Subgroups — C₂×#62994 #10586038

Order 512.

35096 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62994	C₂	1	64	yes	maximal, direct product factor
2	C₂×#3511	C₂	1	3	yes	maximal, complemented
3	C₂×#3494	C₂	1	6	yes	maximal, complemented
4	C₂×#3503	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#3488	C₂	1	2	yes	maximal, complemented
6	C₂×#3524	C₂	1	4	yes	maximal, complemented
7	C₂×#3518	C₂	1	2	yes	maximal, complemented
8	C₂×#3514	C₂	1	12	yes	maximal, complemented
9	C₂×#3493	C₂	1	6	yes	maximal, complemented
10	C₂×#3519	C₂	1	6	yes	maximal, complemented
11	C₂×#3506	C₂	1	3	yes	maximal, complemented
12	C₂×#3483	C₂	1	2	yes	maximal, complemented
13	C₂×#3475	C₂	1	3	yes	maximal, complemented
14	C₂×#3475	C₂	1	6	yes	maximal, complemented
15	C₂²×#555	C₂	1	3	yes	maximal, complemented
16	C₂×D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#3428	C₂	1	2	yes	maximal, complemented
19	C₂²×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	C₂³×#41	C₂²	1	2	yes	—
21	#3524	C₂²	1	128	yes	complemented
22	#3519	C₂²	1	192	yes	complemented
23	#3518	C₂²	1	64	yes	complemented
24	#3514	C₂²	1	384	yes	complemented
25	#3511	C₂²	1	96	yes	complemented
26	#3506	C₂²	1	96	yes	complemented
27	#3503	C₂²	1	32	yes	complemented
28	#3494	C₂²	1	192	yes	complemented
29	#3493	C₂²	1	192	yes	complemented
30	#3488	C₂²	1	64	yes	complemented
31	#3483	C₂²	1	64	yes	complemented
32	C₂×#559	C₂²	1	12	yes	complemented
33	C₂×Q₈²	C₂²	1	2	yes	complemented
34	C₂×#557	C₂²	1	2	yes	complemented
35	#3475	C₂²	1	96	yes	complemented
36	#3475	C₂²	1	192	yes	complemented
37	C₂×#556	C₂²	1	6	yes	complemented
38	C₂×#556	C₂²	1	6	yes	complemented
39	C₂×#556	C₂²	1	12	yes	complemented
40	C₂×#556	C₂²	1	1	yes	characteristic, complemented
41	C₂×#555	C₂²	1	6	yes	complemented
42	C₂×#555	C₂²	1	6	yes	complemented
43	C₂×#555	C₂²	1	12	yes	complemented
44	C₂×#555	C₂²	1	12	yes	complemented
45	C₂×#555	C₂²	1	12	yes	complemented
46	C₂×#555	C₂²	1	3	yes	complemented
47	C₂×#555	C₂²	1	6	yes	complemented
48	C₂×#555	C₂²	1	96	yes	complemented
49	C₂×#554	C₂²	1	6	yes	complemented
50	C₂×#554	C₂²	1	3	yes	complemented
51	C₂×#553	C₂²	1	12	yes	complemented
52	C₂×#553	C₂²	1	12	yes	complemented
53	C₂×#553	C₂²	1	12	yes	complemented
54	C₂×#553	C₂²	1	6	yes	complemented
55	C₂×#552	C₂²	1	6	yes	complemented
56	C₂×#552	C₂²	1	12	yes	complemented
57	C₂×#552	C₂²	1	6	yes	complemented
58	C₂×#551	C₂²	1	12	yes	complemented
59	C₂×#551	C₂²	1	24	yes	complemented
60	D₄×#41	C₂²	1	32	yes	complemented
61	C₂×#550	C₂²	1	6	yes	complemented
62	C₂×#550	C₂²	1	4	yes	complemented
63	C₂×#550	C₂²	1	1	yes	characteristic, complemented
64	C₂×D₄×Q₈	C₂²	1	6	yes	complemented
65	C₂×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
66	C₂×#548	C₂²	1	12	yes	complemented
67	C₂×#548	C₂²	1	4	yes	complemented
68	C₂×#548	C₂²	1	2	yes	complemented
69	C₂×#547	C₂²	1	3	yes	complemented
70	C₂×#547	C₂²	1	6	yes	complemented
71	C₂×#547	C₂²	1	3	yes	complemented
72	C₂×#546	C₂²	1	6	yes	complemented
73	C₂×#546	C₂²	1	24	yes	complemented
74	C₂×#546	C₂²	1	6	yes	complemented
75	C₂×#546	C₂²	1	12	yes	complemented
76	C₂×D₄²	C₂²	1	3	yes	complemented
77	C₂×D₄²	C₂²	1	12	yes	complemented
78	C₂×#544	C₂²	1	6	yes	complemented
79	C₂×#542	C₂²	1	12	yes	complemented
80	C₂×#542	C₂²	1	12	yes	complemented
81	C₂×#540	C₂²	1	12	yes	complemented
82	C₂×#538	C₂²	1	12	yes	complemented
83	C₂×#538	C₂²	1	24	yes	complemented
84	C₂×#537	C₂²	1	6	yes	complemented
85	C₂×#535	C₂²	1	6	yes	complemented
86	C₂×#533	C₂²	1	3	yes	complemented
87	C₂×#533	C₂²	1	6	yes	complemented
88	C₂×#532	C₂²	1	3	yes	complemented
89	C₂×#532	C₂²	1	6	yes	complemented
90	C₂×#532	C₂²	1	12	yes	complemented
91	C₂²×C₄⋊Q₈	C₂²	1	3	yes	complemented
92	C₂×#529	C₂²	1	6	yes	complemented
93	C₂×#529	C₂²	1	24	yes	complemented
94	C₂×#529	C₂²	1	12	yes	complemented
95	C₂×#529	C₂²	1	12	yes	complemented
96	C₂²×#124	C₂²	1	12	yes	complemented
97	C₂×#525	C₂²	1	12	yes	complemented
98	C₂×#525	C₂²	1	6	yes	complemented
99	C₂×#525	C₂²	1	6	yes	complemented
100	C₂²×#121	C₂²	1	6	yes	complemented
101	C₂²×#121	C₂²	1	6	yes	complemented
102	C₄×H(5,𝔽₂)	C₂²	1	32	yes	complemented
103	#3428	C₂²	1	64	yes	complemented
104	C₂×#520	C₂²	1	2	yes	—
105	C₂×#520	C₂²	1	1	yes	characteristic
106	C₂×#520	C₂²	1	6	yes	complemented
107	C₂×#520	C₂²	1	3	yes	complemented
108	C₂×#520	C₂²	1	2	yes	complemented
