C₃	C₂⁵	1	1	yes	characteristic
762	C₃×Q₈	—	4	4	no	—
763	C₃×Q₈	—	4	4	no	—
764	C₃×D₄	—	2	8	no	—
765	C₃×D₄	—	2	8	no	—
766	C₃×D₄	—	4	4	no	—
767	C₃×D₄	—	4	8	no	—
768	C₃×D₄	—	4	4	no	—
769	C₃×D₄	—	4	4	no	—
770	C₃×D₄	—	4	8	no	—
771	C₃×D₄	—	4	8	no	—
772	C₃×D₄	—	4	4	no	—
773	C₃×D₄	—	4	8	no	—
774	C₃×D₄	—	4	8	no	—
775	C₃×D₄	—	4	4	no	—
776	C₃×D₄	—	4	8	no	—
777	C₃×D₄	—	4	4	no	—
778	C₃×D₄	—	4	4	no	—
779	C₃×D₄	—	8	2	no	—
780	C₃×D₄	—	8	2	no	—
781	C₃×D₄	—	8	4	no	—
782	C₃×D₄	—	8	4	no	—
783	C₃×D₄	—	8	4	no	—
784	C₃×D₄	—	8	4	no	—
785	C₃×D₄	—	8	4	no	—
786	C₂×C₃×C₄	—	2	2	no	—
787	C₂×C₃×C₄	—	2	1	no	—
788	C₂×C₃×C₄	—	2	2	no	—
789	C₂×C₃×C₄	—	2	2	no	—
790	C₂×C₃×C₄	—	2	2	no	—
791	C₂×C₃×C₄	—	2	1	no	—
792	C₂×C₃×C₄	—	2	2	no	—
793	C₂×C₃×C₄	—	2	1	no	—
794	C₂×C₃×C₄	—	2	1	no	—
795	C₂×C₃×C₄	—	2	1	no	—
796	C₂×C₃×C₄	—	2	2	no	—
797	C₂×C₃×C₄	—	2	1	no	—
798	C₂×C₃×C₄	—	2	2	no	—
799	C₂×C₃×C₄	—	2	2	no	—
800	C₂×C₃×C₄	—	2	2	no	—
801	C₂×C₃×C₄	—	2	2	no	—
802	C₂×C₃×C₄	—	2	2	no	—
803	C₂×C₃×C₄	—	2	2	no	—
804	C₂×C₃×C₄	—	2	2	no	—
805	C₂×C₃×C₄	—	2	2	no	—
806	C₂×C₃×C₄	—	2	2	no	—
807	C₂×C₃×C₄	—	2	2	no	—
808	C₂×C₃×C₄	—	2	2	no	—
809	C₂×C₃×C₄	—	2	2	no	—
810	C₂×C₃×C₄	—	2	2	no	—
811	C₂×C₃×C₄	—	2	2	no	—
812	C₂×C₃×C₄	—	2	2	no	—
813	C₂×C₃×C₄	—	2	2	no	—
814	C₂×C₃×C₄	—	2	2	no	—
815	C₂×C₃×C₄	—	2	2	no	—
816	C₂×C₃×C₄	—	2	2	no	—
817	C₂×C₃×C₄	—	2	2	no	—
818	C₂×C₃×C₄	—	4	4	no	—
819	C₂×C₃×C₄	—	4	4	no	—
820	C₂×C₃×C₄	—	4	8	no	—
821	C₂×C₃×C₄	—	4	4	no	—
822	C₂×C₃×C₄	—	4	4	no	—
823	C₂×C₃×C₄	—	4	8	no	—
824	C₂×C₃×C₄	—	4	4	no	—
825	C₂×C₃×C₄	—	4	4	no	—
826	C₂×C₃×C₄	—	8	4	no	—
827	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
828	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
829	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
830	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
831	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
832	C₂⁴	—	2	2	no	—
833	C₂⁴	—	2	4	no	—
834	C₂⁴	—	2	2	no	—
835	C₂⁴	—	2	2	no	—
836	C₂⁴	—	2	4	no	—
837	C₂⁴	—	2	4	no	—
838	C₂⁴	—	2	4	no	—
839	C₂⁴	—	2	4	no	—
840	C₂⁴	—	2	2	no	—
841	C₂⁴	—	4	2	no	—
842	C₂⁴	—	4	2	no	—
843	C₂⁴	—	4	2	no	—
844	C₂⁴	—	4	2	no	—
845	C₂⁴	—	4	2	no	—
846	C₂⁴	—	4	1	no	—
847	C₂⁴	—	4	1	no	—
848	C₂⁴	—	4	2	no	—
849	C₂⁴	C₂⁴×C₃	1	2	yes	—
850	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
851	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
852	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
853	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
854	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
855	C₂⁴	C₂⁴×C₃	1	2	yes	—
856	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
857	#41	—	4	16	no	—
858	#41	—	4	16	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	4	2	no	—
862	C₂×Q₈	—	4	2	no	—
863	C₂×D₄	—	2	4	no	—
864	C₂×D₄	—	2	4	no	—
865	C₂×D₄	—	2	4	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	4	no	—
