Subgroups — C₃×#35906 #10654513

Order 768.

2848 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2662	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2661	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2639	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2610	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2603	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2583	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2559	C₂	1	2	yes	maximal, complemented
10	C₃×#2558	C₂	1	2	yes	maximal, complemented
11	C₃×#2543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2445	C₂	1	2	yes	maximal, complemented
13	C₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2430	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2428	C₂	1	2	yes	maximal, complemented
16	C₃×#2424	C₂	1	2	yes	maximal, complemented
17	C₃×#2424	C₂	1	2	yes	maximal, complemented
18	C₃×#2392	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2388	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#2358	C₂	1	2	yes	maximal, complemented
22	C₃×#2358	C₂	1	2	yes	maximal, complemented
23	C₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	#35906	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
27	C₃×#553	—	2	8	no	—
28	C₃×#546	—	2	8	no	—
29	C₂×C₃×#127	C₂²	1	2	yes	—
30	C₂×C₃×#126	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×#126	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#125	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#124	C₂²	1	1	yes	characteristic
34	C₂×C₃×#123	C₂²	1	2	yes	—
35	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×#123	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₃×#121	C₂²	1	2	yes	—
41	C₂×C₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₃×#121	C₂²	1	1	yes	characteristic
43	C₂×C₃×#121	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×#121	C₂²	1	2	yes	complemented
45	C₂×C₃×#121	C₂²	1	2	yes	complemented
46	C₂×C₃×#120	C₂²	1	2	yes	—
47	C₂×C₃×#120	C₂²	1	2	yes	—
48	C₂×C₃×#120	C₂²	1	2	yes	—
49	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
52	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
53	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
54	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
56	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
57	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
58	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
60	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
61	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
62	C₃×#400	C₂²	1	2	yes	complemented
63	C₃×#398	C₂²	1	1	yes	characteristic, complemented
64	C₃×#398	C₂²	1	1	yes	characteristic, complemented
65	C₃×#397	C₂²	1	1	yes	characteristic, complemented
66	C₃×#397	C₂²	1	1	yes	characteristic, complemented
67	C₃×#396	C₂²	1	2	yes	complemented
68	C₃×#396	C₂²	1	2	yes	complemented
69	C₃×#395	C₂²	1	1	yes	characteristic, complemented
70	C₃×#395	C₂²	1	1	yes	characteristic, complemented
71	C₃×#394	C₂²	1	1	yes	characteristic
72	C₃×#394	C₂²	1	1	yes	characteristic
73	C₃×#394	C₂²	1	2	yes	—
74	C₃×#394	C₂²	1	1	yes	characteristic
75	C₃×#394	C₂²	1	2	yes	—
76	C₃×#394	C₂²	1	1	yes	characteristic
77	C₃×#394	C₂²	1	2	yes	complemented
78	C₃×#394	C₂²	1	2	yes	complemented
79	C₃×#394	C₂²	1	2	yes	complemented
80	C₃×#394	C₂²	1	2	yes	complemented
81	C₃×#394	C₂²	1	2	yes	complemented
82	C₃×#393	C₂²	1	1	yes	characteristic, complemented
83	C₃×#393	C₂²	1	1	yes	characteristic, complemented
84	C₃×#392	C₂²	1	1	yes	characteristic
85	C₃×#392	C₂²	1	1	yes	characteristic
86	C₃×#392	C₂²	1	1	yes	characteristic
87	C₃×#392	C₂²	1	1	yes	characteristic
88	C₃×#392	C₂²	1	2	yes	complemented
89	C₃×#392	C₂²	1	2	yes	complemented
90	C₃×#390	C₂²	1	2	yes	—
91	C₃×#390	C₂²	1	2	yes	complemented
92	C₃×#390	C₂²	1	2	yes	complemented
93	C₃×#390	C₂²	1	2	yes	complemented
94	C₃×#390	C₂²	1	2	yes	complemented
95	C₃×#389	C₂²	1	2	yes	complemented
96	C₃×#389	C₂²	1	2	yes	complemented
97	C₃×#388	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×#388	C₂²	1	2	yes	complemented
102	C₃×#388	C₂²	1	2	yes	complemented
103	C₃×#386	C₂²	1	2	yes	—
104	C₃×#386	C₂²	1	2	yes	—
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×#385	C₂²	1	2	yes	—
112	C₃×#385	C₂²	1	2	yes	—
113	C₃×#385	C₂²	1	2	yes	complemented
114	C₃×#385	C₂²	1	2	yes	complemented
115	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
