Subgroups — C₃×#37651 #10656258

Order 768.

3042 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#525	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2681	C₂	1	2	yes	maximal, complemented
7	C₃×#2680	C₂	1	2	yes	maximal, complemented
8	C₃×#2677	C₂	1	2	yes	maximal, complemented
9	C₃×#2674	C₂	1	2	yes	maximal, complemented
10	C₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2616	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2536	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2472	C₂	1	2	yes	maximal, complemented
15	C₃×#2443	C₂	1	2	yes	maximal, complemented
16	C₃×#2440	C₂	1	2	yes	maximal, complemented
17	C₃×#2418	C₂	1	2	yes	maximal, complemented
18	C₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2415	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2409	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2409	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
24	#37651	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
27	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
29	C₃×D₄×Q₈	—	2	8	no	—
30	C₃×#536	—	2	8	no	—
31	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
33	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
34	C₂×C₃×#124	C₂²	1	2	yes	—
35	C₃×#525	—	2	8	no	—
36	C₂×C₃×#123	C₂²	1	1	yes	characteristic
37	C₂×C₃×#123	C₂²	1	1	yes	characteristic
38	C₂×C₃×#123	C₂²	1	2	yes	—
39	C₂×C₃×#123	C₂²	1	2	yes	complemented
40	C₂×C₃×C₂²⋊Q₈	—	2	8	no	—
41	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
46	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
47	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
52	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×#121	C₂²	1	1	yes	characteristic
59	C₂×C₃×#121	C₂²	1	1	yes	characteristic
60	C₂×C₃×#120	C₂²	1	1	yes	characteristic
61	C₂×C₃×#120	C₂²	1	1	yes	characteristic
62	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
64	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
65	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
66	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
67	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
68	C₂×C₃×#117	C₂²	1	1	yes	characteristic
69	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
70	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
72	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₃×#399	C₂²	1	2	yes	—
74	C₃×#399	C₂²	1	2	yes	complemented
75	C₃×#398	C₂²	1	2	yes	complemented
76	C₃×#398	C₂²	1	2	yes	complemented
77	C₃×#398	C₂²	1	2	yes	complemented
78	C₃×#398	C₂²	1	2	yes	complemented
79	C₃×#397	C₂²	1	2	yes	—
80	C₃×#397	C₂²	1	2	yes	—
81	C₃×#397	C₂²	1	2	yes	complemented
82	C₃×#396	C₂²	1	2	yes	complemented
83	C₃×#395	C₂²	1	2	yes	complemented
84	C₃×#395	C₂²	1	2	yes	complemented
85	C₃×#395	C₂²	1	2	yes	complemented
86	C₃×#394	C₂²	1	2	yes	—
87	C₃×#394	C₂²	1	2	yes	—
88	C₃×#394	C₂²	1	2	yes	—
89	C₃×#394	C₂²	1	2	yes	—
90	C₃×#394	C₂²	1	2	yes	complemented
91	C₃×#393	C₂²	1	2	yes	—
92	C₃×#393	C₂²	1	2	yes	complemented
93	C₃×#391	C₂²	1	1	yes	characteristic, complemented
94	C₃×#391	C₂²	1	1	yes	characteristic, complemented
95	C₃×#391	C₂²	1	1	yes	characteristic, complemented
96	C₃×#390	C₂²	1	2	yes	—
97	C₃×#389	C₂²	1	1	yes	characteristic, complemented
98	C₃×#389	C₂²	1	2	yes	complemented
99	C₃×#389	C₂²	1	2	yes	complemented
100	C₃×#388	C₂²	1	2	yes	—
101	C₃×#388	C₂²	1	2	yes	—
102	C₃×#388	C₂²	1	2	yes	—
103	C₃×#388	C₂²	1	2	yes	—
104	C₃×#388	C₂²	1	2	yes	complemented
105	C₃×#388	C₂²	1	2	yes	complemented
106	C₃×#387	C₂²	1	2	yes	complemented
107	C₃×#387	C₂²	1	2	yes	complemented
108	C₃×#386	C₂²	1	2	yes	—
109	C₃×#386	C₂²	1	2	yes	—
110	C₃×#386	C₂²	1	2	yes	—
111	C₃×#386	C₂²	1	2	yes	—
112	C₃×#385	C₂²	1	2	yes	—
113	C₃×#385	C₂²	1	2	yes	—
114	C₃×#385	C₂²	1	2	yes	—
115	C₃×#385	C₂²	1	2	yes	—
116	C₃×#385	C₂²	1	2	yes	complemented
117	C₃×#384	C₂²	1	2	yes	complemented
118	C₃×#382	C₂²	1	1	yes	characteristic, complemented
119	C₃×#380	C₂²	1	1	yes	characteristic
120	C₃×#380	C₂²	1	1	yes	characteristic
121	C₃×#380	C₂²	1	1	yes	characteristic
122	C₃×#380	C₂²	1	2	yes	—
123	C₃×#380	C₂²	1	1	yes	characteristic, complemented
124	C₃×#380	C₂²	1	1	yes	characteristic, complemented
125	C₃×#379	C₂²	1	2	yes	—
126	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
127	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
128	C₂×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
129	C₂×#536	C₂×C₃	1	1	yes	characteristic, complemented
130	C₂×#525	C₂×C₃	1	1	yes	characteristic
131	C₂²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
132	#2848	C₂×C₃	1	1	yes	characteristic, complemented
133	#2681	C₂×C₃	1	2	yes	complemented
134	#2680	C₂×C₃	1	2	yes	complemented
135	#2677	C₂×C₃	1	2	yes	complemented
136	#2674	C₂×C₃	1	2	yes	complemented
137	#2621	C₂×C₃	1	1	yes	characteristic, complemented
138	#2616	C₂×C₃	1	1	yes	characteristic, complemented
139	#2542	C₂×C₃	1	1	yes	characteristic, complemented
