Subgroups — #62912

Order 256.

4039 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	#3558	C₂	1	4	yes	maximal, complemented
2	#3549	C₂	1	2	yes	maximal, complemented
3	#3546	C₂	1	2	yes	maximal, complemented
4	#3546	C₂	1	2	yes	maximal, complemented
5	#3543	C₂	1	4	yes	maximal, complemented
6	#3543	C₂	1	2	yes	maximal, complemented
7	#3542	C₂	1	4	yes	maximal, complemented
8	#3542	C₂	1	4	yes	maximal, complemented
9	#3537	C₂	1	4	yes	maximal, complemented
10	#3532	C₂	1	8	yes	maximal, complemented
11	#3519	C₂	1	2	yes	maximal, complemented
12	#3514	C₂	1	2	yes	maximal, complemented
13	#3508	C₂	1	1	yes	maximal, characteristic, complemented
14	#3506	C₂	1	1	yes	maximal, characteristic, complemented
15	#3498	C₂	1	1	yes	maximal, characteristic, complemented
16	#3498	C₂	1	2	yes	maximal, complemented
17	#3496	C₂	1	2	yes	maximal, complemented
18	#3494	C₂	1	2	yes	maximal, complemented
19	#3488	C₂	1	2	yes	maximal, complemented
20	#3484	C₂	1	2	yes	maximal, complemented
21	#3484	C₂	1	4	yes	maximal, complemented
22	#3475	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
25	#3460	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#535	C₂	1	2	yes	maximal, complemented
27	C₂×H(5,𝔽₂)	C₂²	1	2	yes	complemented
28	C₂×H(5,𝔽₂)	C₂²	1	4	yes	complemented
29	C₂²×#41	C₂²	1	2	yes	complemented
30	C₂³×D₄	C₂²	1	2	yes	complemented
31	C₂³×D₄	C₂²	1	2	yes	complemented
32	#562	C₂²	1	8	yes	complemented
33	H(3,𝔽₄)	C₂²	1	8	yes	complemented
34	#560	C₂²	1	8	yes	complemented
35	#560	C₂²	1	8	yes	complemented
36	#560	C₂²	1	8	yes	complemented
37	#560	C₂²	1	8	yes	complemented
38	#559	C₂²	1	4	yes	complemented
39	#559	C₂²	1	2	yes	complemented
40	#559	C₂²	1	2	yes	complemented
41	#556	C₂²	1	1	yes	characteristic, complemented
42	#556	C₂²	1	2	yes	complemented
43	#555	C₂²	1	1	yes	characteristic, complemented
44	#555	C₂²	1	2	yes	complemented
45	#555	C₂²	1	4	yes	complemented
46	#555	C₂²	1	4	yes	complemented
47	#554	C₂²	1	1	yes	characteristic, complemented
48	#553	C₂²	1	2	yes	complemented
49	#553	C₂²	1	4	yes	complemented
50	#553	C₂²	1	4	yes	complemented
51	#553	C₂²	1	4	yes	complemented
52	#553	C₂²	1	4	yes	complemented
53	#552	C₂²	1	2	yes	complemented
54	#552	C₂²	1	2	yes	complemented
55	#551	C₂²	1	4	yes	complemented
56	#551	C₂²	1	8	yes	complemented
57	#551	C₂²	1	8	yes	complemented
58	#550	C₂²	1	1	yes	characteristic, complemented
59	#550	C₂²	1	2	yes	complemented
60	#550	C₂²	1	4	yes	complemented
61	#550	C₂²	1	4	yes	complemented
62	#550	C₂²	1	2	yes	complemented
63	#550	C₂²	1	2	yes	complemented
64	#550	C₂²	1	2	yes	complemented
65	#550	C₂²	1	2	yes	complemented
66	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
67	#548	C₂²	1	2	yes	complemented
68	#548	C₂²	1	4	yes	complemented
69	#547	C₂²	1	2	yes	complemented
70	#547	C₂²	1	1	yes	characteristic, complemented
71	#547	C₂²	1	2	yes	complemented
72	#547	C₂²	1	1	yes	characteristic, complemented
