Subgroups — C₃×#62822 #10681429

Order 768.

7274 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3560	C₂	1	8	yes	maximal, complemented
2	C₃×#3559	C₂	1	4	yes	maximal, complemented
3	C₃×#3558	C₂	1	4	yes	maximal, complemented
4	C₃×#3545	C₂	1	4	yes	maximal, complemented
5	C₃×#3544	C₂	1	2	yes	maximal, complemented
6	C₃×#3543	C₂	1	2	yes	maximal, complemented
7	C₃×#3522	C₂	1	4	yes	maximal, complemented
8	C₃×#3519	C₂	1	4	yes	maximal, complemented
9	C₃×#3513	C₂	1	8	yes	maximal, complemented
10	C₃×#3505	C₂	1	4	yes	maximal, complemented
11	C₃×#3496	C₂	1	4	yes	maximal, complemented
12	C₃×#3494	C₂	1	8	yes	maximal, complemented
13	C₃×#3485	C₂	1	4	yes	maximal, complemented
14	C₂×C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#529	C₂	1	2	yes	maximal, complemented
16	#62822	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
18	C₂²×C₃×#41	C₂²	1	2	yes	complemented
19	C₃×#563	C₂²	1	8	yes	complemented
20	C₃×#563	C₂²	1	4	yes	complemented
21	C₃×#562	C₂²	1	8	yes	complemented
22	C₃×H(3,𝔽₄)	C₂²	1	4	yes	complemented
23	C₃×#560	C₂²	1	8	yes	complemented
24	C₃×#559	C₂²	1	8	yes	complemented
25	C₃×#559	C₂²	1	2	yes	complemented
26	C₃×Q₈²	C₂²	1	2	yes	complemented
27	C₃×#555	C₂²	1	8	yes	complemented
28	C₃×#555	C₂²	1	2	yes	complemented
29	C₃×#554	C₂²	1	8	yes	complemented
30	C₃×#554	C₂²	1	4	yes	complemented
31	C₃×#553	C₂²	1	16	yes	complemented
32	C₃×#553	C₂²	1	16	yes	complemented
33	C₃×#553	C₂²	1	8	yes	complemented
34	C₃×#553	C₂²	1	8	yes	complemented
35	C₃×#552	C₂²	1	8	yes	complemented
36	C₃×#551	C₂²	1	8	yes	complemented
37	C₃×#551	C₂²	1	16	yes	complemented
38	C₃×#551	C₂²	1	16	yes	complemented
39	C₃×#550	C₂²	1	4	yes	complemented
40	C₃×#548	C₂²	1	8	yes	complemented
41	C₃×#547	C₂²	1	16	yes	complemented
42	C₃×#547	C₂²	1	16	yes	complemented
43	C₃×#547	C₂²	1	8	yes	complemented
44	C₃×#547	C₂²	1	8	yes	complemented
45	C₃×#546	C₂²	1	16	yes	complemented
46	C₃×#546	C₂²	1	16	yes	complemented
47	C₃×#546	C₂²	1	16	yes	complemented
48	C₃×#546	C₂²	1	16	yes	complemented
49	C₃×#546	C₂²	1	8	yes	complemented
50	C₃×#546	C₂²	1	8	yes	complemented
51	C₃×D₄²	C₂²	1	8	yes	complemented
52	C₃×D₄²	C₂²	1	8	yes	complemented
53	C₃×D₄²	C₂²	1	2	yes	complemented
54	C₃×#544	C₂²	1	8	yes	complemented
55	C₃×#542	C₂²	1	8	yes	complemented
56	C₃×#542	C₂²	1	8	yes	complemented
57	C₃×#542	C₂²	1	16	yes	complemented
58	C₃×#540	C₂²	1	8	yes	complemented
59	C₃×#540	C₂²	1	8	yes	complemented
60	C₃×#539	C₂²	1	8	yes	complemented
61	C₃×#539	C₂²	1	16	yes	complemented
62	C₃×#538	C₂²	1	8	yes	complemented
63	C₃×#538	C₂²	1	16	yes	complemented
64	C₃×#538	C₂²	1	16	yes	complemented
65	C₃×#537	C₂²	1	8	yes	complemented
66	C₃×#536	C₂²	1	8	yes	complemented
67	C₃×#535	C₂²	1	8	yes	complemented
68	C₃×#534	C₂²	1	8	yes	complemented
69	C₃×#534	C₂²	1	8	yes	complemented
70	C₃×#534	C₂²	1	8	yes	complemented
71	C₃×#532	C₂²	1	4	yes	complemented
72	C₃×#532	C₂²	1	4	yes	complemented
73	C₃×#532	C₂²	1	4	yes	complemented
74	C₃×#532	C₂²	1	4	yes	complemented
75	C₃×#532	C₂²	1	8	yes	complemented
76	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₃×#127	C₂²	1	1	yes	characteristic, complemented
78	C₃×#529	C₂²	1	4	yes	complemented
79	C₃×#529	C₂²	1	4	yes	complemented
80	C₃×#529	C₂²	1	4	yes	complemented
81	C₃×#529	C₂²	1	4	yes	complemented
82	C₃×#529	C₂²	1	4	yes	complemented
83	C₃×#529	C₂²	1	4	yes	complemented
84	C₃×#529	C₂²	1	4	yes	complemented
85	C₃×#529	C₂²	1	4	yes	complemented
86	C₃×#529	C₂²	1	8	yes	complemented
87	C₂×C₃×#126	C₂²	1	4	yes	complemented
88	C₂×C₃×#125	C₂²	1	2	yes	complemented
89	C₂×C₃×#124	C₂²	1	2	yes	complemented
90	C₂×C₃×#124	C₂²	1	2	yes	complemented
91	C₃×#525	C₂²	1	8	yes	complemented
92	C₃×#525	C₂²	1	8	yes	complemented
93	C₂×C₃×#123	C₂²	1	4	yes	complemented
94	C₂×C₃×#123	C₂²	1	8	yes	complemented
95	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
96	C₂×C₃×#121	C₂²	1	2	yes	—
97	C₂×C₃×#121	C₂²	1	4	yes	complemented
98	C₂×C₃×#121	C₂²	1	8	yes	complemented
99	C₃×#520	C₂²	1	8	yes	complemented
100	C₃×#518	C₂²	1	4	yes	complemented
101	C₃×#518	C₂²	1	8	yes	complemented
102	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
103	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
104	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
105	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
106	C₂×C₃×#117	C₂²	1	4	yes	complemented
107	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
108	#3560	C₂×C₃	1	8	yes	complemented
109	#3559	C₂×C₃	1	4	yes	complemented
110	#3558	C₂×C₃	1	4	yes	complemented
111	#3545	C₂×C₃	1	4	yes	complemented
112	#3544	C₂×C₃	1	2	yes	complemented
113	#3543	C₂×C₃	1	2	yes	complemented
114	#3522	C₂×C₃	1	4	yes	complemented
115	#3519	C₂×C₃	1	4	yes	complemented
116	#3513	C₂×C₃	1	8	yes	complemented
117	#3505	C₂×C₃	1	4	yes	complemented
118	#3496	C₂×C₃	1	4	yes	complemented
119	#3494	C₂×C₃	1	8	yes	complemented
120	#3485	C₂×C₃	1	4	yes	complemented
121	C₂×#532	C₂×C₃	1	1	yes	characteristic, complemented
122	C₂×#529	C₂×C₃	1	2	yes	complemented
