Subgroups — C₂×#63024 #10586344

Order 512.

35128 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#63024	C₂	1	64	yes	maximal, direct product factor
2	C₂×#3500	C₂	1	4	yes	maximal, complemented
3	C₂×#3499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#3511	C₂	1	2	yes	maximal, complemented
5	C₂×#3494	C₂	1	8	yes	maximal, complemented
6	C₂×#3514	C₂	1	4	yes	maximal, complemented
7	C₂×#3519	C₂	1	4	yes	maximal, complemented
8	C₂×#3496	C₂	1	4	yes	maximal, complemented
9	C₂×#3549	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#3545	C₂	1	8	yes	maximal, complemented
11	C₂×#3547	C₂	1	4	yes	maximal, complemented
12	C₂×#3544	C₂	1	2	yes	maximal, complemented
13	C₂×#3551	C₂	1	4	yes	maximal, complemented
14	C₂×#3542	C₂	1	8	yes	maximal, complemented
15	C₂×#3483	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#3481	C₂	1	2	yes	maximal, complemented
17	C₂×#3475	C₂	1	4	yes	maximal, complemented
18	C₂²×#555	C₂	1	2	yes	maximal, complemented
19	C₂²×2₋¹⁺⁴	C₂²	1	2	yes	complemented
20	C₂²×H(5,𝔽₂)	C₂²	1	4	yes	complemented
21	#3551	C₂²	1	128	yes	complemented
22	#3549	C₂²	1	32	yes	complemented
23	#3547	C₂²	1	128	yes	complemented
24	#3545	C₂²	1	256	yes	complemented
25	#3544	C₂²	1	64	yes	complemented
26	#3542	C₂²	1	256	yes	complemented
27	C₂×#563	C₂²	1	8	yes	complemented
28	C₂×#562	C₂²	1	16	yes	complemented
29	C₂×H(3,𝔽₄)	C₂²	1	4	yes	complemented
30	C₂×#560	C₂²	1	8	yes	complemented
31	#3519	C₂²	1	128	yes	complemented
32	#3514	C₂²	1	128	yes	complemented
33	#3511	C₂²	1	64	yes	complemented
34	#3500	C₂²	1	128	yes	complemented
35	#3499	C₂²	1	32	yes	complemented
36	#3496	C₂²	1	128	yes	complemented
37	#3494	C₂²	1	256	yes	complemented
38	#3483	C₂²	1	32	yes	complemented
39	#3481	C₂²	1	64	yes	complemented
40	C₂×#559	C₂²	1	2	yes	complemented
41	C₂×Q₈²	C₂²	1	1	yes	characteristic, complemented
42	#3475	C₂²	1	128	yes	complemented
43	C₂×#556	C₂²	1	4	yes	complemented
44	C₂×#555	C₂²	1	8	yes	complemented
45	C₂×#555	C₂²	1	2	yes	complemented
46	C₂×#555	C₂²	1	4	yes	complemented
47	C₂×#555	C₂²	1	8	yes	complemented
48	C₂×#555	C₂²	1	4	yes	complemented
49	C₂×#555	C₂²	1	4	yes	complemented
50	C₂×#555	C₂²	1	8	yes	complemented
51	C₂×#555	C₂²	1	4	yes	complemented
52	C₂×#555	C₂²	1	1	yes	characteristic, complemented
53	C₂×#555	C₂²	1	64	yes	complemented
54	C₂×#554	C₂²	1	4	yes	complemented
55	C₂×#554	C₂²	1	2	yes	complemented
56	C₂×#554	C₂²	1	2	yes	complemented
57	C₂×#553	C₂²	1	4	yes	complemented
58	C₂×#553	C₂²	1	8	yes	complemented
59	C₂×#553	C₂²	1	8	yes	complemented
60	C₂×#553	C₂²	1	4	yes	complemented
61	C₂×#553	C₂²	1	8	yes	complemented
62	C₂×#552	C₂²	1	8	yes	complemented
63	C₂×#552	C₂²	1	8	yes	complemented
64	C₂×#551	C₂²	1	8	yes	complemented
65	C₂×#551	C₂²	1	8	yes	complemented
66	C₂×#551	C₂²	1	16	yes	complemented
67	C₂×#551	C₂²	1	16	yes	complemented
68	C₂×#550	C₂²	1	2	yes	complemented
69	C₂×#550	C₂²	1	4	yes	complemented
70	C₂×D₄×Q₈	C₂²	1	4	yes	complemented
71	C₂×#548	C₂²	1	8	yes	complemented
72	C₂×#548	C₂²	1	8	yes	complemented
73	C₂×#547	C₂²	1	8	yes	complemented
74	C₂×#547	C₂²	1	4	yes	complemented
75	C₂×#547	C₂²	1	4	yes	complemented
76	C₂×#547	C₂²	1	8	yes	complemented
77	C₂×#546	C₂²	1	8	yes	complemented
78	C₂×#546	C₂²	1	16	yes	complemented
79	C₂×#546	C₂²	1	16	yes	complemented
80	C₂×#546	C₂²	1	8	yes	complemented
81	C₂×#546	C₂²	1	8	yes	complemented
82	C₂×#546	C₂²	1	16	yes	complemented
83	C₂×#546	C₂²	1	4	yes	complemented
84	C₂×#546	C₂²	1	4	yes	complemented
85	C₂×D₄²	C₂²	1	2	yes	—
86	C₂×D₄²	C₂²	1	4	yes	complemented
87	C₂×D₄²	C₂²	1	2	yes	complemented
88	C₂×D₄²	C₂²	1	8	yes	complemented
89	C₂×#544	C₂²	1	8	yes	complemented
90	C₂×#542	C₂²	1	8	yes	complemented
91	C₂×#542	C₂²	1	16	yes	complemented
92	C₂×#542	C₂²	1	8	yes	complemented
93	C₂×#540	C₂²	1	16	yes	complemented
94	C₂×#540	C₂²	1	8	yes	complemented
95	C₂×#538	C₂²	1	16	yes	complemented
96	C₂×#538	C₂²	1	16	yes	complemented
97	C₂×#537	C₂²	1	8	yes	complemented
98	C₂×#537	C₂²	1	4	yes	complemented
99	C₂×#536	C₂²	1	2	yes	complemented
100	C₂×#536	C₂²	1	8	yes	complemented
101	C₂×#536	C₂²	1	4	yes	complemented
102	C₂×#536	C₂²	1	4	yes	complemented
103	C₂×#535	C₂²	1	4	yes	complemented
104	C₂×#535	C₂²	1	8	yes	complemented
105	C₂×#535	C₂²	1	8	yes	complemented
106	C₂×#534	C₂²	1	16	yes	complemented
107	C₂×#533	C₂²	1	4	yes	complemented
108	C₂×#532	C₂²	1	4	yes	complemented
109	C₂×#532	C₂²	1	4	yes	complemented
110	C₂×#532	C₂²	1	2	yes	complemented
111	C₂×#532	C₂²	1	1	yes	characteristic, complemented
112	C₂×#532	C₂²	1	4	yes	complemented
113	C₂×#532	C₂²	1	2	yes	complemented
114	C₂×#532	C₂²	1	8	yes	complemented
115	C₂²×C₄⋊Q₈	C₂²	1	2	yes	complemented
116	C₂²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
117	C₂×#529	C₂²	1	8	yes	complemented
118	C₂×#529	C₂²	1	4	yes	complemented
119	C₂×#529	C₂²	1	4	yes	complemented