109	C₂×#520	C₂²	1	6	yes	complemented
110	C₂×#519	C₂²	1	4	yes	complemented
111	C₂×#518	C₂²	1	12	yes	complemented
112	C₂×#518	C₂²	1	6	yes	complemented
113	C₂×#518	C₂²	1	3	yes	complemented
114	C₂×C₄×#41	C₂²	1	1	yes	characteristic
115	C₂×C₄×#41	C₂²	1	12	yes	complemented
116	C₂×C₄×#41	C₂²	1	2	yes	complemented
117	C₂×C₄×#41	C₂²	1	4	yes	complemented
118	C₂×C₄×#41	C₂²	1	3	yes	complemented
119	C₂×C₄×#41	C₂²	1	6	yes	complemented
120	C₂²×C₄×D₄	C₂²	1	3	yes	complemented
121	C₂²×C₄×D₄	C₂²	1	6	yes	complemented
122	C₂²×C₄×D₄	C₂²	1	3	yes	complemented
123	C₂²×#117	C₂²	1	6	yes	complemented
124	C₂²×#117	C₂²	1	6	yes	complemented
125	C₂²×#117	C₂²	1	6	yes	complemented
126	C₂×H(5,𝔽₂)	—	2	16	no	—
127	C₂×H(5,𝔽₂)	C₂³	1	16	yes	—
128	C₂²×#41	—	2	32	no	—
129	C₂²×#41	C₂³	1	6	yes	—
130	C₂²×#41	C₂³	1	2	yes	—
131	C₂²×#41	C₂³	1	6	yes	—
132	C₂²×#41	C₂³	1	32	yes	—
133	C₂²×#41	C₂³	1	3	yes	—
134	C₂²×#41	C₂³	1	2	yes	—
135	C₂²×#41	C₂³	1	6	yes	—
136	C₂²×#41	C₂³	1	12	yes	—
137	C₂²×#41	C₂³	1	1	yes	characteristic
138	C₂³×Q₈	C₂³	1	2	yes	—
139	C₂³×Q₈	C₂³	1	6	yes	—
140	C₂³×D₄	C₂³	1	6	yes	—
141	C₂³×D₄	C₂³	1	3	yes	—
142	C₂³×D₄	C₂³	1	6	yes	—
143	C₂³×D₄	C₂³	1	3	yes	—
144	C₂³×D₄	C₂³	1	12	yes	—
145	C₂⁴×C₄	C₂³	1	6	yes	—
146	C₂⁴×C₄	C₂³	1	6	yes	—
147	#559	C₂³	1	192	yes	complemented
148	Q₈²	C₂³	1	32	yes	complemented
149	#557	C₂³	1	32	yes	complemented
150	#556	C₂³	1	16	yes	complemented
151	#556	C₂³	1	96	yes	complemented
152	#556	C₂³	1	96	yes	complemented
153	#556	C₂³	1	192	yes	complemented
154	#555	C₂³	1	48	yes	complemented
155	#555	C₂³	1	96	yes	complemented
156	#555	C₂³	1	192	yes	complemented
157	#555	C₂³	1	96	yes	complemented
158	#555	C₂³	1	192	yes	complemented
159	#555	C₂³	1	96	yes	complemented
160	#555	C₂³	1	192	yes	complemented
161	#554	C₂³	1	96	yes	complemented
162	#554	C₂³	1	48	yes	complemented
163	#553	C₂³	1	96	yes	complemented
164	#553	C₂³	1	192	yes	complemented
165	#553	C₂³	1	192	yes	complemented
166	#553	C₂³	1	192	yes	complemented
167	#552	C₂³	1	96	yes	complemented
168	#552	C₂³	1	96	yes	complemented
169	#552	C₂³	1	192	yes	complemented
170	#551	C₂³	1	384	yes	complemented
171	#551	C₂³	1	192	yes	complemented
172	#550	C₂³	1	16	yes	complemented
173	#550	C₂³	1	64	yes	complemented
174	#550	C₂³	1	96	yes	complemented
175	D₄×Q₈	C₂³	1	16	yes	complemented
176	D₄×Q₈	C₂³	1	96	yes	complemented
177	#548	C₂³	1	32	yes	complemented
178	#548	C₂³	1	64	yes	complemented
179	#548	C₂³	1	192	yes	complemented
180	#547	C₂³	1	48	yes	complemented
181	#547	C₂³	1	48	yes	complemented
182	#547	C₂³	1	96	yes	complemented
183	#546	C₂³	1	96	yes	complemented
184	#546	C₂³	1	192	yes	complemented
185	#546	C₂³	1	96	yes	complemented
186	#546	C₂³	1	384	yes	complemented
187	D₄²	C₂³	1	48	yes	complemented
188	D₄²	C₂³	1	192	yes	complemented
189	#544	C₂³	1	96	yes	complemented
190	#542	C₂³	1	192	yes	complemented
191	#542	C₂³	1	192	yes	complemented
192	#540	C₂³	1	192	yes	complemented
193	#538	C₂³	1	384	yes	complemented
194	#538	C₂³	1	192	yes	complemented
195	#537	C₂³	1	96	yes	complemented
196	#535	C₂³	1	96	yes	complemented
197	#533	C₂³	1	48	yes	complemented
198	#533	C₂³	1	96	yes	complemented
199	#532	C₂³	1	48	yes	complemented
200	#532	C₂³	1	192	yes	complemented
201	#532	C₂³	1	96	yes	complemented
202	C₂×C₄⋊Q₈	C₂³	1	3	yes	—
203	C₂×C₄⋊Q₈	C₂³	1	6	yes	—
204	C₂×C₄⋊Q₈	C₂³	1	6	yes	—
205	C₂×C₄⋊Q₈	C₂³	1	6	yes	—
206	C₂×C₄⋊Q₈	C₂³	1	3	yes	—
207	C₂×C₄⋊Q₈	C₂³	1	12	yes	—
208	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	48	yes	complemented
210	C₂×#127	C₂³	1	3	yes	—
211	C₂×#127	C₂³	1	12	yes	—
212	#529	C₂³	1	384	yes	complemented
213	#529	C₂³	1	192	yes	complemented
214	#529	C₂³	1	192	yes	complemented
215	#529	C₂³	1	96	yes	complemented
216	C₂×#126	C₂³	1	4	yes	—
217	C₂×#126	C₂³	1	12	yes	—
218	C₂×#126	C₂³	1	12	yes	—
219	C₂×#126	C₂³	1	24	yes	—
220	C₂×#126	C₂³	1	24	yes	—
221	C₂×#125	C₂³	1	12	yes	—
222	C₂×#125	C₂³	1	6	yes	—
223	C₂×#125	C₂³	1	12	yes	—
224	C₂×#125	C₂³	1	6	yes	—
225	C₂×#124	C₂³	1	12	yes	—
226	C₂×#124	C₂³	1	24	yes	—
227	C₂×#124	C₂³	1	24	yes	—
228	C₂×#124	C₂³	1	24	yes	—
229	C₂×#124	C₂³	1	2	yes	—
230	C₂×#124	C₂³	1	12	yes	—
231	C₂×#124	C₂³	1	12	yes	—
232	C₂×#124	C₂³	1	6	yes	—
233	C₂×#124	C₂³	1	192	yes	complemented
234	#525	C₂³	1	96	yes	complemented
235	#525	C₂³	1	96	yes	complemented
236	#525	C₂³	1	192	yes	complemented