123	C₃×H(5,𝔽₂)	—	4	16	no	—
124	C₂×C₃×#41	—	4	8	no	—
125	C₂×C₃×#41	C₂³	1	8	yes	—
126	C₂×C₃×#41	C₂³	1	8	yes	—
127	C₂×C₃×#41	C₂³	1	8	yes	—
128	C₂×C₃×#41	C₂³	1	16	yes	—
129	C₂×C₃×#41	C₂³	1	8	yes	—
130	C₂²×C₃×Q₈	C₂³	1	2	yes	—
131	C₂²×C₃×Q₈	C₂³	1	2	yes	—
132	C₂²×C₃×D₄	C₂³	1	4	yes	—
133	C₂²×C₃×D₄	C₂³	1	4	yes	—
134	C₂²×C₃×D₄	C₂³	1	2	yes	—
135	C₂²×C₃×D₄	C₂³	1	16	yes	—
136	C₂²×C₃×D₄	C₂³	1	8	yes	—
137	C₂²×C₃×D₄	C₂³	1	2	yes	—
138	C₂²×C₃×D₄	C₂³	1	4	yes	—
139	C₂²×C₃×D₄	C₂³	1	8	yes	—
140	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
141	C₂³×C₃×C₄	C₂³	1	4	yes	—
142	C₂³×C₃×C₄	C₂³	1	2	yes	—
143	C₂³×C₃×C₄	C₂³	1	4	yes	—
144	C₃×C₄⋊Q₈	C₂³	1	8	yes	—
145	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
146	C₃×C₄⋊Q₈	C₂³	1	8	yes	—
147	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
148	C₃×C₄⋊Q₈	C₂³	1	8	yes	—
149	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
150	C₃×#127	C₂³	1	2	yes	—
151	C₃×#127	C₂³	1	8	yes	—
152	C₃×#127	C₂³	1	2	yes	—
153	C₃×#127	C₂³	1	4	yes	—
154	C₃×#126	C₂³	1	8	yes	—
155	C₃×#126	C₂³	1	16	yes	—
156	C₃×#126	C₂³	1	16	yes	—
157	C₃×#126	C₂³	1	8	yes	—
158	C₃×#126	C₂³	1	8	yes	—
159	C₃×#126	C₂³	1	8	yes	—
160	C₃×#126	C₂³	1	16	yes	—
161	C₃×#125	C₂³	1	4	yes	—
162	C₃×#125	C₂³	1	16	yes	—
163	C₃×#125	C₂³	1	4	yes	—
164	C₃×#125	C₂³	1	4	yes	—
165	C₃×#125	C₂³	1	4	yes	—
166	C₃×#125	C₂³	1	8	yes	—
167	C₃×#124	C₂³	1	4	yes	—
168	C₃×#124	C₂³	1	8	yes	—
169	C₃×#124	C₂³	1	16	yes	—
170	C₃×#124	C₂³	1	4	yes	—
171	C₃×#124	C₂³	1	4	yes	—
172	C₃×#124	C₂³	1	8	yes	—
173	C₃×#124	C₂³	1	8	yes	—
174	C₃×#124	C₂³	1	4	yes	—
175	C₃×#124	C₂³	1	4	yes	—
176	C₃×#124	C₂³	1	8	yes	—
177	C₃×#124	C₂³	1	4	yes	—
178	C₃×#124	C₂³	1	16	yes	—
179	C₃×#123	C₂³	1	8	yes	—
180	C₃×#123	C₂³	1	16	yes	—
181	C₃×#123	C₂³	1	16	yes	—
182	C₃×#123	C₂³	1	16	yes	—
183	C₃×#123	C₂³	1	16	yes	—
184	C₃×#123	C₂³	1	16	yes	—
185	C₃×#123	C₂³	1	8	yes	—
186	C₃×#123	C₂³	1	8	yes	—
187	C₃×#123	C₂³	1	8	yes	—
188	C₃×#123	C₂³	1	8	yes	—
189	C₃×#123	C₂³	1	8	yes	—
190	C₃×#123	C₂³	1	16	yes	—
191	C₃×#123	C₂³	1	16	yes	—
192	C₃×#123	C₂³	1	16	yes	—
193	C₃×#123	C₂³	1	16	yes	—
194	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
195	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
196	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
197	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
198	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
199	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
200	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
201	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
202	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
203	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
204	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
205	C₃×#121	C₂³	1	16	yes	—
206	C₃×#121	C₂³	1	16	yes	—
207	C₃×#121	C₂³	1	16	yes	—
208	C₃×#121	C₂³	1	16	yes	—
209	C₃×#121	C₂³	1	16	yes	—
210	C₃×#121	C₂³	1	4	yes	—
211	C₃×#121	C₂³	1	4	yes	—
212	C₃×#121	C₂³	1	4	yes	—
213	C₃×#121	C₂³	1	4	yes	—
214	C₃×#121	C₂³	1	8	yes	—
215	C₃×#121	C₂³	1	8	yes	—
216	C₃×#121	C₂³	1	8	yes	—
217	C₃×#121	C₂³	1	8	yes	—
218	C₃×#121	C₂³	1	16	yes	—
219	C₃×#121	C₂³	1	16	yes	—
220	C₃×#121	C₂³	1	8	yes	—
221	C₃×#121	C₂³	1	8	yes	—
222	C₃×#121	C₂³	1	16	yes	—
223	C₃×#121	C₂³	1	8	yes	—
224	C₃×#121	C₂³	1	16	yes	—
225	C₃×#120	C₂³	1	16	yes	—
226	C₃×#120	C₂³	1	8	yes	—
227	C₃×#120	C₂³	1	8	yes	—
228	C₃×#120	C₂³	1	16	yes	—
229	C₃×#120	C₂³	1	16	yes	—
230	C₃×#120	C₂³	1	16	yes	—
231	C₃×C₄×Q₈	C₂³	1	4	yes	—
232	C₃×C₄×Q₈	C₂³	1	8	yes	—
233	C₃×C₄×Q₈	C₂³	1	4	yes	—
234	C₃×C₄×Q₈	C₂³	1	4	yes	—
235	C₃×C₄×Q₈	C₂³	1	4	yes	—
236	C₃×C₄×D₄	C₂³	1	8	yes	—
237	C₃×C₄×D₄	C₂³	1	8	yes	—
238	C₃×C₄×D₄	C₂³	1	16	yes	—
239	C₃×C₄×D₄	C₂³	1	8	yes	—
240	C₃×C₄×D₄	C₂³	1	4	yes	—
241	C₃×C₄×D₄	C₂³	1	8	yes	—
242	C₃×C₄×D₄	C₂³	1	4	yes	—
243	C₃×C₄×D₄	C₂³	1	8	yes	—
244	C₃×C₄×D₄	C₂³	1	8	yes	—
245	C₃×C₄×D₄	C₂³	1	4	yes	—
246	C₃×C₄×D₄	C₂³	1	8	yes	—
247	C₃×C₄×D₄	C₂³	1	4	yes	—
248	C₃×C₄×D₄	C₂³	1	8	yes	—
249	C₃×C₄×D₄	C₂³	1	8	yes	—
250	C₃×C₄×D₄	C₂³	1	8	yes	—
251	C₃×C₄×D₄	C₂³	1	16	yes	—
252	C₃×C₄×D₄	C₂³	1	16	yes	—
253	C₃×C₄×D₄	C₂³	1	16	yes	—
254	C₃×C₄×D₄	C₂³	1	16	yes	—
255	C₃×C₄×D₄	C₂³	1	8	yes	—
256	C₃×C₄×D₄	C₂³	1	16	yes	—
257	C₃×#117	C₂³	1	8	yes	—
258	C₃×#117	C₂³	1	8	yes	—
259	C₃×#117	C₂³	1	8	yes	—
260	C₃×#117	C₂³	1	8	yes	—
261	C₃×#117	C₂³	1	8	yes	—
262	C₃×#117	C₂³	1	8	yes	—
263	C₃×#117	C₂³	1	16	yes	—
264	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
265	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
266	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
267	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
268	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
269	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
271	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
272	C₂×C₃×C₄⋊C₄	C₂³	1	16	yes	—
273	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
274	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
275	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