120	C₂×#529	C₂²	1	16	yes	complemented
121	C₂²×#124	C₂²	1	8	yes	complemented
122	C₂²×#124	C₂²	1	4	yes	complemented
123	C₂×#525	C₂²	1	8	yes	complemented
124	C₂×#525	C₂²	1	8	yes	complemented
125	C₂²×#121	C₂²	1	8	yes	complemented
126	C₂²×#121	C₂²	1	8	yes	complemented
127	C₂×#520	C₂²	1	4	yes	complemented
128	C₂×#518	C₂²	1	8	yes	complemented
129	C₂×C₄×#41	C₂²	1	4	yes	complemented
130	C₂×C₄×#41	C₂²	1	2	yes	complemented
131	C₂×C₄×#41	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄×#41	C₂²	1	4	yes	complemented
133	C₂²×C₄×D₄	C₂²	1	4	yes	complemented
134	C₂²×C₄×D₄	C₂²	1	4	yes	complemented
135	C₂²×#117	C₂²	1	8	yes	complemented
136	C₂×2₋¹⁺⁴	—	4	16	no	—
137	C₂×2₋¹⁺⁴	C₂³	1	32	yes	complemented
138	C₂×H(5,𝔽₂)	—	4	32	no	—
139	C₂×H(5,𝔽₂)	C₂³	1	64	yes	complemented
140	C₂²×#41	C₂³	1	4	yes	—
141	C₂²×#41	C₂³	1	1	yes	characteristic
142	C₂²×#41	C₂³	1	4	yes	—
143	C₂²×#41	C₂³	1	8	yes	—
144	C₂²×#41	C₂³	1	8	yes	—
145	C₂²×#41	C₂³	1	2	yes	—
146	C₂²×#41	C₂³	1	8	yes	—
147	C₂²×#41	C₂³	1	4	yes	—
148	C₂²×#41	C₂³	1	4	yes	—
149	C₂²×#41	C₂³	1	2	yes	—
150	C₂²×#41	C₂³	1	4	yes	—
151	C₂³×Q₈	C₂³	1	4	yes	—
152	C₂³×Q₈	C₂³	1	4	yes	—
153	C₂³×Q₈	C₂³	1	2	yes	—
154	C₂³×D₄	C₂³	1	4	yes	—
155	C₂³×D₄	C₂³	1	8	yes	—
156	C₂³×D₄	C₂³	1	16	yes	—
157	C₂³×D₄	C₂³	1	4	yes	—
158	C₂³×D₄	C₂³	1	4	yes	—
159	C₂³×D₄	C₂³	1	8	yes	—
160	C₂⁴×C₄	C₂³	1	8	yes	—
161	#563	C₂³	1	128	yes	complemented
162	#562	C₂³	1	256	yes	complemented
163	H(3,𝔽₄)	C₂³	1	64	yes	complemented
164	#560	C₂³	1	128	yes	complemented
165	#559	C₂³	1	32	yes	complemented
166	Q₈²	C₂³	1	16	yes	complemented
167	#556	C₂³	1	64	yes	complemented
168	#555	C₂³	1	16	yes	complemented
169	#555	C₂³	1	128	yes	complemented
170	#555	C₂³	1	64	yes	complemented
171	#555	C₂³	1	128	yes	complemented
172	#555	C₂³	1	32	yes	complemented
173	#555	C₂³	1	128	yes	complemented
174	#555	C₂³	1	64	yes	complemented
175	#555	C₂³	1	64	yes	complemented
176	#555	C₂³	1	64	yes	complemented
177	#554	C₂³	1	32	yes	complemented
178	#554	C₂³	1	32	yes	complemented
179	#554	C₂³	1	64	yes	complemented
180	#553	C₂³	1	128	yes	complemented
181	#553	C₂³	1	64	yes	complemented
182	#553	C₂³	1	64	yes	complemented
183	#553	C₂³	1	128	yes	complemented
184	#553	C₂³	1	128	yes	complemented
185	#552	C₂³	1	128	yes	complemented
186	#552	C₂³	1	128	yes	complemented
187	#551	C₂³	1	256	yes	complemented
188	#551	C₂³	1	128	yes	complemented
189	#551	C₂³	1	128	yes	complemented
190	#551	C₂³	1	256	yes	complemented
191	#550	C₂³	1	32	yes	complemented
192	#550	C₂³	1	64	yes	complemented
193	D₄×Q₈	C₂³	1	64	yes	complemented
194	#548	C₂³	1	128	yes	complemented
195	#548	C₂³	1	128	yes	complemented
196	#547	C₂³	1	64	yes	complemented
197	#547	C₂³	1	128	yes	complemented
198	#547	C₂³	1	128	yes	complemented
199	#547	C₂³	1	64	yes	complemented
200	#546	C₂³	1	128	yes	complemented
201	#546	C₂³	1	64	yes	complemented
202	#546	C₂³	1	64	yes	complemented
203	#546	C₂³	1	256	yes	complemented
204	#546	C₂³	1	256	yes	complemented
205	#546	C₂³	1	128	yes	complemented
206	#546	C₂³	1	256	yes	complemented
207	#546	C₂³	1	128	yes	complemented
208	D₄²	C₂³	1	32	yes	—
209	D₄²	C₂³	1	64	yes	complemented
210	D₄²	C₂³	1	128	yes	complemented
211	D₄²	C₂³	1	32	yes	complemented
212	#544	C₂³	1	128	yes	complemented
213	#542	C₂³	1	256	yes	complemented
214	#542	C₂³	1	128	yes	complemented
215	#542	C₂³	1	128	yes	complemented
216	#540	C₂³	1	256	yes	complemented
217	#540	C₂³	1	128	yes	complemented
218	#538	C₂³	1	256	yes	complemented
219	#538	C₂³	1	256	yes	complemented
220	#537	C₂³	1	128	yes	complemented
221	#537	C₂³	1	64	yes	complemented
222	#536	C₂³	1	64	yes	complemented
223	#536	C₂³	1	32	yes	complemented
224	#536	C₂³	1	128	yes	complemented
225	#536	C₂³	1	64	yes	complemented
226	#535	C₂³	1	128	yes	complemented
227	#535	C₂³	1	128	yes	complemented
228	#535	C₂³	1	64	yes	complemented
229	#534	C₂³	1	256	yes	complemented
230	#533	C₂³	1	64	yes	complemented
231	#532	C₂³	1	32	yes	complemented
232	#532	C₂³	1	64	yes	complemented
233	#532	C₂³	1	16	yes	complemented
234	#532	C₂³	1	64	yes	complemented
235	#532	C₂³	1	128	yes	complemented
236	#532	C₂³	1	64	yes	complemented
237	#532	C₂³	1	32	yes	complemented
238	C₂×C₄⋊Q₈	C₂³	1	2	yes	—
239	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
241	C₂×C₄⋊Q₈	C₂³	1	2	yes	—
242	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
243	C₂×C₄⋊Q₈	C₂³	1	8	yes	—
244	C₂×C₄⋊Q₈	C₂³	1	2	yes	—
245	C₂×C₄⋊Q₈	C₂³	1	8	yes	—
246	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
247	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
248	C₂×C₄⋊Q₈	C₂³	1	32	yes	complemented
249	C₂×C₄⋊Q₈	C₂³	1	16	yes	complemented
250	C₂×#127	C₂³	1	2	yes	—
251	C₂×#127	C₂³	1	1	yes	characteristic
252	C₂×#127	C₂³	1	8	yes	—
253	C₂×#127	C₂³	1	4	yes	—
254	C₂×#127	C₂³	1	4	yes	—
255	#529	C₂³	1	256	yes	complemented
256	#529	C₂³	1	128	yes	complemented
