Subgroups — C₃×#34969 #10653576

Order 768.

1962 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2530	C₂	1	2	yes	maximal, complemented
2	C₃×#2527	C₂	1	2	yes	maximal, complemented
3	C₃×#2511	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2509	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2492	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2477	C₂	1	2	yes	maximal, complemented
8	C₃×#2470	C₂	1	2	yes	maximal, complemented
9	C₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2427	C₂	1	1	yes	maximal, characteristic
12	C₃×#2422	C₂	1	1	yes	maximal, characteristic
13	C₃×#2401	C₂	1	2	yes	maximal, complemented
14	C₃×#2398	C₂	1	2	yes	maximal, complemented
15	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₄×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₄×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₄×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
19	C₃×C₄×#123	C₂	1	2	yes	maximal, complemented
20	C₃×C₄×#121	C₂	1	1	yes	maximal, characteristic
21	C₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	#34969	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₃×#123	C₂²	1	2	yes	—
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
37	C₂×C₃×#117	C₂²	1	1	yes	characteristic
38	C₂×C₃×#117	C₂²	1	1	yes	characteristic
39	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
40	C₂²×C₃×C₄²	C₂²	1	2	yes	—
41	C₃×#401	C₂²	1	2	yes	—
42	C₃×#400	C₂²	1	2	yes	—
43	C₃×#400	C₂²	1	2	yes	—
44	C₃×#400	C₂²	1	2	yes	—
45	C₃×#400	C₂²	1	2	yes	—
46	C₃×#400	C₂²	1	2	yes	—
47	C₃×#397	C₂²	1	2	yes	—
48	C₃×#397	C₂²	1	2	yes	—
49	C₃×#397	C₂²	1	2	yes	—
50	C₃×#397	C₂²	1	2	yes	—
51	C₃×#397	C₂²	1	2	yes	—
52	C₃×#396	C₂²	1	2	yes	—
53	C₃×#394	C₂²	1	2	yes	—
54	C₃×#394	C₂²	1	2	yes	—
55	C₃×#393	C₂²	1	2	yes	—
56	C₃×#393	C₂²	1	2	yes	—
57	C₃×#391	C₂²	1	1	yes	characteristic
58	C₃×#391	C₂²	1	1	yes	characteristic
59	C₃×#391	C₂²	1	1	yes	characteristic
60	C₃×#391	C₂²	1	2	yes	—
61	C₃×#391	C₂²	1	1	yes	characteristic
62	C₃×#391	C₂²	1	2	yes	—
63	C₃×#390	C₂²	1	1	yes	characteristic
64	C₃×#390	C₂²	1	1	yes	characteristic
65	C₃×#389	C₂²	1	1	yes	characteristic
66	C₃×#389	C₂²	1	1	yes	characteristic
67	C₃×#389	C₂²	1	1	yes	characteristic
68	C₃×#389	C₂²	1	1	yes	characteristic
69	C₃×#389	C₂²	1	1	yes	characteristic
70	C₃×#389	C₂²	1	2	yes	—
71	C₃×#389	C₂²	1	2	yes	—
72	C₃×#389	C₂²	1	1	yes	characteristic
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	—
77	C₃×#388	C₂²	1	2	yes	—
78	C₃×#387	C₂²	1	2	yes	—
79	C₃×#387	C₂²	1	2	yes	—
80	C₃×#387	C₂²	1	2	yes	—
81	C₃×#387	C₂²	1	2	yes	—
82	C₃×#387	C₂²	1	2	yes	—
83	C₃×#387	C₂²	1	2	yes	—
84	C₃×#387	C₂²	1	2	yes	—
85	C₃×#386	C₂²	1	2	yes	—
86	C₃×#386	C₂²	1	2	yes	—
87	C₃×#385	C₂²	1	2	yes	—
88	C₃×#385	C₂²	1	2	yes	—
89	C₃×#385	C₂²	1	2	yes	—
90	C₃×#385	C₂²	1	2	yes	—
91	C₃×#384	C₂²	1	1	yes	characteristic
92	C₃×#382	C₂²	1	1	yes	characteristic
93	C₃×#381	C₂²	1	2	yes	—