140	#2536	C₂×C₃	1	1	yes	characteristic, complemented
141	#2472	C₂×C₃	1	2	yes	complemented
142	#2443	C₂×C₃	1	2	yes	complemented
143	#2440	C₂×C₃	1	2	yes	complemented
144	#2418	C₂×C₃	1	2	yes	complemented
145	#2417	C₂×C₃	1	1	yes	characteristic, complemented
146	#2415	C₂×C₃	1	1	yes	characteristic, complemented
147	#2409	C₂×C₃	1	1	yes	characteristic, complemented
148	#2409	C₂×C₃	1	1	yes	characteristic, complemented
149	#2352	C₂×C₃	1	1	yes	characteristic, complemented
150	#2323	C₂×C₃	1	1	yes	characteristic, complemented
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	2	no	—
155	C₂²×C₃×Q₈	—	2	4	no	—
156	C₂²×C₃×Q₈	—	2	4	no	—
157	C₂²×C₃×Q₈	—	2	4	no	—
158	C₂²×C₃×Q₈	—	2	4	no	—
159	C₂²×C₃×Q₈	—	4	2	no	—
160	C₂²×C₃×Q₈	—	4	2	no	—
161	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
162	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
163	C₂²×C₃×Q₈	C₂³	1	2	yes	—
164	C₂²×C₃×Q₈	C₂³	1	2	yes	—
165	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
166	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
167	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
168	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
169	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
170	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
171	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
172	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
173	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
174	C₂³×C₃×C₄	—	2	4	no	—
175	C₂³×C₃×C₄	—	2	4	no	—
176	C₂³×C₃×C₄	—	4	2	no	—
177	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
178	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
179	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
180	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
181	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
182	C₂³×C₃×C₄	C₂³	1	2	yes	—
183	C₂³×C₃×C₄	C₂³	1	2	yes	—
184	C₂³×C₃×C₄	C₂³	1	2	yes	—
185	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
186	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
187	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
188	C₃×C₄⋊Q₈	—	2	8	no	—
189	C₃×C₄⋊Q₈	—	2	8	no	—
190	C₃×C₄⋊Q₈	—	2	4	no	—
191	C₃×#124	—	2	8	no	—
192	C₃×#123	—	2	4	no	—
193	C₃×#123	—	2	8	no	—
194	C₃×#123	—	2	4	no	—
195	C₃×#123	—	2	8	no	—
196	C₃×C₂²⋊Q₈	—	2	4	no	—
197	C₃×C₂²⋊Q₈	—	2	4	no	—
198	C₃×C₂²⋊Q₈	—	2	4	no	—
199	C₃×C₂²⋊Q₈	—	2	4	no	—
200	C₃×C₂²⋊Q₈	—	2	4	no	—
201	C₃×C₂²⋊Q₈	—	2	4	no	—
202	C₃×C₂²⋊Q₈	—	2	4	no	—
203	C₃×C₂²⋊Q₈	—	2	8	no	—
204	C₃×C₂²⋊Q₈	—	2	4	no	—
205	C₃×C₂²⋊Q₈	—	2	4	no	—
206	C₃×C₂²⋊Q₈	—	2	8	no	—
207	C₃×C₂²⋊Q₈	—	2	4	no	—
208	C₃×C₂²⋊Q₈	—	2	8	no	—
209	C₃×C₂²⋊Q₈	—	2	8	no	—
210	C₃×C₂²⋊Q₈	—	4	2	no	—
211	C₃×C₂²⋊Q₈	—	4	2	no	—
212	C₃×C₂²⋊Q₈	D₄	1	8	yes	complemented
213	C₃×#121	—	2	4	no	—
214	C₃×#121	—	2	4	no	—
215	C₃×#120	—	2	4	no	—
216	C₃×#120	—	2	4	no	—
217	C₃×C₄×Q₈	—	2	4	no	—
218	C₃×C₄×D₄	—	2	8	no	—
219	C₃×C₄×D₄	—	2	4	no	—
220	C₃×C₄×D₄	—	2	4	no	—
221	C₃×C₄×D₄	—	2	4	no	—
222	C₃×C₄×D₄	D₄	1	8	yes	—
223	C₃×#117	—	2	4	no	—
224	C₃×#117	—	2	4	no	—
225	C₂×C₃×C₄⋊C₄	—	2	4	no	—
226	C₂×C₃×C₄⋊C₄	—	2	8	no	—
227	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
234	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
241	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
242	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
243	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
248	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
249	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
250	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
251	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
254	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
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	1	yes	characteristic
260	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
266	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
270	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
273	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
274	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
275	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
276	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
277	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
278	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
279	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
281	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₃×C₄²	C₂³	1	2	yes	—
283	C₂×C₃×C₄²	C₂³	1	2	yes	—
284	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
285	C₂×C₃×C₄²	C₂³	1	2	yes	—
286	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
287	C₃×#95	C₂³	1	2	yes	—
288	C₃×#95	C₂³	1	2	yes	—
289	C₃×#95	C₂³	1	2	yes	—
290	C₃×#95	C₂³	1	2	yes	—
291	C₃×#95	C₂³	1	2	yes	—
292	C₃×#95	C₂³	1	2	yes	—
293	C₃×#95	C₂³	1	2	yes	—
294	C₃×#95	C₂³	1	2	yes	—
295	C₃×#95	C₂³	1	2	yes	—
296	C₃×#95	C₂³	1	2	yes	—