73	#547	C₂²	1	4	yes	complemented
74	#546	C₂²	1	2	yes	complemented
75	#546	C₂²	1	8	yes	complemented
76	#546	C₂²	1	4	yes	complemented
77	#546	C₂²	1	4	yes	complemented
78	#546	C₂²	1	4	yes	complemented
79	#546	C₂²	1	8	yes	complemented
80	#546	C₂²	1	2	yes	complemented
81	#546	C₂²	1	4	yes	complemented
82	#546	C₂²	1	8	yes	complemented
83	#546	C₂²	1	8	yes	complemented
84	#546	C₂²	1	8	yes	complemented
85	#546	C₂²	1	4	yes	complemented
86	#546	C₂²	1	4	yes	complemented
87	#546	C₂²	1	4	yes	complemented
88	#546	C₂²	1	4	yes	complemented
89	#546	C₂²	1	4	yes	complemented
90	#546	C₂²	1	4	yes	complemented
91	#546	C₂²	1	4	yes	complemented
92	D₄²	C₂²	1	2	yes	complemented
93	D₄²	C₂²	1	2	yes	complemented
94	D₄²	C₂²	1	4	yes	complemented
95	D₄²	C₂²	1	2	yes	complemented
96	D₄²	C₂²	1	4	yes	complemented
97	D₄²	C₂²	1	2	yes	complemented
98	D₄²	C₂²	1	2	yes	complemented
99	D₄²	C₂²	1	8	yes	complemented
100	D₄²	C₂²	1	4	yes	complemented
101	D₄²	C₂²	1	4	yes	complemented
102	D₄²	C₂²	1	1	yes	characteristic, complemented
103	D₄²	C₂²	1	4	yes	complemented
104	D₄²	C₂²	1	8	yes	complemented
105	D₄²	C₂²	1	8	yes	complemented
106	D₄²	C₂²	1	4	yes	complemented
107	D₄²	C₂²	1	4	yes	complemented
108	D₄²	C₂²	1	4	yes	complemented
109	D₄²	C₂²	1	4	yes	complemented
110	D₄²	C₂²	1	4	yes	complemented
111	D₄²	C₂²	1	4	yes	complemented
112	D₄²	C₂²	1	2	yes	complemented
113	D₄²	C₂²	1	2	yes	complemented
114	#544	C₂²	1	1	yes	characteristic, complemented
115	#542	C₂²	1	2	yes	complemented
116	#542	C₂²	1	2	yes	complemented
117	#542	C₂²	1	4	yes	complemented
118	#542	C₂²	1	4	yes	complemented
119	#540	C₂²	1	2	yes	complemented
120	#540	C₂²	1	2	yes	complemented
121	#540	C₂²	1	4	yes	complemented
122	#540	C₂²	1	4	yes	complemented
123	#540	C₂²	1	8	yes	complemented
124	#540	C₂²	1	4	yes	complemented
125	#538	C₂²	1	4	yes	complemented
126	#538	C₂²	1	4	yes	complemented
127	#538	C₂²	1	8	yes	complemented
128	#538	C₂²	1	8	yes	complemented
129	#538	C₂²	1	8	yes	complemented
130	#538	C₂²	1	8	yes	complemented
131	#538	C₂²	1	8	yes	complemented
132	#537	C₂²	1	1	yes	characteristic, complemented
133	#537	C₂²	1	4	yes	complemented
134	#537	C₂²	1	4	yes	complemented
135	#535	C₂²	1	1	yes	characteristic, complemented
136	#535	C₂²	1	2	yes	complemented
137	#535	C₂²	1	1	yes	characteristic, complemented
138	#535	C₂²	1	2	yes	complemented
139	#535	C₂²	1	2	yes	complemented
140	#535	C₂²	1	8	yes	complemented
141	#535	C₂²	1	8	yes	complemented
142	#535	C₂²	1	8	yes	complemented
143	#535	C₂²	1	4	yes	complemented
144	#535	C₂²	1	4	yes	complemented
145	#535	C₂²	1	4	yes	complemented
146	#535	C₂²	1	4	yes	complemented
147	#535	C₂²	1	4	yes	complemented
148	#535	C₂²	1	4	yes	complemented
149	#535	C₂²	1	4	yes	complemented
150	#535	C₂²	1	4	yes	complemented
151	#535	C₂²	1	4	yes	complemented
152	#534	C₂²	1	8	yes	complemented
153	#534	C₂²	1	8	yes	complemented
154	#534	C₂²	1	8	yes	complemented