257	#529	C₂³	1	64	yes	complemented
258	#529	C₂³	1	64	yes	complemented
259	C₂×#126	C₂³	1	8	yes	—
260	C₂×#126	C₂³	1	16	yes	—
261	C₂×#126	C₂³	1	16	yes	—
262	C₂×#126	C₂³	1	16	yes	—
263	C₂×#126	C₂³	1	8	yes	—
264	C₂×#125	C₂³	1	4	yes	—
265	C₂×#125	C₂³	1	16	yes	—
266	C₂×#125	C₂³	1	4	yes	—
267	C₂×#125	C₂³	1	8	yes	—
268	C₂×#124	C₂³	1	4	yes	—
269	C₂×#124	C₂³	1	8	yes	—
270	C₂×#124	C₂³	1	4	yes	—
271	C₂×#124	C₂³	1	8	yes	—
272	C₂×#124	C₂³	1	8	yes	—
273	C₂×#124	C₂³	1	8	yes	—
274	C₂×#124	C₂³	1	8	yes	—
275	C₂×#124	C₂³	1	16	yes	—
276	C₂×#124	C₂³	1	16	yes	—
277	C₂×#124	C₂³	1	16	yes	—
278	C₂×#124	C₂³	1	4	yes	—
279	C₂×#124	C₂³	1	4	yes	—
280	C₂×#124	C₂³	1	4	yes	—
281	C₂×#124	C₂³	1	2	yes	—
282	C₂×#124	C₂³	1	8	yes	—
283	C₂×#124	C₂³	1	4	yes	—
284	C₂×#124	C₂³	1	128	yes	complemented
285	C₂×#124	C₂³	1	64	yes	complemented
286	#525	C₂³	1	128	yes	complemented
287	#525	C₂³	1	128	yes	complemented
288	C₂×#123	C₂³	1	8	yes	—
289	C₂×#123	C₂³	1	16	yes	—
290	C₂×#123	C₂³	1	8	yes	—
291	C₂×#123	C₂³	1	16	yes	—
292	C₂×#123	C₂³	1	16	yes	—
293	C₂×#123	C₂³	1	8	yes	—
294	C₂×#123	C₂³	1	8	yes	—
295	C₂×#123	C₂³	1	16	yes	—
296	C₂×#123	C₂³	1	16	yes	—
297	C₂×#123	C₂³	1	16	yes	—
298	C₂×#123	C₂³	1	8	yes	—
299	C₂×#123	C₂³	1	16	yes	—
300	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
301	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
302	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
303	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
304	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
305	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
306	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
307	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
308	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
309	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
310	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
311	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
312	C₂×#121	C₂³	1	4	yes	—
313	C₂×#121	C₂³	1	8	yes	—
314	C₂×#121	C₂³	1	4	yes	—
315	C₂×#121	C₂³	1	4	yes	—
316	C₂×#121	C₂³	1	8	yes	—
317	C₂×#121	C₂³	1	16	yes	—
318	C₂×#121	C₂³	1	16	yes	—
319	C₂×#121	C₂³	1	16	yes	—
320	C₂×#121	C₂³	1	8	yes	—
321	C₂×#121	C₂³	1	8	yes	—
322	C₂×#121	C₂³	1	16	yes	—
323	C₂×#121	C₂³	1	8	yes	—
324	C₂×#121	C₂³	1	8	yes	—
325	C₂×#121	C₂³	1	8	yes	—
326	C₂×#121	C₂³	1	8	yes	—
327	C₂×#121	C₂³	1	4	yes	—
328	C₂×#121	C₂³	1	8	yes	—
329	C₂×#121	C₂³	1	8	yes	—
330	C₂×#121	C₂³	1	4	yes	—
331	C₂×#121	C₂³	1	4	yes	—
332	C₂×#121	C₂³	1	4	yes	—
333	C₂×#121	C₂³	1	8	yes	—
334	C₂×#121	C₂³	1	8	yes	—
335	C₂×#121	C₂³	1	16	yes	—
336	C₂×#121	C₂³	1	16	yes	—
337	C₂×#121	C₂³	1	16	yes	—
338	C₂×#121	C₂³	1	128	yes	complemented
339	C₂×#121	C₂³	1	128	yes	complemented
340	C₂×#120	C₂³	1	8	yes	—
341	C₂×#120	C₂³	1	16	yes	—
342	C₂×#120	C₂³	1	8	yes	—
343	C₂×#120	C₂³	1	16	yes	—
344	C₂×#120	C₂³	1	16	yes	—
345	C₂×#120	C₂³	1	8	yes	—
346	C₂×#120	C₂³	1	8	yes	—
347	#520	C₂³	1	64	yes	complemented
348	#518	C₂³	1	128	yes	complemented
349	C₄×#41	C₂³	1	64	yes	complemented
350	C₄×#41	C₂³	1	64	yes	complemented
351	C₄×#41	C₂³	1	16	yes	complemented
352	C₄×#41	C₂³	1	32	yes	complemented
353	C₂×C₄×Q₈	C₂³	1	2	yes	—
354	C₂×C₄×Q₈	C₂³	1	2	yes	—
355	C₂×C₄×Q₈	C₂³	1	2	yes	—
356	C₂×C₄×Q₈	C₂³	1	8	yes	—
357	C₂×C₄×Q₈	C₂³	1	4	yes	—
358	C₂×C₄×Q₈	C₂³	1	8	yes	—
359	C₂×C₄×D₄	C₂³	1	2	yes	—
360	C₂×C₄×D₄	C₂³	1	2	yes	—
361	C₂×C₄×D₄	C₂³	1	4	yes	—
362	C₂×C₄×D₄	C₂³	1	4	yes	—
363	C₂×C₄×D₄	C₂³	1	8	yes	—
364	C₂×C₄×D₄	C₂³	1	8	yes	—
365	C₂×C₄×D₄	C₂³	1	8	yes	—
366	C₂×C₄×D₄	C₂³	1	4	yes	—
367	C₂×C₄×D₄	C₂³	1	4	yes	—
368	C₂×C₄×D₄	C₂³	1	4	yes	—
369	C₂×C₄×D₄	C₂³	1	8	yes	—
370	C₂×C₄×D₄	C₂³	1	4	yes	—
371	C₂×C₄×D₄	C₂³	1	4	yes	—
372	C₂×C₄×D₄	C₂³	1	4	yes	—
373	C₂×C₄×D₄	C₂³	1	4	yes	—
374	C₂×C₄×D₄	C₂³	1	16	yes	—
375	C₂×C₄×D₄	C₂³	1	2	yes	—
376	C₂×C₄×D₄	C₂³	1	4	yes	—
377	C₂×C₄×D₄	C₂³	1	8	yes	—
378	C₂×C₄×D₄	C₂³	1	4	yes	—
379	C₂×C₄×D₄	C₂³	1	8	yes	—
380	C₂×C₄×D₄	C₂³	1	16	yes	—
381	C₂×C₄×D₄	C₂³	1	8	yes	—
382	C₂×C₄×D₄	C₂³	1	8	yes	—
383	C₂×C₄×D₄	C₂³	1	16	yes	—
384	C₂×C₄×D₄	C₂³	1	16	yes	—
385	C₂×C₄×D₄	C₂³	1	8	yes	—
386	C₂×C₄×D₄	C₂³	1	64	yes	complemented
387	C₂×C₄×D₄	C₂³	1	64	yes	complemented
388	C₂×#117	C₂³	1	4	yes	—
389	C₂×#117	C₂³	1	8	yes	—
390	C₂×#117	C₂³	1	8	yes	—
391	C₂×#117	C₂³	1	16	yes	—
392	C₂×#117	C₂³	1	8	yes	—
393	C₂×#117	C₂³	1	16	yes	—
394	C₂×#117	C₂³	1	2	yes	—
395	C₂×#117	C₂³	1	8	yes	—
396	C₂×#117	C₂³	1	8	yes	—
397	C₂×#117	C₂³	1	4	yes	—
398	C₂×#117	C₂³	1	2	yes	—
399	C₂×#117	C₂³	1	1	yes	characteristic
400	C₂×#117	C₂³	1	4	yes	—
401	C₂×#117	C₂³	1	8	yes	—
402	C₂×#117	C₂³	1	128	yes	complemented
403	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
404	C₂²×C₄⋊C₄	C₂³	1	8	yes	—
405	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
406	C₂²×C₄⋊C₄	C₂³	1	8	yes	—
407	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