871	C₂×D₄	—	2	4	no	—
872	C₂×D₄	—	2	4	no	—
873	C₂×D₄	—	2	4	no	—
874	C₂×D₄	—	2	4	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	4	no	—
877	C₂×D₄	—	2	4	no	—
878	C₂×D₄	—	2	4	no	—
879	C₂×D₄	—	2	4	no	—
880	C₂×D₄	—	2	4	no	—
881	C₂×D₄	—	2	4	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	4	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	4	2	no	—
890	C₂×D₄	—	4	2	no	—
891	C₂×D₄	—	4	2	no	—
892	C₂×D₄	—	4	2	no	—
893	C₂×D₄	—	4	2	no	—
894	C₂×D₄	—	4	2	no	—
895	C₂×D₄	—	4	2	no	—
896	C₂×D₄	—	4	2	no	—
897	C₂×D₄	—	4	2	no	—
898	C₂×D₄	—	4	2	no	—
899	C₂×D₄	—	4	2	no	—
900	C₂×D₄	—	4	2	no	—
901	C₂×D₄	—	4	2	no	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	1	no	—
904	C₂×D₄	—	4	2	no	—
905	C₂×D₄	—	4	2	no	—
906	C₂×D₄	—	4	2	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	4	2	no	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	—	4	2	no	—
911	C₂×D₄	—	4	2	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	2	no	—
915	C₂×D₄	—	4	2	no	—
916	C₂×D₄	—	4	2	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	16	no	—
919	C₂×D₄	—	4	16	no	—
920	C₂×D₄	—	4	32	no	—
921	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	4	no	—
925	C₂²×C₄	—	2	4	no	—
926	C₂²×C₄	—	2	4	no	—
927	C₂²×C₄	—	2	4	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	4	no	—
931	C₂²×C₄	—	4	2	no	—
932	C₂²×C₄	—	4	2	no	—
933	C₂²×C₄	—	4	2	no	—
934	C₂²×C₄	—	4	2	no	—
935	C₂²×C₄	—	4	2	no	—
936	C₂²×C₄	—	4	2	no	—
937	C₂²×C₄	—	4	2	no	—
938	C₂²×C₄	—	4	2	no	—
939	C₂²×C₄	—	4	2	no	—
940	C₂²×C₄	—	4	2	no	—
941	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
942	C₂²×C₄	C₂×C₃×D₄	1	4	yes	complemented
943	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
945	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
946	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
948	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
951	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	4	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	4	2	no	—
964	C₄⋊C₄	—	4	2	no	—
965	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	complemented
966	C₂²⋊C₄	—	2	4	no	—
967	C₂²⋊C₄	—	2	4	no	—
968	C₂²⋊C₄	—	2	4	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	4	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	4	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	4	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	2	no	—
985	C₂²⋊C₄	—	4	2	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	2	no	—
996	C₂²⋊C₄	—	4	2	no	—
997	C₂²⋊C₄	—	4	2	no	—
998	C₂²⋊C₄	—	4	2	no	—
999	C₂²⋊C₄	—	4	2	no	—
1000	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
1001	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	complemented
1002	C₄²	—	4	2	no	—
1003	C₄²	C₂×C₃×D₄	1	4	yes	complemented
1004	C₂²×C₃	—	2	2	no	—