297	C₃×#95	C₂³	1	2	yes	—
298	C₃×#95	C₂³	1	2	yes	—
299	C₃×#95	C₂³	1	2	yes	—
300	C₃×#95	C₂³	1	2	yes	—
301	C₃×#95	C₂³	1	2	yes	—
302	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
303	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
304	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
305	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
306	D₄×Q₈	—	2	8	no	—
307	#536	—	2	8	no	—
308	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
309	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
310	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
311	C₂×#124	C₂²×C₃	1	2	yes	—
312	#525	—	2	8	no	—
313	C₂×#123	C₂²×C₃	1	1	yes	characteristic
314	C₂×#123	C₂²×C₃	1	1	yes	characteristic
315	C₂×#123	C₂²×C₃	1	2	yes	—
316	C₂×#123	C₂²×C₃	1	2	yes	complemented
317	C₂×C₂²⋊Q₈	—	2	8	no	—
318	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
319	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
320	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
321	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
322	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
323	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
324	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
325	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
326	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
327	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
328	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
329	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
330	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
331	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
332	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
333	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
334	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
335	C₂×#121	C₂²×C₃	1	1	yes	characteristic
336	C₂×#121	C₂²×C₃	1	1	yes	characteristic
337	C₂×#120	C₂²×C₃	1	1	yes	characteristic
338	C₂×#120	C₂²×C₃	1	1	yes	characteristic
339	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
340	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
342	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
343	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
344	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
345	C₂×#117	C₂²×C₃	1	1	yes	characteristic
346	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
347	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
348	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
349	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
350	#399	C₂²×C₃	1	2	yes	—
351	#399	C₂²×C₃	1	2	yes	complemented
352	#398	C₂²×C₃	1	2	yes	complemented
353	#398	C₂²×C₃	1	2	yes	complemented
354	#398	C₂²×C₃	1	2	yes	complemented
355	#398	C₂²×C₃	1	2	yes	complemented
356	#397	C₂²×C₃	1	2	yes	—
357	#397	C₂²×C₃	1	2	yes	—
358	#397	C₂²×C₃	1	2	yes	complemented
359	#396	C₂²×C₃	1	2	yes	complemented
360	#395	C₂²×C₃	1	2	yes	complemented
361	#395	C₂²×C₃	1	2	yes	complemented
362	#395	C₂²×C₃	1	2	yes	complemented
363	#394	C₂²×C₃	1	2	yes	—
364	#394	C₂²×C₃	1	2	yes	—
365	#394	C₂²×C₃	1	2	yes	—
366	#394	C₂²×C₃	1	2	yes	—
367	#394	C₂²×C₃	1	2	yes	complemented
368	#393	C₂²×C₃	1	2	yes	—
369	#393	C₂²×C₃	1	2	yes	complemented
370	#391	C₂²×C₃	1	1	yes	characteristic, complemented
371	#391	C₂²×C₃	1	1	yes	characteristic, complemented
372	#391	C₂²×C₃	1	1	yes	characteristic, complemented
373	#390	C₂²×C₃	1	2	yes	—
374	#389	C₂²×C₃	1	1	yes	characteristic, complemented
375	#389	C₂²×C₃	1	2	yes	complemented
376	#389	C₂²×C₃	1	2	yes	complemented
377	#388	C₂²×C₃	1	2	yes	—
378	#388	C₂²×C₃	1	2	yes	—
379	#388	C₂²×C₃	1	2	yes	—
380	#388	C₂²×C₃	1	2	yes	—
381	#388	C₂²×C₃	1	2	yes	complemented
382	#388	C₂²×C₃	1	2	yes	complemented
383	#387	C₂²×C₃	1	2	yes	complemented
384	#387	C₂²×C₃	1	2	yes	complemented
385	#386	C₂²×C₃	1	2	yes	—
386	#386	C₂²×C₃	1	2	yes	—
387	#386	C₂²×C₃	1	2	yes	—
388	#386	C₂²×C₃	1	2	yes	—
389	#385	C₂²×C₃	1	2	yes	—
390	#385	C₂²×C₃	1	2	yes	—
391	#385	C₂²×C₃	1	2	yes	—
392	#385	C₂²×C₃	1	2	yes	—
393	#385	C₂²×C₃	1	2	yes	complemented
394	#384	C₂²×C₃	1	2	yes	complemented
395	#382	C₂²×C₃	1	1	yes	characteristic, complemented
396	#380	C₂²×C₃	1	1	yes	characteristic
397	#380	C₂²×C₃	1	1	yes	characteristic
398	#380	C₂²×C₃	1	1	yes	characteristic
399	#380	C₂²×C₃	1	2	yes	—
400	#380	C₂²×C₃	1	1	yes	characteristic, complemented
401	#380	C₂²×C₃	1	1	yes	characteristic, complemented
402	#379	C₂²×C₃	1	2	yes	—
403	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
404	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
405	C₂⁴×C₃	—	2	2	no	—
406	C₂⁴×C₃	—	2	2	no	—
407	C₂⁴×C₃	—	2	2	no	—
408	C₂⁴×C₃	—	2	2	no	—
409	C₂⁴×C₃	—	2	2	no	—
410	C₂⁴×C₃	—	4	1	no	—
411	C₂⁴×C₃	—	4	1	no	—
412	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
413	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
414	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