276	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
277	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
278	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
279	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	—
280	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
281	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	—
282	C₂×C₃×C₄²	C₂³	1	2	yes	—
283	C₂×C₃×C₄²	C₂³	1	2	yes	—
284	C₂×C₃×C₄²	C₂³	1	2	yes	—
285	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
286	C₂×C₃×C₄²	C₂³	1	2	yes	—
287	C₂×C₃×C₄²	C₂³	1	2	yes	—
288	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
289	C₂×C₃×C₄²	C₂³	1	4	yes	—
290	C₂×H(5,𝔽₂)	C₂²×C₃	1	4	yes	complemented
291	C₂²×#41	C₂²×C₃	1	2	yes	complemented
292	#563	C₂²×C₃	1	8	yes	complemented
293	#563	C₂²×C₃	1	4	yes	complemented
294	#562	C₂²×C₃	1	8	yes	complemented
295	H(3,𝔽₄)	C₂²×C₃	1	4	yes	complemented
296	#560	C₂²×C₃	1	8	yes	complemented
297	#559	C₂²×C₃	1	8	yes	complemented
298	#559	C₂²×C₃	1	2	yes	complemented
299	Q₈²	C₂²×C₃	1	2	yes	complemented
300	#555	C₂²×C₃	1	8	yes	complemented
301	#555	C₂²×C₃	1	2	yes	complemented
302	#554	C₂²×C₃	1	8	yes	complemented
303	#554	C₂²×C₃	1	4	yes	complemented
304	#553	C₂²×C₃	1	16	yes	complemented
305	#553	C₂²×C₃	1	16	yes	complemented
306	#553	C₂²×C₃	1	8	yes	complemented
307	#553	C₂²×C₃	1	8	yes	complemented
308	#552	C₂²×C₃	1	8	yes	complemented
309	#551	C₂²×C₃	1	8	yes	complemented
310	#551	C₂²×C₃	1	16	yes	complemented
311	#551	C₂²×C₃	1	16	yes	complemented
312	#550	C₂²×C₃	1	4	yes	complemented
313	#548	C₂²×C₃	1	8	yes	complemented
314	#547	C₂²×C₃	1	16	yes	complemented
315	#547	C₂²×C₃	1	16	yes	complemented
316	#547	C₂²×C₃	1	8	yes	complemented
317	#547	C₂²×C₃	1	8	yes	complemented
318	#546	C₂²×C₃	1	16	yes	complemented
319	#546	C₂²×C₃	1	16	yes	complemented
320	#546	C₂²×C₃	1	16	yes	complemented
321	#546	C₂²×C₃	1	16	yes	complemented
322	#546	C₂²×C₃	1	8	yes	complemented
323	#546	C₂²×C₃	1	8	yes	complemented
324	D₄²	C₂²×C₃	1	8	yes	complemented
325	D₄²	C₂²×C₃	1	8	yes	complemented
326	D₄²	C₂²×C₃	1	2	yes	complemented
327	#544	C₂²×C₃	1	8	yes	complemented
328	#542	C₂²×C₃	1	8	yes	complemented
329	#542	C₂²×C₃	1	8	yes	complemented
330	#542	C₂²×C₃	1	16	yes	complemented
331	#540	C₂²×C₃	1	8	yes	complemented
332	#540	C₂²×C₃	1	8	yes	complemented
333	#539	C₂²×C₃	1	8	yes	complemented
334	#539	C₂²×C₃	1	16	yes	complemented
335	#538	C₂²×C₃	1	8	yes	complemented
336	#538	C₂²×C₃	1	16	yes	complemented
337	#538	C₂²×C₃	1	16	yes	complemented
338	#537	C₂²×C₃	1	8	yes	complemented
339	#536	C₂²×C₃	1	8	yes	complemented
340	#535	C₂²×C₃	1	8	yes	complemented
341	#534	C₂²×C₃	1	8	yes	complemented
342	#534	C₂²×C₃	1	8	yes	complemented
343	#534	C₂²×C₃	1	8	yes	complemented
344	#532	C₂²×C₃	1	4	yes	complemented
345	#532	C₂²×C₃	1	4	yes	complemented
346	#532	C₂²×C₃	1	4	yes	complemented
347	#532	C₂²×C₃	1	4	yes	complemented
348	#532	C₂²×C₃	1	8	yes	complemented
349	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
350	C₂×#127	C₂²×C₃	1	1	yes	characteristic, complemented
351	#529	C₂²×C₃	1	4	yes	complemented
352	#529	C₂²×C₃	1	4	yes	complemented
353	#529	C₂²×C₃	1	4	yes	complemented
354	#529	C₂²×C₃	1	4	yes	complemented
355	#529	C₂²×C₃	1	4	yes	complemented
356	#529	C₂²×C₃	1	4	yes	complemented
357	#529	C₂²×C₃	1	4	yes	complemented
358	#529	C₂²×C₃	1	4	yes	complemented
359	#529	C₂²×C₃	1	8	yes	complemented
360	C₂×#126	C₂²×C₃	1	4	yes	complemented
361	C₂×#125	C₂²×C₃	1	2	yes	complemented
362	C₂×#124	C₂²×C₃	1	2	yes	complemented
363	C₂×#124	C₂²×C₃	1	2	yes	complemented
364	#525	C₂²×C₃	1	8	yes	complemented
365	#525	C₂²×C₃	1	8	yes	complemented
366	C₂×#123	C₂²×C₃	1	4	yes	complemented
367	C₂×#123	C₂²×C₃	1	8	yes	complemented
368	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
369	C₂×#121	C₂²×C₃	1	2	yes	—
370	C₂×#121	C₂²×C₃	1	4	yes	complemented
371	C₂×#121	C₂²×C₃	1	8	yes	complemented
372	#520	C₂²×C₃	1	8	yes	complemented
373	#518	C₂²×C₃	1	4	yes	complemented
374	#518	C₂²×C₃	1	8	yes	complemented
375	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
376	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
377	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
378	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
379	C₂×#117	C₂²×C₃	1	4	yes	complemented
380	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
381	C₂⁴×C₃	C₂⁴	1	4	yes	—
382	C₂⁴×C₃	C₂⁴	1	4	yes	—
383	C₂⁴×C₃	C₂⁴	1	8	yes	—
384	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
385	C₃×#41	—	4	16	no	—
386	C₃×#41	—	4	16	no	—
387	C₃×#41	—	4	16	no	—
388	C₃×#41	—	4	32	no	—
389	C₃×#41	—	4	16	no	—
390	C₂×C₃×Q₈	—	4	4	no	—
391	C₂×C₃×Q₈	—	4	4	no	—
392	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
393	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
394	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
395	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
396	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
397	C₂×C₃×D₄	—	2	16	no	—