1005	C₂²×C₃	—	2	2	no	—
1006	C₂²×C₃	—	2	4	no	—
1007	C₂²×C₃	—	2	4	no	—
1008	C₂²×C₃	—	2	2	no	—
1009	C₂²×C₃	—	2	4	no	—
1010	C₂²×C₃	—	2	2	no	—
1011	C₂²×C₃	—	2	2	no	—
1012	C₂²×C₃	—	2	2	no	—
1013	C₂²×C₃	—	2	4	no	—
1014	C₂²×C₃	—	2	4	no	—
1015	C₂²×C₃	—	2	4	no	—
1016	C₂²×C₃	—	4	1	no	—
1017	C₂²×C₃	—	4	2	no	—
1018	C₂²×C₃	—	4	1	no	—
1019	C₂²×C₃	—	4	2	no	—
1020	C₂²×C₃	—	4	2	no	—
1021	C₂²×C₃	—	4	2	no	—
1022	C₂²×C₃	—	4	2	no	—
1023	C₂²×C₃	—	4	2	no	—
1024	C₂²×C₃	—	4	2	no	—
1025	C₂²×C₃	—	4	1	no	—
1026	C₂²×C₃	—	4	1	no	—
1027	C₂²×C₃	—	4	1	no	—
1028	C₂²×C₃	—	4	2	no	—
1029	C₂²×C₃	—	4	2	no	—
1030	C₂²×C₃	—	4	1	no	—
1031	C₂²×C₃	—	4	1	no	—
1032	C₂²×C₃	—	4	1	no	—
1033	C₂²×C₃	—	4	1	no	—
1034	C₂²×C₃	—	4	2	no	—
1035	C₂²×C₃	—	4	1	no	—
1036	C₂²×C₃	—	4	1	no	—
1037	C₂²×C₃	—	4	2	no	—
1038	C₂²×C₃	—	4	2	no	—
1039	C₂²×C₃	—	4	2	no	—
1040	C₂²×C₃	—	4	2	no	—
1041	C₂²×C₃	—	4	2	no	—
1042	C₂²×C₃	—	4	2	no	—
1043	C₂²×C₃	—	4	2	no	—
1044	C₂²×C₃	—	4	2	no	—
1045	C₂²×C₃	—	4	2	no	—
1046	C₂²×C₃	—	4	2	no	—
1047	C₂²×C₃	—	8	16	no	—
1048	C₂²×C₃	—	8	8	no	—
1049	C₂²×C₃	—	8	8	no	—
1050	C₂²×C₃	#535	1	4	yes	—
1051	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1052	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
1053	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
1054	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1055	C₂²×C₃	#585	1	1	yes	characteristic
1056	C₃×C₄	—	2	2	no	—
1057	C₃×C₄	—	2	2	no	—
1058	C₃×C₄	—	2	2	no	—
1059	C₃×C₄	—	2	2	no	—
1060	C₃×C₄	—	2	2	no	—
1061	C₃×C₄	—	4	1	no	—
1062	C₃×C₄	—	4	1	no	—
1063	C₃×C₄	—	4	1	no	—
1064	C₃×C₄	—	4	1	no	—
1065	C₃×C₄	—	4	2	no	—
1066	C₃×C₄	—	4	2	no	—
1067	C₃×C₄	—	4	2	no	—
1068	C₃×C₄	—	4	2	no	—
1069	C₃×C₄	—	4	2	no	—
1070	C₃×C₄	—	4	2	no	—
1071	C₂³	—	2	2	no	—
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	1	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	2	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	2	no	—
1079	C₂³	—	2	2	no	—
1080	C₂³	—	2	2	no	—
1081	C₂³	—	2	2	no	—
1082	C₂³	—	2	2	no	—
1083	C₂³	—	2	2	no	—
1084	C₂³	—	2	2	no	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	2	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	1	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	2	no	—
1096	C₂³	—	2	2	no	—
1097	C₂³	—	2	2	no	—
1098	C₂³	—	2	2	no	—
1099	C₂³	—	2	2	no	—
1100	C₂³	—	2	2	no	—
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	2	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	1	no	—
1106	C₂³	—	2	1	no	—
1107	C₂³	—	2	1	no	—
1108	C₂³	—	2	2	no	—
1109	C₂³	—	2	1	no	—
1110	C₂³	—	4	8	no	—
1111	C₂³	—	4	8	no	—
1112	C₂³	—	4	8	no	—
1113	C₂³	—	4	4	no	—
1114	C₂³	—	4	8	no	—
1115	C₂³	—	4	4	no	—
1116	C₂³	—	4	4	no	—
1117	C₂³	—	4	4	no	—
1118	C₂³	—	4	8	no	—
1119	C₂³	—	8	2	no	—
1120	C₂³	—	8	4	no	—
1121	C₂³	—	8	4	no	—
1122	C₂³	—	8	4	no	—
1123	C₂³	—	8	4	no	—