415	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
416	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
417	C₃×#41	—	4	16	no	—
418	C₂×C₃×Q₈	—	2	2	no	—
419	C₂×C₃×Q₈	—	2	4	no	—
420	C₂×C₃×Q₈	—	2	2	no	—
421	C₂×C₃×Q₈	—	2	2	no	—
422	C₂×C₃×Q₈	—	2	2	no	—
423	C₂×C₃×Q₈	—	2	4	no	—
424	C₂×C₃×Q₈	—	2	4	no	—
425	C₂×C₃×Q₈	—	2	2	no	—
426	C₂×C₃×Q₈	—	2	2	no	—
427	C₂×C₃×Q₈	—	2	4	no	—
428	C₂×C₃×Q₈	—	2	2	no	—
429	C₂×C₃×Q₈	—	2	2	no	—
430	C₂×C₃×Q₈	—	2	2	no	—
431	C₂×C₃×Q₈	—	2	2	no	—
432	C₂×C₃×Q₈	—	4	2	no	—
433	C₂×C₃×Q₈	—	4	2	no	—
434	C₂×C₃×Q₈	—	4	1	no	—
435	C₂×C₃×Q₈	—	4	16	no	—
436	C₂×C₃×Q₈	—	4	16	no	—
437	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
438	C₂×C₃×D₄	—	2	2	no	—
439	C₂×C₃×D₄	—	2	2	no	—
440	C₂×C₃×D₄	—	2	2	no	—
441	C₂×C₃×D₄	—	2	2	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	—	2	2	no	—
447	C₂×C₃×D₄	—	2	2	no	—
448	C₂×C₃×D₄	—	2	2	no	—
449	C₂×C₃×D₄	—	2	2	no	—
450	C₂×C₃×D₄	—	2	2	no	—
451	C₂×C₃×D₄	—	2	2	no	—
452	C₂×C₃×D₄	—	2	2	no	—
453	C₂×C₃×D₄	—	4	1	no	—
454	C₂×C₃×D₄	—	4	1	no	—
455	C₂×C₃×D₄	—	4	1	no	—
456	C₂×C₃×D₄	—	4	1	no	—
457	C₂×C₃×D₄	—	4	1	no	—
458	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
459	C₂²×C₃×C₄	—	2	2	no	—
460	C₂²×C₃×C₄	—	2	2	no	—
461	C₂²×C₃×C₄	—	2	2	no	—
462	C₂²×C₃×C₄	—	2	2	no	—
463	C₂²×C₃×C₄	—	2	2	no	—
464	C₂²×C₃×C₄	—	2	2	no	—
465	C₂²×C₃×C₄	—	2	4	no	—
466	C₂²×C₃×C₄	—	2	4	no	—
467	C₂²×C₃×C₄	—	2	2	no	—
468	C₂²×C₃×C₄	—	2	2	no	—
469	C₂²×C₃×C₄	—	2	4	no	—
470	C₂²×C₃×C₄	—	2	4	no	—
471	C₂²×C₃×C₄	—	2	4	no	—
472	C₂²×C₃×C₄	—	2	2	no	—
473	C₂²×C₃×C₄	—	2	2	no	—
474	C₂²×C₃×C₄	—	2	2	no	—
475	C₂²×C₃×C₄	—	2	2	no	—
476	C₂²×C₃×C₄	—	2	2	no	—
477	C₂²×C₃×C₄	—	2	2	no	—
478	C₂²×C₃×C₄	—	2	2	no	—
479	C₂²×C₃×C₄	—	2	2	no	—
480	C₂²×C₃×C₄	—	2	4	no	—
481	C₂²×C₃×C₄	—	2	2	no	—
482	C₂²×C₃×C₄	—	2	2	no	—
483	C₂²×C₃×C₄	—	4	1	no	—
484	C₂²×C₃×C₄	—	4	1	no	—
485	C₂²×C₃×C₄	—	4	1	no	—
486	C₂²×C₃×C₄	—	4	2	no	—
487	C₂²×C₃×C₄	—	4	2	no	—
488	C₂²×C₃×C₄	—	4	2	no	—
489	C₂²×C₃×C₄	—	4	16	no	—
490	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
491	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
492	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
493	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
494	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
495	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
496	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
497	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
498	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
499	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
500	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
501	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
502	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
503	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
504	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
505	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	C₃×C₄⋊C₄	—	2	4	no	—
512	C₃×C₄⋊C₄	—	2	2	no	—
513	C₃×C₄⋊C₄	—	2	4	no	—
514	C₃×C₄⋊C₄	—	2	4	no	—
515	C₃×C₄⋊C₄	—	2	4	no	—
516	C₃×C₄⋊C₄	—	2	2	no	—
517	C₃×C₄⋊C₄	—	2	2	no	—
518	C₃×C₄⋊C₄	—	2	2	no	—
519	C₃×C₄⋊C₄	—	2	2	no	—
520	C₃×C₄⋊C₄	—	2	2	no	—
521	C₃×C₄⋊C₄	—	2	2	no	—
522	C₃×C₄⋊C₄	—	2	4	no	—
523	C₃×C₄⋊C₄	—	2	4	no	—
524	C₃×C₄⋊C₄	—	2	2	no	—
525	C₃×C₄⋊C₄	—	2	4	no	—
526	C₃×C₄⋊C₄	—	2	4	no	—
527	C₃×C₄⋊C₄	—	2	4	no	—
528	C₃×C₄⋊C₄	—	2	4	no	—
529	C₃×C₄⋊C₄	—	2	4	no	—
530	C₃×C₄⋊C₄	—	2	4	no	—
531	C₃×C₄⋊C₄	—	2	2	no	—
532	C₃×C₄⋊C₄	—	4	2	no	—
533	C₃×C₄⋊C₄	—	4	2	no	—
534	C₃×C₄⋊C₄	—	4	2	no	—
535	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
536	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
537	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
538	C₃×C₂²⋊C₄	—	2	4	no	—
539	C₃×C₂²⋊C₄	—	2	2	no	—
540	C₃×C₂²⋊C₄	—	2	2	no	—
541	C₃×C₂²⋊C₄	—	2	4	no	—
542	C₃×C₂²⋊C₄	—	2	4	no	—
543	C₃×C₂²⋊C₄	—	2	4	no	—
544	C₃×C₂²⋊C₄	—	2	4	no	—
545	C₃×C₂²⋊C₄	—	2	4	no	—
546	C₃×C₂²⋊C₄	—	2	4	no	—
547	C₃×C₂²⋊C₄	—	2	4	no	—
548	C₃×C₂²⋊C₄	—	2	2	no	—
549	C₃×C₂²⋊C₄	—	2	2	no	—
550	C₃×C₂²⋊C₄	—	2	4	no	—
551	C₃×C₂²⋊C₄	—	2	2	no	—
552	C₃×C₂²⋊C₄	—	2	2	no	—
553	C₃×C₂²⋊C₄	—	2	2	no	—
554	C₃×C₂²⋊C₄	—	2	2	no	—
555	C₃×C₂²⋊C₄	—	2	4	no	—
556	C₃×C₂²⋊C₄	—	2	4	no	—
557	C₃×C₂²⋊C₄	—	4	2	no	—
558	C₃×C₂²⋊C₄	—	4	2	no	—
559	C₃×C₂²⋊C₄	—	4	2	no	—
560	C₃×C₂²⋊C₄	—	4	2	no	—
561	C₃×C₂²⋊C₄	—	4	2	no	—
562	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
563	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
564	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
565	C₃×C₄²	—	2	2	no	—
566	C₃×C₄²	—	2	4	no	—
567	C₃×C₄²	—	2	4	no	—
568	C₃×C₄²	—	4	2	no	—
569	C₃×C₄²	C₂×D₄	1	4	yes	—
570	C₂⁵	C₂³×C₃	1	1	yes	characteristic
571	C₂×#41	—	2	4	no	—
572	C₂×#41	—	2	4	no	—
573	C₂×#41	—	4	2	no	—
574	C₂²×Q₈	—	2	4	no	—
575	C₂²×Q₈	—	2	4	no	—
576	C₂²×Q₈	—	2	4	no	—
577	C₂²×Q₈	—	2	4	no	—
578	C₂²×Q₈	—	4	2	no	—
579	C₂²×Q₈	—	4	2	no	—
580	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