237	C₂×#123	C₂³	1	12	yes	—
238	C₂×#123	C₂³	1	12	yes	—
239	C₂×#123	C₂³	1	24	yes	—
240	C₂×#123	C₂³	1	12	yes	—
241	C₂×#123	C₂³	1	12	yes	—
242	C₂×#123	C₂³	1	24	yes	—
243	C₂×#123	C₂³	1	12	yes	—
244	C₂×C₂²⋊Q₈	C₂³	1	2	yes	—
245	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
246	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
247	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
248	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
249	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
250	C₂×C₂²⋊Q₈	C₂³	1	24	yes	—
251	C₂×C₂²⋊Q₈	C₂³	1	12	yes	—
252	C₂×C₂²⋊Q₈	C₂³	1	12	yes	—
253	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
254	C₂×C₂²⋊Q₈	C₂³	1	12	yes	—
255	C₂×#121	C₂³	1	6	yes	—
256	C₂×#121	C₂³	1	6	yes	—
257	C₂×#121	C₂³	1	12	yes	—
258	C₂×#121	C₂³	1	12	yes	—
259	C₂×#121	C₂³	1	12	yes	—
260	C₂×#121	C₂³	1	24	yes	—
261	C₂×#121	C₂³	1	12	yes	—
262	C₂×#121	C₂³	1	6	yes	—
263	C₂×#121	C₂³	1	6	yes	—
264	C₂×#121	C₂³	1	6	yes	—
265	C₂×#121	C₂³	1	6	yes	—
266	C₂×#121	C₂³	1	24	yes	—
267	C₂×#121	C₂³	1	12	yes	—
268	C₂×#121	C₂³	1	12	yes	—
269	C₂×#121	C₂³	1	6	yes	—
270	C₂×#121	C₂³	1	24	yes	—
271	C₂×#121	C₂³	1	96	yes	complemented
272	C₂×#121	C₂³	1	96	yes	complemented
273	C₂×#120	C₂³	1	24	yes	—
274	C₂×#120	C₂³	1	12	yes	—
275	C₂×#120	C₂³	1	12	yes	—
276	#520	C₂³	1	16	yes	—
277	#520	C₂³	1	32	yes	—
278	#520	C₂³	1	96	yes	complemented
279	#520	C₂³	1	96	yes	complemented
280	#520	C₂³	1	48	yes	complemented
281	#520	C₂³	1	32	yes	complemented
282	#519	C₂³	1	64	yes	complemented
283	#518	C₂³	1	192	yes	complemented
284	#518	C₂³	1	48	yes	complemented
285	#518	C₂³	1	96	yes	complemented
286	C₄×#41	C₂³	1	16	yes	—
287	C₄×#41	C₂³	1	192	yes	complemented
288	C₄×#41	C₂³	1	64	yes	complemented
289	C₄×#41	C₂³	1	48	yes	complemented
290	C₄×#41	C₂³	1	32	yes	complemented
291	C₄×#41	C₂³	1	96	yes	complemented
292	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
293	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
294	C₂×C₄×Q₈	C₂³	1	2	yes	—
295	C₂×C₄×Q₈	C₂³	1	2	yes	—
296	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
297	C₂×C₄×Q₈	C₂³	1	4	yes	—
298	C₂×C₄×Q₈	C₂³	1	12	yes	—
299	C₂×C₄×Q₈	C₂³	1	12	yes	—
300	C₂×C₄×Q₈	C₂³	1	3	yes	—
301	C₂×C₄×Q₈	C₂³	1	6	yes	—
302	C₂×C₄×Q₈	C₂³	1	12	yes	—
303	C₂×C₄×Q₈	C₂³	1	6	yes	—
304	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂³	1	3	yes	—
306	C₂×C₄×D₄	C₂³	1	6	yes	—
307	C₂×C₄×D₄	C₂³	1	3	yes	—
308	C₂×C₄×D₄	C₂³	1	6	yes	—
309	C₂×C₄×D₄	C₂³	1	6	yes	—
310	C₂×C₄×D₄	C₂³	1	3	yes	—
311	C₂×C₄×D₄	C₂³	1	12	yes	—
312	C₂×C₄×D₄	C₂³	1	6	yes	—
313	C₂×C₄×D₄	C₂³	1	6	yes	—
314	C₂×C₄×D₄	C₂³	1	6	yes	—
315	C₂×C₄×D₄	C₂³	1	6	yes	—
316	C₂×C₄×D₄	C₂³	1	3	yes	—
317	C₂×C₄×D₄	C₂³	1	6	yes	—
318	C₂×C₄×D₄	C₂³	1	3	yes	—
319	C₂×C₄×D₄	C₂³	1	3	yes	—
320	C₂×C₄×D₄	C₂³	1	6	yes	—
321	C₂×C₄×D₄	C₂³	1	3	yes	—
322	C₂×C₄×D₄	C₂³	1	6	yes	—
323	C₂×C₄×D₄	C₂³	1	12	yes	—
324	C₂×C₄×D₄	C₂³	1	24	yes	—
325	C₂×C₄×D₄	C₂³	1	12	yes	—
326	C₂×C₄×D₄	C₂³	1	24	yes	—
327	C₂×C₄×D₄	C₂³	1	12	yes	—
328	C₂×C₄×D₄	C₂³	1	12	yes	—
329	C₂×C₄×D₄	C₂³	1	6	yes	—
330	C₂×C₄×D₄	C₂³	1	12	yes	—
331	C₂×C₄×D₄	C₂³	1	6	yes	—
332	C₂×C₄×D₄	C₂³	1	12	yes	—
333	C₂×C₄×D₄	C₂³	1	24	yes	—
334	C₂×C₄×D₄	C₂³	1	48	yes	complemented
335	C₂×C₄×D₄	C₂³	1	96	yes	complemented
336	C₂×C₄×D₄	C₂³	1	48	yes	complemented
337	C₂×#117	C₂³	1	6	yes	—
338	C₂×#117	C₂³	1	2	yes	—
339	C₂×#117	C₂³	1	3	yes	—
340	C₂×#117	C₂³	1	6	yes	—
341	C₂×#117	C₂³	1	12	yes	—
342	C₂×#117	C₂³	1	12	yes	—
343	C₂×#117	C₂³	1	12	yes	—
344	C₂×#117	C₂³	1	12	yes	—
345	C₂×#117	C₂³	1	6	yes	—
346	C₂×#117	C₂³	1	12	yes	—
347	C₂×#117	C₂³	1	12	yes	—
348	C₂×#117	C₂³	1	24	yes	—
349	C₂×#117	C₂³	1	3	yes	—
350	C₂×#117	C₂³	1	6	yes	—
351	C₂×#117	C₂³	1	6	yes	—
352	C₂×#117	C₂³	1	12	yes	—
353	C₂×#117	C₂³	1	96	yes	complemented
354	C₂×#117	C₂³	1	96	yes	complemented
355	C₂×#117	C₂³	1	96	yes	complemented
356	C₂²×C₄⋊C₄	C₂³	1	3	yes	—
357	C₂²×C₄⋊C₄	C₂³	1	3	yes	—
358	C₂²×C₄⋊C₄	C₂³	1	6	yes	—
359	C₂²×C₄⋊C₄	C₂³	1	6	yes	—
360	C₂²×C₄⋊C₄	C₂³	1	6	yes	—
361	C₂²×C₄⋊C₄	C₂³	1	6	yes	—
362	C₂²×C₄⋊C₄	C₂³	1	6	yes	—
363	C₂²×C₂²⋊C₄	C₂³	1	12	yes	—
364	C₂²×C₂²⋊C₄	C₂³	1	12	yes	—
365	C₂²×C₂²⋊C₄	C₂³	1	12	yes	—
366	C₂²×C₂²⋊C₄	C₂³	1	6	yes	—
367	C₂²×C₂²⋊C₄	C₂³	1	12	yes	—
368	C₂²×C₂²⋊C₄	C₂³	1	6	yes	—
369	C₂²×C₄²	C₂³	1	12	yes	—
370	C₂²×C₄²	C₂³	1	12	yes	—
371	C₂²×C₄²	C₂³	1	3	yes	—
372	C₂²×C₄²	C₂³	1	6	yes	—