94	C₃×#380	C₂²	1	1	yes	characteristic
95	C₃×#380	C₂²	1	2	yes	—
96	C₃×#380	C₂²	1	1	yes	characteristic
97	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
99	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
100	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
108	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
109	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
110	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
117	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
119	C₃×#376	C₂²	1	2	yes	—
120	C₃×#376	C₂²	1	1	yes	characteristic
121	C₃×#376	C₂²	1	1	yes	characteristic
122	C₃×C₄³	C₂²	1	1	yes	characteristic
123	C₃×C₄³	C₂²	1	1	yes	characteristic
124	#2530	C₂×C₃	1	2	yes	complemented
125	#2527	C₂×C₃	1	2	yes	complemented
126	#2511	C₂×C₃	1	1	yes	characteristic, complemented
127	#2509	C₂×C₃	1	1	yes	characteristic, complemented
128	#2494	C₂×C₃	1	1	yes	characteristic, complemented
129	#2492	C₂×C₃	1	1	yes	characteristic, complemented
130	#2477	C₂×C₃	1	2	yes	complemented
131	#2470	C₂×C₃	1	2	yes	complemented
132	#2452	C₂×C₃	1	1	yes	characteristic, complemented
133	#2447	C₂×C₃	1	1	yes	characteristic, complemented
134	#2427	C₂×C₃	1	1	yes	characteristic
135	#2422	C₂×C₃	1	1	yes	characteristic
136	#2401	C₂×C₃	1	2	yes	complemented
137	#2398	C₂×C₃	1	2	yes	complemented
138	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
139	C₄×#124	C₂×C₃	1	1	yes	characteristic, complemented
140	C₄×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
141	C₄×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
142	C₄×#123	C₂×C₃	1	2	yes	complemented
143	C₄×#121	C₂×C₃	1	1	yes	characteristic
144	#2295	C₂×C₃	1	1	yes	characteristic, complemented
145	C₄²×D₄	C₂×C₃	1	1	yes	characteristic, complemented
146	C₄×#117	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
148	C₂²×C₃×Q₈	C₂³	1	2	yes	—
149	C₂²×C₃×D₄	C₂³	1	2	yes	—
150	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
151	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
152	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂³×C₃×C₄	C₂³	1	2	yes	—
155	C₂³×C₃×C₄	C₂³	1	2	yes	—
156	C₂³×C₃×C₄	C₂³	1	2	yes	—
157	C₃×C₄⋊Q₈	—	2	4	no	—
158	C₃×#124	—	2	4	no	—
159	C₃×#123	—	2	8	no	—
160	C₃×C₂²⋊Q₈	—	2	8	no	—
161	C₃×C₂²⋊Q₈	—	2	4	no	—
162	C₃×#121	—	2	4	no	—
163	C₃×C₄×Q₈	—	2	4	no	—
164	C₃×C₄×Q₈	—	4	4	no	—
165	C₃×C₄×D₄	—	2	4	no	—
166	C₃×C₄×D₄	—	2	4	no	—
167	C₃×C₄×D₄	—	2	4	no	—
168	C₃×C₄×D₄	—	4	4	no	—
169	C₃×#117	—	2	4	no	—
170	C₃×#117	—	2	4	no	—
171	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₃×C₄²	—	2	4	no	—
210	C₂×C₃×C₄²	—	4	4	no	—
211	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
212	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
214	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
219	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₄²	C₂³	1	2	yes	—
226	C₂×C₃×C₄²	C₂³	1	2	yes	—
227	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