155	#534	C₂²	1	8	yes	complemented
156	#534	C₂²	1	8	yes	complemented
157	#533	C₂²	1	1	yes	characteristic, complemented
158	#532	C₂²	1	1	yes	characteristic, complemented
159	#532	C₂²	1	2	yes	complemented
160	#532	C₂²	1	2	yes	complemented
161	#532	C₂²	1	2	yes	complemented
162	#532	C₂²	1	4	yes	complemented
163	#532	C₂²	1	2	yes	complemented
164	#532	C₂²	1	2	yes	complemented
165	#532	C₂²	1	2	yes	complemented
166	C₂×#127	C₂²	1	1	yes	characteristic, complemented
167	C₂×#127	C₂²	1	4	yes	complemented
168	C₂×#127	C₂²	1	2	yes	complemented
169	#529	C₂²	1	4	yes	complemented
170	#529	C₂²	1	2	yes	complemented
171	#529	C₂²	1	2	yes	complemented
172	#529	C₂²	1	2	yes	complemented
173	#529	C₂²	1	4	yes	complemented
174	C₂×#124	C₂²	1	4	yes	complemented
175	#525	C₂²	1	2	yes	complemented
176	#525	C₂²	1	2	yes	complemented
177	#525	C₂²	1	4	yes	complemented
178	#525	C₂²	1	4	yes	complemented
179	#525	C₂²	1	4	yes	complemented
180	#525	C₂²	1	4	yes	complemented
181	C₂×#121	C₂²	1	2	yes	complemented
182	C₂×#121	C₂²	1	2	yes	complemented
183	C₂×#121	C₂²	1	4	yes	complemented
184	C₂×#121	C₂²	1	4	yes	complemented
185	C₂×#121	C₂²	1	4	yes	complemented
186	C₂×#120	C₂²	1	4	yes	complemented
187	C₂×#120	C₂²	1	8	yes	complemented
188	C₂×#120	C₂²	1	8	yes	complemented
189	#520	C₂²	1	2	yes	complemented
190	#518	C₂²	1	2	yes	complemented
191	#518	C₂²	1	4	yes	complemented
192	C₄×#41	C₂²	1	1	yes	characteristic, complemented
193	C₄×#41	C₂²	1	1	yes	characteristic, complemented
194	C₄×#41	C₂²	1	2	yes	complemented
195	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
197	C₂×C₄×D₄	C₂²	1	2	yes	complemented
198	C₂×#117	C₂²	1	2	yes	complemented
199	C₂⁵	C₂³	1	4	yes	—
200	H(5,𝔽₂)	—	4	16	no	—
201	H(5,𝔽₂)	—	4	8	no	—
202	C₂×#41	—	4	8	no	—
203	C₂×#41	C₂³	1	1	yes	characteristic
204	C₂×#41	C₂³	1	1	yes	characteristic
205	C₂×#41	C₂³	1	2	yes	—
206	C₂×#41	C₂³	1	2	yes	—
207	C₂×#41	C₂³	1	4	yes	—
208	C₂×#41	C₂³	1	4	yes	complemented
209	C₂×#41	C₂³	1	4	yes	complemented
210	C₂×#41	C₂³	1	4	yes	complemented
211	C₂×#41	C₂³	1	4	yes	complemented
212	C₂×#41	C₂³	1	8	yes	complemented
213	C₂×#41	C₂³	1	4	yes	complemented
214	C₂×#41	C₂³	1	4	yes	complemented
215	C₂×#41	C₂³	1	2	yes	complemented
216	C₂×#41	C₂³	1	2	yes	complemented
217	C₂×#41	C₂³	1	4	yes	complemented
218	C₂²×Q₈	C₂³	1	2	yes	complemented
219	C₂²×D₄	—	4	8	no	—
220	C₂²×D₄	—	4	8	no	—
221	C₂²×D₄	C₂³	1	1	yes	characteristic
222	C₂²×D₄	C₂³	1	2	yes	—
223	C₂²×D₄	C₂³	1	1	yes	characteristic
224	C₂²×D₄	C₂³	1	2	yes	—
225	C₂²×D₄	C₂³	1	4	yes	—
226	C₂²×D₄	C₂³	1	4	yes	—
227	C₂²×D₄	C₂³	1	4	yes	—
228	C₂²×D₄	C₂³	1	4	yes	—
229	C₂²×D₄	C₂³	1	8	yes	—
230	C₂²×D₄	C₂³	1	4	yes	—
231	C₂²×D₄	C₂³	1	2	yes	—
232	C₂²×D₄	C₂³	1	4	yes	—
233	C₂²×D₄	C₂³	1	8	yes	—
234	C₂²×D₄	C₂³	1	4	yes	—
235	C₂²×D₄	C₂³	1	4	yes	—
236	C₂²×D₄	C₂³	1	4	yes	—
237	C₂²×D₄	C₂³	1	2	yes	—
238	C₂²×D₄	C₂³	1	8	yes	complemented
239	C₂²×D₄	C₂³	1	8	yes	complemented