117	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₃×#376	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₃×#95	C₂²	1	1	yes	characteristic
125	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
126	C₂×#553	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×#546	C₂×C₃	1	1	yes	characteristic, complemented
128	#2662	C₂×C₃	1	1	yes	characteristic, complemented
129	#2661	C₂×C₃	1	1	yes	characteristic, complemented
130	#2639	C₂×C₃	1	1	yes	characteristic, complemented
131	#2610	C₂×C₃	1	1	yes	characteristic, complemented
132	#2603	C₂×C₃	1	1	yes	characteristic, complemented
133	#2583	C₂×C₃	1	1	yes	characteristic, complemented
134	#2559	C₂×C₃	1	2	yes	complemented
135	#2558	C₂×C₃	1	2	yes	complemented
136	#2543	C₂×C₃	1	1	yes	characteristic, complemented
137	#2445	C₂×C₃	1	2	yes	complemented
138	#2433	C₂×C₃	1	1	yes	characteristic, complemented
139	#2430	C₂×C₃	1	1	yes	characteristic, complemented
140	#2428	C₂×C₃	1	2	yes	complemented
141	#2424	C₂×C₃	1	2	yes	complemented
142	#2424	C₂×C₃	1	2	yes	complemented
143	#2392	C₂×C₃	1	1	yes	characteristic, complemented
144	#2388	C₂×C₃	1	1	yes	characteristic, complemented
145	C₂×#394	C₂×C₃	1	1	yes	characteristic, complemented
146	#2358	C₂×C₃	1	2	yes	complemented
147	#2358	C₂×C₃	1	2	yes	complemented
148	#2275	C₂×C₃	1	1	yes	characteristic, complemented
149	C₂⁵×C₃	C₂³	1	2	yes	—
150	C₂×C₃×#41	—	2	4	no	—
151	C₂×C₃×#41	—	4	4	no	—
152	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₃×D₄	—	2	4	no	—
154	C₂²×C₃×D₄	—	4	4	no	—
155	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	2	yes	—
159	C₂²×C₃×D₄	C₂³	1	2	yes	—
160	C₂²×C₃×D₄	C₂³	1	2	yes	—
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
163	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
164	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
165	C₂²×C₃×D₄	C₂³	1	2	yes	—
166	C₂²×C₃×D₄	C₂³	1	2	yes	—
167	C₂²×C₃×D₄	C₂³	1	2	yes	—
168	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
169	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
170	C₂³×C₃×C₄	C₂³	1	2	yes	—
171	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
172	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
173	C₂³×C₃×C₄	C₂³	1	2	yes	—
174	C₂³×C₃×C₄	C₂³	1	2	yes	—
175	C₂³×C₃×C₄	C₂³	1	2	yes	—
176	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
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	C₃×#127	—	4	4	no	—
181	C₃×#126	—	2	4	no	—
182	C₃×#126	—	2	4	no	—
183	C₃×#125	—	2	4	no	—
184	C₃×#124	—	2	4	no	—
185	C₃×#123	—	2	4	no	—
186	C₃×#123	—	2	8	no	—
187	C₃×#123	—	2	4	no	—
188	C₃×C₂²⋊Q₈	—	2	4	no	—
189	C₃×#121	—	2	4	no	—
190	C₃×#121	—	2	4	no	—
191	C₃×#121	—	2	4	no	—
192	C₃×#121	—	2	4	no	—
193	C₃×#121	—	2	8	no	—
194	C₃×#121	—	2	4	no	—
195	C₃×#121	—	4	4	no	—
196	C₃×#121	—	4	4	no	—
197	C₃×#120	—	2	8	no	—
198	C₃×#120	—	2	8	no	—
199	C₃×#120	—	2	8	no	—
200	C₃×C₄×D₄	—	2	4	no	—
201	C₃×C₄×D₄	—	2	4	no	—
202	C₃×C₄×D₄	—	2	4	no	—
203	C₃×C₄×D₄	—	2	8	no	—
204	C₃×C₄×D₄	—	2	4	no	—
205	C₃×C₄×D₄	—	4	4	no	—
206	C₃×C₄×D₄	—	4	4	no	—
207	C₃×C₄×D₄	D₄	1	8	yes	complemented
208	C₃×#117	—	2	4	no	—
209	C₂×C₃×C₄⋊C₄	—	2	4	no	—
210	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
225	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
228	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
229	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
242	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
244	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
246	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
247	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
248	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
261	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
263	C₂×C₃×C₄²	C₂³	1	2	yes	—
264	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
265	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
266	C₂×C₃×C₄²	C₂³	1	2	yes	—
267	C₂×C₃×C₄²	C₂³	1	2	yes	—
268	C₂×C₃×C₄²	C₂³	1	2	yes	—
269	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
270	C₃×#95	C₂³	1	1	yes	characteristic
271	C₃×#95	C₂³	1	1	yes	characteristic
272	C₃×#95	C₂³	1	2	yes	—
273	C₃×#95	C₂³	1	2	yes	—
274	C₃×#95	C₂³	1	1	yes	characteristic
275	C₃×#95	C₂³	1	2	yes	—
276	C₃×#95	C₂³	1	1	yes	characteristic
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	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
286	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
287	#553	—	2	8	no	—
288	#546	—	2	8	no	—
289	C₂×#127	C₂²×C₃	1	2	yes	—
290	C₂×#126	C₂²×C₃	1	1	yes	characteristic, complemented