228	C₂×C₃×C₄²	C₂³	1	2	yes	—
229	C₂×C₃×C₄²	C₂³	1	2	yes	—
230	C₂×C₃×C₄²	C₂³	1	2	yes	—
231	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
232	C₃×#95	C₂³	1	1	yes	characteristic
233	C₃×#95	C₂³	1	1	yes	characteristic
234	C₃×#95	C₂³	1	1	yes	characteristic
235	C₃×#95	C₂³	1	1	yes	characteristic
236	C₃×#95	C₂³	1	1	yes	characteristic
237	C₃×#95	C₂³	1	1	yes	characteristic
238	C₃×#95	C₂³	1	1	yes	characteristic
239	C₃×#95	C₂³	1	1	yes	characteristic
240	C₃×#95	C₂³	1	2	yes	—
241	C₃×#95	C₂³	1	2	yes	—
242	C₃×#95	C₂³	1	2	yes	—
243	C₃×#95	C₂³	1	2	yes	—
244	C₃×#95	C₂³	1	2	yes	—
245	C₃×#95	C₂³	1	2	yes	—
246	C₃×#95	C₂³	1	2	yes	—
247	C₃×#95	C₂³	1	2	yes	—
248	C₃×#95	C₂³	1	2	yes	—
249	C₃×#95	C₂³	1	2	yes	—
250	C₃×#95	C₂³	1	2	yes	—
251	C₃×#95	C₂³	1	2	yes	—
252	C₃×#95	C₂³	1	2	yes	—
253	C₃×#95	C₂³	1	2	yes	—
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
263	C₂×#124	C₂²×C₃	1	1	yes	characteristic
264	C₂×#123	C₂²×C₃	1	2	yes	—
265	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
266	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
267	C₂×#121	C₂²×C₃	1	1	yes	characteristic
268	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
269	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
270	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
271	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
274	C₂×#117	C₂²×C₃	1	1	yes	characteristic
275	C₂×#117	C₂²×C₃	1	1	yes	characteristic
276	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
277	C₂²×C₄²	C₂²×C₃	1	2	yes	—
278	#401	C₂²×C₃	1	2	yes	—
279	#400	C₂²×C₃	1	2	yes	—
280	#400	C₂²×C₃	1	2	yes	—
281	#400	C₂²×C₃	1	2	yes	—
282	#400	C₂²×C₃	1	2	yes	—
283	#400	C₂²×C₃	1	2	yes	—
284	#397	C₂²×C₃	1	2	yes	—
285	#397	C₂²×C₃	1	2	yes	—
286	#397	C₂²×C₃	1	2	yes	—
287	#397	C₂²×C₃	1	2	yes	—
288	#397	C₂²×C₃	1	2	yes	—
289	#396	C₂²×C₃	1	2	yes	—
290	#394	C₂²×C₃	1	2	yes	—
291	#394	C₂²×C₃	1	2	yes	—
292	#393	C₂²×C₃	1	2	yes	—
293	#393	C₂²×C₃	1	2	yes	—
294	#391	C₂²×C₃	1	2	yes	—
295	#391	C₂²×C₃	1	1	yes	characteristic
296	#391	C₂²×C₃	1	1	yes	characteristic
297	#391	C₂²×C₃	1	1	yes	characteristic
298	#391	C₂²×C₃	1	1	yes	characteristic
299	#391	C₂²×C₃	1	2	yes	—
300	#390	C₂²×C₃	1	1	yes	characteristic
301	#390	C₂²×C₃	1	1	yes	characteristic
302	#389	C₂²×C₃	1	1	yes	characteristic
303	#389	C₂²×C₃	1	1	yes	characteristic
304	#389	C₂²×C₃	1	2	yes	—
305	#389	C₂²×C₃	1	1	yes	characteristic
306	#389	C₂²×C₃	1	1	yes	characteristic
307	#389	C₂²×C₃	1	1	yes	characteristic
308	#389	C₂²×C₃	1	2	yes	—
309	#389	C₂²×C₃	1	1	yes	characteristic
310	#388	C₂²×C₃	1	2	yes	—
311	#388	C₂²×C₃	1	2	yes	—
312	#388	C₂²×C₃	1	2	yes	—
313	#388	C₂²×C₃	1	2	yes	—
314	#388	C₂²×C₃	1	2	yes	—
315	#387	C₂²×C₃	1	2	yes	—
316	#387	C₂²×C₃	1	2	yes	—
317	#387	C₂²×C₃	1	2	yes	—
318	#387	C₂²×C₃	1	2	yes	—
319	#387	C₂²×C₃	1	2	yes	—
320	#387	C₂²×C₃	1	2	yes	—
321	#387	C₂²×C₃	1	2	yes	—
322	#386	C₂²×C₃	1	2	yes	—