373	C₂⁵	C₂⁴	1	6	yes	—
374	C₂⁵	C₂⁴	1	6	yes	—
375	H(5,𝔽₂)	—	2	128	no	—
376	C₂×#41	—	2	256	no	—
377	C₂×#41	—	2	16	no	—
378	C₂×#41	—	2	16	no	—
379	C₂×#41	—	2	48	no	—
380	C₂×#41	—	2	48	no	—
381	C₂×#41	—	2	24	no	—
382	C₂×#41	—	4	24	no	—
383	C₂×#41	—	8	24	no	—
384	C₂×#41	#41	1	16	yes	complemented
385	C₂×#41	C₂⁴	1	48	yes	—
386	C₂×#41	C₂⁴	1	16	yes	—
387	C₂×#41	C₂⁴	1	24	yes	—
388	C₂×#41	C₂⁴	1	16	yes	—
389	C₂×#41	C₂⁴	1	48	yes	—
390	C₂×#41	C₂⁴	1	48	yes	—
391	C₂×#41	C₂⁴	1	96	yes	—
392	C₂×#41	C₂⁴	1	8	yes	—
393	C₂²×Q₈	—	2	16	no	—
394	C₂²×Q₈	—	8	12	no	—
395	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
396	C₂²×Q₈	C₂⁴	1	2	yes	—
397	C₂²×Q₈	C₂⁴	1	6	yes	—
398	C₂²×Q₈	C₂⁴	1	16	yes	—
399	C₂²×Q₈	C₂⁴	1	6	yes	—
400	C₂²×Q₈	C₂⁴	1	12	yes	—
401	C₂²×Q₈	C₂⁴	1	48	yes	—
402	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
403	C₂²×D₄	—	2	48	no	—
404	C₂²×D₄	—	2	48	no	—
405	C₂²×D₄	—	2	24	no	—
406	C₂²×D₄	—	4	12	no	—
407	C₂²×D₄	—	8	24	no	—
408	C₂²×D₄	C₂⁴	1	12	yes	—
409	C₂²×D₄	C₂⁴	1	6	yes	—
410	C₂²×D₄	C₂⁴	1	3	yes	—
411	C₂²×D₄	C₂⁴	1	1	yes	characteristic
412	C₂²×D₄	C₂⁴	1	3	yes	—
413	C₂²×D₄	C₂⁴	1	6	yes	—
414	C₂²×D₄	C₂⁴	1	6	yes	—
415	C₂²×D₄	C₂⁴	1	24	yes	—
416	C₂²×D₄	C₂⁴	1	48	yes	—
417	C₂²×D₄	C₂⁴	1	48	yes	—
418	C₂²×D₄	C₂⁴	1	12	yes	—
419	C₂²×D₄	C₂⁴	1	6	yes	—
420	C₂²×D₄	C₂⁴	1	6	yes	—
421	C₂²×D₄	C₂⁴	1	12	yes	—
422	C₂²×D₄	C₂⁴	1	24	yes	—
423	C₂²×D₄	C₂⁴	1	24	yes	—
424	C₂²×D₄	C₂⁴	1	96	yes	—
425	C₂²×D₄	C₂⁴	1	3	yes	—
426	C₂³×C₄	—	2	48	no	—
427	C₂³×C₄	—	4	24	no	—
428	C₂³×C₄	C₂⁴	1	6	yes	—
429	C₂³×C₄	C₂⁴	1	3	yes	—
430	C₂³×C₄	C₂⁴	1	6	yes	—
431	C₂³×C₄	C₂⁴	1	6	yes	—
432	C₂³×C₄	C₂⁴	1	2	yes	—
433	C₂³×C₄	C₂⁴	1	6	yes	—
434	C₂³×C₄	C₂⁴	1	6	yes	—
435	C₂³×C₄	C₂⁴	1	6	yes	—
436	C₂³×C₄	C₂⁴	1	48	yes	—
437	C₂³×C₄	C₂⁴	1	3	yes	—
438	C₂³×C₄	C₂⁴	1	6	yes	—
439	C₂³×C₄	C₂⁴	1	12	yes	—
440	C₂³×C₄	C₂⁴	1	6	yes	—
441	C₂³×C₄	C₂⁴	1	12	yes	—
442	C₂³×C₄	C₂⁴	1	12	yes	—
443	C₂³×C₄	C₂⁴	1	12	yes	—
444	C₂³×C₄	C₂⁴	1	48	yes	—
445	C₂³×C₄	C₂⁴	1	3	yes	—
446	C₄⋊Q₈	C₂⁴	1	24	yes	—
447	C₄⋊Q₈	C₂⁴	1	48	yes	—
448	C₄⋊Q₈	C₂⁴	1	48	yes	—
449	C₄⋊Q₈	C₂⁴	1	48	yes	—
450	C₄⋊Q₈	C₂⁴	1	24	yes	—
451	C₄⋊Q₈	C₂⁴	1	96	yes	—
452	C₄⋊Q₈	C₂⁴	1	8	yes	—
453	#127	C₂⁴	1	24	yes	—
454	#127	C₂⁴	1	96	yes	—
455	#126	C₂⁴	1	32	yes	—
456	#126	C₂⁴	1	96	yes	—
457	#126	C₂⁴	1	96	yes	—
458	#126	C₂⁴	1	192	yes	—
459	#126	C₂⁴	1	192	yes	—
460	#125	C₂⁴	1	96	yes	—
461	#125	C₂⁴	1	48	yes	—
462	#125	C₂⁴	1	96	yes	—
463	#125	C₂⁴	1	48	yes	—
464	#124	C₂⁴	1	96	yes	—
465	#124	C₂⁴	1	192	yes	—
466	#124	C₂⁴	1	192	yes	—
467	#124	C₂⁴	1	192	yes	—
468	#124	C₂⁴	1	16	yes	—
469	#124	C₂⁴	1	96	yes	—
470	#124	C₂⁴	1	96	yes	—
471	#124	C₂⁴	1	48	yes	—
472	#123	C₂⁴	1	96	yes	—
473	#123	C₂⁴	1	96	yes	—
474	#123	C₂⁴	1	192	yes	—
475	#123	C₂⁴	1	96	yes	—
476	#123	C₂⁴	1	96	yes	—
477	#123	C₂⁴	1	192	yes	—
478	#123	C₂⁴	1	96	yes	—
479	C₂²⋊Q₈	C₂⁴	1	16	yes	—
480	C₂²⋊Q₈	C₂⁴	1	48	yes	—
481	C₂²⋊Q₈	C₂⁴	1	48	yes	—
482	C₂²⋊Q₈	C₂⁴	1	48	yes	—
483	C₂²⋊Q₈	C₂⁴	1	48	yes	—
484	C₂²⋊Q₈	C₂⁴	1	48	yes	—
485	C₂²⋊Q₈	C₂⁴	1	192	yes	—
486	C₂²⋊Q₈	C₂⁴	1	96	yes	—
487	C₂²⋊Q₈	C₂⁴	1	96	yes	—
488	C₂²⋊Q₈	C₂⁴	1	48	yes	—
489	C₂²⋊Q₈	C₂⁴	1	96	yes	—
490	#121	C₂⁴	1	48	yes	—
491	#121	C₂⁴	1	48	yes	—
492	#121	C₂⁴	1	96	yes	—
493	#121	C₂⁴	1	96	yes	—
494	#121	C₂⁴	1	96	yes	—
495	#121	C₂⁴	1	192	yes	—
496	#121	C₂⁴	1	96	yes	—
497	#121	C₂⁴	1	48	yes	—
498	#121	C₂⁴	1	48	yes	—
499	#121	C₂⁴	1	48	yes	—
500	#121	C₂⁴	1	48	yes	—
501	#121	C₂⁴	1	192	yes	—
502	#121	C₂⁴	1	96	yes	—
503	#121	C₂⁴	1	96	yes	—
504	#121	C₂⁴	1	48	yes	—
505	#121	C₂⁴	1	192	yes	—
506	#120	C₂⁴	1	192	yes	—
507	#120	C₂⁴	1	96	yes	—
508	#120	C₂⁴	1	96	yes	—
509	C₄×Q₈	C₂⁴	1	8	yes	—
510	C₄×Q₈	C₂⁴	1	8	yes	—
511	C₄×Q₈	C₂⁴	1	16	yes	—
512	C₄×Q₈	C₂⁴	1	16	yes	—
513	C₄×Q₈	C₂⁴	1	8	yes	—
514	C₄×Q₈	C₂⁴	1	32	yes	—
515	C₄×Q₈	C₂⁴	1	96	yes	—
516	C₄×Q₈	C₂⁴	1	96	yes	—
517	C₄×Q₈	C₂⁴	1	24	yes	—
518	C₄×Q₈	C₂⁴	1	48	yes	—
519	C₄×Q₈	C₂⁴	1	96	yes	—
520	C₄×Q₈	C₂⁴	1	48	yes	—
521	C₄×D₄	C₂⁴	1	8	yes	—
522	C₄×D₄	C₂⁴	1	24	yes	—
523	C₄×D₄	C₂⁴	1	48	yes	—
524	C₄×D₄	C₂⁴	1	24	yes	—
525	C₄×D₄	C₂⁴	1	48	yes	—
526	C₄×D₄	C₂⁴	1	48	yes	—
527	C₄×D₄	C₂⁴	1	24	yes	—
528	C₄×D₄	C₂⁴	1	96	yes	—
529	C₄×D₄	C₂⁴	1	48	yes	—
530	C₄×D₄	C₂⁴	1	48	yes	—
531	C₄×D₄	C₂⁴	1	48	yes	—
532	C₄×D₄	C₂⁴	1	48	yes	—
533	C₄×D₄	C₂⁴	1	24	yes	—
534	C₄×D₄	C₂⁴	1	48	yes	—
535	C₄×D₄	C₂⁴	1	24	yes	—
536	C₄×D₄	C₂⁴	1	24	yes	—
537	C₄×D₄	C₂⁴	1	48	yes	—
538	C₄×D₄	C₂⁴	1	24	yes	—
539	C₄×D₄	C₂⁴	1	48	yes	—