291	C₂×#126	C₂²×C₃	1	1	yes	characteristic, complemented
292	C₂×#125	C₂²×C₃	1	1	yes	characteristic, complemented
293	C₂×#124	C₂²×C₃	1	1	yes	characteristic
294	C₂×#123	C₂²×C₃	1	2	yes	—
295	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₂×#123	C₂²×C₃	1	1	yes	characteristic, complemented
297	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
298	C₂×#121	C₂²×C₃	1	1	yes	characteristic
299	C₂×#121	C₂²×C₃	1	1	yes	characteristic
300	C₂×#121	C₂²×C₃	1	1	yes	characteristic
301	C₂×#121	C₂²×C₃	1	1	yes	characteristic
302	C₂×#121	C₂²×C₃	1	2	yes	—
303	C₂×#121	C₂²×C₃	1	1	yes	characteristic, complemented
304	C₂×#121	C₂²×C₃	1	2	yes	complemented
305	C₂×#121	C₂²×C₃	1	2	yes	complemented
306	C₂×#120	C₂²×C₃	1	2	yes	—
307	C₂×#120	C₂²×C₃	1	2	yes	—
308	C₂×#120	C₂²×C₃	1	2	yes	—
309	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
310	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
311	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
312	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
313	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
314	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
315	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
316	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
317	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
318	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
319	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
320	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
321	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
322	#400	C₂²×C₃	1	2	yes	complemented
323	#398	C₂²×C₃	1	1	yes	characteristic, complemented
324	#398	C₂²×C₃	1	1	yes	characteristic, complemented
325	#397	C₂²×C₃	1	1	yes	characteristic, complemented
326	#397	C₂²×C₃	1	1	yes	characteristic, complemented
327	#396	C₂²×C₃	1	2	yes	complemented
328	#396	C₂²×C₃	1	2	yes	complemented
329	#395	C₂²×C₃	1	1	yes	characteristic, complemented
330	#395	C₂²×C₃	1	1	yes	characteristic, complemented
331	#394	C₂²×C₃	1	1	yes	characteristic
332	#394	C₂²×C₃	1	1	yes	characteristic
333	#394	C₂²×C₃	1	1	yes	characteristic
334	#394	C₂²×C₃	1	1	yes	characteristic
335	#394	C₂²×C₃	1	2	yes	—
336	#394	C₂²×C₃	1	2	yes	—
337	#394	C₂²×C₃	1	2	yes	complemented
338	#394	C₂²×C₃	1	2	yes	complemented
339	#394	C₂²×C₃	1	2	yes	complemented
340	#394	C₂²×C₃	1	2	yes	complemented
341	#394	C₂²×C₃	1	2	yes	complemented
342	#393	C₂²×C₃	1	1	yes	characteristic, complemented
343	#393	C₂²×C₃	1	1	yes	characteristic, complemented
344	#392	C₂²×C₃	1	1	yes	characteristic
345	#392	C₂²×C₃	1	1	yes	characteristic
346	#392	C₂²×C₃	1	1	yes	characteristic
347	#392	C₂²×C₃	1	1	yes	characteristic
348	#392	C₂²×C₃	1	2	yes	complemented
349	#392	C₂²×C₃	1	2	yes	complemented
350	#390	C₂²×C₃	1	2	yes	—
351	#390	C₂²×C₃	1	2	yes	complemented
352	#390	C₂²×C₃	1	2	yes	complemented
353	#390	C₂²×C₃	1	2	yes	complemented
354	#390	C₂²×C₃	1	2	yes	complemented
355	#389	C₂²×C₃	1	2	yes	complemented
356	#389	C₂²×C₃	1	2	yes	complemented
357	#388	C₂²×C₃	1	2	yes	complemented
358	#388	C₂²×C₃	1	2	yes	complemented
359	#388	C₂²×C₃	1	2	yes	complemented
360	#388	C₂²×C₃	1	2	yes	complemented
361	#388	C₂²×C₃	1	2	yes	complemented
362	#388	C₂²×C₃	1	2	yes	complemented
363	#386	C₂²×C₃	1	2	yes	—
364	#386	C₂²×C₃	1	2	yes	—
365	#386	C₂²×C₃	1	2	yes	complemented
366	#386	C₂²×C₃	1	2	yes	complemented
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	#385	C₂²×C₃	1	2	yes	—
372	#385	C₂²×C₃	1	2	yes	—
373	#385	C₂²×C₃	1	2	yes	complemented
374	#385	C₂²×C₃	1	2	yes	complemented
375	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
376	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
377	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
378	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
379	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
380	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
381	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
382	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
383	#376	C₂²×C₃	1	1	yes	characteristic, complemented
384	C₂×#95	C₂²×C₃	1	1	yes	characteristic
385	C₂×#95	C₂²×C₃	1	1	yes	characteristic, complemented
386	C₂⁴×C₃	—	2	4	no	—
387	C₂⁴×C₃	—	2	4	no	—
388	C₂⁴×C₃	—	2	4	no	—
389	C₂⁴×C₃	—	2	4	no	—
390	C₂⁴×C₃	—	4	2	no	—
391	C₂⁴×C₃	—	4	2	no	—
392	C₂⁴×C₃	—	4	2	no	—
393	C₂⁴×C₃	C₂⁴	1	2	yes	—
394	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