323	#386	C₂²×C₃	1	2	yes	—
324	#385	C₂²×C₃	1	2	yes	—
325	#385	C₂²×C₃	1	2	yes	—
326	#385	C₂²×C₃	1	2	yes	—
327	#385	C₂²×C₃	1	2	yes	—
328	#384	C₂²×C₃	1	1	yes	characteristic
329	#382	C₂²×C₃	1	1	yes	characteristic
330	#381	C₂²×C₃	1	2	yes	—
331	#380	C₂²×C₃	1	1	yes	characteristic
332	#380	C₂²×C₃	1	2	yes	—
333	#380	C₂²×C₃	1	1	yes	characteristic
334	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
335	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
336	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
337	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
338	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
339	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
341	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
342	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
345	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
346	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
347	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
348	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
349	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
351	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
353	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
354	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
355	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
356	#376	C₂²×C₃	1	2	yes	—
357	#376	C₂²×C₃	1	1	yes	characteristic
358	#376	C₂²×C₃	1	1	yes	characteristic
359	C₄³	C₂²×C₃	1	1	yes	characteristic
360	C₄³	C₂²×C₃	1	1	yes	characteristic
361	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
362	C₂⁴×C₃	C₂⁴	1	2	yes	—
363	C₂×C₃×Q₈	—	2	2	no	—
364	C₂×C₃×Q₈	—	2	4	no	—
365	C₂×C₃×Q₈	—	2	2	no	—
366	C₂×C₃×Q₈	—	2	2	no	—
367	C₂×C₃×Q₈	—	2	4	no	—
368	C₂×C₃×Q₈	—	4	2	no	—
369	C₂×C₃×D₄	—	2	4	no	—
370	C₂×C₃×D₄	—	2	4	no	—
371	C₂×C₃×D₄	—	2	2	no	—
372	C₂×C₃×D₄	—	2	2	no	—
373	C₂×C₃×D₄	—	4	2	no	—
374	C₂×C₃×D₄	#41	1	4	yes	—
375	C₂²×C₃×C₄	—	2	2	no	—
376	C₂²×C₃×C₄	—	2	2	no	—
377	C₂²×C₃×C₄	—	2	2	no	—
378	C₂²×C₃×C₄	—	2	4	no	—
379	C₂²×C₃×C₄	—	2	2	no	—
380	C₂²×C₃×C₄	—	2	2	no	—
381	C₂²×C₃×C₄	—	2	4	no	—
382	C₂²×C₃×C₄	—	2	4	no	—
383	C₂²×C₃×C₄	—	2	2	no	—
384	C₂²×C₃×C₄	—	2	4	no	—
385	C₂²×C₃×C₄	—	2	2	no	—
386	C₂²×C₃×C₄	—	2	4	no	—
387	C₂²×C₃×C₄	—	2	4	no	—
388	C₂²×C₃×C₄	—	2	2	no	—
389	C₂²×C₃×C₄	—	2	2	no	—
390	C₂²×C₃×C₄	—	2	4	no	—
391	C₂²×C₃×C₄	—	4	2	no	—
392	C₂²×C₃×C₄	—	4	2	no	—
393	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
394	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
395	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
397	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
398	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
399	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
400	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
401	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
402	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