540	C₄×D₄	C₂⁴	1	96	yes	—
541	C₄×D₄	C₂⁴	1	192	yes	—
542	C₄×D₄	C₂⁴	1	96	yes	—
543	C₄×D₄	C₂⁴	1	192	yes	—
544	C₄×D₄	C₂⁴	1	96	yes	—
545	C₄×D₄	C₂⁴	1	96	yes	—
546	C₄×D₄	C₂⁴	1	48	yes	—
547	C₄×D₄	C₂⁴	1	96	yes	—
548	C₄×D₄	C₂⁴	1	48	yes	—
549	C₄×D₄	C₂⁴	1	96	yes	—
550	C₄×D₄	C₂⁴	1	192	yes	—
551	#117	C₂⁴	1	48	yes	—
552	#117	C₂⁴	1	16	yes	—
553	#117	C₂⁴	1	24	yes	—
554	#117	C₂⁴	1	48	yes	—
555	#117	C₂⁴	1	96	yes	—
556	#117	C₂⁴	1	96	yes	—
557	#117	C₂⁴	1	96	yes	—
558	#117	C₂⁴	1	96	yes	—
559	#117	C₂⁴	1	48	yes	—
560	#117	C₂⁴	1	96	yes	—
561	#117	C₂⁴	1	96	yes	—
562	#117	C₂⁴	1	192	yes	—
563	#117	C₂⁴	1	24	yes	—
564	#117	C₂⁴	1	48	yes	—
565	#117	C₂⁴	1	48	yes	—
566	#117	C₂⁴	1	96	yes	—
567	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂⁴	1	3	yes	—
569	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
571	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
572	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
573	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
574	C₂×C₄⋊C₄	C₂⁴	1	3	yes	—
575	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
576	C₂×C₄⋊C₄	C₂⁴	1	3	yes	—
577	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
578	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
579	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
580	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
581	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
582	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
583	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
584	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
585	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
586	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
587	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
588	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
589	C₂×C₄⋊C₄	C₂⁴	1	3	yes	—
590	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
591	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
592	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
593	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
594	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
595	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
596	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
598	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
600	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
602	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
603	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
604	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
605	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
606	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
607	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
608	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
609	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
610	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
611	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
612	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
613	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
614	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
615	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
616	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
617	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
618	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
619	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
620	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
621	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
622	C₂×C₄²	C₂⁴	1	12	yes	—
623	C₂×C₄²	C₂⁴	1	6	yes	—
624	C₂×C₄²	C₂⁴	1	24	yes	—
625	C₂×C₄²	C₂⁴	1	6	yes	—
626	C₂×C₄²	C₂⁴	1	4	yes	—
627	C₂×C₄²	C₂⁴	1	3	yes	—
628	C₂×C₄²	C₂⁴	1	3	yes	—
629	C₂×C₄²	C₂⁴	1	12	yes	—
630	C₂×C₄²	C₂⁴	1	96	yes	—
631	C₂×C₄²	C₂⁴	1	96	yes	—
632	C₂×C₄²	C₂⁴	1	1	yes	characteristic
633	C₂×C₄²	C₂⁴	1	2	yes	—
634	C₂×C₄²	C₂⁴	1	3	yes	—
635	C₂×C₄²	C₂⁴	1	24	yes	—
636	C₂×C₄²	C₂⁴	1	48	yes	—
637	C₂⁴	—	2	24	no	—
638	C₂⁴	—	2	24	no	—
639	C₂⁴	—	4	12	no	—
640	C₂⁴	—	4	12	no	—
641	C₂⁴	—	4	12	no	—
642	C₂⁴	—	4	12	no	—
643	C₂⁴	C₂⁵	1	2	yes	—
644	C₂⁴	C₂⁵	1	6	yes	—
645	C₂⁴	C₂⁵	1	6	yes	—
646	C₂⁴	C₂⁵	1	3	yes	—
647	C₂⁴	C₂⁵	1	24	yes	—
648	C₂⁴	C₂⁵	1	24	yes	—
649	#41	—	2	64	no	—
650	#41	—	2	64	no	—
651	#41	—	2	192	no	—