408	C₂²×C₂²⋊C₄	C₂³	1	16	yes	—
409	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
410	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
411	C₂²×C₂²⋊C₄	C₂³	1	16	yes	—
412	C₂²×C₂²⋊C₄	C₂³	1	16	yes	—
413	C₂²×C₄²	C₂³	1	8	yes	—
414	C₂²×C₄²	C₂³	1	2	yes	—
415	C₂²×C₄²	C₂³	1	4	yes	—
416	C₂²×C₄²	C₂³	1	4	yes	—
417	C₂²×C₄²	C₂³	1	1	yes	characteristic
418	C₂⁵	C₂⁴	1	8	yes	—
419	C₂⁵	C₂⁴	1	8	yes	—
420	2₋¹⁺⁴	—	4	128	no	—
421	H(5,𝔽₂)	—	4	256	no	—
422	C₂×#41	—	2	32	no	—
423	C₂×#41	—	2	8	no	—
424	C₂×#41	—	4	16	no	—
425	C₂×#41	—	4	16	no	—
426	C₂×#41	—	4	8	no	—
427	C₂×#41	—	4	32	no	—
428	C₂×#41	—	4	32	no	—
429	C₂×#41	—	4	16	no	—
430	C₂×#41	—	4	16	no	—
431	C₂×#41	—	4	8	no	—
432	C₂×#41	—	4	32	no	—
433	C₂×#41	C₂⁴	1	8	yes	—
434	C₂×#41	C₂⁴	1	32	yes	—
435	C₂×#41	C₂⁴	1	32	yes	—
436	C₂×#41	C₂⁴	1	16	yes	—
437	C₂×#41	C₂⁴	1	32	yes	—
438	C₂×#41	C₂⁴	1	16	yes	—
439	C₂×#41	C₂⁴	1	32	yes	—
440	C₂×#41	C₂⁴	1	64	yes	—
441	C₂×#41	C₂⁴	1	32	yes	—
442	C₂×#41	C₂⁴	1	64	yes	—
443	C₂×#41	C₂⁴	1	64	yes	—
444	C₂²×Q₈	—	4	16	no	—
445	C₂²×Q₈	—	4	16	no	—
446	C₂²×Q₈	—	4	8	no	—
447	C₂²×Q₈	C₂⁴	1	2	yes	—
448	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
449	C₂²×Q₈	C₂⁴	1	4	yes	—
450	C₂²×Q₈	C₂⁴	1	4	yes	—
451	C₂²×Q₈	C₂⁴	1	4	yes	—
452	C₂²×Q₈	C₂⁴	1	8	yes	—
453	C₂²×Q₈	C₂⁴	1	4	yes	—
454	C₂²×Q₈	C₂⁴	1	2	yes	—
455	C₂²×Q₈	C₂⁴	1	32	yes	—
456	C₂²×Q₈	C₂⁴	1	32	yes	—
457	C₂²×Q₈	C₂⁴	1	16	yes	—
458	C₂²×D₄	—	2	32	no	—
459	C₂²×D₄	—	4	16	no	—
460	C₂²×D₄	—	4	32	no	—
461	C₂²×D₄	—	4	16	no	—
462	C₂²×D₄	—	4	32	no	—
463	C₂²×D₄	—	4	64	no	—
464	C₂²×D₄	C₂⁴	1	4	yes	—
465	C₂²×D₄	C₂⁴	1	2	yes	—
466	C₂²×D₄	C₂⁴	1	4	yes	—
467	C₂²×D₄	C₂⁴	1	2	yes	—
468	C₂²×D₄	C₂⁴	1	8	yes	—
469	C₂²×D₄	C₂⁴	1	8	yes	—
470	C₂²×D₄	C₂⁴	1	4	yes	—
471	C₂²×D₄	C₂⁴	1	32	yes	—
472	C₂²×D₄	C₂⁴	1	4	yes	—
473	C₂²×D₄	C₂⁴	1	8	yes	—
474	C₂²×D₄	C₂⁴	1	8	yes	—
475	C₂²×D₄	C₂⁴	1	16	yes	—
476	C₂²×D₄	C₂⁴	1	8	yes	—
477	C₂²×D₄	C₂⁴	1	4	yes	—
478	C₂²×D₄	C₂⁴	1	32	yes	—
479	C₂²×D₄	C₂⁴	1	64	yes	—
480	C₂²×D₄	C₂⁴	1	2	yes	—
481	C₂²×D₄	C₂⁴	1	8	yes	—
482	C₂²×D₄	C₂⁴	1	4	yes	—
483	C₂²×D₄	C₂⁴	1	16	yes	—
484	C₂²×D₄	C₂⁴	1	8	yes	—
485	C₂²×D₄	C₂⁴	1	4	yes	—
486	C₂²×D₄	C₂⁴	1	64	yes	—
487	C₂²×D₄	C₂⁴	1	128	yes	—
488	C₂²×D₄	C₂⁴	1	32	yes	—
489	C₂²×D₄	C₂⁴	1	1	yes	characteristic
490	C₂³×C₄	—	4	32	no	—
491	C₂³×C₄	C₂⁴	1	2	yes	—
492	C₂³×C₄	C₂⁴	1	8	yes	—
493	C₂³×C₄	C₂⁴	1	4	yes	—
494	C₂³×C₄	C₂⁴	1	2	yes	—
495	C₂³×C₄	C₂⁴	1	8	yes	—
496	C₂³×C₄	C₂⁴	1	4	yes	—
497	C₂³×C₄	C₂⁴	1	4	yes	—
498	C₂³×C₄	C₂⁴	1	1	yes	characteristic
499	C₂³×C₄	C₂⁴	1	4	yes	—
500	C₂³×C₄	C₂⁴	1	8	yes	—
501	C₂³×C₄	C₂⁴	1	8	yes	—
502	C₂³×C₄	C₂⁴	1	8	yes	—
503	C₂³×C₄	C₂⁴	1	4	yes	—
504	C₂³×C₄	C₂⁴	1	8	yes	—
505	C₂³×C₄	C₂⁴	1	8	yes	—
506	C₂³×C₄	C₂⁴	1	16	yes	—
507	C₂³×C₄	C₂⁴	1	4	yes	—
508	C₂³×C₄	C₂⁴	1	64	yes	—
509	C₄⋊Q₈	C₂⁴	1	16	yes	—
510	C₄⋊Q₈	C₂⁴	1	8	yes	—
511	C₄⋊Q₈	C₂⁴	1	32	yes	—
512	C₄⋊Q₈	C₂⁴	1	16	yes	—
513	C₄⋊Q₈	C₂⁴	1	32	yes	—
514	C₄⋊Q₈	C₂⁴	1	64	yes	—
515	C₄⋊Q₈	C₂⁴	1	16	yes	—
516	C₄⋊Q₈	C₂⁴	1	64	yes	—
517	C₄⋊Q₈	C₂⁴	1	32	yes	—
518	C₄⋊Q₈	C₂⁴	1	32	yes	—
519	#127	C₂⁴	1	16	yes	—
520	#127	C₂⁴	1	8	yes	—
521	#127	C₂⁴	1	64	yes	—
522	#127	C₂⁴	1	32	yes	—
523	#127	C₂⁴	1	32	yes	—
524	#126	C₂⁴	1	64	yes	—
525	#126	C₂⁴	1	128	yes	—
526	#126	C₂⁴	1	128	yes	—
527	#126	C₂⁴	1	128	yes	—
528	#126	C₂⁴	1	64	yes	—
529	#125	C₂⁴	1	32	yes	—
530	#125	C₂⁴	1	128	yes	—
531	#125	C₂⁴	1	32	yes	—
532	#125	C₂⁴	1	64	yes	—
533	#124	C₂⁴	1	32	yes	—
534	#124	C₂⁴	1	64	yes	—
535	#124	C₂⁴	1	32	yes	—
536	#124	C₂⁴	1	64	yes	—
537	#124	C₂⁴	1	64	yes	—
538	#124	C₂⁴	1	64	yes	—
539	#124	C₂⁴	1	64	yes	—
540	#124	C₂⁴	1	128	yes	—
541	#124	C₂⁴	1	128	yes	—
542	#124	C₂⁴	1	128	yes	—
543	#124	C₂⁴	1	32	yes	—
544	#124	C₂⁴	1	32	yes	—
545	#124	C₂⁴	1	32	yes	—
546	#124	C₂⁴	1	16	yes	—
547	#124	C₂⁴	1	64	yes	—
548	#124	C₂⁴	1	32	yes	—
549	#123	C₂⁴	1	64	yes	—
550	#123	C₂⁴	1	128	yes	—
551	#123	C₂⁴	1	64	yes	—
552	#123	C₂⁴	1	128	yes	—
553	#123	C₂⁴	1	128	yes	—
554	#123	C₂⁴	1	64	yes	—
555	#123	C₂⁴	1	64	yes	—
556	#123	C₂⁴	1	128	yes	—
557	#123	C₂⁴	1	128	yes	—
558	#123	C₂⁴	1	128	yes	—
559	#123	C₂⁴	1	64	yes	—
560	#123	C₂⁴	1	128	yes	—
561	C₂²⋊Q₈	C₂⁴	1	32	yes	—
562	C₂²⋊Q₈	C₂⁴	1	64	yes	—
563	C₂²⋊Q₈	C₂⁴	1	64	yes	—
564	C₂²⋊Q₈	C₂⁴	1	64	yes	—
565	C₂²⋊Q₈	C₂⁴	1	32	yes	—
566	C₂²⋊Q₈	C₂⁴	1	64	yes	—
567	C₂²⋊Q₈	C₂⁴	1	64	yes	—
568	C₂²⋊Q₈	C₂⁴	1	64	yes	—
569	C₂²⋊Q₈	C₂⁴	1	128	yes	—
570	C₂²⋊Q₈	C₂⁴	1	128	yes	—
571	C₂²⋊Q₈	C₂⁴	1	128	yes	—
572	C₂²⋊Q₈	C₂⁴	1	128	yes	—
573	#121	C₂⁴	1	32	yes	—
574	#121	C₂⁴	1	64	yes	—
575	#121	C₂⁴	1	32	yes	—
576	#121	C₂⁴	1	32	yes	—
577	#121	C₂⁴	1	64	yes	—
578	#121	C₂⁴	1	128	yes	—
579	#121	C₂⁴	1	128	yes	—
580	#121	C₂⁴	1	128	yes	—
581	#121	C₂⁴	1	64	yes	—
582	#121	C₂⁴	1	64	yes	—
583	#121	C₂⁴	1	128	yes	—
584	#121	C₂⁴	1	64	yes	—
585	#121	C₂⁴	1	64	yes	—
586	#121	C₂⁴	1	64	yes	—
587	#121	C₂⁴	1	64	yes	—
588	#121	C₂⁴	1	32	yes	—
589	#121	C₂⁴	1	64	yes	—
590	#121	C₂⁴	1	64	yes	—
591	#121	C₂⁴	1	32	yes	—