240	C₂²×D₄	C₂³	1	8	yes	complemented
241	C₂²×D₄	C₂³	1	4	yes	complemented
242	C₂²×D₄	C₂³	1	2	yes	complemented
243	C₂²×D₄	C₂³	1	4	yes	complemented
244	C₂²×D₄	C₂³	1	4	yes	complemented
245	C₂²×D₄	C₂³	1	8	yes	complemented
246	C₂²×D₄	C₂³	1	8	yes	complemented
247	C₂²×D₄	C₂³	1	4	yes	complemented
248	C₂³×C₄	C₂³	1	2	yes	—
249	C₂³×C₄	C₂³	1	2	yes	—
250	C₂³×C₄	C₂³	1	4	yes	complemented
251	C₄⋊Q₈	C₂³	1	2	yes	complemented
252	C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
253	C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
254	C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
255	C₄⋊Q₈	C₂³	1	2	yes	complemented
256	C₄⋊Q₈	C₂³	1	2	yes	complemented
257	#127	C₂³	1	2	yes	—
258	#127	C₂³	1	2	yes	—
259	#127	C₂³	1	2	yes	—
260	#127	C₂³	1	2	yes	—
261	#127	C₂³	1	4	yes	—
262	#127	C₂³	1	2	yes	—
263	#127	C₂³	1	2	yes	—
264	#127	C₂³	1	2	yes	—
265	#127	C₂³	1	4	yes	complemented
266	#127	C₂³	1	1	yes	characteristic, complemented
267	#127	C₂³	1	8	yes	complemented
268	#127	C₂³	1	4	yes	complemented
269	#127	C₂³	1	8	yes	complemented
270	#127	C₂³	1	4	yes	complemented
271	#127	C₂³	1	4	yes	complemented
272	#127	C₂³	1	8	yes	complemented
273	#126	C₂³	1	4	yes	complemented
274	#126	C₂³	1	4	yes	complemented
275	#126	C₂³	1	4	yes	complemented
276	#126	C₂³	1	4	yes	complemented
277	#126	C₂³	1	4	yes	complemented
278	#126	C₂³	1	8	yes	complemented
279	#126	C₂³	1	8	yes	complemented
280	#126	C₂³	1	8	yes	complemented
281	#125	C₂³	1	2	yes	complemented
282	#125	C₂³	1	4	yes	complemented
283	#125	C₂³	1	2	yes	complemented
284	#125	C₂³	1	2	yes	complemented
285	#125	C₂³	1	2	yes	complemented
286	#124	C₂³	1	2	yes	—
287	#124	C₂³	1	4	yes	—
288	#124	C₂³	1	2	yes	—
289	#124	C₂³	1	2	yes	—
290	#124	C₂³	1	4	yes	complemented
291	#124	C₂³	1	8	yes	complemented
292	#124	C₂³	1	4	yes	complemented
293	#124	C₂³	1	8	yes	complemented
294	#124	C₂³	1	4	yes	complemented
295	#124	C₂³	1	4	yes	complemented
296	#124	C₂³	1	2	yes	complemented
297	#124	C₂³	1	8	yes	complemented
298	#124	C₂³	1	4	yes	complemented
299	#124	C₂³	1	4	yes	complemented
300	#124	C₂³	1	4	yes	complemented
301	#124	C₂³	1	4	yes	complemented
302	#124	C₂³	1	8	yes	complemented
303	#124	C₂³	1	8	yes	complemented
304	#124	C₂³	1	8	yes	complemented
305	#123	C₂³	1	4	yes	—
306	#123	C₂³	1	4	yes	—
307	#123	C₂³	1	4	yes	—
308	#123	C₂³	1	4	yes	complemented
309	#123	C₂³	1	4	yes	complemented
310	#123	C₂³	1	8	yes	complemented
311	#123	C₂³	1	4	yes	complemented
312	#123	C₂³	1	8	yes	complemented
313	#123	C₂³	1	4	yes	complemented
314	#123	C₂³	1	4	yes	complemented
315	#123	C₂³	1	4	yes	complemented
316	#123	C₂³	1	8	yes	complemented
317	#123	C₂³	1	4	yes	complemented
318	#123	C₂³	1	4	yes	complemented
319	#123	C₂³	1	8	yes	complemented
320	#123	C₂³	1	8	yes	complemented
321	#123	C₂³	1	8	yes	complemented
322	#123	C₂³	1	8	yes	complemented
323	#123	C₂³	1	8	yes	complemented
324	#123	C₂³	1	8	yes	complemented
325	#123	C₂³	1	8	yes	complemented