398	C₂×C₃×D₄	—	2	16	no	—
399	C₂×C₃×D₄	—	4	8	no	—
400	C₂×C₃×D₄	—	4	4	no	—
401	C₂×C₃×D₄	—	4	16	no	—
402	C₂×C₃×D₄	—	4	4	no	—
403	C₂×C₃×D₄	—	4	16	no	—
404	C₂×C₃×D₄	—	4	32	no	—
405	C₂×C₃×D₄	C₂⁴	1	4	yes	—
406	C₂×C₃×D₄	C₂⁴	1	8	yes	—
407	C₂×C₃×D₄	C₂⁴	1	8	yes	—
408	C₂×C₃×D₄	C₂⁴	1	16	yes	—
409	C₂×C₃×D₄	C₂⁴	1	8	yes	—
410	C₂×C₃×D₄	C₂⁴	1	16	yes	—
411	C₂×C₃×D₄	C₂⁴	1	4	yes	—
412	C₂×C₃×D₄	C₂⁴	1	16	yes	—
413	C₂×C₃×D₄	C₂⁴	1	8	yes	—
414	C₂×C₃×D₄	C₂⁴	1	8	yes	—
415	C₂×C₃×D₄	C₂⁴	1	4	yes	—
416	C₂×C₃×D₄	C₂⁴	1	4	yes	—
417	C₂×C₃×D₄	C₂⁴	1	16	yes	—
418	C₂²×C₃×C₄	—	2	4	no	—
419	C₂²×C₃×C₄	—	4	4	no	—
420	C₂²×C₃×C₄	—	4	8	no	—
421	C₂²×C₃×C₄	—	4	8	no	—
422	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
423	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
424	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
425	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
426	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
427	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
430	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
431	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
432	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
433	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
434	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
435	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
436	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
437	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
438	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
439	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
440	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
441	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
442	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
443	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
444	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
445	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
446	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
447	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
448	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
449	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
450	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
451	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
452	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
453	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
454	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
455	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
456	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
457	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
458	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
459	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
460	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
461	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
462	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
463	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
464	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
465	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
466	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
467	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
468	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
469	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
470	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
471	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
472	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
473	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
474	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
475	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
476	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
477	C₃×C₄²	C₂⁴	1	1	yes	characteristic
478	C₃×C₄²	C₂⁴	1	2	yes	—
479	C₃×C₄²	C₂⁴	1	2	yes	—
480	C₃×C₄²	C₂⁴	1	2	yes	—
481	C₃×C₄²	C₂⁴	1	2	yes	—
482	C₃×C₄²	C₂⁴	1	1	yes	characteristic
483	C₃×C₄²	C₂⁴	1	2	yes	—
484	C₃×C₄²	C₂⁴	1	2	yes	—
485	C₃×C₄²	C₂⁴	1	1	yes	characteristic
486	C₃×C₄²	C₂⁴	1	1	yes	characteristic
487	C₃×C₄²	C₂⁴	1	8	yes	—
488	C₃×C₄²	C₂⁴	1	8	yes	—
489	C₃×C₄²	C₂⁴	1	8	yes	—
490	C₃×C₄²	C₂⁴	1	8	yes	—
491	H(5,𝔽₂)	—	4	16	no	—
492	C₂×#41	—	4	8	no	—
493	C₂×#41	C₂³×C₃	1	8	yes	—
494	C₂×#41	C₂³×C₃	1	8	yes	—
495	C₂×#41	C₂³×C₃	1	8	yes	—
496	C₂×#41	C₂³×C₃	1	8	yes	—
497	C₂×#41	C₂³×C₃	1	16	yes	—
498	C₂²×Q₈	C₂³×C₃	1	2	yes	—
499	C₂²×Q₈	C₂³×C₃	1	2	yes	—
500	C₂²×D₄	C₂³×C₃	1	4	yes	—
501	C₂²×D₄	C₂³×C₃	1	4	yes	—
502	C₂²×D₄	C₂³×C₃	1	2	yes	—
503	C₂²×D₄	C₂³×C₃	1	4	yes	—
504	C₂²×D₄	C₂³×C₃	1	8	yes	—
505	C₂²×D₄	C₂³×C₃	1	16	yes	—
506	C₂²×D₄	C₂³×C₃	1	8	yes	—
507	C₂²×D₄	C₂³×C₃	1	2	yes	—
508	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₃	1	4	yes	—
510	C₂³×C₄	C₂³×C₃	1	2	yes	—
511	C₂³×C₄	C₂³×C₃	1	4	yes	—
512	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
513	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