1124	C₂³	—	8	2	no	—
1125	C₂³	—	8	4	no	—
1126	C₂³	—	8	4	no	—
1127	C₂³	C₂²×C₃×D₄	1	2	yes	—
1128	C₂³	C₂²×C₃×D₄	1	2	yes	—
1129	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
1130	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
1131	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
1132	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1133	Q₈	—	4	4	no	—
1134	Q₈	—	4	4	no	—
1135	D₄	—	2	8	no	—
1136	D₄	—	2	8	no	—
1137	D₄	—	4	8	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	4	no	—
1140	D₄	—	4	4	no	—
1141	D₄	—	4	8	no	—
1142	D₄	—	4	8	no	—
1143	D₄	—	4	4	no	—
1144	D₄	—	4	8	no	—
1145	D₄	—	4	8	no	—
1146	D₄	—	4	4	no	—
1147	D₄	—	4	8	no	—
1148	D₄	—	4	4	no	—
1149	D₄	—	4	4	no	—
1150	D₄	—	8	2	no	—
1151	D₄	—	8	2	no	—
1152	D₄	—	8	4	no	—
1153	D₄	—	8	4	no	—
1154	D₄	—	8	4	no	—
1155	D₄	—	8	4	no	—
1156	D₄	—	8	4	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	2	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	2	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	2	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	2	no	—
1186	C₂×C₄	—	2	2	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	2	2	no	—
1189	C₂×C₄	—	4	4	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	8	no	—
1192	C₂×C₄	—	4	4	no	—
1193	C₂×C₄	—	4	4	no	—
1194	C₂×C₄	—	4	8	no	—
1195	C₂×C₄	—	4	4	no	—
1196	C₂×C₄	—	4	4	no	—
1197	C₂×C₄	—	8	4	no	—
1198	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1199	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1200	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1201	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1202	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1203	C₂×C₃	—	2	4	no	—
1204	C₂×C₃	—	4	2	no	—
1205	C₂×C₃	—	4	4	no	—
1206	C₂×C₃	—	4	2	no	—
1207	C₂×C₃	—	8	1	no	—
1208	C₂×C₃	—	8	1	no	—
1209	C₂×C₃	—	8	1	no	—
1210	C₂×C₃	—	8	2	no	—
1211	C₂×C₃	C₂×#535	1	1	yes	characteristic
1212	C₂×C₃	#3484	1	1	yes	characteristic
1213	C₂×C₃	#3488	1	1	yes	characteristic
1214	C₂×C₃	#3532	1	2	yes	—
1215	C₂×C₃	#3534	1	2	yes	—
1216	C₂²	—	2	2	no	—
1217	C₂²	—	2	2	no	—
1218	C₂²	—	2	4	no	—
1219	C₂²	—	2	4	no	—
1220	C₂²	—	2	2	no	—
1221	C₂²	—	2	4	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	2	no	—
1225	C₂²	—	2	4	no	—
1226	C₂²	—	2	4	no	—
1227	C₂²	—	2	4	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	2	no	—
1232	C₂²	—	4	2	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	2	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	1	no	—
1238	C₂²	—	4	1	no	—
1239	C₂²	—	4	1	no	—
1240	C₂²	—	4	2	no	—
1241	C₂²	—	4	2	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	1	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	4	2	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	4	2	no	—
1250	C₂²	—	4	2	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	2	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	2	no	—