395	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
396	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
397	C₂⁴×C₃	C₂⁴	1	2	yes	—
398	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
399	C₃×#41	—	4	16	no	—
400	C₂×C₃×Q₈	—	2	2	no	—
401	C₂×C₃×Q₈	—	4	2	no	—
402	C₂×C₃×D₄	—	2	4	no	—
403	C₂×C₃×D₄	—	2	4	no	—
404	C₂×C₃×D₄	—	2	2	no	—
405	C₂×C₃×D₄	—	2	2	no	—
406	C₂×C₃×D₄	—	2	2	no	—
407	C₂×C₃×D₄	—	2	4	no	—
408	C₂×C₃×D₄	—	2	4	no	—
409	C₂×C₃×D₄	—	2	4	no	—
410	C₂×C₃×D₄	—	2	4	no	—
411	C₂×C₃×D₄	—	2	4	no	—
412	C₂×C₃×D₄	—	2	4	no	—
413	C₂×C₃×D₄	—	2	4	no	—
414	C₂×C₃×D₄	—	2	4	no	—
415	C₂×C₃×D₄	—	2	2	no	—
416	C₂×C₃×D₄	—	2	2	no	—
417	C₂×C₃×D₄	—	2	4	no	—
418	C₂×C₃×D₄	—	2	2	no	—
419	C₂×C₃×D₄	—	2	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	4	no	—
424	C₂×C₃×D₄	—	2	2	no	—
425	C₂×C₃×D₄	—	4	2	no	—
426	C₂×C₃×D₄	—	4	2	no	—
427	C₂×C₃×D₄	—	4	2	no	—
428	C₂×C₃×D₄	—	4	2	no	—
429	C₂×C₃×D₄	—	4	1	no	—
430	C₂×C₃×D₄	—	4	2	no	—
431	C₂×C₃×D₄	—	4	2	no	—
432	C₂×C₃×D₄	—	4	2	no	—
433	C₂×C₃×D₄	—	4	2	no	—
434	C₂×C₃×D₄	—	4	2	no	—
435	C₂×C₃×D₄	—	4	2	no	—
436	C₂×C₃×D₄	—	4	2	no	—
437	C₂×C₃×D₄	—	4	2	no	—
438	C₂×C₃×D₄	—	4	2	no	—
439	C₂×C₃×D₄	—	4	16	no	—
440	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
441	C₂²×C₃×C₄	—	2	2	no	—
442	C₂²×C₃×C₄	—	2	4	no	—
443	C₂²×C₃×C₄	—	2	2	no	—
444	C₂²×C₃×C₄	—	2	4	no	—
445	C₂²×C₃×C₄	—	2	4	no	—
446	C₂²×C₃×C₄	—	2	2	no	—
447	C₂²×C₃×C₄	—	2	2	no	—
448	C₂²×C₃×C₄	—	2	2	no	—
449	C₂²×C₃×C₄	—	2	4	no	—
450	C₂²×C₃×C₄	—	2	2	no	—
451	C₂²×C₃×C₄	—	2	4	no	—
452	C₂²×C₃×C₄	—	4	1	no	—
453	C₂²×C₃×C₄	—	4	1	no	—
454	C₂²×C₃×C₄	—	4	2	no	—
455	C₂²×C₃×C₄	—	4	2	no	—
456	C₂²×C₃×C₄	—	4	2	no	—
457	C₂²×C₃×C₄	—	4	2	no	—
458	C₂²×C₃×C₄	—	4	2	no	—
459	C₂²×C₃×C₄	—	4	2	no	—
460	C₂²×C₃×C₄	—	4	2	no	—
461	C₂²×C₃×C₄	—	4	2	no	—
462	C₂²×C₃×C₄	—	4	2	no	—
463	C₂²×C₃×C₄	—	4	2	no	—
464	C₂²×C₃×C₄	—	4	2	no	—
465	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
466	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
467	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
468	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
469	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
470	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
471	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
472	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
473	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
474	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
475	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
476	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
477	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
478	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
479	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
480	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
481	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
482	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
483	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
484	C₃×C₄⋊C₄	—	2	2	no	—
485	C₃×C₄⋊C₄	—	2	2	no	—
486	C₃×C₄⋊C₄	—	2	2	no	—
487	C₃×C₄⋊C₄	—	2	2	no	—
488	C₃×C₄⋊C₄	—	2	2	no	—
489	C₃×C₄⋊C₄	—	2	2	no	—
490	C₃×C₄⋊C₄	—	2	2	no	—
491	C₃×C₄⋊C₄	—	2	2	no	—
492	C₃×C₄⋊C₄	—	2	4	no	—
493	C₃×C₄⋊C₄	—	2	2	no	—
494	C₃×C₄⋊C₄	—	2	2	no	—
495	C₃×C₄⋊C₄	—	2	4	no	—
496	C₃×C₄⋊C₄	—	2	4	no	—
497	C₃×C₄⋊C₄	—	4	2	no	—
498	C₃×C₄⋊C₄	—	4	2	no	—
499	C₃×C₄⋊C₄	—	4	2	no	—
500	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
501	C₃×C₂²⋊C₄	—	2	4	no	—
502	C₃×C₂²⋊C₄	—	2	2	no	—
503	C₃×C₂²⋊C₄	—	2	2	no	—
504	C₃×C₂²⋊C₄	—	2	4	no	—
505	C₃×C₂²⋊C₄	—	2	4	no	—
506	C₃×C₂²⋊C₄	—	2	4	no	—
507	C₃×C₂²⋊C₄	—	2	4	no	—
508	C₃×C₂²⋊C₄	—	2	2	no	—
509	C₃×C₂²⋊C₄	—	2	2	no	—
510	C₃×C₂²⋊C₄	—	2	4	no	—
511	C₃×C₂²⋊C₄	—	2	2	no	—
512	C₃×C₂²⋊C₄	—	2	2	no	—
513	C₃×C₂²⋊C₄	—	2	2	no	—
514	C₃×C₂²⋊C₄	—	2	4	no	—
515	C₃×C₂²⋊C₄	—	2	2	no	—
516	C₃×C₂²⋊C₄	—	2	4	no	—
517	C₃×C₂²⋊C₄	—	2	4	no	—
518	C₃×C₂²⋊C₄	—	2	4	no	—
519	C₃×C₂²⋊C₄	—	2	4	no	—
520	C₃×C₂²⋊C₄	—	2	4	no	—
521	C₃×C₂²⋊C₄	—	2	4	no	—
522	C₃×C₂²⋊C₄	—	2	4	no	—
523	C₃×C₂²⋊C₄	—	4	2	no	—
524	C₃×C₂²⋊C₄	—	4	2	no	—
525	C₃×C₂²⋊C₄	—	4	2	no	—
526	C₃×C₂²⋊C₄	—	4	2	no	—
527	C₃×C₂²⋊C₄	—	4	2	no	—
528	C₃×C₂²⋊C₄	—	4	2	no	—
529	C₃×C₂²⋊C₄	—	4	2	no	—
530	C₃×C₂²⋊C₄	—	4	2	no	—
531	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
532	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
533	C₃×C₂²⋊C₄	#41	1	8	yes	complemented
534	C₃×C₄²	—	2	2	no	—
535	C₃×C₄²	—	2	2	no	—
536	C₃×C₄²	—	2	4	no	—
537	C₃×C₄²	—	4	2	no	—
538	C₃×C₄²	—	4	2	no	—