581	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
582	C₂²×Q₈	C₂³×C₃	1	2	yes	—
583	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
584	C₂²×Q₈	C₂³×C₃	1	2	yes	—
585	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
586	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
587	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
590	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
591	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
592	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
593	C₂³×C₄	—	2	4	no	—
594	C₂³×C₄	—	2	4	no	—
595	C₂³×C₄	—	4	2	no	—
596	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₃	1	2	yes	—
599	C₂³×C₄	C₂³×C₃	1	2	yes	—
600	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₃	1	2	yes	—
602	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
603	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	8	no	—
608	C₄⋊Q₈	—	2	8	no	—
609	C₄⋊Q₈	—	2	4	no	—
610	#124	—	2	8	no	—
611	#123	—	2	4	no	—
612	#123	—	2	8	no	—
613	#123	—	2	4	no	—
614	#123	—	2	8	no	—
615	C₂²⋊Q₈	—	2	4	no	—
616	C₂²⋊Q₈	—	2	4	no	—
617	C₂²⋊Q₈	—	2	4	no	—
618	C₂²⋊Q₈	—	2	4	no	—
619	C₂²⋊Q₈	—	2	4	no	—
620	C₂²⋊Q₈	—	2	4	no	—
621	C₂²⋊Q₈	—	2	4	no	—
622	C₂²⋊Q₈	—	2	8	no	—
623	C₂²⋊Q₈	—	2	4	no	—
624	C₂²⋊Q₈	—	2	4	no	—
625	C₂²⋊Q₈	—	2	8	no	—
626	C₂²⋊Q₈	—	2	4	no	—
627	C₂²⋊Q₈	—	2	8	no	—
628	C₂²⋊Q₈	—	2	8	no	—
629	C₂²⋊Q₈	—	4	2	no	—
630	C₂²⋊Q₈	—	4	2	no	—
631	C₂²⋊Q₈	C₃×D₄	1	8	yes	complemented
632	#121	—	2	4	no	—
633	#121	—	2	4	no	—
634	#120	—	2	4	no	—
635	#120	—	2	4	no	—
636	C₄×Q₈	—	2	4	no	—
637	C₄×D₄	—	2	8	no	—
638	C₄×D₄	—	2	4	no	—
639	C₄×D₄	—	2	4	no	—
640	C₄×D₄	—	2	4	no	—
641	C₄×D₄	C₃×D₄	1	8	yes	—
642	#117	—	2	4	no	—
643	#117	—	2	4	no	—
644	C₂×C₄⋊C₄	—	2	4	no	—
645	C₂×C₄⋊C₄	—	2	8	no	—
646	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	—	2	8	no	—
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	1	yes	characteristic
678	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
684	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
686	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₃	1	2	yes	—
703	C₂×C₄²	C₂³×C₃	1	2	yes	—
704	C₂×C₄²	C₂³×C₃	1	2	yes	—
705	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
706	#95	C₂³×C₃	1	2	yes	—
707	#95	C₂³×C₃	1	2	yes	—
708	#95	C₂³×C₃	1	2	yes	—
709	#95	C₂³×C₃	1	2	yes	—
710	#95	C₂³×C₃	1	2	yes	—
711	#95	C₂³×C₃	1	2	yes	—
712	#95	C₂³×C₃	1	2	yes	—
713	#95	C₂³×C₃	1	2	yes	—
714	#95	C₂³×C₃	1	2	yes	—
715	#95	C₂³×C₃	1	2	yes	—
716	#95	C₂³×C₃	1	2	yes	—
717	#95	C₂³×C₃	1	2	yes	—
718	#95	C₂³×C₃	1	2	yes	—
719	#95	C₂³×C₃	1	2	yes	—
720	#95	C₂³×C₃	1	2	yes	—
721	C₂³×C₃	—	2	1	no	—
722	C₂³×C₃	—	2	1	no	—
723	C₂³×C₃	—	2	1	no	—
724	C₂³×C₃	—	2	1	no	—
725	C₂³×C₃	—	2	8	no	—
726	C₂³×C₃	—	2	1	no	—
727	C₂³×C₃	—	2	1	no	—
728	C₂³×C₃	—	2	1	no	—
729	C₂³×C₃	—	2	1	no	—
730	C₂³×C₃	—	2	1	no	—
731	C₂³×C₃	—	2	1	no	—
732	C₂³×C₃	—	2	1	no	—
733	C₂³×C₃	—	2	1	no	—
734	C₂³×C₃	—	2	1	no	—
735	C₂³×C₃	—	2	1	no	—
736	C₂³×C₃	—	2	1	no	—
737	C₂³×C₃	—	2	1	no	—
738	C₂³×C₃	—	2	1	no	—
739	C₂³×C₃	—	2	1	no	—
740	C₂³×C₃	—	2	1	no	—
741	C₂³×C₃	—	2	1	no	—
742	C₂³×C₃	—	2	1	no	—
743	C₂³×C₃	—	2	1	no	—
744	C₂³×C₃	—	2	1	no	—
745	C₂³×C₃	—	2	1	no	—
746	C₂³×C₃	—	2	1	no	—
747	C₂³×C₃	—	2	1	no	—
748	C₂³×C₃	—	2	1	no	—
749	C₂³×C₃	—	2	1	no	—
750	C₂³×C₃	—	2	1	no	—
751	C₂³×C₃	—	4	4	no	—
752	C₂³×C₃	—	4	4	no	—
753	C₂³×C₃	—	4	4	no	—
754	C₂³×C₃	—	4	4	no	—
755	C₂³×C₃	—	4	4	no	—
756	C₂³×C₃	—	4	4	no	—
757	C₂³×C₃	C₂²×D₄	1	2	yes	—
758	C₂³×C₃	C₂²×D₄	1	2	yes	—
759	C₂³×C₃	C₂²×D₄	1	2	yes	—
760	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
761	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
762	C₂³×C₃	2₋¹⁺⁴	1	2	yes	—
763	C₂³×C₃	C₂⁵	1	1	yes	characteristic
764	C₃×Q₈	—	2	8	no	—
765	C₃×Q₈	—	4	8	no	—
766	C₃×Q₈	—	4	8	no	—
767	C₃×Q₈	—	4	4	no	—
768	C₃×Q₈	—	4	4	no	—
769	C₃×Q₈	—	4	4	no	—
770	C₃×D₄	—	2	8	no	—
771	C₃×D₄	—	4	4	no	—
772	C₃×D₄	—	4	4	no	—
773	C₃×D₄	—	4	4	no	—
774	C₃×D₄	—	4	4	no	—
775	C₃×D₄	—	4	4	no	—
776	C₃×D₄	—	4	4	no	—
777	C₂×C₃×C₄	—	2	1	no	—
778	C₂×C₃×C₄	—	2	2	no	—
779	C₂×C₃×C₄	—	2	1	no	—
780	C₂×C₃×C₄	—	2	1	no	—
781	C₂×C₃×C₄	—	2	1	no	—
782	C₂×C₃×C₄	—	2	1	no	—
783	C₂×C₃×C₄	—	2	1	no	—
784	C₂×C₃×C₄	—	2	2	no	—
785	C₂×C₃×C₄	—	2	2	no	—
786	C₂×C₃×C₄	—	2	1	no	—
787	C₂×C₃×C₄	—	2	1	no	—
788	C₂×C₃×C₄	—	2	1	no	—
789	C₂×C₃×C₄	—	2	1	no	—
790	C₂×C₃×C₄	—	2	2	no	—
791	C₂×C₃×C₄	—	2	8	no	—
792	C₂×C₃×C₄	—	2	8	no	—
793	C₂×C₃×C₄	—	2	8	no	—
794	C₂×C₃×C₄	—	2	2	no	—
795	C₂×C₃×C₄	—	2	1	no	—
796	C₂×C₃×C₄	—	2	1	no	—
797	C₂×C₃×C₄	—	2	2	no	—
798	C₂×C₃×C₄	—	2	2	no	—
799	C₂×C₃×C₄	—	2	1	no	—
800	C₂×C₃×C₄	—	2	1	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	1	no	—
806	C₂×C₃×C₄	—	2	1	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	1	no	—
811	C₂×C₃×C₄	—	2	1	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	1	no	—
818	C₂×C₃×C₄	—	2	1	no	—
819	C₂×C₃×C₄	—	2	1	no	—
820	C₂×C₃×C₄	—	2	2	no	—
821	C₂×C₃×C₄	—	2	2	no	—
822	C₂×C₃×C₄	—	2	2	no	—