514	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₃	1	8	yes	—
516	C₄⋊Q₈	C₂³×C₃	1	8	yes	—
517	C₄⋊Q₈	C₂³×C₃	1	8	yes	—
518	#127	C₂³×C₃	1	4	yes	—
519	#127	C₂³×C₃	1	2	yes	—
520	#127	C₂³×C₃	1	2	yes	—
521	#127	C₂³×C₃	1	8	yes	—
522	#126	C₂³×C₃	1	8	yes	—
523	#126	C₂³×C₃	1	8	yes	—
524	#126	C₂³×C₃	1	8	yes	—
525	#126	C₂³×C₃	1	8	yes	—
526	#126	C₂³×C₃	1	16	yes	—
527	#126	C₂³×C₃	1	16	yes	—
528	#126	C₂³×C₃	1	16	yes	—
529	#125	C₂³×C₃	1	4	yes	—
530	#125	C₂³×C₃	1	4	yes	—
531	#125	C₂³×C₃	1	4	yes	—
532	#125	C₂³×C₃	1	4	yes	—
533	#125	C₂³×C₃	1	8	yes	—
534	#125	C₂³×C₃	1	16	yes	—
535	#124	C₂³×C₃	1	4	yes	—
536	#124	C₂³×C₃	1	4	yes	—
537	#124	C₂³×C₃	1	4	yes	—
538	#124	C₂³×C₃	1	4	yes	—
539	#124	C₂³×C₃	1	8	yes	—
540	#124	C₂³×C₃	1	4	yes	—
541	#124	C₂³×C₃	1	4	yes	—
542	#124	C₂³×C₃	1	8	yes	—
543	#124	C₂³×C₃	1	16	yes	—
544	#124	C₂³×C₃	1	8	yes	—
545	#124	C₂³×C₃	1	8	yes	—
546	#124	C₂³×C₃	1	16	yes	—
547	#123	C₂³×C₃	1	8	yes	—
548	#123	C₂³×C₃	1	8	yes	—
549	#123	C₂³×C₃	1	8	yes	—
550	#123	C₂³×C₃	1	8	yes	—
551	#123	C₂³×C₃	1	16	yes	—
552	#123	C₂³×C₃	1	16	yes	—
553	#123	C₂³×C₃	1	16	yes	—
554	#123	C₂³×C₃	1	16	yes	—
555	#123	C₂³×C₃	1	16	yes	—
556	#123	C₂³×C₃	1	16	yes	—
557	#123	C₂³×C₃	1	16	yes	—
558	#123	C₂³×C₃	1	8	yes	—
559	#123	C₂³×C₃	1	8	yes	—
560	#123	C₂³×C₃	1	16	yes	—
561	#123	C₂³×C₃	1	16	yes	—
562	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
563	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
564	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
565	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
566	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
567	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
568	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
569	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
570	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
571	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
572	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
573	#121	C₂³×C₃	1	4	yes	—
574	#121	C₂³×C₃	1	4	yes	—
575	#121	C₂³×C₃	1	4	yes	—
576	#121	C₂³×C₃	1	4	yes	—
577	#121	C₂³×C₃	1	8	yes	—
578	#121	C₂³×C₃	1	8	yes	—
579	#121	C₂³×C₃	1	8	yes	—
580	#121	C₂³×C₃	1	8	yes	—
581	#121	C₂³×C₃	1	16	yes	—
582	#121	C₂³×C₃	1	16	yes	—
583	#121	C₂³×C₃	1	8	yes	—
584	#121	C₂³×C₃	1	8	yes	—
585	#121	C₂³×C₃	1	16	yes	—
586	#121	C₂³×C₃	1	8	yes	—
587	#121	C₂³×C₃	1	16	yes	—
588	#121	C₂³×C₃	1	16	yes	—
589	#121	C₂³×C₃	1	16	yes	—
590	#121	C₂³×C₃	1	16	yes	—
591	#121	C₂³×C₃	1	16	yes	—
592	#121	C₂³×C₃	1	16	yes	—
593	#120	C₂³×C₃	1	16	yes	—
594	#120	C₂³×C₃	1	16	yes	—
595	#120	C₂³×C₃	1	8	yes	—
596	#120	C₂³×C₃	1	16	yes	—
597	#120	C₂³×C₃	1	8	yes	—
598	#120	C₂³×C₃	1	16	yes	—
599	C₄×Q₈	C₂³×C₃	1	4	yes	—
600	C₄×Q₈	C₂³×C₃	1	4	yes	—
601	C₄×Q₈	C₂³×C₃	1	4	yes	—
602	C₄×Q₈	C₂³×C₃	1	4	yes	—
603	C₄×Q₈	C₂³×C₃	1	8	yes	—
604	C₄×D₄	C₂³×C₃	1	4	yes	—
605	C₄×D₄	C₂³×C₃	1	8	yes	—
606	C₄×D₄	C₂³×C₃	1	4	yes	—
607	C₄×D₄	C₂³×C₃	1	8	yes	—
608	C₄×D₄	C₂³×C₃	1	8	yes	—
609	C₄×D₄	C₂³×C₃	1	4	yes	—
610	C₄×D₄	C₂³×C₃	1	8	yes	—
611	C₄×D₄	C₂³×C₃	1	4	yes	—
612	C₄×D₄	C₂³×C₃	1	8	yes	—
613	C₄×D₄	C₂³×C₃	1	8	yes	—
614	C₄×D₄	C₂³×C₃	1	8	yes	—
615	C₄×D₄	C₂³×C₃	1	8	yes	—
616	C₄×D₄	C₂³×C₃	1	16	yes	—
617	C₄×D₄	C₂³×C₃	1	16	yes	—
618	C₄×D₄	C₂³×C₃	1	16	yes	—
619	C₄×D₄	C₂³×C₃	1	16	yes	—
620	C₄×D₄	C₂³×C₃	1	8	yes	—
621	C₄×D₄	C₂³×C₃	1	8	yes	—
622	C₄×D₄	C₂³×C₃	1	16	yes	—
623	C₄×D₄	C₂³×C₃	1	8	yes	—
624	C₄×D₄	C₂³×C₃	1	16	yes	—
625	#117	C₂³×C₃	1	8	yes	—
626	#117	C₂³×C₃	1	8	yes	—
627	#117	C₂³×C₃	1	8	yes	—
628	#117	C₂³×C₃	1	8	yes	—
629	#117	C₂³×C₃	1	8	yes	—
630	#117	C₂³×C₃	1	8	yes	—
631	#117	C₂³×C₃	1	16	yes	—
632	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
633	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
634	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
635	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
637	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
639	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
640	C₂×C₄⋊C₄	C₂³×C₃	1	16	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
650	C₂×C₄²	C₂³×C₃	1	2	yes	—
651	C₂×C₄²	C₂³×C₃	1	4	yes	—
652	C₂×C₄²	C₂³×C₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₃	1	2	yes	—
657	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
658	C₂³×C₃	—	2	8	no	—
659	C₂³×C₃	—	2	8	no	—
660	C₂³×C₃	—	4	2	no	—
661	C₂³×C₃	—	4	4	no	—
662	C₂³×C₃	—	4	4	no	—
663	C₂³×C₃	—	4	8	no	—
664	C₂³×C₃	—	4	8	no	—
665	C₂³×C₃	—	4	16	no	—
666	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
667	C₂³×C₃	C₂⁵	1	8	yes	—
668	C₂³×C₃	C₂⁵	1	8	yes	—
669	C₂³×C₃	C₂⁵	1	1	yes	characteristic
670	C₂³×C₃	C₂⁵	1	2	yes	—
671	C₃×Q₈	—	2	8	no	—
672	C₃×Q₈	—	4	4	no	—
673	C₃×Q₈	—	4	4	no	—
674	C₃×Q₈	—	4	4	no	—
675	C₃×Q₈	—	4	8	no	—
676	C₃×D₄	—	2	16	no	—
677	C₃×D₄	—	2	16	no	—
678	C₃×D₄	—	2	32	no	—
679	C₃×D₄	—	2	8	no	—
680	C₃×D₄	—	2	16	no	—
681	C₃×D₄	—	4	16	no	—
682	C₃×D₄	—	4	8	no	—
683	C₃×D₄	—	4	16	no	—
684	C₃×D₄	—	4	8	no	—
685	C₃×D₄	—	4	4	no	—
686	C₃×D₄	—	4	4	no	—
687	C₃×D₄	—	4	4	no	—
688	C₃×D₄	—	4	16	no	—
689	C₂×C₃×C₄	—	2	2	no	—