539	C₃×C₄²	—	4	2	no	—
540	C₃×C₄²	C₂×D₄	1	4	yes	—
541	C₂⁵	C₂³×C₃	1	2	yes	—
542	C₂×#41	—	2	4	no	—
543	C₂×#41	—	4	4	no	—
544	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
545	C₂²×D₄	—	2	4	no	—
546	C₂²×D₄	—	4	4	no	—
547	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
548	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
550	C₂²×D₄	C₂³×C₃	1	2	yes	—
551	C₂²×D₄	C₂³×C₃	1	2	yes	—
552	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
553	C₂²×D₄	C₂³×C₃	1	2	yes	—
554	C₂²×D₄	C₂³×C₃	1	2	yes	—
555	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₃	1	2	yes	—
557	C₂²×D₄	C₂³×C₃	1	2	yes	—
558	C₂²×D₄	C₂³×C₃	1	2	yes	—
559	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
560	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₃	1	2	yes	—
564	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₃	1	2	yes	—
567	C₂³×C₄	C₂³×C₃	1	2	yes	—
568	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
569	C₂³×C₄	C₂³×C₃	1	2	yes	—
570	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
572	#127	—	4	4	no	—
573	#126	—	2	4	no	—
574	#126	—	2	4	no	—
575	#125	—	2	4	no	—
576	#124	—	2	4	no	—
577	#123	—	2	4	no	—
578	#123	—	2	8	no	—
579	#123	—	2	4	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	#121	—	2	4	no	—
582	#121	—	2	4	no	—
583	#121	—	2	4	no	—
584	#121	—	2	4	no	—
585	#121	—	2	8	no	—
586	#121	—	2	4	no	—
587	#121	—	4	4	no	—
588	#121	—	4	4	no	—
589	#120	—	2	8	no	—
590	#120	—	2	8	no	—
591	#120	—	2	8	no	—
592	C₄×D₄	—	2	4	no	—
593	C₄×D₄	—	2	4	no	—
594	C₄×D₄	—	2	4	no	—
595	C₄×D₄	—	2	8	no	—
596	C₄×D₄	—	2	4	no	—
597	C₄×D₄	—	4	4	no	—
598	C₄×D₄	—	4	4	no	—
599	C₄×D₄	C₃×D₄	1	8	yes	complemented
600	#117	—	2	4	no	—
601	C₂×C₄⋊C₄	—	2	4	no	—
602	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	—	2	8	no	—
620	C₂×C₂²⋊C₄	—	4	4	no	—
621	C₂×C₂²⋊C₄	—	4	4	no	—
622	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
655	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₃	1	2	yes	—
658	C₂×C₄²	C₂³×C₃	1	2	yes	—
659	C₂×C₄²	C₂³×C₃	1	2	yes	—
660	C₂×C₄²	C₂³×C₃	1	2	yes	—
661	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
662	#95	C₂³×C₃	1	1	yes	characteristic
663	#95	C₂³×C₃	1	1	yes	characteristic
664	#95	C₂³×C₃	1	2	yes	—
665	#95	C₂³×C₃	1	2	yes	—
666	#95	C₂³×C₃	1	1	yes	characteristic
667	#95	C₂³×C₃	1	2	yes	—
668	#95	C₂³×C₃	1	1	yes	characteristic
669	#95	C₂³×C₃	1	2	yes	—
670	#95	C₂³×C₃	1	2	yes	—
671	#95	C₂³×C₃	1	2	yes	—
672	#95	C₂³×C₃	1	2	yes	—
673	#95	C₂³×C₃	1	2	yes	—
674	#95	C₂³×C₃	1	2	yes	—
675	#95	C₂³×C₃	1	2	yes	—
676	#95	C₂³×C₃	1	2	yes	—
677	C₂³×C₃	—	2	1	no	—
678	C₂³×C₃	—	2	2	no	—
679	C₂³×C₃	—	2	1	no	—
680	C₂³×C₃	—	2	2	no	—
681	C₂³×C₃	—	2	2	no	—
682	C₂³×C₃	—	2	2	no	—
683	C₂³×C₃	—	2	2	no	—
684	C₂³×C₃	—	2	2	no	—
685	C₂³×C₃	—	2	2	no	—
686	C₂³×C₃	—	2	1	no	—
687	C₂³×C₃	—	2	2	no	—
688	C₂³×C₃	—	2	2	no	—
689	C₂³×C₃	—	2	1	no	—
690	C₂³×C₃	—	2	1	no	—
691	C₂³×C₃	—	2	1	no	—
692	C₂³×C₃	—	2	2	no	—
693	C₂³×C₃	—	2	2	no	—
694	C₂³×C₃	—	2	2	no	—
695	C₂³×C₃	—	2	2	no	—
696	C₂³×C₃	—	2	2	no	—
697	C₂³×C₃	—	2	2	no	—
698	C₂³×C₃	—	2	1	no	—
699	C₂³×C₃	—	2	1	no	—
700	C₂³×C₃	—	2	2	no	—
701	C₂³×C₃	—	2	2	no	—
702	C₂³×C₃	—	2	2	no	—
703	C₂³×C₃	—	2	2	no	—
704	C₂³×C₃	—	2	1	no	—
705	C₂³×C₃	—	2	1	no	—
706	C₂³×C₃	—	2	2	no	—
707	C₂³×C₃	—	4	8	no	—
708	C₂³×C₃	—	4	8	no	—
709	C₂³×C₃	—	4	8	no	—
710	C₂³×C₃	—	4	8	no	—
711	C₂³×C₃	—	8	4	no	—
712	C₂³×C₃	—	8	4	no	—
713	C₂³×C₃	—	8	4	no	—
714	C₂³×C₃	C₂²×D₄	1	2	yes	—
715	C₂³×C₃	C₂²×D₄	1	2	yes	—
716	C₂³×C₃	C₂×#41	1	4	yes	—
717	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
718	C₂³×C₃	C₂⁵	1	1	yes	characteristic
719	C₃×Q₈	—	4	4	no	—
720	C₃×D₄	—	2	8	no	—
721	C₃×D₄	—	2	8	no	—
722	C₃×D₄	—	4	4	no	—
723	C₃×D₄	—	4	8	no	—
724	C₃×D₄	—	4	8	no	—
725	C₃×D₄	—	4	8	no	—
726	C₃×D₄	—	4	4	no	—
727	C₃×D₄	—	4	8	no	—
728	C₃×D₄	—	4	4	no	—
729	C₃×D₄	—	4	4	no	—
730	C₃×D₄	—	8	2	no	—
731	C₃×D₄	—	8	4	no	—
732	C₃×D₄	—	8	4	no	—
733	C₃×D₄	—	8	2	no	—
734	C₃×D₄	—	8	4	no	—
735	C₂×C₃×C₄	—	2	1	no	—
736	C₂×C₃×C₄	—	2	2	no	—
737	C₂×C₃×C₄	—	2	2	no	—
738	C₂×C₃×C₄	—	2	1	no	—
739	C₂×C₃×C₄	—	2	2	no	—
740	C₂×C₃×C₄	—	2	2	no	—
741	C₂×C₃×C₄	—	2	2	no	—
742	C₂×C₃×C₄	—	2	2	no	—
743	C₂×C₃×C₄	—	2	2	no	—
744	C₂×C₃×C₄	—	2	2	no	—
745	C₂×C₃×C₄	—	2	1	no	—
746	C₂×C₃×C₄	—	2	1	no	—
747	C₂×C₃×C₄	—	2	1	no	—
748	C₂×C₃×C₄	—	2	1	no	—
749	C₂×C₃×C₄	—	2	1	no	—
750	C₂×C₃×C₄	—	2	1	no	—
751	C₂×C₃×C₄	—	2	2	no	—
752	C₂×C₃×C₄	—	2	2	no	—
753	C₂×C₃×C₄	—	2	1	no	—
754	C₂×C₃×C₄	—	2	2	no	—
755	C₂×C₃×C₄	—	2	2	no	—
756	C₂×C₃×C₄	—	2	2	no	—
757	C₂×C₃×C₄	—	2	2	no	—