1258	C₂²	—	4	2	no	—
1259	C₂²	—	8	8	no	—
1260	C₂²	—	8	16	no	—
1261	C₂²	—	8	8	no	—
1262	C₂²	C₃×#535	1	4	yes	—
1263	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1264	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1265	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1266	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1267	C₂²	C₃×#585	1	1	yes	characteristic
1268	C₄	—	2	2	no	—
1269	C₄	—	2	2	no	—
1270	C₄	—	2	2	no	—
1271	C₄	—	2	2	no	—
1272	C₄	—	2	2	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	2	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	2	no	—
1280	C₄	—	4	2	no	—
1281	C₄	—	4	2	no	—
1282	C₄	—	4	2	no	—
1283	C₃	#40588	1	1	yes	characteristic, direct product factor, Sylow
1284	C₂	—	2	4	no	—
1285	C₂	—	4	2	no	—
1286	C₂	—	4	2	no	—
1287	C₂	—	4	4	no	—
1288	C₂	—	8	1	no	—
1289	C₂	—	8	1	no	—
1290	C₂	—	8	2	no	—
1291	C₂	—	8	1	no	—
1292	C₂	C₂×C₃×#535	1	1	yes	characteristic
1293	C₂	C₃×#3484	1	1	yes	characteristic
1294	C₂	C₃×#3488	1	1	yes	characteristic
1295	C₂	C₃×#3532	1	2	yes	—
1296	C₂	C₃×#3534	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×#546	C₂	semidirect
2. C₂×C₃×#546	C₂	semidirect
3. C₃×#2819	C₂	semidirect
4. C₃×#2815	C₂	semidirect
5. C₃×#2703	C₂	semidirect
6. C₃×#2696	C₂	semidirect
7. C₃×#2673	C₂	semidirect
8. C₃×#2669	C₂	semidirect
9. C₃×#2639	C₂	semidirect
10. C₃×#2631	C₂	semidirect
11. C₃×#2631	C₂	semidirect
12. C₃×#2617	C₂	semidirect
13. C₃×#2615	C₂	semidirect
14. C₃×#2561	C₂	semidirect
15. C₃×#2535	C₂	semidirect
16. C₃×#2433	C₂	semidirect
17. C₃×#2412	C₂	semidirect
18. C₃×#2410	C₂	semidirect
19. C₃×#2404	C₂	semidirect
20. C₃×#2404	C₂	semidirect
21. C₃×#2403	C₂	semidirect
22. C₂×C₃×#392	C₂	semidirect
23. C₃×#2318	C₂	semidirect
24. #40588	C₃	direct (N × H)
26. C₂²×C₃×#41	C₂²	semidirect
29. C₂³×C₃×D₄	C₂²	semidirect
32. C₂×C₃×#127	C₂²	semidirect
33. C₂×C₃×#124	C₂²	semidirect
34. C₂×C₃×#124	C₂²	semidirect
36. C₂×C₃×#123	C₂²	semidirect
37. C₂×C₃×#123	C₂²	semidirect
38. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
39. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₃×#121	C₂²	semidirect
42. C₂×C₃×#121	C₂²	semidirect
43. C₂×C₃×#121	C₂²	semidirect
44. C₂×C₃×#121	C₂²	semidirect
45. C₂×C₃×#121	C₂²	semidirect
46. C₂×C₃×#121	C₂²	semidirect
50. C₂×C₃×#120	C₂²	semidirect
51. C₂×C₃×#120	C₂²	semidirect
52. C₂×C₃×#120	C₂²	semidirect
53. C₂×C₃×#120	C₂²	semidirect
55. C₂×C₃×C₄×D₄	C₂²	semidirect
56. C₂×C₃×C₄×D₄	C₂²	semidirect
58. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
59. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
60. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
61. C₃×#400	C₂²	semidirect
62. C₃×#397	C₂²	semidirect
63. C₃×#397	C₂²	semidirect
64. C₃×#397	C₂²	semidirect