326	#123	C₂³	1	8	yes	complemented
327	C₂²⋊Q₈	C₂³	1	2	yes	—
328	C₂²⋊Q₈	C₂³	1	4	yes	—
329	C₂²⋊Q₈	C₂³	1	2	yes	—
330	C₂²⋊Q₈	C₂³	1	2	yes	complemented
331	C₂²⋊Q₈	C₂³	1	2	yes	complemented
332	C₂²⋊Q₈	C₂³	1	2	yes	complemented
333	C₂²⋊Q₈	C₂³	1	2	yes	complemented
334	C₂²⋊Q₈	C₂³	1	4	yes	complemented
335	C₂²⋊Q₈	C₂³	1	4	yes	complemented
336	C₂²⋊Q₈	C₂³	1	4	yes	complemented
337	C₂²⋊Q₈	C₂³	1	2	yes	complemented
338	C₂²⋊Q₈	C₂³	1	4	yes	complemented
339	C₂²⋊Q₈	C₂³	1	2	yes	complemented
340	C₂²⋊Q₈	C₂³	1	2	yes	complemented
341	C₂²⋊Q₈	C₂³	1	4	yes	complemented
342	C₂²⋊Q₈	C₂³	1	8	yes	complemented
343	C₂²⋊Q₈	C₂³	1	8	yes	complemented
344	#121	C₂³	1	4	yes	—
345	#121	C₂³	1	2	yes	—
346	#121	C₂³	1	2	yes	—
347	#121	C₂³	1	4	yes	—
348	#121	C₂³	1	4	yes	—
349	#121	C₂³	1	4	yes	—
350	#121	C₂³	1	4	yes	—
351	#121	C₂³	1	4	yes	—
352	#121	C₂³	1	4	yes	—
353	#121	C₂³	1	8	yes	—
354	#121	C₂³	1	4	yes	—
355	#121	C₂³	1	2	yes	—
356	#121	C₂³	1	4	yes	—
357	#121	C₂³	1	4	yes	—
358	#121	C₂³	1	4	yes	—
359	#121	C₂³	1	2	yes	—
360	#121	C₂³	1	2	yes	—
361	#121	C₂³	1	2	yes	—
362	#121	C₂³	1	2	yes	—
363	#121	C₂³	1	2	yes	—
364	#121	C₂³	1	2	yes	complemented
365	#121	C₂³	1	4	yes	complemented
366	#121	C₂³	1	2	yes	complemented
367	#121	C₂³	1	4	yes	complemented
368	#121	C₂³	1	8	yes	complemented
369	#121	C₂³	1	8	yes	complemented
370	#121	C₂³	1	8	yes	complemented
371	#121	C₂³	1	8	yes	complemented
372	#121	C₂³	1	4	yes	complemented
373	#121	C₂³	1	4	yes	complemented
374	#121	C₂³	1	8	yes	complemented
375	#121	C₂³	1	8	yes	complemented
376	#121	C₂³	1	2	yes	complemented
377	#121	C₂³	1	4	yes	complemented
378	#121	C₂³	1	2	yes	complemented
379	#121	C₂³	1	4	yes	complemented
380	#121	C₂³	1	2	yes	complemented
381	#121	C₂³	1	4	yes	complemented
382	#121	C₂³	1	4	yes	complemented
383	#121	C₂³	1	4	yes	complemented
384	#121	C₂³	1	8	yes	complemented
385	#121	C₂³	1	4	yes	complemented
386	#121	C₂³	1	2	yes	complemented
387	#121	C₂³	1	4	yes	complemented
388	#121	C₂³	1	4	yes	complemented
389	#121	C₂³	1	2	yes	complemented
390	#121	C₂³	1	4	yes	complemented
391	#121	C₂³	1	4	yes	complemented
392	#121	C₂³	1	8	yes	complemented
393	#121	C₂³	1	8	yes	complemented
394	#121	C₂³	1	8	yes	complemented
395	#121	C₂³	1	8	yes	complemented
396	#121	C₂³	1	8	yes	complemented
397	#121	C₂³	1	8	yes	complemented
398	#121	C₂³	1	8	yes	complemented
399	#121	C₂³	1	8	yes	complemented
400	#121	C₂³	1	8	yes	complemented
401	#121	C₂³	1	8	yes	complemented
402	#121	C₂³	1	8	yes	complemented
403	#121	C₂³	1	8	yes	complemented
404	#121	C₂³	1	8	yes	complemented
405	#121	C₂³	1	8	yes	complemented
406	#120	C₂³	1	4	yes	—
407	#120	C₂³	1	8	yes	—
408	#120	C₂³	1	4	yes	—
409	#120	C₂³	1	4	yes	—
410	#120	C₂³	1	4	yes	—
411	#120	C₂³	1	8	yes	—
412	#120	C₂³	1	8	yes	—
413	#120	C₂³	1	8	yes	—
414	#120	C₂³	1	8	yes	—
415	#120	C₂³	1	8	yes	—
416	#120	C₂³	1	8	yes	—
417	#120	C₂³	1	4	yes	—
418	#120	C₂³	1	8	yes	complemented