758	C₂×C₃×C₄	—	2	2	no	—
759	C₂×C₃×C₄	—	2	2	no	—
760	C₂×C₃×C₄	—	2	2	no	—
761	C₂×C₃×C₄	—	2	2	no	—
762	C₂×C₃×C₄	—	2	2	no	—
763	C₂×C₃×C₄	—	2	2	no	—
764	C₂×C₃×C₄	—	2	1	no	—
765	C₂×C₃×C₄	—	2	2	no	—
766	C₂×C₃×C₄	—	2	2	no	—
767	C₂×C₃×C₄	—	2	2	no	—
768	C₂×C₃×C₄	—	2	1	no	—
769	C₂×C₃×C₄	—	2	2	no	—
770	C₂×C₃×C₄	—	4	4	no	—
771	C₂×C₃×C₄	—	4	4	no	—
772	C₂×C₃×C₄	—	4	4	no	—
773	C₂×C₃×C₄	—	4	4	no	—
774	C₂×C₃×C₄	—	4	8	no	—
775	C₂×C₃×C₄	—	8	2	no	—
776	C₂×C₃×C₄	—	8	4	no	—
777	C₂×C₃×C₄	—	8	4	no	—
778	C₂×C₃×C₄	—	8	2	no	—
779	C₂×C₃×C₄	—	8	4	no	—
780	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
781	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
782	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
783	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
784	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
785	C₂×C₃×C₄	C₂×#41	1	4	yes	—
786	C₂×C₃×C₄	C₂×#41	1	4	yes	—
787	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
788	C₂⁴	—	2	4	no	—
789	C₂⁴	—	2	4	no	—
790	C₂⁴	—	2	4	no	—
791	C₂⁴	—	2	4	no	—
792	C₂⁴	—	4	2	no	—
793	C₂⁴	—	4	2	no	—
794	C₂⁴	—	4	2	no	—
795	C₂⁴	C₂⁴×C₃	1	2	yes	—
796	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
797	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
798	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
799	C₂⁴	C₂⁴×C₃	1	2	yes	—
800	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
801	#41	—	4	16	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	4	2	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	4	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	4	no	—
812	C₂×D₄	—	2	4	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	2	2	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	4	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	1	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	4	2	no	—
836	C₂×D₄	—	4	2	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	4	2	no	—
839	C₂×D₄	—	4	2	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	16	no	—
842	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	4	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	4	no	—
847	C₂²×C₄	—	2	4	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	4	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	4	no	—
854	C₂²×C₄	—	4	2	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	1	no	—
858	C₂²×C₄	—	4	1	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
868	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
869	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
870	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
871	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	4	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	4	no	—
898	C₄⋊C₄	—	2	4	no	—
899	C₄⋊C₄	—	4	2	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₄⋊C₄	—	4	2	no	—
902	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
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	4	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	2	4	no	—
923	C₂²⋊C₄	—	2	4	no	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	2	no	—
928	C₂²⋊C₄	—	4	2	no	—
929	C₂²⋊C₄	—	4	2	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
934	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
935	C₂²⋊C₄	C₃×#41	1	8	yes	complemented
936	C₄²	—	2	2	no	—
937	C₄²	—	2	2	no	—
938	C₄²	—	2	4	no	—
939	C₄²	—	4	2	no	—
940	C₄²	—	4	2	no	—
941	C₄²	—	4	2	no	—
942	C₄²	C₂×C₃×D₄	1	4	yes	—
943	C₂²×C₃	—	2	2	no	—
944	C₂²×C₃	—	2	2	no	—
945	C₂²×C₃	—	2	4	no	—
946	C₂²×C₃	—	2	4	no	—
947	C₂²×C₃	—	2	2	no	—
948	C₂²×C₃	—	2	4	no	—
949	C₂²×C₃	—	2	2	no	—
950	C₂²×C₃	—	2	2	no	—
951	C₂²×C₃	—	2	4	no	—
952	C₂²×C₃	—	2	4	no	—
953	C₂²×C₃	—	4	2	no	—
954	C₂²×C₃	—	4	2	no	—
955	C₂²×C₃	—	4	2	no	—
956	C₂²×C₃	—	4	2	no	—
957	C₂²×C₃	—	4	2	no	—
958	C₂²×C₃	—	4	2	no	—
959	C₂²×C₃	—	4	1	no	—
960	C₂²×C₃	—	4	1	no	—
961	C₂²×C₃	—	4	2	no	—
962	C₂²×C₃	—	4	1	no	—
963	C₂²×C₃	—	4	2	no	—
964	C₂²×C₃	—	4	1	no	—
965	C₂²×C₃	—	4	1	no	—
966	C₂²×C₃	—	4	1	no	—
967	C₂²×C₃	—	4	2	no	—
968	C₂²×C₃	—	4	2	no	—
969	C₂²×C₃	—	4	2	no	—
970	C₂²×C₃	—	4	2	no	—
971	C₂²×C₃	—	4	2	no	—
972	C₂²×C₃	—	4	2	no	—
973	C₂²×C₃	—	4	2	no	—
974	C₂²×C₃	—	4	2	no	—
975	C₂²×C₃	—	4	2	no	—
976	C₂²×C₃	—	8	16	no	—
977	C₂²×C₃	#532	1	4	yes	—
978	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
979	C₂²×C₃	C₂²×#41	1	2	yes	—
980	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
981	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