592	#121	C₂⁴	1	32	yes	—
593	#121	C₂⁴	1	32	yes	—
594	#121	C₂⁴	1	64	yes	—
595	#121	C₂⁴	1	64	yes	—
596	#121	C₂⁴	1	128	yes	—
597	#121	C₂⁴	1	128	yes	—
598	#121	C₂⁴	1	128	yes	—
599	#120	C₂⁴	1	64	yes	—
600	#120	C₂⁴	1	128	yes	—
601	#120	C₂⁴	1	64	yes	—
602	#120	C₂⁴	1	128	yes	—
603	#120	C₂⁴	1	128	yes	—
604	#120	C₂⁴	1	64	yes	—
605	#120	C₂⁴	1	64	yes	—
606	C₄×Q₈	C₂⁴	1	16	yes	—
607	C₄×Q₈	C₂⁴	1	16	yes	—
608	C₄×Q₈	C₂⁴	1	16	yes	—
609	C₄×Q₈	C₂⁴	1	64	yes	—
610	C₄×Q₈	C₂⁴	1	32	yes	—
611	C₄×Q₈	C₂⁴	1	64	yes	—
612	C₄×D₄	C₂⁴	1	16	yes	—
613	C₄×D₄	C₂⁴	1	16	yes	—
614	C₄×D₄	C₂⁴	1	32	yes	—
615	C₄×D₄	C₂⁴	1	32	yes	—
616	C₄×D₄	C₂⁴	1	64	yes	—
617	C₄×D₄	C₂⁴	1	64	yes	—
618	C₄×D₄	C₂⁴	1	64	yes	—
619	C₄×D₄	C₂⁴	1	32	yes	—
620	C₄×D₄	C₂⁴	1	32	yes	—
621	C₄×D₄	C₂⁴	1	32	yes	—
622	C₄×D₄	C₂⁴	1	64	yes	—
623	C₄×D₄	C₂⁴	1	32	yes	—
624	C₄×D₄	C₂⁴	1	32	yes	—
625	C₄×D₄	C₂⁴	1	32	yes	—
626	C₄×D₄	C₂⁴	1	32	yes	—
627	C₄×D₄	C₂⁴	1	128	yes	—
628	C₄×D₄	C₂⁴	1	16	yes	—
629	C₄×D₄	C₂⁴	1	32	yes	—
630	C₄×D₄	C₂⁴	1	64	yes	—
631	C₄×D₄	C₂⁴	1	32	yes	—
632	C₄×D₄	C₂⁴	1	64	yes	—
633	C₄×D₄	C₂⁴	1	128	yes	—
634	C₄×D₄	C₂⁴	1	64	yes	—
635	C₄×D₄	C₂⁴	1	64	yes	—
636	C₄×D₄	C₂⁴	1	128	yes	—
637	C₄×D₄	C₂⁴	1	128	yes	—
638	C₄×D₄	C₂⁴	1	64	yes	—
639	#117	C₂⁴	1	32	yes	—
640	#117	C₂⁴	1	64	yes	—
641	#117	C₂⁴	1	64	yes	—
642	#117	C₂⁴	1	128	yes	—
643	#117	C₂⁴	1	64	yes	—
644	#117	C₂⁴	1	128	yes	—
645	#117	C₂⁴	1	16	yes	—
646	#117	C₂⁴	1	64	yes	—
647	#117	C₂⁴	1	64	yes	—
648	#117	C₂⁴	1	32	yes	—
649	#117	C₂⁴	1	16	yes	—
650	#117	C₂⁴	1	8	yes	—
651	#117	C₂⁴	1	32	yes	—
652	#117	C₂⁴	1	64	yes	—
653	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
654	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
655	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
656	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
657	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
658	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
659	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
660	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
661	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
662	C₂×C₄⋊C₄	C₂⁴	1	32	yes	—
663	C₂×C₄⋊C₄	C₂⁴	1	64	yes	—
664	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
665	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
666	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
667	C₂×C₄⋊C₄	C₂⁴	1	32	yes	—
668	C₂×C₄⋊C₄	C₂⁴	1	64	yes	—
669	C₂×C₄⋊C₄	C₂⁴	1	32	yes	—
670	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
671	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
672	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
673	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
674	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
675	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
676	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
677	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
678	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
679	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
680	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
681	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
682	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
683	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
684	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
685	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
686	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
687	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
688	C₂×C₂²⋊C₄	C₂⁴	1	128	yes	—
689	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
690	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
691	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
692	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
693	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
694	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
695	C₂×C₂²⋊C₄	C₂⁴	1	64	yes	—
696	C₂×C₂²⋊C₄	C₂⁴	1	64	yes	—
697	C₂×C₂²⋊C₄	C₂⁴	1	128	yes	—
698	C₂×C₂²⋊C₄	C₂⁴	1	128	yes	—
699	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
700	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
701	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
702	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
703	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
704	C₂×C₄²	C₂⁴	1	4	yes	—
705	C₂×C₄²	C₂⁴	1	1	yes	characteristic
706	C₂×C₄²	C₂⁴	1	8	yes	—
707	C₂×C₄²	C₂⁴	1	4	yes	—
708	C₂×C₄²	C₂⁴	1	16	yes	—
709	C₂×C₄²	C₂⁴	1	4	yes	—
710	C₂×C₄²	C₂⁴	1	4	yes	—
711	C₂×C₄²	C₂⁴	1	2	yes	—
712	C₂×C₄²	C₂⁴	1	4	yes	—
713	C₂×C₄²	C₂⁴	1	64	yes	—
714	C₂×C₄²	C₂⁴	1	2	yes	—
715	C₂×C₄²	C₂⁴	1	1	yes	characteristic
716	C₂×C₄²	C₂⁴	1	4	yes	—
717	C₂×C₄²	C₂⁴	1	16	yes	—
718	C₂×C₄²	C₂⁴	1	32	yes	—
719	C₂×C₄²	C₂⁴	1	32	yes	—
720	C₂×C₄²	C₂⁴	1	8	yes	—
721	C₂⁴	—	2	32	no	—
722	C₂⁴	—	4	16	no	—
723	C₂⁴	—	4	16	no	—