419	#120	C₂³	1	8	yes	complemented
420	#120	C₂³	1	8	yes	complemented
421	#120	C₂³	1	8	yes	complemented
422	#120	C₂³	1	8	yes	complemented
423	#120	C₂³	1	8	yes	complemented
424	#120	C₂³	1	8	yes	complemented
425	#120	C₂³	1	8	yes	complemented
426	#120	C₂³	1	8	yes	complemented
427	#120	C₂³	1	4	yes	complemented
428	#120	C₂³	1	8	yes	complemented
429	#120	C₂³	1	8	yes	complemented
430	#120	C₂³	1	8	yes	complemented
431	#120	C₂³	1	8	yes	complemented
432	#120	C₂³	1	8	yes	complemented
433	#120	C₂³	1	8	yes	complemented
434	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
435	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
436	C₄×Q₈	C₂³	1	2	yes	complemented
437	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
438	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
439	C₄×Q₈	C₂³	1	2	yes	complemented
440	C₄×Q₈	C₂³	1	4	yes	complemented
441	C₄×Q₈	C₂³	1	2	yes	complemented
442	C₄×D₄	C₂³	1	1	yes	characteristic
443	C₄×D₄	C₂³	1	1	yes	characteristic
444	C₄×D₄	C₂³	1	2	yes	—
445	C₄×D₄	C₂³	1	2	yes	—
446	C₄×D₄	C₂³	1	2	yes	—
447	C₄×D₄	C₂³	1	1	yes	characteristic
448	C₄×D₄	C₂³	1	2	yes	—
449	C₄×D₄	C₂³	1	2	yes	—
450	C₄×D₄	C₂³	1	1	yes	characteristic
451	C₄×D₄	C₂³	1	2	yes	—
452	C₄×D₄	C₂³	1	2	yes	—
453	C₄×D₄	C₂³	1	2	yes	—
454	C₄×D₄	C₂³	1	2	yes	—
455	C₄×D₄	C₂³	1	2	yes	—
456	C₄×D₄	C₂³	1	2	yes	—
457	C₄×D₄	C₂³	1	2	yes	—
458	C₄×D₄	C₂³	1	8	yes	—
459	C₄×D₄	C₂³	1	4	yes	complemented
460	C₄×D₄	C₂³	1	2	yes	complemented
461	C₄×D₄	C₂³	1	4	yes	complemented
462	C₄×D₄	C₂³	1	2	yes	complemented
463	C₄×D₄	C₂³	1	4	yes	complemented
464	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
465	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
466	C₄×D₄	C₂³	1	4	yes	complemented
467	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
468	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
469	C₄×D₄	C₂³	1	8	yes	complemented
470	C₄×D₄	C₂³	1	8	yes	complemented
471	C₄×D₄	C₂³	1	4	yes	complemented
472	C₄×D₄	C₂³	1	4	yes	complemented
473	C₄×D₄	C₂³	1	4	yes	complemented
474	C₄×D₄	C₂³	1	4	yes	complemented
475	C₄×D₄	C₂³	1	4	yes	complemented
476	C₄×D₄	C₂³	1	4	yes	complemented
477	C₄×D₄	C₂³	1	4	yes	complemented
478	C₄×D₄	C₂³	1	4	yes	complemented
479	C₄×D₄	C₂³	1	2	yes	complemented
480	C₄×D₄	C₂³	1	4	yes	complemented
481	C₄×D₄	C₂³	1	4	yes	complemented
482	C₄×D₄	C₂³	1	4	yes	complemented
483	C₄×D₄	C₂³	1	8	yes	complemented
484	C₄×D₄	C₂³	1	8	yes	complemented
485	C₄×D₄	C₂³	1	4	yes	complemented
486	C₄×D₄	C₂³	1	8	yes	complemented
487	C₄×D₄	C₂³	1	4	yes	complemented
488	#117	C₂³	1	1	yes	characteristic
489	#117	C₂³	1	2	yes	—
490	#117	C₂³	1	4	yes	—
491	#117	C₂³	1	1	yes	characteristic
492	#117	C₂³	1	4	yes	complemented
493	#117	C₂³	1	2	yes	complemented
494	#117	C₂³	1	2	yes	complemented
495	#117	C₂³	1	2	yes	complemented
496	#117	C₂³	1	2	yes	complemented
497	#117	C₂³	1	4	yes	complemented
498	#117	C₂³	1	2	yes	complemented
499	#117	C₂³	1	4	yes	complemented