982	C₂²×C₃	#585	1	1	yes	characteristic
983	C₃×C₄	—	2	2	no	—
984	C₃×C₄	—	2	2	no	—
985	C₃×C₄	—	2	2	no	—
986	C₃×C₄	—	2	2	no	—
987	C₃×C₄	—	2	2	no	—
988	C₃×C₄	—	2	2	no	—
989	C₃×C₄	—	2	4	no	—
990	C₃×C₄	—	2	4	no	—
991	C₃×C₄	—	4	1	no	—
992	C₃×C₄	—	4	1	no	—
993	C₃×C₄	—	4	2	no	—
994	C₃×C₄	—	4	1	no	—
995	C₃×C₄	—	4	1	no	—
996	C₃×C₄	—	4	1	no	—
997	C₃×C₄	—	4	2	no	—
998	C₃×C₄	—	4	2	no	—
999	C₃×C₄	—	4	2	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	2	2	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	2	2	no	—
1024	C₂³	—	2	2	no	—
1025	C₂³	—	2	2	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	4	8	no	—
1031	C₂³	—	4	8	no	—
1032	C₂³	—	4	8	no	—
1033	C₂³	—	4	8	no	—
1034	C₂³	—	8	4	no	—
1035	C₂³	—	8	4	no	—
1036	C₂³	—	8	4	no	—
1037	C₂³	C₂²×C₃×D₄	1	2	yes	—
1038	C₂³	C₂²×C₃×D₄	1	2	yes	—
1039	C₂³	C₂×C₃×#41	1	4	yes	—
1040	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
1041	C₂³	C₂⁵×C₃	1	1	yes	characteristic
1042	Q₈	—	4	4	no	—
1043	D₄	—	2	8	no	—
1044	D₄	—	2	8	no	—
1045	D₄	—	4	8	no	—
1046	D₄	—	4	4	no	—
1047	D₄	—	4	8	no	—
1048	D₄	—	4	8	no	—
1049	D₄	—	4	4	no	—
1050	D₄	—	4	8	no	—
1051	D₄	—	4	4	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	4	no	—
1055	D₄	—	8	4	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	4	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	4	4	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	4	no	—
1096	C₂×C₄	—	4	8	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	4	no	—
1100	C₂×C₄	—	8	4	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	4	no	—
1103	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1104	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1105	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1106	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1107	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
1108	C₂×C₄	C₂×C₃×#41	1	4	yes	—
1109	C₂×C₄	C₂×C₃×#41	1	4	yes	—
1110	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1111	C₂×C₃	—	2	4	no	—
1112	C₂×C₃	—	4	2	no	—
1113	C₂×C₃	—	4	4	no	—
1114	C₂×C₃	—	8	1	no	—
1115	C₂×C₃	—	8	1	no	—
1116	C₂×C₃	—	8	2	no	—
1117	C₂×C₃	C₂×#532	1	1	yes	characteristic
1118	C₂×C₃	#3484	1	1	yes	characteristic
1119	C₂×C₃	#3488	1	1	yes	characteristic
1120	C₂×C₃	#3513	1	2	yes	—
1121	C₂×C₃	#3519	1	2	yes	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	4	no	—
1125	C₂²	—	2	4	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	4	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	4	no	—
1131	C₂²	—	2	4	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	8	16	no	—
1156	C₂²	C₃×#532	1	4	yes	—
1157	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
1158	C₂²	C₂²×C₃×#41	1	2	yes	—
1159	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1160	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1161	C₂²	C₃×#585	1	1	yes	characteristic
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	2	2	no	—
1168	C₄	—	2	4	no	—
1169	C₄	—	2	4	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	2	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	1	no	—
1175	C₄	—	4	1	no	—
1176	C₄	—	4	2	no	—
1177	C₄	—	4	2	no	—
1178	C₄	—	4	2	no	—
1179	C₃	#35906	1	1	yes	characteristic, direct product factor, Sylow
1180	C₂	—	2	4	no	—
1181	C₂	—	4	4	no	—
1182	C₂	—	4	2	no	—
1183	C₂	—	8	2	no	—
1184	C₂	—	8	1	no	—
1185	C₂	—	8	1	no	—
1186	C₂	C₂×C₃×#532	1	1	yes	characteristic
1187	C₂	C₃×#3484	1	1	yes	characteristic
1188	C₂	C₃×#3488	1	1	yes	characteristic
1189	C₂	C₃×#3513	1	2	yes	—
1190	C₂	C₃×#3519	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×#553	C₂	semidirect
2. C₂×C₃×#546	C₂	semidirect
3. C₃×#2662	C₂	semidirect
4. C₃×#2661	C₂	semidirect
5. C₃×#2639	C₂	semidirect
6. C₃×#2610	C₂	semidirect
7. C₃×#2603	C₂	semidirect
8. C₃×#2583	C₂	semidirect
9. C₃×#2559	C₂	semidirect
10. C₃×#2558	C₂	semidirect
11. C₃×#2543	C₂	semidirect
12. C₃×#2445	C₂	semidirect
13. C₃×#2433	C₂	semidirect
14. C₃×#2430	C₂	semidirect
15. C₃×#2428	C₂	semidirect
16. C₃×#2424	C₂	semidirect
17. C₃×#2424	C₂	semidirect
18. C₃×#2392	C₂	semidirect
19. C₃×#2388	C₂	semidirect
20. C₂×C₃×#394	C₂	semidirect
21. C₃×#2358	C₂	semidirect
22. C₃×#2358	C₂	semidirect
23. C₃×#2275	C₂	semidirect
24. #35906	C₃	direct (N × H)
30. C₂×C₃×#126	C₂²	semidirect
31. C₂×C₃×#126	C₂²	semidirect
32. C₂×C₃×#125	C₂²	semidirect
35. C₂×C₃×#123	C₂²	semidirect
36. C₂×C₃×#123	C₂²	semidirect
43. C₂×C₃×#121	C₂²	semidirect
44. C₂×C₃×#121	C₂²	semidirect
45. C₂×C₃×#121	C₂²	semidirect
54. C₂×C₃×C₄×D₄	C₂²	semidirect