724	C₂⁴	—	4	16	no	—
725	C₂⁴	—	4	32	no	—
726	C₂⁴	C₂⁵	1	8	yes	—
727	C₂⁴	C₂⁵	1	4	yes	—
728	C₂⁴	C₂⁵	1	4	yes	—
729	C₂⁴	C₂⁵	1	1	yes	characteristic
730	C₂⁴	C₂⁵	1	2	yes	—
731	C₂⁴	C₂⁵	1	32	yes	—
732	C₂⁴	C₂⁵	1	32	yes	—
733	#41	—	2	128	no	—
734	#41	—	2	32	no	—
735	#41	—	4	64	no	—
736	#41	—	4	64	no	—
737	#41	—	4	32	no	—
738	#41	—	4	128	no	—
739	#41	—	4	128	no	—
740	#41	—	4	64	no	—
741	#41	—	4	64	no	—
742	#41	—	4	32	no	—
743	#41	—	4	128	no	—
744	C₂×Q₈	—	2	4	no	—
745	C₂×Q₈	—	2	16	no	—
746	C₂×Q₈	—	2	8	no	—
747	C₂×Q₈	—	4	4	no	—
748	C₂×Q₈	—	4	16	no	—
749	C₂×Q₈	—	4	8	no	—
750	C₂×Q₈	—	4	64	no	—
751	C₂×Q₈	—	4	8	no	—
752	C₂×Q₈	—	4	8	no	—
753	C₂×Q₈	—	4	64	no	—
754	C₂×Q₈	—	4	32	no	—
755	C₂×Q₈	C₂⁵	1	8	yes	—
756	C₂×Q₈	C₂⁵	1	4	yes	—
757	C₂×Q₈	C₂⁵	1	16	yes	—
758	C₂×Q₈	C₂⁵	1	16	yes	—
759	C₂×Q₈	C₂⁵	1	16	yes	—
760	C₂×Q₈	C₂⁵	1	32	yes	—
761	C₂×Q₈	C₂⁵	1	16	yes	—
762	C₂×Q₈	C₂⁵	1	8	yes	—
763	C₂×D₄	—	2	32	no	—
764	C₂×D₄	—	2	32	no	—
765	C₂×D₄	—	2	8	no	—
766	C₂×D₄	—	2	128	no	—
767	C₂×D₄	—	2	16	no	—
768	C₂×D₄	—	2	16	no	—
769	C₂×D₄	—	2	8	no	—
770	C₂×D₄	—	2	16	no	—
771	C₂×D₄	—	4	64	no	—
772	C₂×D₄	—	4	128	no	—
773	C₂×D₄	—	4	64	no	—
774	C₂×D₄	—	4	8	no	—
775	C₂×D₄	—	4	16	no	—
776	C₂×D₄	—	4	16	no	—
777	C₂×D₄	—	4	32	no	—
778	C₂×D₄	—	4	16	no	—
779	C₂×D₄	—	4	32	no	—
780	C₂×D₄	—	4	128	no	—
781	C₂×D₄	—	4	16	no	—
782	C₂×D₄	—	4	8	no	—
783	C₂×D₄	—	4	16	no	—
784	C₂×D₄	—	4	8	no	—
785	C₂×D₄	—	4	8	no	—
786	C₂×D₄	—	4	4	no	—
787	C₂×D₄	—	4	256	no	—
788	C₂×D₄	H(5,𝔽₂)	1	8	yes	—
789	C₂×D₄	C₂⁵	1	16	yes	—
790	C₂×D₄	C₂⁵	1	8	yes	—
791	C₂×D₄	C₂⁵	1	16	yes	—
792	C₂×D₄	C₂⁵	1	8	yes	—
793	C₂×D₄	C₂⁵	1	32	yes	—
794	C₂×D₄	C₂⁵	1	32	yes	—
795	C₂×D₄	C₂⁵	1	16	yes	—
796	C₂×D₄	C₂⁵	1	16	yes	—
797	C₂×D₄	C₂⁵	1	32	yes	—
798	C₂×D₄	C₂⁵	1	32	yes	—
799	C₂×D₄	C₂⁵	1	64	yes	—
800	C₂×D₄	C₂⁵	1	32	yes	—
801	C₂×D₄	C₂⁵	1	16	yes	—
802	C₂×D₄	C₂⁵	1	8	yes	—
803	C₂×D₄	C₂⁵	1	32	yes	—
804	C₂×D₄	C₂⁵	1	16	yes	—
805	C₂×D₄	C₂⁵	1	64	yes	—
806	C₂×D₄	C₂⁵	1	32	yes	—
807	C₂×D₄	C₂⁵	1	16	yes	—
808	C₂×D₄	C₂⁵	1	4	yes	—
809	C₂²×C₄	—	2	32	no	—
810	C₂²×C₄	—	2	8	no	—
811	C₂²×C₄	—	2	16	no	—
812	C₂²×C₄	—	2	16	no	—
813	C₂²×C₄	—	2	4	no	—
814	C₂²×C₄	—	2	16	no	—
815	C₂²×C₄	—	2	16	no	—
816	C₂²×C₄	—	2	32	no	—
817	C₂²×C₄	—	2	8	no	—
818	C₂²×C₄	—	4	128	no	—
819	C₂²×C₄	—	4	16	no	—
820	C₂²×C₄	—	4	16	no	—
821	C₂²×C₄	—	4	16	no	—
822	C₂²×C₄	—	4	32	no	—
823	C₂²×C₄	—	4	8	no	—
824	C₂²×C₄	—	4	16	no	—
825	C₂²×C₄	—	4	16	no	—
826	C₂²×C₄	—	4	8	no	—
827	C₂²×C₄	C₂⁵	1	8	yes	—
828	C₂²×C₄	C₂⁵	1	32	yes	—
829	C₂²×C₄	C₂⁵	1	16	yes	—
830	C₂²×C₄	C₂⁵	1	8	yes	—
831	C₂²×C₄	C₂⁵	1	16	yes	—
832	C₂²×C₄	C₂⁵	1	16	yes	—
833	C₂²×C₄	C₂⁵	1	4	yes	—
834	C₂²×C₄	C₂⁵	1	16	yes	—
835	C₂²×C₄	C₂⁵	1	32	yes	—
836	C₂²×C₄	C₂⁵	1	4	yes	—
837	C₂²×C₄	C₂⁵	1	2	yes	—
838	C₂²×C₄	C₂⁵	1	1	yes	characteristic
839	C₂²×C₄	C₂⁵	1	8	yes	—
840	C₂²×C₄	C₂⁵	1	4	yes	—
841	C₂²×C₄	C₂⁵	1	4	yes	—
842	C₂²×C₄	C₂⁵	1	2	yes	—
843	C₂²×C₄	C₂⁵	1	4	yes	—
844	C₂²×C₄	C₂⁵	1	8	yes	—
845	C₂²×C₄	C₂⁵	1	4	yes	—
846	C₂²×C₄	C₂⁵	1	32	yes	—
847	C₂²×C₄	C₂⁵	1	32	yes	—
848	C₂²×C₄	C₂⁵	1	16	yes	—
849	C₂²×C₄	C₂⁵	1	32	yes	—
850	C₂²×C₄	C₂⁵	1	32	yes	—
851	C₂²×C₄	C₂⁵	1	32	yes	—
852	C₂²×C₄	C₂⁵	1	64	yes	—
853	C₂²×C₄	C₂⁵	1	16	yes	—
854	C₂²×C₄	C₂⁵	1	1	yes	characteristic
855	C₂²×C₄	C₂⁵	1	2	yes	—
856	C₄⋊C₄	C₂⁵	1	8	yes	—
857	C₄⋊C₄	C₂⁵	1	32	yes	—
858	C₄⋊C₄	C₂⁵	1	8	yes	—
859	C₄⋊C₄	C₂⁵	1	16	yes	—
860	C₄⋊C₄	C₂⁵	1	8	yes	—
861	C₄⋊C₄	C₂⁵	1	16	yes	—
862	C₄⋊C₄	C₂⁵	1	32	yes	—
863	C₄⋊C₄	C₂⁵	1	16	yes	—
864	C₄⋊C₄	C₂⁵	1	64	yes	—
865	C₄⋊C₄	C₂⁵	1	32	yes	—
866	C₄⋊C₄	C₂⁵	1	64	yes	—
867	C₄⋊C₄	C₂⁵	1	32	yes	—
868	C₄⋊C₄	C₂⁵	1	16	yes	—
869	C₄⋊C₄	C₂⁵	1	32	yes	—
870	C₄⋊C₄	C₂⁵	1	32	yes	—
871	C₄⋊C₄	C₂⁵	1	64	yes	—
872	C₄⋊C₄	C₂⁵	1	16	yes	—
873	C₄⋊C₄	C₂⁵	1	32	yes	—
874	C₄⋊C₄	C₂⁵	1	16	yes	—
875	C₂²⋊C₄	C₂⁵	1	64	yes	—
876	C₂²⋊C₄	C₂⁵	1	32	yes	—
877	C₂²⋊C₄	C₂⁵	1	32	yes	—
878	C₂²⋊C₄	C₂⁵	1	16	yes	—
879	C₂²⋊C₄	C₂⁵	1	32	yes	—
880	C₂²⋊C₄	C₂⁵	1	16	yes	—
881	C₂²⋊C₄	C₂⁵	1	32	yes	—
882	C₂²⋊C₄	C₂⁵	1	32	yes	—
883	C₂²⋊C₄	C₂⁵	1	32	yes	—
884	C₂²⋊C₄	C₂⁵	1	64	yes	—
885	C₂²⋊C₄	C₂⁵	1	64	yes	—
886	C₂²⋊C₄	C₂⁵	1	64	yes	—
887	C₂²⋊C₄	C₂⁵	1	32	yes	—
888	C₂²⋊C₄	C₂⁵	1	32	yes	—
889	C₂²⋊C₄	C₂⁵	1	32	yes	—
890	C₂²⋊C₄	C₂⁵	1	64	yes	—
891	C₂²⋊C₄	C₂⁵	1	32	yes	—
892	C₂²⋊C₄	C₂⁵	1	16	yes	—
893	C₂²⋊C₄	C₂⁵	1	16	yes	—
894	C₂²⋊C₄	C₂⁵	1	32	yes	—
895	C₂²⋊C₄	C₂⁵	1	32	yes	—
896	C₂²⋊C₄	C₂⁵	1	8	yes	—
897	C₄²	C₂⁵	1	16	yes	—
898	C₄²	C₂⁵	1	8	yes	—
899	C₄²	C₂⁵	1	4	yes	—
900	C₄²	C₂⁵	1	16	yes	—
901	C₄²	C₂⁵	1	4	yes	—
902	C₄²	C₂⁵	1	32	yes	—
903	C₄²	C₂⁵	1	16	yes	—
904	C₄²	C₂⁵	1	64	yes	—
905	C₄²	C₂⁵	1	16	yes	—
906	C₄²	C₂⁵	1	16	yes	—
907	C₄²	C₂⁵	1	8	yes	—
908	C₄²	C₂⁵	1	16	yes	—
909	C₂³	—	2	8	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	8	no	—
912	C₂³	—	2	8	no	—
913	C₂³	—	2	16	no	—
914	C₂³	—	2	8	no	—
915	C₂³	—	2	16	no	—
916	C₂³	—	2	4	no	—
917	C₂³	—	2	8	no	—
918	C₂³	—	2	16	no	—
919	C₂³	—	2	16	no	—
920	C₂³	—	2	64	no	—