500	#117	C₂³	1	4	yes	complemented
501	#117	C₂³	1	4	yes	complemented
502	#117	C₂³	1	8	yes	complemented
503	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³	1	2	yes	complemented
506	C₂×C₄⋊C₄	C₂³	1	2	yes	complemented
507	C₂×C₄⋊C₄	C₂³	1	2	yes	complemented
508	C₂×C₄⋊C₄	C₂³	1	4	yes	complemented
509	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
513	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³	1	4	yes	complemented
515	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
516	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
517	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
518	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
519	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
520	C₂×C₄²	C₂³	1	1	yes	characteristic
521	C₂×C₄²	C₂³	1	4	yes	complemented
522	C₂×C₄²	C₂³	1	2	yes	complemented
523	C₂×C₄²	C₂³	1	2	yes	complemented
524	C₂⁴	—	4	8	no	—
525	C₂⁴	—	4	8	no	—
526	C₂⁴	—	8	4	no	—
527	C₂⁴	C₂⁴	1	2	yes	—
528	C₂⁴	C₂⁴	1	4	yes	—
529	C₂⁴	C₂⁴	1	2	yes	—
530	C₂⁴	C₂⁴	1	8	yes	—
531	C₂⁴	C₂⁴	1	4	yes	—
532	C₂⁴	C₂⁴	1	8	yes	—
533	C₂⁴	C₂⁴	1	8	yes	—
534	#41	—	2	8	no	—
535	#41	—	2	4	no	—
536	#41	—	2	8	no	—
537	#41	—	2	4	no	—
538	#41	—	4	8	no	—
539	#41	—	4	8	no	—
540	#41	—	4	8	no	—
541	#41	—	4	16	no	—
542	#41	—	4	4	no	—
543	#41	—	4	4	no	—
544	#41	—	4	8	no	—
545	#41	—	4	8	no	—
546	#41	—	4	8	no	—
547	#41	—	4	8	no	—
548	#41	—	8	4	no	—
549	C₂×Q₈	—	4	4	no	—
550	C₂×Q₈	C₂⁴	1	2	yes	—
551	C₂×Q₈	C₂⁴	1	1	yes	characteristic
552	C₂×Q₈	C₂⁴	1	1	yes	characteristic
553	C₂×Q₈	C₂⁴	1	2	yes	—
554	C₂×Q₈	C₂⁴	1	2	yes	—
555	C₂×Q₈	C₂⁴	1	4	yes	—
556	C₂×Q₈	C₂⁴	1	4	yes	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	16	no	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	8	no	—
562	C₂×D₄	—	4	8	no	—
563	C₂×D₄	—	4	8	no	—
564	C₂×D₄	—	4	8	no	—
565	C₂×D₄	—	4	8	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	8	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	8	no	—
570	C₂×D₄	—	4	8	no	—
571	C₂×D₄	—	4	8	no	—
572	C₂×D₄	—	4	8	no	—
573	C₂×D₄	—	4	16	no	—
574	C₂×D₄	—	4	16	no	—
575	C₂×D₄	—	4	8	no	—
576	C₂×D₄	—	4	8	no	—
577	C₂×D₄	—	4	16	no	—
578	C₂×D₄	—	4	16	no	—
579	C₂×D₄	—	4	16	no	—
580	C₂×D₄	—	8	2	no	—
581	C₂×D₄	—	8	4	no	—
582	C₂×D₄	—	8	8	no	—
583	C₂×D₄	—	8	8	no	—
584	C₂×D₄	C₂⁴	1	2	yes	—
585	C₂×D₄	C₂⁴	1	4	yes	—
586	C₂×D₄	C₂⁴	1	2	yes	—
587	C₂×D₄	C₂⁴	1	2	yes	—
588	C₂×D₄	C₂⁴	1	2	yes	—
589	C₂×D₄	C₂⁴	1	1	yes	characteristic
590	C₂×D₄	C₂⁴	1	2	yes	—
591	C₂×D₄	C₂⁴	1	8	yes	—
592	C₂×D₄	C₂⁴	1	4	yes	—
593	C₂×D₄	C₂⁴	1	4	yes	—
594	C₂×D₄	C₂⁴	1	4	yes	—
595	C₂×D₄	C₂⁴	1	4	yes	—
596	C₂×D₄	C₂⁴	1	4	yes	—
597	C₂×D₄	C₂⁴	1	2	yes	—
598	C₂×D₄	C₂⁴	1	1	yes	characteristic
599	C₂×D₄	C₂⁴	1	2	yes	—
600	C₂×D₄	C₂⁴	1	1	yes	characteristic
601	C₂×D₄	C₂⁴	1	4	yes	—
602	C₂×D₄	C₂⁴	1	4	yes	—
603	C₂×D₄	C₂⁴	1	4	yes	—
604	C₂×D₄	C₂⁴	1	4	yes	—
605	C₂×D₄	C₂⁴	1	4	yes	—
606	C₂×D₄	C₂⁴	1	8	yes	—
607	C₂×D₄	C₂⁴	1	8	yes	—
608	C₂×D₄	C₂⁴	1	4	yes	—