403	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
404	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
407	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
408	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
411	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
412	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
414	C₃×C₄⋊C₄	—	2	2	no	—
415	C₃×C₄⋊C₄	—	2	2	no	—
416	C₃×C₄⋊C₄	—	2	2	no	—
417	C₃×C₄⋊C₄	—	2	2	no	—
418	C₃×C₄⋊C₄	—	2	2	no	—
419	C₃×C₄⋊C₄	—	2	2	no	—
420	C₃×C₄⋊C₄	—	2	4	no	—
421	C₃×C₄⋊C₄	—	2	2	no	—
422	C₃×C₄⋊C₄	—	2	4	no	—
423	C₃×C₄⋊C₄	—	2	4	no	—
424	C₃×C₄⋊C₄	—	2	4	no	—
425	C₃×C₄⋊C₄	—	2	4	no	—
426	C₃×C₄⋊C₄	—	2	4	no	—
427	C₃×C₄⋊C₄	—	2	4	no	—
428	C₃×C₄⋊C₄	—	2	2	no	—
429	C₃×C₄⋊C₄	—	4	2	no	—
430	C₃×C₄⋊C₄	—	4	2	no	—
431	C₃×C₄⋊C₄	—	4	2	no	—
432	C₃×C₄⋊C₄	—	4	2	no	—
433	C₃×C₄⋊C₄	#41	1	4	yes	—
434	C₃×C₄⋊C₄	#41	1	4	yes	—
435	C₃×C₂²⋊C₄	—	2	2	no	—
436	C₃×C₂²⋊C₄	—	2	4	no	—
437	C₃×C₂²⋊C₄	—	2	4	no	—
438	C₃×C₂²⋊C₄	—	2	4	no	—
439	C₃×C₂²⋊C₄	—	2	4	no	—
440	C₃×C₂²⋊C₄	—	2	4	no	—
441	C₃×C₂²⋊C₄	—	2	2	no	—
442	C₃×C₂²⋊C₄	—	2	2	no	—
443	C₃×C₂²⋊C₄	—	2	4	no	—
444	C₃×C₂²⋊C₄	—	2	4	no	—
445	C₃×C₂²⋊C₄	—	2	4	no	—
446	C₃×C₂²⋊C₄	—	2	4	no	—
447	C₃×C₂²⋊C₄	—	2	4	no	—
448	C₃×C₂²⋊C₄	—	2	4	no	—
449	C₃×C₂²⋊C₄	—	4	2	no	—
450	C₃×C₂²⋊C₄	—	4	2	no	—
451	C₃×C₂²⋊C₄	#41	1	4	yes	—
452	C₃×C₄²	—	2	2	no	—
453	C₃×C₄²	—	2	2	no	—
454	C₃×C₄²	—	2	2	no	—
455	C₃×C₄²	—	2	2	no	—
456	C₃×C₄²	—	2	2	no	—
457	C₃×C₄²	—	2	2	no	—
458	C₃×C₄²	—	2	2	no	—
459	C₃×C₄²	—	2	2	no	—
460	C₃×C₄²	—	2	2	no	—
461	C₃×C₄²	—	2	4	no	—
462	C₃×C₄²	—	2	2	no	—
463	C₃×C₄²	—	2	2	no	—
464	C₃×C₄²	—	2	2	no	—
465	C₃×C₄²	—	2	4	no	—
466	C₃×C₄²	—	2	4	no	—
467	C₃×C₄²	—	2	2	no	—
468	C₃×C₄²	—	2	2	no	—
469	C₃×C₄²	—	2	2	no	—
470	C₃×C₄²	—	4	2	no	—
471	C₃×C₄²	—	4	2	no	—
472	C₃×C₄²	#41	1	4	yes	—
473	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
474	C₂²×Q₈	C₂³×C₃	1	2	yes	—
475	C₂²×D₄	C₂³×C₃	1	2	yes	—
476	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₃	1	2	yes	—
480	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₃	1	2	yes	—
482	C₂³×C₄	C₂³×C₃	1	2	yes	—
483	C₄⋊Q₈	—	2	4	no	—
484	#124	—	2	4	no	—
485	#123	—	2	8	no	—
486	C₂²⋊Q₈	—	2	8	no	—
487	C₂²⋊Q₈	—	2	4	no	—
488	#121	—	2	4	no	—
489	C₄×Q₈	—	2	4	no	—
490	C₄×Q₈	—	4	4	no	—
491	C₄×D₄	—	2	4	no	—
492	C₄×D₄	—	2	4	no	—
493	C₄×D₄	—	2	4	no	—
494	C₄×D₄	—	4	4	no	—
495	#117	—	2	4	no	—
496	#117	—	2	4	no	—
497	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₄²	—	2	4	no	—
536	C₂×C₄²	—	4	4	no	—
537	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₃	1	2	yes	—
542	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₃	1	2	yes	—
546	C₂×C₄²	C₂³×C₃	1	2	yes	—
547	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₃	1	2	yes	—
556	C₂×C₄²	C₂³×C₃	1	2	yes	—
557	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
558	#95	C₂³×C₃	1	1	yes	characteristic
559	#95	C₂³×C₃	1	1	yes	characteristic