921	C₂³	—	4	32	no	—
922	C₂³	—	4	32	no	—
923	C₂³	—	4	32	no	—
924	C₂³	—	4	64	no	—
925	C₂³	—	8	64	no	—
926	C₂³	—	16	32	no	—
927	C₂³	C₂×H(5,𝔽₂)	1	8	yes	—
928	C₂³	C₂⁶	1	16	yes	—
929	C₂³	C₂⁶	1	8	yes	—
930	C₂³	C₂⁶	1	8	yes	—
931	C₂³	C₂⁶	1	2	yes	—
932	C₂³	C₂⁶	1	4	yes	—
933	C₂³	C₂⁶	1	1	yes	characteristic
934	Q₈	—	2	8	no	—
935	Q₈	—	2	32	no	—
936	Q₈	—	2	16	no	—
937	Q₈	—	4	8	no	—
938	Q₈	—	4	32	no	—
939	Q₈	—	4	16	no	—
940	Q₈	—	4	16	no	—
941	Q₈	—	4	16	no	—
942	D₄	—	2	64	no	—
943	D₄	—	2	64	no	—
944	D₄	—	2	16	no	—
945	D₄	—	2	32	no	—
946	D₄	—	2	32	no	—
947	D₄	—	2	16	no	—
948	D₄	—	2	32	no	—
949	D₄	—	4	16	no	—
950	D₄	—	4	32	no	—
951	D₄	—	4	32	no	—
952	D₄	—	4	64	no	—
953	D₄	—	4	32	no	—
954	D₄	—	4	64	no	—
955	D₄	—	4	32	no	—
956	D₄	—	4	16	no	—
957	D₄	—	4	32	no	—
958	D₄	—	4	16	no	—
959	D₄	—	4	16	no	—
960	D₄	—	4	8	no	—
961	D₄	C₂×H(5,𝔽₂)	1	16	yes	—
962	C₂×C₄	—	2	8	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	8	no	—
965	C₂×C₄	—	2	16	no	—
966	C₂×C₄	—	2	4	no	—
967	C₂×C₄	—	2	64	no	—
968	C₂×C₄	—	2	16	no	—
969	C₂×C₄	—	2	8	no	—
970	C₂×C₄	—	2	8	no	—
971	C₂×C₄	—	2	16	no	—
972	C₂×C₄	—	2	4	no	—
973	C₂×C₄	—	2	8	no	—
974	C₂×C₄	—	2	32	no	—
975	C₂×C₄	—	2	32	no	—
976	C₂×C₄	—	2	8	no	—
977	C₂×C₄	—	2	32	no	—
978	C₂×C₄	—	2	32	no	—
979	C₂×C₄	—	2	64	no	—
980	C₂×C₄	—	2	16	no	—
981	C₂×C₄	—	4	32	no	—
982	C₂×C₄	—	4	32	no	—
983	C₂×C₄	—	4	32	no	—
984	C₂×C₄	—	4	64	no	—
985	C₂×C₄	—	4	16	no	—
986	C₂×C₄	—	4	32	no	—
987	C₂×C₄	—	4	32	no	—
988	C₂×C₄	—	4	16	no	—
989	C₂×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
990	C₂×C₄	#585	1	8	yes	—
991	C₂×C₄	C₂⁶	1	8	yes	—
992	C₂×C₄	C₂⁶	1	4	yes	—
993	C₂×C₄	C₂⁶	1	2	yes	—
994	C₂×C₄	C₂⁶	1	16	yes	—
995	C₂×C₄	C₂⁶	1	8	yes	—
996	C₂×C₄	C₂⁶	1	8	yes	—
997	C₂×C₄	C₂⁶	1	4	yes	—
998	C₂×C₄	C₂⁶	1	8	yes	—
999	C₂×C₄	C₂⁶	1	16	yes	—
1000	C₂×C₄	C₂⁶	1	8	yes	—
1001	C₂×C₄	C₂⁶	1	2	yes	—
1002	C₂×C₄	C₂⁶	1	4	yes	—
1003	C₂²	—	2	16	no	—
1004	C₂²	—	2	8	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	8	no	—
1007	C₂²	—	2	8	no	—
1008	C₂²	—	2	16	no	—
1009	C₂²	—	2	8	no	—
1010	C₂²	—	2	16	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	8	no	—
1013	C₂²	—	2	16	no	—
1014	C₂²	—	2	16	no	—
1015	C₂²	—	4	4	no	—
1016	C₂²	—	4	16	no	—
1017	C₂²	—	4	32	no	—
1018	C₂²	—	4	16	no	—
1019	C₂²	—	8	64	no	—
1020	C₂²	—	16	32	no	—
1021	C₂²	C₂²×H(5,𝔽₂)	1	8	yes	—
1022	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
1023	C₂²	C₂×#585	1	4	yes	—
1024	C₂²	C₂⁷	1	1	yes	characteristic
1025	C₄	—	2	8	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	8	no	—
1028	C₄	—	2	16	no	—
1029	C₄	—	2	4	no	—
1030	C₄	—	2	8	no	—
1031	C₄	—	2	8	no	—
1032	C₄	—	2	16	no	—
1033	C₄	—	2	4	no	—
1034	C₄	—	2	8	no	—
1035	C₄	C₂²×H(5,𝔽₂)	1	4	yes	—
1036	C₄	C₂×#585	1	8	yes	—
1037	C₂	—	2	8	no	—
1038	C₂	—	4	2	no	—
1039	C₂	—	4	8	no	—
1040	C₂	—	4	16	no	—
1041	C₂	—	4	8	no	—
1042	C₂	#63024	1	4	yes	direct product factor
1043	C₂	C₂³×H(5,𝔽₂)	1	1	yes	characteristic
1044	C₂	C₂²×#585	1	2	yes	—

	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. #63024	C₂	direct (N × H)
2. C₂×#3500	C₂	semidirect
3. C₂×#3499	C₂	semidirect
4. C₂×#3511	C₂	semidirect
5. C₂×#3494	C₂	semidirect
6. C₂×#3514	C₂	semidirect
7. C₂×#3519	C₂	semidirect
8. C₂×#3496	C₂	semidirect
9. C₂×#3549	C₂	semidirect
10. C₂×#3545	C₂	semidirect
11. C₂×#3547	C₂	semidirect
12. C₂×#3544	C₂	semidirect
13. C₂×#3551	C₂	semidirect
14. C₂×#3542	C₂	semidirect
15. C₂×#3483	C₂	semidirect
16. C₂×#3481	C₂	semidirect
17. C₂×#3475	C₂	semidirect
18. C₂²×#555	C₂	semidirect
19. C₂²×2₋¹⁺⁴	C₂²	semidirect
20. C₂²×H(5,𝔽₂)	C₂²	semidirect
21. #3551	C₂²	semidirect
22. #3549	C₂²	semidirect
23. #3547	C₂²	semidirect
24. #3545	C₂²	semidirect
25. #3544	C₂²	semidirect
26. #3542	C₂²	semidirect
27. C₂×#563	C₂²	semidirect
28. C₂×#562	C₂²	semidirect
29. C₂×H(3,𝔽₄)	C₂²	semidirect
30. C₂×#560	C₂²	semidirect
31. #3519	C₂²	semidirect
32. #3514	C₂²	semidirect
33. #3511	C₂²	semidirect
34. #3500	C₂²	semidirect
35. #3499	C₂²	semidirect
36. #3496	C₂²	semidirect
37. #3494	C₂²	semidirect
38. #3483	C₂²	semidirect
39. #3481	C₂²	semidirect
40. C₂×#559	C₂²	semidirect
41. C₂×Q₈²	C₂²	semidirect
42. #3475	C₂²	semidirect
43. C₂×#556	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×#555	C₂²	semidirect
50. C₂×#555	C₂²	semidirect
51. C₂×#555	C₂²	semidirect
52. C₂×#555	C₂²	semidirect
53. C₂×#555	C₂²	semidirect
54. C₂×#554	C₂²	semidirect
55. C₂×#554	C₂²	semidirect
56. C₂×#554	C₂²	semidirect
57. C₂×#553	C₂²	semidirect
58. C₂×#553	C₂²	semidirect
59. C₂×#553	C₂²	semidirect
60. C₂×#553	C₂²	semidirect
61. C₂×#553	C₂²	semidirect
62. C₂×#552	C₂²	semidirect
63. C₂×#552	C₂²	semidirect
64. C₂×#551	C₂²	semidirect
65. C₂×#551	C₂²	semidirect
66. C₂×#551	C₂²	semidirect
67. C₂×#551	C₂²	semidirect
68. C₂×#550	C₂²	semidirect
69. C₂×#550	C₂²	semidirect
70. C₂×D₄×Q₈	C₂²	semidirect
71. C₂×#548	C₂²	semidirect