55. C₂×C₃×C₄×D₄	C₂²	semidirect
56. C₂×C₃×C₄×D₄	C₂²	semidirect
57. C₂×C₃×#117	C₂²	semidirect
62. C₃×#400	C₂²	semidirect
63. C₃×#398	C₂²	semidirect
64. C₃×#398	C₂²	semidirect
65. C₃×#397	C₂²	semidirect
66. C₃×#397	C₂²	semidirect
67. C₃×#396	C₂²	semidirect
68. C₃×#396	C₂²	semidirect
69. C₃×#395	C₂²	semidirect
70. C₃×#395	C₂²	semidirect
77. C₃×#394	C₂²	semidirect
78. C₃×#394	C₂²	semidirect
79. C₃×#394	C₂²	semidirect
80. C₃×#394	C₂²	semidirect
81. C₃×#394	C₂²	semidirect
82. C₃×#393	C₂²	semidirect
83. C₃×#393	C₂²	semidirect
88. C₃×#392	C₂²	semidirect
89. C₃×#392	C₂²	semidirect
91. C₃×#390	C₂²	semidirect
92. C₃×#390	C₂²	semidirect
93. C₃×#390	C₂²	semidirect
94. C₃×#390	C₂²	semidirect
95. C₃×#389	C₂²	semidirect
96. C₃×#389	C₂²	semidirect
97. C₃×#388	C₂²	semidirect
98. C₃×#388	C₂²	semidirect
99. C₃×#388	C₂²	semidirect
100. C₃×#388	C₂²	semidirect
101. C₃×#388	C₂²	semidirect
102. C₃×#388	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
113. C₃×#385	C₂²	semidirect
114. C₃×#385	C₂²	semidirect
115. C₃×C₄×C₄⋊C₄	C₂²	semidirect
116. C₃×C₄×C₄⋊C₄	C₂²	semidirect
119. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
120. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
121. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
122. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
123. C₃×#376	C₂²	semidirect
125. C₂×C₃×#95	C₂²	semidirect
126. C₂×#553	C₂×C₃	semidirect
127. C₂×#546	C₂×C₃	semidirect
128. #2662	C₂×C₃	semidirect
129. #2661	C₂×C₃	semidirect
130. #2639	C₂×C₃	semidirect
131. #2610	C₂×C₃	semidirect
132. #2603	C₂×C₃	semidirect
133. #2583	C₂×C₃	semidirect
134. #2559	C₂×C₃	semidirect
135. #2558	C₂×C₃	semidirect
136. #2543	C₂×C₃	semidirect
137. #2445	C₂×C₃	semidirect
138. #2433	C₂×C₃	semidirect
139. #2430	C₂×C₃	semidirect
140. #2428	C₂×C₃	semidirect
141. #2424	C₂×C₃	semidirect
142. #2424	C₂×C₃	semidirect
143. #2392	C₂×C₃	semidirect
144. #2388	C₂×C₃	semidirect
145. C₂×#394	C₂×C₃	semidirect
146. #2358	C₂×C₃	semidirect
147. #2358	C₂×C₃	semidirect
148. #2275	C₂×C₃	semidirect
207. C₃×C₄×D₄	D₄	semidirect
290. C₂×#126	C₂²×C₃	semidirect
291. C₂×#126	C₂²×C₃	semidirect
292. C₂×#125	C₂²×C₃	semidirect
295. C₂×#123	C₂²×C₃	semidirect
296. C₂×#123	C₂²×C₃	semidirect
303. C₂×#121	C₂²×C₃	semidirect
304. C₂×#121	C₂²×C₃	semidirect
305. C₂×#121	C₂²×C₃	semidirect
314. C₂×C₄×D₄	C₂²×C₃	semidirect
315. C₂×C₄×D₄	C₂²×C₃	semidirect
316. C₂×C₄×D₄	C₂²×C₃	semidirect
317. C₂×#117	C₂²×C₃	semidirect
322. #400	C₂²×C₃	semidirect
323. #398	C₂²×C₃	semidirect
324. #398	C₂²×C₃	semidirect
325. #397	C₂²×C₃	semidirect
326. #397	C₂²×C₃	semidirect
327. #396	C₂²×C₃	semidirect
328. #396	C₂²×C₃	semidirect
329. #395	C₂²×C₃	semidirect
330. #395	C₂²×C₃	semidirect
337. #394	C₂²×C₃	semidirect
338. #394	C₂²×C₃	semidirect
339. #394	C₂²×C₃	semidirect
340. #394	C₂²×C₃	semidirect
341. #394	C₂²×C₃	semidirect
342. #393	C₂²×C₃	semidirect
343. #393	C₂²×C₃	semidirect
348. #392	C₂²×C₃	semidirect
349. #392	C₂²×C₃	semidirect
351. #390	C₂²×C₃	semidirect
352. #390	C₂²×C₃	semidirect
353. #390	C₂²×C₃	semidirect
354. #390	C₂²×C₃	semidirect
355. #389	C₂²×C₃	semidirect
356. #389	C₂²×C₃	semidirect
357. #388	C₂²×C₃	semidirect
358. #388	C₂²×C₃	semidirect
359. #388	C₂²×C₃	semidirect
360. #388	C₂²×C₃	semidirect
361. #388	C₂²×C₃	semidirect
362. #388	C₂²×C₃	semidirect
365. #386	C₂²×C₃	semidirect
366. #386	C₂²×C₃	semidirect
367. #386	C₂²×C₃	semidirect
368. #386	C₂²×C₃	semidirect
369. #386	C₂²×C₃	semidirect
370. #386	C₂²×C₃	semidirect
373. #385	C₂²×C₃	semidirect
374. #385	C₂²×C₃	semidirect
375. C₄×C₄⋊C₄	C₂²×C₃	semidirect
376. C₄×C₄⋊C₄	C₂²×C₃	semidirect
379. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
380. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
381. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
382. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
383. #376	C₂²×C₃	semidirect
385. C₂×#95	C₂²×C₃	semidirect
533. C₃×C₂²⋊C₄	#41	semidirect
599. C₄×D₄	C₃×D₄	semidirect
935. C₂²⋊C₄	C₃×#41	semidirect
1179. C₃	#35906	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×#553	2
C₂×C₃×#546	2
C₃×#2662	2
C₃×#2661	2
C₃×#2639	2
C₃×#2610	2
C₃×#2603	2
C₃×#2583	2
C₃×#2559	2
C₃×#2558	2
C₃×#2543	2
C₃×#2445	2
C₃×#2433	2
C₃×#2430	2
C₃×#2428	2
C₃×#2424	2
C₃×#2392	2
C₃×#2388	2
C₂×C₃×#394	2
C₃×#2358	2
C₃×#2275	2
#35906	3

Subgroups — C3×#35906 #10654513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35906 #10654513