690	C₂×C₃×C₄	—	2	2	no	—
691	C₂×C₃×C₄	—	2	4	no	—
692	C₂×C₃×C₄	—	2	4	no	—
693	C₂×C₃×C₄	—	2	8	no	—
694	C₂×C₃×C₄	—	2	8	no	—
695	C₂×C₃×C₄	—	2	4	no	—
696	C₂×C₃×C₄	—	2	4	no	—
697	C₂×C₃×C₄	—	2	4	no	—
698	C₂×C₃×C₄	—	2	16	no	—
699	C₂×C₃×C₄	—	4	8	no	—
700	C₂×C₃×C₄	—	4	2	no	—
701	C₂×C₃×C₄	—	4	2	no	—
702	C₂×C₃×C₄	—	4	4	no	—
703	C₂×C₃×C₄	—	4	2	no	—
704	C₂×C₃×C₄	—	4	16	no	—
705	C₂×C₃×C₄	—	4	8	no	—
706	C₂×C₃×C₄	—	4	16	no	—
707	C₂×C₃×C₄	—	4	4	no	—
708	C₂×C₃×C₄	—	4	16	no	—
709	C₂×C₃×C₄	C₂⁵	1	2	yes	—
710	C₂×C₃×C₄	C₂⁵	1	2	yes	—
711	C₂×C₃×C₄	C₂⁵	1	8	yes	—
712	C₂×C₃×C₄	C₂⁵	1	2	yes	—
713	C₂×C₃×C₄	C₂⁵	1	2	yes	—
714	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
715	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
716	C₂×C₃×C₄	C₂⁵	1	8	yes	—
717	C₂×C₃×C₄	C₂⁵	1	8	yes	—
718	C₂×C₃×C₄	C₂⁵	1	8	yes	—
719	C₂×C₃×C₄	C₂⁵	1	2	yes	—
720	C₂⁴	C₂⁴×C₃	1	4	yes	—
721	C₂⁴	C₂⁴×C₃	1	4	yes	—
722	C₂⁴	C₂⁴×C₃	1	8	yes	—
723	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
724	#41	—	4	16	no	—
725	#41	—	4	16	no	—
726	#41	—	4	16	no	—
727	#41	—	4	32	no	—
728	#41	—	4	16	no	—
729	C₂×Q₈	—	4	4	no	—
730	C₂×Q₈	—	4	4	no	—
731	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
732	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
733	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
734	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
735	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
736	C₂×D₄	—	2	16	no	—
737	C₂×D₄	—	2	16	no	—
738	C₂×D₄	—	4	8	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	—	4	16	no	—
741	C₂×D₄	—	4	4	no	—
742	C₂×D₄	—	4	16	no	—
743	C₂×D₄	—	4	32	no	—
744	C₂×D₄	C₂⁴×C₃	1	4	yes	—
745	C₂×D₄	C₂⁴×C₃	1	8	yes	—
746	C₂×D₄	C₂⁴×C₃	1	8	yes	—
747	C₂×D₄	C₂⁴×C₃	1	16	yes	—
748	C₂×D₄	C₂⁴×C₃	1	8	yes	—
749	C₂×D₄	C₂⁴×C₃	1	16	yes	—
750	C₂×D₄	C₂⁴×C₃	1	4	yes	—
751	C₂×D₄	C₂⁴×C₃	1	16	yes	—
752	C₂×D₄	C₂⁴×C₃	1	8	yes	—
753	C₂×D₄	C₂⁴×C₃	1	8	yes	—
754	C₂×D₄	C₂⁴×C₃	1	4	yes	—
755	C₂×D₄	C₂⁴×C₃	1	4	yes	—
756	C₂×D₄	C₂⁴×C₃	1	16	yes	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	4	4	no	—
759	C₂²×C₄	—	4	8	no	—
760	C₂²×C₄	—	4	8	no	—
761	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
769	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
770	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
771	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
775	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
776	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
777	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
778	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
779	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
780	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
781	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
782	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
783	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
784	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
785	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
786	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
787	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
788	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
789	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
790	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
791	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
792	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
793	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
794	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
795	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
796	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
797	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
798	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
799	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
800	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
801	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
802	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
803	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
804	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
805	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
806	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
807	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
808	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
809	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
810	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
811	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
812	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
813	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
814	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
815	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
816	C₄²	C₂⁴×C₃	1	1	yes	characteristic
817	C₄²	C₂⁴×C₃	1	2	yes	—
818	C₄²	C₂⁴×C₃	1	2	yes	—
819	C₄²	C₂⁴×C₃	1	2	yes	—
820	C₄²	C₂⁴×C₃	1	2	yes	—
821	C₄²	C₂⁴×C₃	1	1	yes	characteristic
822	C₄²	C₂⁴×C₃	1	2	yes	—