72. C₂×#548	C₂²	semidirect
73. C₂×#547	C₂²	semidirect
74. C₂×#547	C₂²	semidirect
75. C₂×#547	C₂²	semidirect
76. C₂×#547	C₂²	semidirect
77. C₂×#546	C₂²	semidirect
78. C₂×#546	C₂²	semidirect
79. C₂×#546	C₂²	semidirect
80. C₂×#546	C₂²	semidirect
81. C₂×#546	C₂²	semidirect
82. C₂×#546	C₂²	semidirect
83. C₂×#546	C₂²	semidirect
84. C₂×#546	C₂²	semidirect
86. C₂×D₄²	C₂²	semidirect
87. C₂×D₄²	C₂²	semidirect
88. C₂×D₄²	C₂²	semidirect
89. C₂×#544	C₂²	semidirect
90. C₂×#542	C₂²	semidirect
91. C₂×#542	C₂²	semidirect
92. C₂×#542	C₂²	semidirect
93. C₂×#540	C₂²	semidirect
94. C₂×#540	C₂²	semidirect
95. C₂×#538	C₂²	semidirect
96. C₂×#538	C₂²	semidirect
97. C₂×#537	C₂²	semidirect
98. C₂×#537	C₂²	semidirect
99. C₂×#536	C₂²	semidirect
100. C₂×#536	C₂²	semidirect
101. C₂×#536	C₂²	semidirect
102. C₂×#536	C₂²	semidirect
103. C₂×#535	C₂²	semidirect
104. C₂×#535	C₂²	semidirect
105. C₂×#535	C₂²	semidirect
106. C₂×#534	C₂²	semidirect
107. C₂×#533	C₂²	semidirect
108. C₂×#532	C₂²	semidirect
109. C₂×#532	C₂²	semidirect
110. C₂×#532	C₂²	semidirect
111. C₂×#532	C₂²	semidirect
112. C₂×#532	C₂²	semidirect
113. C₂×#532	C₂²	semidirect
114. C₂×#532	C₂²	semidirect
115. C₂²×C₄⋊Q₈	C₂²	semidirect
116. C₂²×C₄⋊Q₈	C₂²	semidirect
117. C₂×#529	C₂²	semidirect
118. C₂×#529	C₂²	semidirect
119. C₂×#529	C₂²	semidirect
120. C₂×#529	C₂²	semidirect
121. C₂²×#124	C₂²	semidirect
122. C₂²×#124	C₂²	semidirect
123. C₂×#525	C₂²	semidirect
124. C₂×#525	C₂²	semidirect
125. C₂²×#121	C₂²	semidirect
126. C₂²×#121	C₂²	semidirect
127. C₂×#520	C₂²	semidirect
128. C₂×#518	C₂²	semidirect
129. C₂×C₄×#41	C₂²	semidirect
130. C₂×C₄×#41	C₂²	semidirect
131. C₂×C₄×#41	C₂²	semidirect
132. C₂×C₄×#41	C₂²	semidirect
133. C₂²×C₄×D₄	C₂²	semidirect
134. C₂²×C₄×D₄	C₂²	semidirect
135. C₂²×#117	C₂²	semidirect
137. C₂×2₋¹⁺⁴	C₂³	semidirect
139. C₂×H(5,𝔽₂)	C₂³	semidirect
161. #563	C₂³	semidirect
162. #562	C₂³	semidirect
163. H(3,𝔽₄)	C₂³	semidirect
164. #560	C₂³	semidirect
165. #559	C₂³	semidirect
166. Q₈²	C₂³	semidirect
167. #556	C₂³	semidirect
168. #555	C₂³	semidirect
169. #555	C₂³	semidirect
170. #555	C₂³	semidirect
171. #555	C₂³	semidirect
172. #555	C₂³	semidirect
173. #555	C₂³	semidirect
174. #555	C₂³	semidirect
175. #555	C₂³	semidirect
176. #555	C₂³	semidirect
177. #554	C₂³	semidirect
178. #554	C₂³	semidirect
179. #554	C₂³	semidirect
180. #553	C₂³	semidirect
181. #553	C₂³	semidirect
182. #553	C₂³	semidirect
183. #553	C₂³	semidirect
184. #553	C₂³	semidirect
185. #552	C₂³	semidirect
186. #552	C₂³	semidirect
187. #551	C₂³	semidirect
188. #551	C₂³	semidirect
189. #551	C₂³	semidirect
190. #551	C₂³	semidirect
191. #550	C₂³	semidirect
192. #550	C₂³	semidirect
193. D₄×Q₈	C₂³	semidirect
194. #548	C₂³	semidirect
195. #548	C₂³	semidirect
196. #547	C₂³	semidirect
197. #547	C₂³	semidirect
198. #547	C₂³	semidirect
199. #547	C₂³	semidirect
200. #546	C₂³	semidirect
201. #546	C₂³	semidirect
202. #546	C₂³	semidirect
203. #546	C₂³	semidirect
204. #546	C₂³	semidirect
205. #546	C₂³	semidirect
206. #546	C₂³	semidirect
207. #546	C₂³	semidirect
209. D₄²	C₂³	semidirect
210. D₄²	C₂³	semidirect
211. D₄²	C₂³	semidirect
212. #544	C₂³	semidirect
213. #542	C₂³	semidirect
214. #542	C₂³	semidirect
215. #542	C₂³	semidirect
216. #540	C₂³	semidirect
217. #540	C₂³	semidirect
218. #538	C₂³	semidirect
219. #538	C₂³	semidirect
220. #537	C₂³	semidirect
221. #537	C₂³	semidirect
222. #536	C₂³	semidirect
223. #536	C₂³	semidirect
224. #536	C₂³	semidirect
225. #536	C₂³	semidirect
226. #535	C₂³	semidirect
227. #535	C₂³	semidirect
228. #535	C₂³	semidirect
229. #534	C₂³	semidirect
230. #533	C₂³	semidirect
231. #532	C₂³	semidirect
232. #532	C₂³	semidirect
233. #532	C₂³	semidirect
234. #532	C₂³	semidirect
235. #532	C₂³	semidirect
236. #532	C₂³	semidirect
237. #532	C₂³	semidirect
248. C₂×C₄⋊Q₈	C₂³	semidirect
249. C₂×C₄⋊Q₈	C₂³	semidirect
255. #529	C₂³	semidirect
256. #529	C₂³	semidirect
257. #529	C₂³	semidirect
258. #529	C₂³	semidirect
284. C₂×#124	C₂³	semidirect
285. C₂×#124	C₂³	semidirect
286. #525	C₂³	semidirect
287. #525	C₂³	semidirect
338. C₂×#121	C₂³	semidirect
339. C₂×#121	C₂³	semidirect
347. #520	C₂³	semidirect
348. #518	C₂³	semidirect
349. C₄×#41	C₂³	semidirect
350. C₄×#41	C₂³	semidirect
351. C₄×#41	C₂³	semidirect
352. C₄×#41	C₂³	semidirect
386. C₂×C₄×D₄	C₂³	semidirect
387. C₂×C₄×D₄	C₂³	semidirect
402. C₂×#117	C₂³	semidirect
1042. C₂	#63024	direct (N × H)

Maximal subgroups

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

subgroup	index
#63024	2
C₂×#3500	2
C₂×#3499	2
C₂×#3511	2
C₂×#3494	2
C₂×#3514	2
C₂×#3519	2
C₂×#3496	2
C₂×#3549	2
C₂×#3545	2
C₂×#3547	2
C₂×#3544	2
C₂×#3551	2
C₂×#3542	2
C₂×#3483	2
C₂×#3481	2
C₂×#3475	2
C₂²×#555	2

Subgroups — C2×#63024 #10586344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63024 #10586344