65. C₃×#397	C₂²	semidirect
66. C₃×#397	C₂²	semidirect
67. C₃×#397	C₂²	semidirect
68. C₃×#394	C₂²	semidirect
69. C₃×#394	C₂²	semidirect
70. C₃×#394	C₂²	semidirect
71. C₃×#394	C₂²	semidirect
72. C₃×#394	C₂²	semidirect
73. C₃×#393	C₂²	semidirect
74. C₃×#393	C₂²	semidirect
75. C₃×#393	C₂²	semidirect
76. C₃×#393	C₂²	semidirect
77. C₃×#393	C₂²	semidirect
78. C₃×#393	C₂²	semidirect
82. C₃×#392	C₂²	semidirect
83. C₃×#392	C₂²	semidirect
84. C₃×#392	C₂²	semidirect
85. C₃×#392	C₂²	semidirect
86. C₃×#392	C₂²	semidirect
87. C₃×#392	C₂²	semidirect
88. C₃×#392	C₂²	semidirect
89. C₃×#392	C₂²	semidirect
90. C₃×#392	C₂²	semidirect
91. C₃×#392	C₂²	semidirect
92. C₃×#392	C₂²	semidirect
93. C₃×#392	C₂²	semidirect
94. C₃×#392	C₂²	semidirect
95. C₃×#392	C₂²	semidirect
96. C₃×#392	C₂²	semidirect
97. C₃×#390	C₂²	semidirect
98. C₃×#388	C₂²	semidirect
99. C₃×#388	C₂²	semidirect
100. C₃×#388	C₂²	semidirect
101. C₃×#387	C₂²	semidirect
104. C₃×#386	C₂²	semidirect
105. C₃×#386	C₂²	semidirect
106. C₃×#386	C₂²	semidirect
107. C₃×#386	C₂²	semidirect
108. C₃×#386	C₂²	semidirect
109. C₃×#386	C₂²	semidirect
110. C₃×#386	C₂²	semidirect
111. C₃×#386	C₂²	semidirect
112. C₃×#386	C₂²	semidirect
113. C₃×#386	C₂²	semidirect
114. C₃×#386	C₂²	semidirect
115. C₃×#385	C₂²	semidirect
116. C₃×#383	C₂²	semidirect
117. C₃×#382	C₂²	semidirect
118. C₃×#381	C₂²	semidirect
119. C₃×#381	C₂²	semidirect
120. C₃×#380	C₂²	semidirect
121. C₃×#380	C₂²	semidirect
122. C₃×#380	C₂²	semidirect
124. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
125. C₂×C₃×#95	C₂²	semidirect
126. C₂×#546	C₂×C₃	semidirect
127. C₂×#546	C₂×C₃	semidirect
128. #2819	C₂×C₃	semidirect
129. #2815	C₂×C₃	semidirect
130. #2703	C₂×C₃	semidirect
131. #2696	C₂×C₃	semidirect
132. #2673	C₂×C₃	semidirect
133. #2669	C₂×C₃	semidirect
134. #2639	C₂×C₃	semidirect
135. #2631	C₂×C₃	semidirect
136. #2631	C₂×C₃	semidirect
137. #2617	C₂×C₃	semidirect
138. #2615	C₂×C₃	semidirect
139. #2561	C₂×C₃	semidirect
140. #2535	C₂×C₃	semidirect
141. #2433	C₂×C₃	semidirect
142. #2412	C₂×C₃	semidirect
143. #2410	C₂×C₃	semidirect
144. #2404	C₂×C₃	semidirect
145. #2404	C₂×C₃	semidirect
146. #2403	C₂×C₃	semidirect
147. C₂×#392	C₂×C₃	semidirect
148. #2318	C₂×C₃	semidirect
220. C₃×C₄×D₄	D₄	semidirect
289. C₂²×#41	C₂²×C₃	semidirect
292. C₂³×D₄	C₂²×C₃	semidirect
295. C₂×#127	C₂²×C₃	semidirect
296. C₂×#124	C₂²×C₃	semidirect
297. C₂×#124	C₂²×C₃	semidirect
299. C₂×#123	C₂²×C₃	semidirect
300. C₂×#123	C₂²×C₃	semidirect
301. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
302. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
304. C₂×#121	C₂²×C₃	semidirect
305. C₂×#121	C₂²×C₃	semidirect
306. C₂×#121	C₂²×C₃	semidirect
307. C₂×#121	C₂²×C₃	semidirect
308. C₂×#121	C₂²×C₃	semidirect
309. C₂×#121	C₂²×C₃	semidirect