560	#95	C₂³×C₃	1	1	yes	characteristic
561	#95	C₂³×C₃	1	1	yes	characteristic
562	#95	C₂³×C₃	1	1	yes	characteristic
563	#95	C₂³×C₃	1	1	yes	characteristic
564	#95	C₂³×C₃	1	1	yes	characteristic
565	#95	C₂³×C₃	1	1	yes	characteristic
566	#95	C₂³×C₃	1	2	yes	—
567	#95	C₂³×C₃	1	2	yes	—
568	#95	C₂³×C₃	1	2	yes	—
569	#95	C₂³×C₃	1	2	yes	—
570	#95	C₂³×C₃	1	2	yes	—
571	#95	C₂³×C₃	1	2	yes	—
572	#95	C₂³×C₃	1	2	yes	—
573	#95	C₂³×C₃	1	2	yes	—
574	#95	C₂³×C₃	1	2	yes	—
575	#95	C₂³×C₃	1	2	yes	—
576	#95	C₂³×C₃	1	2	yes	—
577	#95	C₂³×C₃	1	2	yes	—
578	#95	C₂³×C₃	1	2	yes	—
579	#95	C₂³×C₃	1	2	yes	—
580	#95	C₂³×C₃	1	2	yes	—
581	#95	C₂³×C₃	1	2	yes	—
582	#95	C₂³×C₃	1	2	yes	—
583	#95	C₂³×C₃	1	2	yes	—
584	#95	C₂³×C₃	1	2	yes	—
585	#95	C₂³×C₃	1	2	yes	—
586	#95	C₂³×C₃	1	2	yes	—
587	#95	C₂³×C₃	1	2	yes	—
588	C₂³×C₃	—	2	1	no	—
589	C₂³×C₃	—	2	1	no	—
590	C₂³×C₃	—	2	2	no	—
591	C₂³×C₃	—	2	2	no	—
592	C₂³×C₃	—	2	2	no	—
593	C₂³×C₃	—	2	2	no	—
594	C₂³×C₃	—	2	1	no	—
595	C₂³×C₃	—	2	1	no	—
596	C₂³×C₃	—	2	1	no	—
597	C₂³×C₃	—	2	2	no	—
598	C₂³×C₃	—	2	1	no	—
599	C₂³×C₃	—	2	2	no	—
600	C₂³×C₃	C₂×#41	1	4	yes	—
601	C₂³×C₃	C₂×#41	1	2	yes	—
602	C₂³×C₃	C₂⁵	1	1	yes	characteristic
603	C₃×Q₈	—	4	8	no	—
604	C₃×Q₈	—	4	4	no	—
605	C₃×D₄	—	2	8	no	—
606	C₃×D₄	—	4	8	no	—
607	C₂×C₃×C₄	—	2	8	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	1	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	2	1	no	—
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	2	no	—
633	C₂×C₃×C₄	—	2	2	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	2	2	no	—
638	C₂×C₃×C₄	—	2	2	no	—
639	C₂×C₃×C₄	—	2	2	no	—
640	C₂×C₃×C₄	—	2	2	no	—
641	C₂×C₃×C₄	—	2	2	no	—
642	C₂×C₃×C₄	—	2	2	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	2	no	—
647	C₂×C₃×C₄	—	2	2	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	2	no	—
651	C₂×C₃×C₄	—	2	2	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	1	no	—
656	C₂×C₃×C₄	—	2	1	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	4	8	no	—
659	C₂×C₃×C₄	—	4	8	no	—
660	C₂×C₃×C₄	—	4	4	no	—
661	C₂×C₃×C₄	—	4	4	no	—
662	C₂×C₃×C₄	—	4	8	no	—
663	C₂×C₃×C₄	C₂×#41	1	2	yes	—
664	C₂×C₃×C₄	C₂×#41	1	2	yes	—
665	C₂×C₃×C₄	C₂×#41	1	2	yes	—
666	C₂×C₃×C₄	C₂×#41	1	2	yes	—
667	C₂×C₃×C₄	C₂×#41	1	2	yes	—
668	C₂×C₃×C₄	C₂×#41	1	2	yes	—
669	C₂×C₃×C₄	C₂×#41	1	4	yes	—
670	C₂×C₃×C₄	C₂×#41	1	2	yes	—
671	C₂×C₃×C₄	C₂×#41	1	2	yes	—
672	C₂×C₃×C₄	C₂×#41	1	2	yes	—
673	C₂×C₃×C₄	C₂×#41	1	2	yes	—
674	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
675	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
676	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
677	C₂⁴	C₂⁴×C₃	1	2	yes	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	4	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	4	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	C₃×#41	1	4	yes	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	C₃×#41	1	4	yes	—