823	C₂×C₃×C₄	—	2	1	no	—
824	C₂×C₃×C₄	—	4	4	no	—
825	C₂×C₃×C₄	—	4	8	no	—
826	C₂×C₃×C₄	—	4	4	no	—
827	C₂×C₃×C₄	—	4	4	no	—
828	C₂×C₃×C₄	—	4	8	no	—
829	C₂×C₃×C₄	—	4	8	no	—
830	C₂×C₃×C₄	—	4	4	no	—
831	C₂×C₃×C₄	—	4	4	no	—
832	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
833	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
834	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
835	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
836	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
837	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
838	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
839	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
840	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
841	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
842	C₂⁴	—	2	2	no	—
843	C₂⁴	—	2	2	no	—
844	C₂⁴	—	2	2	no	—
845	C₂⁴	—	2	2	no	—
846	C₂⁴	—	2	2	no	—
847	C₂⁴	—	4	1	no	—
848	C₂⁴	—	4	1	no	—
849	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
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	#41	—	4	16	no	—
855	C₂×Q₈	—	2	2	no	—
856	C₂×Q₈	—	2	4	no	—
857	C₂×Q₈	—	2	2	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	4	no	—
861	C₂×Q₈	—	2	4	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	4	no	—
865	C₂×Q₈	—	2	2	no	—
866	C₂×Q₈	—	2	2	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	2	2	no	—
869	C₂×Q₈	—	4	2	no	—
870	C₂×Q₈	—	4	2	no	—
871	C₂×Q₈	—	4	1	no	—
872	C₂×Q₈	—	4	16	no	—
873	C₂×Q₈	—	4	16	no	—
874	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	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	—	2	2	no	—
890	C₂×D₄	—	4	1	no	—
891	C₂×D₄	—	4	1	no	—
892	C₂×D₄	—	4	1	no	—
893	C₂×D₄	—	4	1	no	—
894	C₂×D₄	—	4	1	no	—
895	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	4	no	—
903	C₂²×C₄	—	2	4	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	4	no	—
907	C₂²×C₄	—	2	4	no	—
908	C₂²×C₄	—	2	4	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	4	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	4	1	no	—
921	C₂²×C₄	—	4	1	no	—
922	C₂²×C₄	—	4	1	no	—
923	C₂²×C₄	—	4	2	no	—
924	C₂²×C₄	—	4	2	no	—
925	C₂²×C₄	—	4	2	no	—
926	C₂²×C₄	—	4	16	no	—
927	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
928	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
929	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
930	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
932	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
933	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
935	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
936	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
938	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
939	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
945	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
948	C₄⋊C₄	—	2	4	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	4	no	—
951	C₄⋊C₄	—	2	4	no	—
952	C₄⋊C₄	—	2	4	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	4	no	—
960	C₄⋊C₄	—	2	4	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	4	no	—
963	C₄⋊C₄	—	2	4	no	—
964	C₄⋊C₄	—	2	4	no	—
965	C₄⋊C₄	—	2	4	no	—
966	C₄⋊C₄	—	2	4	no	—
967	C₄⋊C₄	—	2	4	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	4	2	no	—
970	C₄⋊C₄	—	4	2	no	—
971	C₄⋊C₄	—	4	2	no	—
972	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
973	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
974	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
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	4	no	—
980	C₂²⋊C₄	—	2	4	no	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	2	4	no	—
983	C₂²⋊C₄	—	2	4	no	—
984	C₂²⋊C₄	—	2	4	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	4	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	4	no	—
993	C₂²⋊C₄	—	2	4	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	C₂×C₃×D₄	1	8	yes	—
1000	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
1001	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	4	no	—
1004	C₄²	—	2	4	no	—
1005	C₄²	—	4	2	no	—
1006	C₄²	C₂×C₃×D₄	1	4	yes	—
1007	C₂²×C₃	—	2	2	no	—
1008	C₂²×C₃	—	2	2	no	—
1009	C₂²×C₃	—	2	2	no	—
1010	C₂²×C₃	—	2	2	no	—
1011	C₂²×C₃	—	2	2	no	—
1012	C₂²×C₃	—	2	2	no	—
1013	C₂²×C₃	—	2	2	no	—
1014	C₂²×C₃	—	2	2	no	—
1015	C₂²×C₃	—	2	2	no	—
1016	C₂²×C₃	—	2	2	no	—
1017	C₂²×C₃	—	2	2	no	—
1018	C₂²×C₃	—	2	2	no	—
1019	C₂²×C₃	—	2	2	no	—
1020	C₂²×C₃	—	2	2	no	—
1021	C₂²×C₃	—	2	2	no	—
1022	C₂²×C₃	—	4	16	no	—
1023	C₂²×C₃	—	4	1	no	—
1024	C₂²×C₃	—	4	1	no	—
1025	C₂²×C₃	—	4	1	no	—
1026	C₂²×C₃	—	4	1	no	—
1027	C₂²×C₃	—	4	1	no	—
1028	C₂²×C₃	—	4	1	no	—
1029	C₂²×C₃	—	4	1	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	1	no	—
1035	C₂²×C₃	—	4	1	no	—
1036	C₂²×C₃	—	4	1	no	—
1037	C₂²×C₃	—	4	1	no	—
1038	C₂²×C₃	—	4	1	no	—
1039	C₂²×C₃	—	4	1	no	—
1040	C₂²×C₃	—	4	1	no	—
1041	C₂²×C₃	—	4	1	no	—
1042	C₂²×C₃	#536	1	4	yes	complemented