823	C₄²	C₂⁴×C₃	1	2	yes	—
824	C₄²	C₂⁴×C₃	1	1	yes	characteristic
825	C₄²	C₂⁴×C₃	1	1	yes	characteristic
826	C₄²	C₂⁴×C₃	1	8	yes	—
827	C₄²	C₂⁴×C₃	1	8	yes	—
828	C₄²	C₂⁴×C₃	1	8	yes	—
829	C₄²	C₂⁴×C₃	1	8	yes	—
830	C₂²×C₃	—	2	2	no	—
831	C₂²×C₃	—	2	2	no	—
832	C₂²×C₃	—	2	2	no	—
833	C₂²×C₃	—	2	8	no	—
834	C₂²×C₃	—	2	8	no	—
835	C₂²×C₃	—	2	8	no	—
836	C₂²×C₃	—	2	16	no	—
837	C₂²×C₃	—	2	8	no	—
838	C₂²×C₃	—	4	4	no	—
839	C₂²×C₃	—	8	8	no	—
840	C₂²×C₃	—	8	8	no	—
841	C₂²×C₃	—	16	8	no	—
842	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
843	C₂²×C₃	C₂×H(5,𝔽₂)	1	4	yes	—
844	C₂²×C₃	C₂⁶	1	1	yes	characteristic
845	C₃×C₄	—	2	2	no	—
846	C₃×C₄	—	2	1	no	—
847	C₃×C₄	—	2	1	no	—
848	C₃×C₄	—	2	8	no	—
849	C₃×C₄	—	2	8	no	—
850	C₃×C₄	—	2	2	no	—
851	C₃×C₄	—	2	8	no	—
852	C₃×C₄	—	2	2	no	—
853	C₃×C₄	—	2	2	no	—
854	C₃×C₄	—	2	8	no	—
855	C₃×C₄	#585	1	4	yes	—
856	C₂³	—	2	8	no	—
857	C₂³	—	2	8	no	—
858	C₂³	—	4	2	no	—
859	C₂³	—	4	4	no	—
860	C₂³	—	4	4	no	—
861	C₂³	—	4	8	no	—
862	C₂³	—	4	8	no	—
863	C₂³	—	4	16	no	—
864	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
865	C₂³	C₂⁵×C₃	1	8	yes	—
866	C₂³	C₂⁵×C₃	1	8	yes	—
867	C₂³	C₂⁵×C₃	1	1	yes	characteristic
868	C₂³	C₂⁵×C₃	1	2	yes	—
869	Q₈	—	2	8	no	—
870	Q₈	—	4	4	no	—
871	Q₈	—	4	4	no	—
872	Q₈	—	4	4	no	—
873	Q₈	—	4	8	no	—
874	D₄	—	2	16	no	—
875	D₄	—	2	16	no	—
876	D₄	—	2	32	no	—
877	D₄	—	2	8	no	—
878	D₄	—	2	16	no	—
879	D₄	—	4	16	no	—
880	D₄	—	4	8	no	—
881	D₄	—	4	4	no	—
882	D₄	—	4	4	no	—
883	D₄	—	4	16	no	—
884	D₄	—	4	8	no	—
885	D₄	—	4	4	no	—
886	D₄	—	4	16	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	4	no	—
890	C₂×C₄	—	2	4	no	—
891	C₂×C₄	—	2	8	no	—
892	C₂×C₄	—	2	8	no	—
893	C₂×C₄	—	2	4	no	—
894	C₂×C₄	—	2	4	no	—
895	C₂×C₄	—	2	4	no	—
896	C₂×C₄	—	2	16	no	—
897	C₂×C₄	—	4	16	no	—
898	C₂×C₄	—	4	8	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	2	no	—
903	C₂×C₄	—	4	8	no	—
904	C₂×C₄	—	4	16	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	16	no	—
907	C₂×C₄	C₂⁵×C₃	1	2	yes	—
908	C₂×C₄	C₂⁵×C₃	1	2	yes	—
909	C₂×C₄	C₂⁵×C₃	1	8	yes	—
910	C₂×C₄	C₂⁵×C₃	1	2	yes	—
911	C₂×C₄	C₂⁵×C₃	1	2	yes	—
912	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
913	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
914	C₂×C₄	C₂⁵×C₃	1	8	yes	—
915	C₂×C₄	C₂⁵×C₃	1	8	yes	—
916	C₂×C₄	C₂⁵×C₃	1	8	yes	—
917	C₂×C₄	C₂⁵×C₃	1	2	yes	—
918	C₂×C₃	—	2	2	no	—
919	C₂×C₃	—	2	4	no	—
920	C₂×C₃	—	4	8	no	—
921	C₂×C₃	—	4	8	no	—
922	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
923	C₂×C₃	C₂×#585	1	2	yes	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	8	no	—
928	C₂²	—	2	8	no	—
929	C₂²	—	2	8	no	—
930	C₂²	—	2	16	no	—
931	C₂²	—	2	8	no	—
932	C₂²	—	4	4	no	—
933	C₂²	—	8	8	no	—
934	C₂²	—	8	8	no	—
935	C₂²	—	16	8	no	—
936	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
937	C₂²	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
938	C₂²	C₂⁶×C₃	1	1	yes	characteristic
939	C₄	—	2	2	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	8	no	—
943	C₄	—	2	8	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	8	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	8	no	—
949	C₄	C₃×#585	1	4	yes	—
950	C₃	#62822	1	1	yes	characteristic, direct product factor, Sylow
951	C₂	—	2	2	no	—
952	C₂	—	2	4	no	—
953	C₂	—	4	8	no	—
954	C₂	—	4	8	no	—
955	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
956	C₂	C₂×C₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3560	C₂	semidirect
2. C₃×#3559	C₂	semidirect
3. C₃×#3558	C₂	semidirect
4. C₃×#3545	C₂	semidirect
5. C₃×#3544	C₂	semidirect
6. C₃×#3543	C₂	semidirect
7. C₃×#3522	C₂	semidirect
8. C₃×#3519	C₂	semidirect
9. C₃×#3513	C₂	semidirect
10. C₃×#3505	C₂	semidirect
11. C₃×#3496	C₂	semidirect
12. C₃×#3494	C₂	semidirect
13. C₃×#3485	C₂	semidirect
14. C₂×C₃×#532	C₂	semidirect
15. C₂×C₃×#529	C₂	semidirect
16. #62822	C₃	direct (N × H)
17. C₂×C₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂²×C₃×#41	C₂²	semidirect
19. C₃×#563	C₂²	semidirect
20. C₃×#563	C₂²	semidirect
21. C₃×#562	C₂²	semidirect
22. C₃×H(3,𝔽₄)	C₂²	semidirect
23. C₃×#560	C₂²	semidirect
24. C₃×#559	C₂²	semidirect
25. C₃×#559	C₂²	semidirect
26. C₃×Q₈²	C₂²	semidirect
27. C₃×#555	C₂²	semidirect
28. C₃×#555	C₂²	semidirect
29. C₃×#554	C₂²	semidirect
30. C₃×#554	C₂²	semidirect
31. C₃×#553	C₂²	semidirect
32. C₃×#553	C₂²	semidirect
33. C₃×#553	C₂²	semidirect
34. C₃×#553	C₂²	semidirect
35. C₃×#552	C₂²	semidirect
36. C₃×#551	C₂²	semidirect
37. C₃×#551	C₂²	semidirect
38. C₃×#551	C₂²	semidirect
39. C₃×#550	C₂²	semidirect
40. C₃×#548	C₂²	semidirect
41. C₃×#547	C₂²	semidirect
42. C₃×#547	C₂²	semidirect
43. C₃×#547	C₂²	semidirect
44. C₃×#547	C₂²	semidirect
45. C₃×#546	C₂²	semidirect
46. C₃×#546	C₂²	semidirect
47. C₃×#546	C₂²	semidirect
48. C₃×#546	C₂²	semidirect
49. C₃×#546	C₂²	semidirect
50. C₃×#546	C₂²	semidirect
51. C₃×D₄²	C₂²	semidirect
52. C₃×D₄²	C₂²	semidirect
53. C₃×D₄²	C₂²	semidirect
54. C₃×#544	C₂²	semidirect
55. C₃×#542	C₂²	semidirect
56. C₃×#542	C₂²	semidirect
57. C₃×#542	C₂²	semidirect