749	C₄⋊C₄	C₃×#41	1	4	yes	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	C₃×#41	1	4	yes	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	4	no	—
781	C₄²	—	2	4	no	—
782	C₄²	—	2	2	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	4	2	no	—
786	C₄²	—	4	2	no	—
787	C₄²	C₃×#41	1	4	yes	—
788	C₂²×C₃	—	2	4	no	—
789	C₂²×C₃	—	2	2	no	—
790	C₂²×C₃	—	2	4	no	—
791	C₂²×C₃	—	2	2	no	—
792	C₂²×C₃	—	2	2	no	—
793	C₂²×C₃	—	2	4	no	—
794	C₂²×C₃	—	4	1	no	—
795	C₂²×C₃	—	4	2	no	—
796	C₂²×C₃	—	4	2	no	—
797	C₂²×C₃	—	4	1	no	—
798	C₂²×C₃	—	4	2	no	—
799	C₂²×C₃	—	4	1	no	—
800	C₂²×C₃	—	4	2	no	—
801	C₂²×C₃	—	4	1	no	—
802	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
803	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
804	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
805	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
806	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
807	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
808	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
809	C₃×C₄	—	2	2	no	—
810	C₃×C₄	—	2	2	no	—
811	C₃×C₄	—	2	2	no	—
812	C₃×C₄	—	2	2	no	—
813	C₃×C₄	—	2	4	no	—
814	C₃×C₄	—	2	2	no	—
815	C₃×C₄	—	2	2	no	—
816	C₃×C₄	—	4	1	no	—
817	C₃×C₄	—	4	2	no	—
818	C₃×C₄	—	4	2	no	—
819	C₃×C₄	—	4	1	no	—
820	C₃×C₄	—	4	2	no	—
821	C₃×C₄	—	4	1	no	—
822	C₃×C₄	—	4	2	no	—
823	C₃×C₄	—	4	2	no	—
824	C₃×C₄	—	4	2	no	—
825	C₃×C₄	—	4	1	no	—
826	C₃×C₄	—	4	1	no	—
827	C₃×C₄	—	4	1	no	—
828	C₃×C₄	#529	1	4	yes	—
829	C₃×C₄	#542	1	4	yes	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	2	no	—
842	C₂³	C₂×C₃×#41	1	4	yes	—
843	C₂³	C₂×C₃×#41	1	2	yes	—
844	C₂³	C₂⁵×C₃	1	1	yes	characteristic
845	Q₈	—	4	8	no	—
846	Q₈	—	4	4	no	—
847	D₄	—	2	8	no	—
848	D₄	—	4	8	no	—
849	C₂×C₄	—	2	8	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	4	8	no	—
901	C₂×C₄	—	4	8	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	8	no	—
905	C₂×C₄	C₂×C₃×#41	1	2	yes	—
906	C₂×C₄	C₂×C₃×#41	1	2	yes	—
907	C₂×C₄	C₂×C₃×#41	1	2	yes	—
908	C₂×C₄	C₂×C₃×#41	1	2	yes	—
909	C₂×C₄	C₂×C₃×#41	1	2	yes	—
910	C₂×C₄	C₂×C₃×#41	1	2	yes	—
911	C₂×C₄	C₂×C₃×#41	1	4	yes	—
912	C₂×C₄	C₂×C₃×#41	1	2	yes	—
913	C₂×C₄	C₂×C₃×#41	1	2	yes	—
914	C₂×C₄	C₂×C₃×#41	1	2	yes	—
915	C₂×C₄	C₂×C₃×#41	1	2	yes	—
916	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
917	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
918	C₂×C₃	—	4	4	no	—
919	C₂×C₃	—	4	2	no	—
920	C₂×C₃	C₂×#529	1	1	yes	characteristic
921	C₂×C₃	#3444	1	1	yes	characteristic
922	C₂×C₃	C₂×#542	1	1	yes	characteristic
923	C₂×C₃	#3481	1	1	yes	characteristic
924	C₂×C₃	#3481	1	1	yes	characteristic
925	C₂×C₃	#3482	1	1	yes	characteristic
926	C₂×C₃	#3482	1	1	yes	characteristic
927	C₂²	—	2	4	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	4	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	4	no	—
933	C₂²	—	4	1	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	1	no	—
941	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