313. C₂×#120	C₂²×C₃	semidirect
314. C₂×#120	C₂²×C₃	semidirect
315. C₂×#120	C₂²×C₃	semidirect
316. C₂×#120	C₂²×C₃	semidirect
318. C₂×C₄×D₄	C₂²×C₃	semidirect
319. C₂×C₄×D₄	C₂²×C₃	semidirect
321. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
322. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
323. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
324. #400	C₂²×C₃	semidirect
325. #397	C₂²×C₃	semidirect
326. #397	C₂²×C₃	semidirect
327. #397	C₂²×C₃	semidirect
328. #397	C₂²×C₃	semidirect
329. #397	C₂²×C₃	semidirect
330. #397	C₂²×C₃	semidirect
331. #394	C₂²×C₃	semidirect
332. #394	C₂²×C₃	semidirect
333. #394	C₂²×C₃	semidirect
334. #394	C₂²×C₃	semidirect
335. #394	C₂²×C₃	semidirect
336. #393	C₂²×C₃	semidirect
337. #393	C₂²×C₃	semidirect
338. #393	C₂²×C₃	semidirect
339. #393	C₂²×C₃	semidirect
340. #393	C₂²×C₃	semidirect
341. #393	C₂²×C₃	semidirect
345. #392	C₂²×C₃	semidirect
346. #392	C₂²×C₃	semidirect
347. #392	C₂²×C₃	semidirect
348. #392	C₂²×C₃	semidirect
349. #392	C₂²×C₃	semidirect
350. #392	C₂²×C₃	semidirect
351. #392	C₂²×C₃	semidirect
352. #392	C₂²×C₃	semidirect
353. #392	C₂²×C₃	semidirect
354. #392	C₂²×C₃	semidirect
355. #392	C₂²×C₃	semidirect
356. #392	C₂²×C₃	semidirect
357. #392	C₂²×C₃	semidirect
358. #392	C₂²×C₃	semidirect
359. #392	C₂²×C₃	semidirect
360. #390	C₂²×C₃	semidirect
361. #388	C₂²×C₃	semidirect
362. #388	C₂²×C₃	semidirect
363. #388	C₂²×C₃	semidirect
364. #387	C₂²×C₃	semidirect
367. #386	C₂²×C₃	semidirect
368. #386	C₂²×C₃	semidirect
369. #386	C₂²×C₃	semidirect
370. #386	C₂²×C₃	semidirect
371. #386	C₂²×C₃	semidirect
372. #386	C₂²×C₃	semidirect
373. #386	C₂²×C₃	semidirect
374. #386	C₂²×C₃	semidirect
375. #386	C₂²×C₃	semidirect
376. #386	C₂²×C₃	semidirect
377. #386	C₂²×C₃	semidirect
378. #385	C₂²×C₃	semidirect
379. #383	C₂²×C₃	semidirect
380. #382	C₂²×C₃	semidirect
381. #381	C₂²×C₃	semidirect
382. #381	C₂²×C₃	semidirect
383. #380	C₂²×C₃	semidirect
384. #380	C₂²×C₃	semidirect
385. #380	C₂²×C₃	semidirect
387. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
388. C₂×#95	C₂²×C₃	semidirect
499. C₂²×C₃×C₄	C₂×D₄	semidirect
522. C₃×C₄⋊C₄	C₂×D₄	semidirect
558. C₃×C₂²⋊C₄	C₂×D₄	semidirect
560. C₃×C₄²	C₂×D₄	semidirect
632. C₄×D₄	C₃×D₄	semidirect
942. C₂²×C₄	C₂×C₃×D₄	semidirect
965. C₄⋊C₄	C₂×C₃×D₄	semidirect
1001. C₂²⋊C₄	C₂×C₃×D₄	semidirect
1003. C₄²	C₂×C₃×D₄	semidirect
1283. C₃	#40588	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#546	2
C₃×#2819	2
C₃×#2815	2
C₃×#2703	2
C₃×#2696	2
C₃×#2673	2
C₃×#2669	2
C₃×#2639	2
C₃×#2631	2
C₃×#2617	2
C₃×#2615	2
C₃×#2561	2
C₃×#2535	2
C₃×#2433	2
C₃×#2412	2
C₃×#2410	2
C₃×#2404	2
C₃×#2403	2
C₂×C₃×#392	2
C₃×#2318	2
#40588	3

Subgroups — C3×#40588 #10659195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#40588 #10659195