652	#41	—	2	192	no	—
653	#41	—	2	96	no	—
654	#41	—	4	96	no	—
655	#41	—	8	96	no	—
656	#41	C₂×#41	1	64	yes	complemented
657	C₂×Q₈	—	2	64	no	—
658	C₂×Q₈	—	2	24	no	—
659	C₂×Q₈	—	2	4	no	—
660	C₂×Q₈	—	2	8	no	—
661	C₂×Q₈	—	4	12	no	—
662	C₂×Q₈	—	4	24	no	—
663	C₂×Q₈	—	8	48	no	—
664	C₂×Q₈	C₂×#41	1	8	yes	—
665	C₂×Q₈	C₂⁵	1	4	yes	—
666	C₂×Q₈	C₂⁵	1	8	yes	—
667	C₂×Q₈	C₂⁵	1	24	yes	—
668	C₂×Q₈	C₂⁵	1	24	yes	—
669	C₂×Q₈	C₂⁵	1	48	yes	—
670	C₂×Q₈	C₂⁵	1	4	yes	—
671	C₂×D₄	—	2	24	no	—
672	C₂×D₄	—	2	48	no	—
673	C₂×D₄	—	2	192	no	—
674	C₂×D₄	—	2	192	no	—
675	C₂×D₄	—	2	12	no	—
676	C₂×D₄	—	2	24	no	—
677	C₂×D₄	—	2	24	no	—
678	C₂×D₄	—	2	96	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	12	no	—
681	C₂×D₄	—	4	48	no	—
682	C₂×D₄	—	4	12	no	—
683	C₂×D₄	—	4	24	no	—
684	C₂×D₄	—	4	48	no	—
685	C₂×D₄	—	4	24	no	—
686	C₂×D₄	—	4	12	no	—
687	C₂×D₄	—	8	96	no	—
688	C₂×D₄	C₂×#41	1	24	yes	—
689	C₂×D₄	C₂⁵	1	48	yes	—
690	C₂×D₄	C₂⁵	1	24	yes	—
691	C₂×D₄	C₂⁵	1	12	yes	—
692	C₂×D₄	C₂⁵	1	4	yes	—
693	C₂×D₄	C₂⁵	1	12	yes	—
694	C₂×D₄	C₂⁵	1	24	yes	—
695	C₂×D₄	C₂⁵	1	24	yes	—
696	C₂×D₄	C₂⁵	1	48	yes	—
697	C₂×D₄	C₂⁵	1	24	yes	—
698	C₂×D₄	C₂⁵	1	24	yes	—
699	C₂×D₄	C₂⁵	1	48	yes	—
700	C₂×D₄	C₂⁵	1	96	yes	—
701	C₂×D₄	C₂⁵	1	12	yes	—
702	C₂²×C₄	—	2	24	no	—
703	C₂²×C₄	—	2	8	no	—
704	C₂²×C₄	—	2	24	no	—
705	C₂²×C₄	—	2	24	no	—
706	C₂²×C₄	—	2	24	no	—
707	C₂²×C₄	—	2	192	no	—
708	C₂²×C₄	—	2	24	no	—
709	C₂²×C₄	—	2	12	no	—
710	C₂²×C₄	—	2	24	no	—
711	C₂²×C₄	—	4	96	no	—
712	C₂²×C₄	—	4	12	no	—
713	C₂²×C₄	—	4	24	no	—
714	C₂²×C₄	—	4	24	no	—
715	C₂²×C₄	—	4	6	no	—
716	C₂²×C₄	—	4	24	no	—
717	C₂²×C₄	—	4	24	no	—
718	C₂²×C₄	—	4	12	no	—
719	C₂²×C₄	C₂×#41	1	24	yes	—
720	C₂²×C₄	C₂⁵	1	24	yes	—
721	C₂²×C₄	C₂⁵	1	24	yes	—
722	C₂²×C₄	C₂⁵	1	12	yes	—
723	C₂²×C₄	C₂⁵	1	24	yes	—
724	C₂²×C₄	C₂⁵	1	24	yes	—
725	C₂²×C₄	C₂⁵	1	24	yes	—
726	C₂²×C₄	C₂⁵	1	8	yes	—
727	C₂²×C₄	C₂⁵	1	24	yes	—
728	C₂²×C₄	C₂⁵	1	2	yes	—
729	C₂²×C₄	C₂⁵	1	6	yes	—
730	C₂²×C₄	C₂⁵	1	2	yes	—
731	C₂²×C₄	C₂⁵	1	1	yes	characteristic
732	C₂²×C₄	C₂⁵	1	6	yes	—
733	C₂²×C₄	C₂⁵	1	3	yes	—
734	C₂²×C₄	C₂⁵	1	2	yes	—
735	C₂²×C₄	C₂⁵	1	4	yes	—
736	C₂²×C₄	C₂⁵	1	12	yes	—
737	C₂²×C₄	C₂⁵	1	3	yes	—
738	C₂²×C₄	C₂⁵	1	24	yes	—
739	C₂²×C₄	C₂⁵	1	12	yes	—
740	C₂²×C₄	C₂⁵	1	48	yes	—
741	C₂²×C₄	C₂⁵	1	24	yes	—
742	C₂²×C₄	C₂⁵	1	48	yes	—
743	C₂²×C₄	C₂⁵	1	48	yes	—
744	C₂²×C₄	C₂⁵	1	48	yes	—
745	C₂²×C₄	C₂⁵	1	12	yes	—
746	C₂²×C₄	C₂⁵	1	3	yes	—
747	C₂²×C₄	C₂⁵	1	1	yes	characteristic
748	C₂²×C₄	C₂⁵	1	1	yes	characteristic
749	C₄⋊C₄	C₂⁵	1	4	yes	—
750	C₄⋊C₄	C₂⁵	1	12	yes	—
751	C₄⋊C₄	C₂⁵	1	4	yes	—
752	C₄⋊C₄	C₂⁵	1	8	yes	—
753	C₄⋊C₄	C₂⁵	1	24	yes	—
754	C₄⋊C₄	C₂⁵	1	24	yes	—
755	C₄⋊C₄	C₂⁵	1	24	yes	—
756	C₄⋊C₄	C₂⁵	1	12	yes	—
757	C₄⋊C₄	C₂⁵	1	24	yes	—
758	C₄⋊C₄	C₂⁵	1	12	yes	—
759	C₄⋊C₄	C₂⁵	1	24	yes	—
760	C₄⋊C₄	C₂⁵	1	48	yes	—
761	C₄⋊C₄	C₂⁵	1	48	yes	—
762	C₄⋊C₄	C₂⁵	1	48	yes	—
763	C₄⋊C₄	C₂⁵	1	48	yes	—
764	C₄⋊C₄	C₂⁵	1	12	yes	—
765	C₄⋊C₄	C₂⁵	1	8	yes	—
766	C₄⋊C₄	C₂⁵	1	16	yes	—
767	C₄⋊C₄	C₂⁵	1	48	yes	—
768	C₄⋊C₄	C₂⁵	1	48	yes	—
769	C₄⋊C₄	C₂⁵	1	48	yes	—
770	C₄⋊C₄	C₂⁵	1	24	yes	—
771	C₄⋊C₄	C₂⁵	1	8	yes	—
772	C₂²⋊C₄	C₂⁵	1	24	yes	—
773	C₂²⋊C₄	C₂⁵	1	16	yes	—
774	C₂²⋊C₄	C₂⁵	1	48	yes	—
775	C₂²⋊C₄	C₂⁵	1	8	yes	—
776	C₂²⋊C₄	C₂⁵	1	48	yes	—
777	C₂²⋊C₄	C₂⁵	1	24	yes	—
778	C₂²⋊C₄	C₂⁵	1	24	yes	—
779	C₂²⋊C₄	C₂⁵	1	48	yes	—
780	C₂²⋊C₄	C₂⁵	1	24	yes	—
781	C₂²⋊C₄	C₂⁵	1	48	yes	—
782	C₂²⋊C₄	C₂⁵	1	96	yes	—
783	C₂²⋊C₄	C₂⁵	1	24	yes	—
784	C₂²⋊C₄	C₂⁵	1	96	yes	—
785	C₂²⋊C₄	C₂⁵	1	24	yes	—
786	C₂²⋊C₄	C₂⁵	1	24	yes	—
787	C₂²⋊C₄	C₂⁵	1	48	yes	—
788	C₂²⋊C₄	C₂⁵	1	16	yes	—
789	C₂²⋊C₄	C₂⁵	1	48	yes	—
790	C₂²⋊C₄	C₂⁵	1	48	yes	—
791	C₄²	C₂⁵	1	48	yes	—
792	C₄²	C₂⁵	1	24	yes	—
793	C₄²	C₂⁵	1	16	yes	—
794	C₄²	C₂⁵	1	4	yes	—
795	C₄²	C₂⁵	1	8	yes	—
796	C₄²	C₂⁵	1	12	yes	—
797	C₄²	C₂⁵	1	96	yes	—
798	C₄²	C₂⁵	1	24	yes	—
799	C₄²	C₂⁵	1	12	yes	—
800	C₄²	C₂⁵	1	12	yes	—
801	C₄²	C₂⁵	1	48	yes	—
802	C₂³	—	2	6	no	—
803	C₂³	—	2	6	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	12	no	—
806	C₂³	—	2	12	no	—
807	C₂³	—	2	12	no	—
808	C₂³	—	2	12	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	2	12	no	—
811	C₂³	—	2	12	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	2	48	no	—
814	C₂³	—	2	48	no	—
815	C₂³	—	4	24	no	—
816	C₂³	—	4	24	no	—
817	C₂³	—	4	24	no	—
818	C₂³	—	4	24	no	—
819	C₂³	—	8	48	no	—
820	C₂³	—	8	48	no	—
821	C₂³	C₂²×#41	1	12	yes	—
822	C₂³	C₂⁶	1	4	yes	—
823	C₂³	C₂⁶	1	12	yes	—