1043	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1044	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1045	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1046	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1047	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1048	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1049	C₂²×C₃	#585	1	1	yes	characteristic
1050	C₃×C₄	—	2	2	no	—
1051	C₃×C₄	—	2	2	no	—
1052	C₃×C₄	—	2	2	no	—
1053	C₃×C₄	—	2	2	no	—
1054	C₃×C₄	—	2	4	no	—
1055	C₃×C₄	—	2	4	no	—
1056	C₃×C₄	—	2	2	no	—
1057	C₃×C₄	—	4	1	no	—
1058	C₃×C₄	—	4	1	no	—
1059	C₃×C₄	—	4	1	no	—
1060	C₃×C₄	—	4	2	no	—
1061	C₃×C₄	—	4	2	no	—
1062	C₃×C₄	—	4	2	no	—
1063	C₃×C₄	—	4	2	no	—
1064	C₃×C₄	—	4	2	no	—
1065	C₃×C₄	—	4	1	no	—
1066	C₃×C₄	—	4	2	no	—
1067	C₃×C₄	D₄²	1	4	yes	—
1068	C₂³	—	2	1	no	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	1	no	—
1072	C₂³	—	2	8	no	—
1073	C₂³	—	2	1	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	1	no	—
1076	C₂³	—	2	1	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	1	no	—
1079	C₂³	—	2	1	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	2	1	no	—
1082	C₂³	—	2	1	no	—
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	2	1	no	—
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	1	no	—
1093	C₂³	—	2	1	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	1	no	—
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	1	no	—
1098	C₂³	—	4	4	no	—
1099	C₂³	—	4	4	no	—
1100	C₂³	—	4	4	no	—
1101	C₂³	—	4	4	no	—
1102	C₂³	—	4	4	no	—
1103	C₂³	—	4	4	no	—
1104	C₂³	C₂²×C₃×D₄	1	2	yes	—
1105	C₂³	C₂²×C₃×D₄	1	2	yes	—
1106	C₂³	C₂²×C₃×D₄	1	2	yes	—
1107	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
1108	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
1109	C₂³	C₃×2₋¹⁺⁴	1	2	yes	—
1110	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1111	Q₈	—	2	8	no	—
1112	Q₈	—	4	8	no	—
1113	Q₈	—	4	8	no	—
1114	Q₈	—	4	4	no	—
1115	Q₈	—	4	4	no	—
1116	Q₈	—	4	4	no	—
1117	D₄	—	2	8	no	—
1118	D₄	—	4	4	no	—
1119	D₄	—	4	4	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	4	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	2	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	8	no	—
1139	C₂×C₄	—	2	8	no	—
1140	C₂×C₄	—	2	8	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	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	2	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	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	4	4	no	—
1172	C₂×C₄	—	4	4	no	—
1173	C₂×C₄	—	4	4	no	—
1174	C₂×C₄	—	4	8	no	—
1175	C₂×C₄	—	4	8	no	—
1176	C₂×C₄	—	4	8	no	—
1177	C₂×C₄	—	4	4	no	—
1178	C₂×C₄	—	4	4	no	—
1179	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1180	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1181	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1182	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
1183	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1184	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1185	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1186	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1187	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1188	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1189	C₂×C₃	—	2	4	no	—
1190	C₂×C₃	—	4	2	no	—
1191	C₂×C₃	—	4	2	no	—
1192	C₂×C₃	—	4	2	no	—
1193	C₂×C₃	—	8	1	no	—
1194	C₂×C₃	C₂×#536	1	1	yes	characteristic
1195	C₂×C₃	C₂×D₄²	1	1	yes	characteristic
1196	C₂×C₃	#3486	1	1	yes	characteristic
1197	C₂×C₃	#3489	1	1	yes	characteristic
1198	C₂×C₃	#3489	1	1	yes	characteristic
1199	C₂×C₃	#3538	1	1	yes	characteristic
1200	C₂×C₃	#3541	1	1	yes	characteristic
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	2	2	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	2	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	2	2	no	—
1210	C₂²	—	2	2	no	—
1211	C₂²	—	2	2	no	—
1212	C₂²	—	2	2	no	—
1213	C₂²	—	2	2	no	—
1214	C₂²	—	2	2	no	—
1215	C₂²	—	2	2	no	—
1216	C₂²	—	4	16	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	1	no	—
1234	C₂²	—	4	1	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	C₃×#536	1	4	yes	complemented
1237	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1238	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1239	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1240	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1241	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1242	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1243	C₂²	C₃×#585	1	1	yes	characteristic
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	2	2	no	—
1247	C₄	—	2	2	no	—
1248	C₄	—	2	4	no	—
1249	C₄	—	2	4	no	—
1250	C₄	—	2	2	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	2	no	—
1255	C₄	—	4	2	no	—
1256	C₄	—	4	2	no	—
1257	C₄	—	4	2	no	—
1258	C₄	—	4	1	no	—
1259	C₄	—	4	2	no	—
1260	C₄	—	4	2	no	—
1261	C₄	C₃×D₄²	1	4	yes	—