942	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
943	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
944	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
945	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
946	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
947	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
948	C₄	—	2	2	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	2	no	—
952	C₄	—	2	4	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	1	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	1	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	C₃×#529	1	4	yes	—
968	C₄	C₃×#542	1	4	yes	—
969	C₃	#34969	1	1	yes	characteristic, direct product factor, Sylow
970	C₂	—	4	4	no	—
971	C₂	—	4	2	no	—
972	C₂	C₂×C₃×#529	1	1	yes	characteristic
973	C₂	C₃×#3444	1	1	yes	characteristic
974	C₂	C₂×C₃×#542	1	1	yes	characteristic
975	C₂	C₃×#3481	1	1	yes	characteristic
976	C₂	C₃×#3481	1	1	yes	characteristic
977	C₂	C₃×#3482	1	1	yes	characteristic
978	C₂	C₃×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
socle	C₂³×C₃	C₂⁵
prime radical	C₂×C₃×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2530	C₂	semidirect
2. C₃×#2527	C₂	semidirect
3. C₃×#2511	C₂	semidirect
4. C₃×#2509	C₂	semidirect
5. C₃×#2494	C₂	semidirect
6. C₃×#2492	C₂	semidirect
7. C₃×#2477	C₂	semidirect
8. C₃×#2470	C₂	semidirect
9. C₃×#2452	C₂	semidirect
10. C₃×#2447	C₂	semidirect
13. C₃×#2401	C₂	semidirect
14. C₃×#2398	C₂	semidirect
15. C₃×C₄×C₄⋊Q₈	C₂	semidirect
16. C₃×C₄×#124	C₂	semidirect
17. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
18. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
19. C₃×C₄×#123	C₂	semidirect
21. C₃×#2295	C₂	semidirect
22. C₃×C₄²×D₄	C₂	semidirect
23. C₃×C₄×#117	C₂	semidirect
24. #34969	C₃	direct (N × H)
124. #2530	C₂×C₃	semidirect
125. #2527	C₂×C₃	semidirect
126. #2511	C₂×C₃	semidirect
127. #2509	C₂×C₃	semidirect
128. #2494	C₂×C₃	semidirect
129. #2492	C₂×C₃	semidirect
130. #2477	C₂×C₃	semidirect
131. #2470	C₂×C₃	semidirect
132. #2452	C₂×C₃	semidirect
133. #2447	C₂×C₃	semidirect
136. #2401	C₂×C₃	semidirect
137. #2398	C₂×C₃	semidirect
138. C₄×C₄⋊Q₈	C₂×C₃	semidirect
139. C₄×#124	C₂×C₃	semidirect
140. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
141. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
142. C₄×#123	C₂×C₃	semidirect
144. #2295	C₂×C₃	semidirect
145. C₄²×D₄	C₂×C₃	semidirect
146. C₄×#117	C₂×C₃	semidirect
969. C₃	#34969	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#2530	2
C₃×#2527	2
C₃×#2511	2
C₃×#2509	2
C₃×#2494	2
C₃×#2492	2
C₃×#2477	2
C₃×#2470	2
C₃×#2452	2
C₃×#2447	2
C₃×#2427	2
C₃×#2422	2
C₃×#2401	2
C₃×#2398	2
C₃×C₄×C₄⋊Q₈	2
C₃×C₄×#124	2
C₃×C₄×C₂²⋊Q₈	2
C₃×C₄×#123	2
C₃×C₄×#121	2
C₃×#2295	2
C₃×C₄²×D₄	2
C₃×C₄×#117	2
#34969	3

Subgroups — C3×#34969 #10653576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34969 #10653576