824	C₂³	C₂⁶	1	12	yes	—
825	C₂³	C₂⁶	1	6	yes	—
826	C₂³	C₂⁶	1	1	yes	characteristic
827	Q₈	—	2	48	no	—
828	Q₈	—	2	8	no	—
829	Q₈	—	2	16	no	—
830	Q₈	—	4	24	no	—
831	Q₈	—	4	48	no	—
832	Q₈	C₂²×#41	1	16	yes	—
833	D₄	—	2	48	no	—
834	D₄	—	2	96	no	—
835	D₄	—	2	24	no	—
836	D₄	—	2	48	no	—
837	D₄	—	2	48	no	—
838	D₄	—	2	8	no	—
839	D₄	—	2	24	no	—
840	D₄	—	4	24	no	—
841	D₄	—	4	48	no	—
842	D₄	—	4	96	no	—
843	D₄	—	4	48	no	—
844	D₄	—	4	24	no	—
845	D₄	C₂²×#41	1	48	yes	—
846	C₂×C₄	—	2	4	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	12	no	—
849	C₂×C₄	—	2	48	no	—
850	C₂×C₄	—	2	12	no	—
851	C₂×C₄	—	2	6	no	—
852	C₂×C₄	—	2	8	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	24	no	—
855	C₂×C₄	—	2	6	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	16	no	—
858	C₂×C₄	—	2	48	no	—
859	C₂×C₄	—	2	48	no	—
860	C₂×C₄	—	2	48	no	—
861	C₂×C₄	—	2	48	no	—
862	C₂×C₄	—	2	24	no	—
863	C₂×C₄	—	2	48	no	—
864	C₂×C₄	—	4	24	no	—
865	C₂×C₄	—	4	48	no	—
866	C₂×C₄	—	4	48	no	—
867	C₂×C₄	—	4	12	no	—
868	C₂×C₄	—	4	48	no	—
869	C₂×C₄	—	4	48	no	—
870	C₂×C₄	—	4	24	no	—
871	C₂×C₄	C₂²×#41	1	4	yes	—
872	C₂×C₄	C₂²×#41	1	12	yes	—
873	C₂×C₄	C₂²×#41	1	48	yes	—
874	C₂×C₄	#585	1	4	yes	—
875	C₂×C₄	C₂⁶	1	4	yes	—
876	C₂×C₄	C₂⁶	1	12	yes	—
877	C₂×C₄	C₂⁶	1	4	yes	—
878	C₂×C₄	C₂⁶	1	2	yes	—
879	C₂×C₄	C₂⁶	1	12	yes	—
880	C₂×C₄	C₂⁶	1	6	yes	—
881	C₂×C₄	C₂⁶	1	4	yes	—
882	C₂×C₄	C₂⁶	1	8	yes	—
883	C₂×C₄	C₂⁶	1	24	yes	—
884	C₂×C₄	C₂⁶	1	6	yes	—
885	C₂×C₄	C₂⁶	1	6	yes	—
886	C₂×C₄	C₂⁶	1	2	yes	—
887	C₂×C₄	C₂⁶	1	2	yes	—
888	C₂²	—	2	24	no	—
889	C₂²	—	2	6	no	—
890	C₂²	—	2	6	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	12	no	—
893	C₂²	—	2	12	no	—
894	C₂²	—	2	12	no	—
895	C₂²	—	2	12	no	—
896	C₂²	—	2	4	no	—
897	C₂²	—	2	12	no	—
898	C₂²	—	2	12	no	—
899	C₂²	—	2	4	no	—
900	C₂²	—	4	24	no	—
901	C₂²	—	4	24	no	—
902	C₂²	—	4	8	no	—
903	C₂²	—	8	48	no	—
904	C₂²	—	8	48	no	—
905	C₂²	C₂³×#41	1	12	yes	—
906	C₂²	C₂³×#41	1	2	yes	—
907	C₂²	C₂×#585	1	2	yes	—
908	C₂²	H(7,𝔽₂)	1	2	yes	—
909	C₂²	C₂⁷	1	1	yes	characteristic
910	C₄	—	2	4	no	—
911	C₄	—	2	4	no	—
912	C₄	—	2	12	no	—
913	C₄	—	2	12	no	—
914	C₄	—	2	6	no	—
915	C₄	—	2	8	no	—
916	C₄	—	2	4	no	—
917	C₄	—	2	24	no	—
918	C₄	—	2	6	no	—
919	C₄	—	2	2	no	—
920	C₄	C₂³×#41	1	4	yes	—
921	C₄	C₂³×#41	1	12	yes	—
922	C₄	C₂×#585	1	4	yes	—
923	C₂	—	2	12	no	—
924	C₂	—	4	12	no	—
925	C₂	—	4	12	no	—
926	C₂	—	4	4	no	—
927	C₂	#62994	1	4	yes	direct product factor
928	C₂	C₂⁴×#41	1	1	yes	characteristic
929	C₂	C₂²×#585	1	1	yes	characteristic
930	C₂	C₂×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁷
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #62994	C₂	direct (N × H)
2. C₂×#3511	C₂	semidirect
3. C₂×#3494	C₂	semidirect
4. C₂×#3503	C₂	semidirect
5. C₂×#3488	C₂	semidirect
6. C₂×#3524	C₂	semidirect
7. C₂×#3518	C₂	semidirect
8. C₂×#3514	C₂	semidirect
9. C₂×#3493	C₂	semidirect
10. C₂×#3519	C₂	semidirect
11. C₂×#3506	C₂	semidirect
12. C₂×#3483	C₂	semidirect
13. C₂×#3475	C₂	semidirect
14. C₂×#3475	C₂	semidirect
15. C₂²×#555	C₂	semidirect
16. C₂×D₄×#41	C₂	semidirect
17. C₂×C₄×H(5,𝔽₂)	C₂	semidirect
18. C₂×#3428	C₂	semidirect
21. #3524	C₂²	semidirect
22. #3519	C₂²	semidirect
23. #3518	C₂²	semidirect
24. #3514	C₂²	semidirect
25. #3511	C₂²	semidirect
26. #3506	C₂²	semidirect
27. #3503	C₂²	semidirect
28. #3494	C₂²	semidirect
29. #3493	C₂²	semidirect
30. #3488	C₂²	semidirect
31. #3483	C₂²	semidirect
32. C₂×#559	C₂²	semidirect
33. C₂×Q₈²	C₂²	semidirect
34. C₂×#557	C₂²	semidirect
35. #3475	C₂²	semidirect
36. #3475	C₂²	semidirect
37. C₂×#556	C₂²	semidirect
38. C₂×#556	C₂²	semidirect
39. C₂×#556	C₂²	semidirect
40. C₂×#556	C₂²	semidirect
41. C₂×#555	C₂²	semidirect
42. C₂×#555	C₂²	semidirect
43. C₂×#555	C₂²	semidirect
44. C₂×#555	C₂²	semidirect
45. C₂×#555	C₂²	semidirect
46. C₂×#555	C₂²	semidirect
47. C₂×#555	C₂²	semidirect
48. C₂×#555	C₂²	semidirect
49. C₂×#554	C₂²	semidirect
50. C₂×#554	C₂²	semidirect
51. C₂×#553	C₂²	semidirect
52. C₂×#553	C₂²	semidirect
53. C₂×#553	C₂²	semidirect
54. C₂×#553	C₂²	semidirect
55. C₂×#552	C₂²	semidirect
56. C₂×#552	C₂²	semidirect
57. C₂×#552	C₂²	semidirect
58. C₂×#551	C₂²	semidirect
59. C₂×#551	C₂²	semidirect
60. D₄×#41	C₂²	semidirect
61. C₂×#550	C₂²	semidirect
62. C₂×#550	C₂²	semidirect
63. C₂×#550	C₂²	semidirect
64. C₂×D₄×Q₈	C₂²	semidirect
65. C₂×D₄×Q₈	C₂²	semidirect