1262	C₃	#37651	1	1	yes	characteristic, direct product factor, Sylow
1263	C₂	—	2	4	no	—
1264	C₂	—	4	2	no	—
1265	C₂	—	4	2	no	—
1266	C₂	—	4	2	no	—
1267	C₂	—	8	1	no	—
1268	C₂	C₂×C₃×#536	1	1	yes	characteristic
1269	C₂	C₂×C₃×D₄²	1	1	yes	characteristic
1270	C₂	C₃×#3486	1	1	yes	characteristic
1271	C₂	C₃×#3489	1	1	yes	characteristic
1272	C₂	C₃×#3489	1	1	yes	characteristic
1273	C₂	C₃×#3538	1	1	yes	characteristic
1274	C₂	C₃×#3541	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#525	C₂
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×D₄×Q₈	C₂	semidirect
2. C₂×C₃×#536	C₂	semidirect
4. C₂²×C₃×C₂²⋊Q₈	C₂	semidirect
5. C₃×#2848	C₂	semidirect
6. C₃×#2681	C₂	semidirect
7. C₃×#2680	C₂	semidirect
8. C₃×#2677	C₂	semidirect
9. C₃×#2674	C₂	semidirect
10. C₃×#2621	C₂	semidirect
11. C₃×#2616	C₂	semidirect
12. C₃×#2542	C₂	semidirect
13. C₃×#2536	C₂	semidirect
14. C₃×#2472	C₂	semidirect
15. C₃×#2443	C₂	semidirect
16. C₃×#2440	C₂	semidirect
17. C₃×#2418	C₂	semidirect
18. C₃×#2417	C₂	semidirect
19. C₃×#2415	C₂	semidirect
20. C₃×#2409	C₂	semidirect
21. C₃×#2409	C₂	semidirect
22. C₃×#2352	C₂	semidirect
23. C₃×#2323	C₂	semidirect
24. #37651	C₃	direct (N × H)
27. C₂³×C₃×Q₈	C₂²	semidirect
31. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
32. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₃×#123	C₂²	semidirect
53. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
57. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₃×C₄×Q₈	C₂²	semidirect
69. C₂×C₃×#117	C₂²	semidirect
74. C₃×#399	C₂²	semidirect
75. C₃×#398	C₂²	semidirect
76. C₃×#398	C₂²	semidirect
77. C₃×#398	C₂²	semidirect
78. C₃×#398	C₂²	semidirect
81. C₃×#397	C₂²	semidirect
82. C₃×#396	C₂²	semidirect
83. C₃×#395	C₂²	semidirect
84. C₃×#395	C₂²	semidirect
85. C₃×#395	C₂²	semidirect
90. C₃×#394	C₂²	semidirect
92. C₃×#393	C₂²	semidirect
93. C₃×#391	C₂²	semidirect
94. C₃×#391	C₂²	semidirect
95. C₃×#391	C₂²	semidirect
97. C₃×#389	C₂²	semidirect
98. C₃×#389	C₂²	semidirect
99. C₃×#389	C₂²	semidirect
104. C₃×#388	C₂²	semidirect
105. C₃×#388	C₂²	semidirect
106. C₃×#387	C₂²	semidirect
107. C₃×#387	C₂²	semidirect
116. C₃×#385	C₂²	semidirect
117. C₃×#384	C₂²	semidirect
118. C₃×#382	C₂²	semidirect
123. C₃×#380	C₂²	semidirect
124. C₃×#380	C₂²	semidirect
126. C₃×C₄×C₄⋊C₄	C₂²	semidirect
128. C₂×D₄×Q₈	C₂×C₃	semidirect
129. C₂×#536	C₂×C₃	semidirect
131. C₂²×C₂²⋊Q₈	C₂×C₃	semidirect
132. #2848	C₂×C₃	semidirect
133. #2681	C₂×C₃	semidirect
134. #2680	C₂×C₃	semidirect
135. #2677	C₂×C₃	semidirect
136. #2674	C₂×C₃	semidirect
137. #2621	C₂×C₃	semidirect
138. #2616	C₂×C₃	semidirect
139. #2542	C₂×C₃	semidirect
140. #2536	C₂×C₃	semidirect
141. #2472	C₂×C₃	semidirect
142. #2443	C₂×C₃	semidirect
143. #2440	C₂×C₃	semidirect
144. #2418	C₂×C₃	semidirect
145. #2417	C₂×C₃	semidirect
146. #2415	C₂×C₃	semidirect
147. #2409	C₂×C₃	semidirect
148. #2409	C₂×C₃	semidirect
149. #2352	C₂×C₃	semidirect
150. #2323	C₂×C₃	semidirect
212. C₃×C₂²⋊Q₈	D₄	semidirect
304. C₂³×Q₈	C₂²×C₃	semidirect
308. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
309. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
310. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
316. C₂×#123	C₂²×C₃	semidirect
330. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
331. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
332. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
333. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
334. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
339. C₂×C₄×Q₈	C₂²×C₃	semidirect
346. C₂×#117	C₂²×C₃	semidirect
351. #399	C₂²×C₃	semidirect
352. #398	C₂²×C₃	semidirect
353. #398	C₂²×C₃	semidirect
354. #398	C₂²×C₃	semidirect
355. #398	C₂²×C₃	semidirect
358. #397	C₂²×C₃	semidirect
359. #396	C₂²×C₃	semidirect
360. #395	C₂²×C₃	semidirect
361. #395	C₂²×C₃	semidirect
362. #395	C₂²×C₃	semidirect
367. #394	C₂²×C₃	semidirect
369. #393	C₂²×C₃	semidirect
370. #391	C₂²×C₃	semidirect
371. #391	C₂²×C₃	semidirect
372. #391	C₂²×C₃	semidirect
374. #389	C₂²×C₃	semidirect
375. #389	C₂²×C₃	semidirect
376. #389	C₂²×C₃	semidirect
381. #388	C₂²×C₃	semidirect
382. #388	C₂²×C₃	semidirect
383. #387	C₂²×C₃	semidirect
384. #387	C₂²×C₃	semidirect
393. #385	C₂²×C₃	semidirect
394. #384	C₂²×C₃	semidirect
395. #382	C₂²×C₃	semidirect
400. #380	C₂²×C₃	semidirect
401. #380	C₂²×C₃	semidirect
403. C₄×C₄⋊C₄	C₂²×C₃	semidirect
631. C₂²⋊Q₈	C₃×D₄	semidirect
1042. C₂²×C₃	#536	semidirect
1236. C₂²	C₃×#536	semidirect
1262. C₃	#37651	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×D₄×Q₈	2
C₂×C₃×#536	2
C₂×C₃×#525	2
C₂²×C₃×C₂²⋊Q₈	2
C₃×#2848	2
C₃×#2681	2
C₃×#2680	2
C₃×#2677	2
C₃×#2674	2
C₃×#2621	2
C₃×#2616	2
C₃×#2542	2
C₃×#2536	2
C₃×#2472	2
C₃×#2443	2
C₃×#2440	2
C₃×#2418	2
C₃×#2417	2
C₃×#2415	2
C₃×#2409	2
C₃×#2352	2
C₃×#2323	2
#37651	3

Subgroups — C3×#37651 #10656258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37651 #10656258