58. C₃×#540	C₂²	semidirect
59. C₃×#540	C₂²	semidirect
60. C₃×#539	C₂²	semidirect
61. C₃×#539	C₂²	semidirect
62. C₃×#538	C₂²	semidirect
63. C₃×#538	C₂²	semidirect
64. C₃×#538	C₂²	semidirect
65. C₃×#537	C₂²	semidirect
66. C₃×#536	C₂²	semidirect
67. C₃×#535	C₂²	semidirect
68. C₃×#534	C₂²	semidirect
69. C₃×#534	C₂²	semidirect
70. C₃×#534	C₂²	semidirect
71. C₃×#532	C₂²	semidirect
72. C₃×#532	C₂²	semidirect
73. C₃×#532	C₂²	semidirect
74. C₃×#532	C₂²	semidirect
75. C₃×#532	C₂²	semidirect
76. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
77. C₂×C₃×#127	C₂²	semidirect
78. C₃×#529	C₂²	semidirect
79. C₃×#529	C₂²	semidirect
80. C₃×#529	C₂²	semidirect
81. C₃×#529	C₂²	semidirect
82. C₃×#529	C₂²	semidirect
83. C₃×#529	C₂²	semidirect
84. C₃×#529	C₂²	semidirect
85. C₃×#529	C₂²	semidirect
86. C₃×#529	C₂²	semidirect
87. C₂×C₃×#126	C₂²	semidirect
88. C₂×C₃×#125	C₂²	semidirect
89. C₂×C₃×#124	C₂²	semidirect
90. C₂×C₃×#124	C₂²	semidirect
91. C₃×#525	C₂²	semidirect
92. C₃×#525	C₂²	semidirect
93. C₂×C₃×#123	C₂²	semidirect
94. C₂×C₃×#123	C₂²	semidirect
95. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
97. C₂×C₃×#121	C₂²	semidirect
98. C₂×C₃×#121	C₂²	semidirect
99. C₃×#520	C₂²	semidirect
100. C₃×#518	C₂²	semidirect
101. C₃×#518	C₂²	semidirect
102. C₂×C₃×C₄×Q₈	C₂²	semidirect
103. C₂×C₃×C₄×D₄	C₂²	semidirect
104. C₂×C₃×C₄×D₄	C₂²	semidirect
105. C₂×C₃×C₄×D₄	C₂²	semidirect
106. C₂×C₃×#117	C₂²	semidirect
107. C₂²×C₃×C₄²	C₂²	semidirect
108. #3560	C₂×C₃	semidirect
109. #3559	C₂×C₃	semidirect
110. #3558	C₂×C₃	semidirect
111. #3545	C₂×C₃	semidirect
112. #3544	C₂×C₃	semidirect
113. #3543	C₂×C₃	semidirect
114. #3522	C₂×C₃	semidirect
115. #3519	C₂×C₃	semidirect
116. #3513	C₂×C₃	semidirect
117. #3505	C₂×C₃	semidirect
118. #3496	C₂×C₃	semidirect
119. #3494	C₂×C₃	semidirect
120. #3485	C₂×C₃	semidirect
121. C₂×#532	C₂×C₃	semidirect
122. C₂×#529	C₂×C₃	semidirect
290. C₂×H(5,𝔽₂)	C₂²×C₃	semidirect
291. C₂²×#41	C₂²×C₃	semidirect
292. #563	C₂²×C₃	semidirect
293. #563	C₂²×C₃	semidirect
294. #562	C₂²×C₃	semidirect
295. H(3,𝔽₄)	C₂²×C₃	semidirect
296. #560	C₂²×C₃	semidirect
297. #559	C₂²×C₃	semidirect
298. #559	C₂²×C₃	semidirect
299. Q₈²	C₂²×C₃	semidirect
300. #555	C₂²×C₃	semidirect
301. #555	C₂²×C₃	semidirect
302. #554	C₂²×C₃	semidirect
303. #554	C₂²×C₃	semidirect
304. #553	C₂²×C₃	semidirect
305. #553	C₂²×C₃	semidirect
306. #553	C₂²×C₃	semidirect
307. #553	C₂²×C₃	semidirect
308. #552	C₂²×C₃	semidirect
309. #551	C₂²×C₃	semidirect
310. #551	C₂²×C₃	semidirect
311. #551	C₂²×C₃	semidirect
312. #550	C₂²×C₃	semidirect
313. #548	C₂²×C₃	semidirect
314. #547	C₂²×C₃	semidirect
315. #547	C₂²×C₃	semidirect
316. #547	C₂²×C₃	semidirect
317. #547	C₂²×C₃	semidirect
318. #546	C₂²×C₃	semidirect
319. #546	C₂²×C₃	semidirect
320. #546	C₂²×C₃	semidirect
321. #546	C₂²×C₃	semidirect
322. #546	C₂²×C₃	semidirect
323. #546	C₂²×C₃	semidirect
324. D₄²	C₂²×C₃	semidirect
325. D₄²	C₂²×C₃	semidirect
326. D₄²	C₂²×C₃	semidirect
327. #544	C₂²×C₃	semidirect
328. #542	C₂²×C₃	semidirect
329. #542	C₂²×C₃	semidirect
330. #542	C₂²×C₃	semidirect
331. #540	C₂²×C₃	semidirect
332. #540	C₂²×C₃	semidirect
333. #539	C₂²×C₃	semidirect
334. #539	C₂²×C₃	semidirect
335. #538	C₂²×C₃	semidirect
336. #538	C₂²×C₃	semidirect
337. #538	C₂²×C₃	semidirect
338. #537	C₂²×C₃	semidirect
339. #536	C₂²×C₃	semidirect
340. #535	C₂²×C₃	semidirect
341. #534	C₂²×C₃	semidirect
342. #534	C₂²×C₃	semidirect
343. #534	C₂²×C₃	semidirect
344. #532	C₂²×C₃	semidirect
345. #532	C₂²×C₃	semidirect
346. #532	C₂²×C₃	semidirect
347. #532	C₂²×C₃	semidirect
348. #532	C₂²×C₃	semidirect
349. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
350. C₂×#127	C₂²×C₃	semidirect
351. #529	C₂²×C₃	semidirect
352. #529	C₂²×C₃	semidirect
353. #529	C₂²×C₃	semidirect
354. #529	C₂²×C₃	semidirect
355. #529	C₂²×C₃	semidirect
356. #529	C₂²×C₃	semidirect
357. #529	C₂²×C₃	semidirect
358. #529	C₂²×C₃	semidirect
359. #529	C₂²×C₃	semidirect
360. C₂×#126	C₂²×C₃	semidirect
361. C₂×#125	C₂²×C₃	semidirect
362. C₂×#124	C₂²×C₃	semidirect
363. C₂×#124	C₂²×C₃	semidirect
364. #525	C₂²×C₃	semidirect
365. #525	C₂²×C₃	semidirect
366. C₂×#123	C₂²×C₃	semidirect
367. C₂×#123	C₂²×C₃	semidirect
368. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
370. C₂×#121	C₂²×C₃	semidirect
371. C₂×#121	C₂²×C₃	semidirect
372. #520	C₂²×C₃	semidirect
373. #518	C₂²×C₃	semidirect
374. #518	C₂²×C₃	semidirect
375. C₂×C₄×Q₈	C₂²×C₃	semidirect
376. C₂×C₄×D₄	C₂²×C₃	semidirect
377. C₂×C₄×D₄	C₂²×C₃	semidirect
378. C₂×C₄×D₄	C₂²×C₃	semidirect
379. C₂×#117	C₂²×C₃	semidirect
380. C₂²×C₄²	C₂²×C₃	semidirect
950. C₃	#62822	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×#3560	2
C₃×#3559	2
C₃×#3558	2
C₃×#3545	2
C₃×#3544	2
C₃×#3543	2
C₃×#3522	2
C₃×#3519	2
C₃×#3513	2
C₃×#3505	2
C₃×#3496	2
C₃×#3494	2
C₃×#3485	2
C₂×C₃×#532	2
C₂×C₃×#529	2
#62822	3

Subgroups — C3×#62822 #10681429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#62822 #10681429