66. C₂×#548	C₂²	semidirect
67. C₂×#548	C₂²	semidirect
68. C₂×#548	C₂²	semidirect
69. C₂×#547	C₂²	semidirect
70. C₂×#547	C₂²	semidirect
71. C₂×#547	C₂²	semidirect
72. C₂×#546	C₂²	semidirect
73. C₂×#546	C₂²	semidirect
74. C₂×#546	C₂²	semidirect
75. C₂×#546	C₂²	semidirect
76. C₂×D₄²	C₂²	semidirect
77. C₂×D₄²	C₂²	semidirect
78. C₂×#544	C₂²	semidirect
79. C₂×#542	C₂²	semidirect
80. C₂×#542	C₂²	semidirect
81. C₂×#540	C₂²	semidirect
82. C₂×#538	C₂²	semidirect
83. C₂×#538	C₂²	semidirect
84. C₂×#537	C₂²	semidirect
85. C₂×#535	C₂²	semidirect
86. C₂×#533	C₂²	semidirect
87. C₂×#533	C₂²	semidirect
88. C₂×#532	C₂²	semidirect
89. C₂×#532	C₂²	semidirect
90. C₂×#532	C₂²	semidirect
91. C₂²×C₄⋊Q₈	C₂²	semidirect
92. C₂×#529	C₂²	semidirect
93. C₂×#529	C₂²	semidirect
94. C₂×#529	C₂²	semidirect
95. C₂×#529	C₂²	semidirect
96. C₂²×#124	C₂²	semidirect
97. C₂×#525	C₂²	semidirect
98. C₂×#525	C₂²	semidirect
99. C₂×#525	C₂²	semidirect
100. C₂²×#121	C₂²	semidirect
101. C₂²×#121	C₂²	semidirect
102. C₄×H(5,𝔽₂)	C₂²	semidirect
103. #3428	C₂²	semidirect
106. C₂×#520	C₂²	semidirect
107. C₂×#520	C₂²	semidirect
108. C₂×#520	C₂²	semidirect
109. C₂×#520	C₂²	semidirect
110. C₂×#519	C₂²	semidirect
111. C₂×#518	C₂²	semidirect
112. C₂×#518	C₂²	semidirect
113. C₂×#518	C₂²	semidirect
115. C₂×C₄×#41	C₂²	semidirect
116. C₂×C₄×#41	C₂²	semidirect
117. C₂×C₄×#41	C₂²	semidirect
118. C₂×C₄×#41	C₂²	semidirect
119. C₂×C₄×#41	C₂²	semidirect
120. C₂²×C₄×D₄	C₂²	semidirect
121. C₂²×C₄×D₄	C₂²	semidirect
122. C₂²×C₄×D₄	C₂²	semidirect
123. C₂²×#117	C₂²	semidirect
124. C₂²×#117	C₂²	semidirect
125. C₂²×#117	C₂²	semidirect
147. #559	C₂³	semidirect
148. Q₈²	C₂³	semidirect
149. #557	C₂³	semidirect
150. #556	C₂³	semidirect
151. #556	C₂³	semidirect
152. #556	C₂³	semidirect
153. #556	C₂³	semidirect
154. #555	C₂³	semidirect
155. #555	C₂³	semidirect
156. #555	C₂³	semidirect
157. #555	C₂³	semidirect
158. #555	C₂³	semidirect
159. #555	C₂³	semidirect
160. #555	C₂³	semidirect
161. #554	C₂³	semidirect
162. #554	C₂³	semidirect
163. #553	C₂³	semidirect
164. #553	C₂³	semidirect
165. #553	C₂³	semidirect
166. #553	C₂³	semidirect
167. #552	C₂³	semidirect
168. #552	C₂³	semidirect
169. #552	C₂³	semidirect
170. #551	C₂³	semidirect
171. #551	C₂³	semidirect
172. #550	C₂³	semidirect
173. #550	C₂³	semidirect
174. #550	C₂³	semidirect
175. D₄×Q₈	C₂³	semidirect
176. D₄×Q₈	C₂³	semidirect
177. #548	C₂³	semidirect
178. #548	C₂³	semidirect
179. #548	C₂³	semidirect
180. #547	C₂³	semidirect
181. #547	C₂³	semidirect
182. #547	C₂³	semidirect
183. #546	C₂³	semidirect
184. #546	C₂³	semidirect
185. #546	C₂³	semidirect
186. #546	C₂³	semidirect
187. D₄²	C₂³	semidirect
188. D₄²	C₂³	semidirect
189. #544	C₂³	semidirect
190. #542	C₂³	semidirect
191. #542	C₂³	semidirect
192. #540	C₂³	semidirect
193. #538	C₂³	semidirect
194. #538	C₂³	semidirect
195. #537	C₂³	semidirect
196. #535	C₂³	semidirect
197. #533	C₂³	semidirect
198. #533	C₂³	semidirect
199. #532	C₂³	semidirect
200. #532	C₂³	semidirect
201. #532	C₂³	semidirect
209. C₂×C₄⋊Q₈	C₂³	semidirect
212. #529	C₂³	semidirect
213. #529	C₂³	semidirect
214. #529	C₂³	semidirect
215. #529	C₂³	semidirect
233. C₂×#124	C₂³	semidirect
234. #525	C₂³	semidirect
235. #525	C₂³	semidirect
236. #525	C₂³	semidirect
271. C₂×#121	C₂³	semidirect
272. C₂×#121	C₂³	semidirect
278. #520	C₂³	semidirect
279. #520	C₂³	semidirect
280. #520	C₂³	semidirect
281. #520	C₂³	semidirect
282. #519	C₂³	semidirect
283. #518	C₂³	semidirect
284. #518	C₂³	semidirect
285. #518	C₂³	semidirect
287. C₄×#41	C₂³	semidirect
288. C₄×#41	C₂³	semidirect
289. C₄×#41	C₂³	semidirect
290. C₄×#41	C₂³	semidirect
291. C₄×#41	C₂³	semidirect
334. C₂×C₄×D₄	C₂³	semidirect
335. C₂×C₄×D₄	C₂³	semidirect
336. C₂×C₄×D₄	C₂³	semidirect
353. C₂×#117	C₂³	semidirect
354. C₂×#117	C₂³	semidirect
355. C₂×#117	C₂³	semidirect
384. C₂×#41	#41	semidirect
656. #41	C₂×#41	semidirect
927. C₂	#62994	direct (N × H)

Maximal subgroups

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

subgroup	index
#62994	2
C₂×#3511	2
C₂×#3494	2
C₂×#3503	2
C₂×#3488	2
C₂×#3524	2
C₂×#3518	2
C₂×#3514	2
C₂×#3493	2
C₂×#3519	2
C₂×#3506	2
C₂×#3483	2
C₂×#3475	2
C₂²×#555	2
C₂×D₄×#41	2
C₂×C₄×H(5,𝔽₂)	2
C₂×#3428	2

Subgroups — C2×#62994 #10586038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#62994 #10586038