609	C₂×D₄	C₂⁴	1	8	yes	—
610	C₂×D₄	C₂⁴	1	2	yes	—
611	C₂×D₄	C₂⁴	1	8	yes	—
612	C₂×D₄	C₂⁴	1	8	yes	—
613	C₂×D₄	C₂⁴	1	8	yes	—
614	C₂×D₄	C₂⁴	1	4	yes	—
615	C₂×D₄	C₂⁴	1	4	yes	—
616	C₂×D₄	C₂⁴	1	8	yes	—
617	C₂×D₄	C₂⁴	1	4	yes	—
618	C₂×D₄	C₂⁴	1	8	yes	—
619	C₂×D₄	C₂⁴	1	8	yes	—
620	C₂×D₄	C₂⁴	1	4	yes	—
621	C₂×D₄	C₂⁴	1	8	yes	—
622	C₂×D₄	C₂⁴	1	8	yes	—
623	C₂×D₄	C₂⁴	1	4	yes	—
624	C₂×D₄	C₂⁴	1	4	yes	—
625	C₂×D₄	C₂⁴	1	4	yes	—
626	C₂×D₄	C₂⁴	1	1	yes	characteristic
627	C₂²×C₄	—	2	8	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	—	4	8	no	—
630	C₂²×C₄	C₂⁴	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴	1	2	yes	—
632	C₂²×C₄	C₂⁴	1	4	yes	—
633	C₂²×C₄	C₂⁴	1	2	yes	—
634	C₂²×C₄	C₂⁴	1	2	yes	—
635	C₂²×C₄	C₂⁴	1	2	yes	—
636	C₂²×C₄	C₂⁴	1	2	yes	—
637	C₂²×C₄	C₂⁴	1	2	yes	—
638	C₂²×C₄	C₂⁴	1	2	yes	—
639	C₂²×C₄	C₂⁴	1	4	yes	—
640	C₂²×C₄	C₂⁴	1	2	yes	—
641	C₂²×C₄	C₂⁴	1	2	yes	—
642	C₂²×C₄	C₂⁴	1	4	yes	—
643	C₂²×C₄	C₂⁴	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴	1	4	yes	—
645	C₂²×C₄	C₂⁴	1	2	yes	—
646	C₂²×C₄	C₂⁴	1	2	yes	—
647	C₂²×C₄	C₂⁴	1	2	yes	—
648	C₂²×C₄	C₂⁴	1	8	yes	—
649	C₂²×C₄	C₂⁴	1	8	yes	—
650	C₂²×C₄	C₂⁴	1	4	yes	—
651	C₂²×C₄	C₂⁴	1	8	yes	—
652	C₂²×C₄	C₂⁴	1	4	yes	—
653	C₂²×C₄	C₂⁴	1	8	yes	—
654	C₂²×C₄	C₂⁴	1	4	yes	—
655	C₂²×C₄	C₂⁴	1	4	yes	—
656	C₂²×C₄	C₂⁴	1	1	yes	characteristic
657	C₄⋊C₄	C₂⁴	1	2	yes	—
658	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
659	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
660	C₄⋊C₄	C₂⁴	1	2	yes	—
661	C₄⋊C₄	C₂⁴	1	2	yes	—
662	C₄⋊C₄	C₂⁴	1	2	yes	—
663	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
664	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
665	C₄⋊C₄	C₂⁴	1	2	yes	—
666	C₄⋊C₄	C₂⁴	1	4	yes	—
667	C₄⋊C₄	C₂⁴	1	4	yes	—
668	C₄⋊C₄	C₂⁴	1	2	yes	—
669	C₄⋊C₄	C₂⁴	1	8	yes	—
670	C₄⋊C₄	C₂⁴	1	4	yes	—
671	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
672	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
673	C₄⋊C₄	C₂⁴	1	2	yes	—
674	C₄⋊C₄	C₂⁴	1	4	yes	—
675	C₄⋊C₄	C₂⁴	1	4	yes	—
676	C₄⋊C₄	C₂⁴	1	2	yes	—
677	C₄⋊C₄	C₂⁴	1	2	yes	—
678	C₄⋊C₄	C₂⁴	1	2	yes	—
679	C₄⋊C₄	C₂⁴	1	2	yes	—
680	C₄⋊C₄	C₂⁴	1	4	yes	—
681	C₄⋊C₄	C₂⁴	1	4	yes	—
682	C₄⋊C₄	C₂⁴	1	4	yes	—
683	C₄⋊C₄	C₂⁴	1	4	yes	—
684	C₄⋊C₄	C₂⁴	1	2	yes	—
685	C₄⋊C₄	C₂⁴	1	4	yes	—
686	C₄⋊C₄	C₂⁴	1	4	yes	—
687	C₄⋊C₄	C₂⁴	1	4	yes	—
688	C₄⋊C₄	C₂⁴	1	2	yes	—
689	C₂²⋊C₄	C₂⁴	1	2	yes	—
690	C₂²⋊C₄	C₂⁴	1	4	yes	—
691	C₂²⋊C₄	C₂⁴	1	2	yes	—
692	C₂²⋊C₄	C₂⁴	1	2	yes	—
693	C₂²⋊C₄	C₂⁴	1	8	yes	—
694	C₂²⋊C₄	C₂⁴	1	2	yes	—
695	C₂²⋊C₄	C₂⁴	1	4	yes	—
696	C₂²⋊C₄	C₂⁴	1	4	yes	—
697	C₂²⋊C₄	C₂⁴	1	8	yes	—
698	C₂²⋊C₄	C₂⁴	1	4	yes	—
699	C₂²⋊C₄	C₂⁴	1	2	yes	—
700	C₂²⋊C₄	C₂⁴	1	2	yes	—
701	C₂²⋊C₄	C₂⁴	1	4	yes	—
702	C₂²⋊C₄	C₂⁴	1	8	yes	—
703	C₂²⋊C₄	C₂⁴	1	8	yes	—
704	C₂²⋊C₄	C₂⁴	1	4	yes	—
705	C₂²⋊C₄	C₂⁴	1	4	yes	—
706	C₂²⋊C₄	C₂⁴	1	4	yes	—
707	C₂²⋊C₄	C₂⁴	1	8	yes	—
708	C₂²⋊C₄	C₂⁴	1	4	yes	—
709	C₂²⋊C₄	C₂⁴	1	4	yes	—
710	C₂²⋊C₄	C₂⁴	1	8	yes	—
711	C₂²⋊C₄	C₂⁴	1	4	yes	—
712	C₂²⋊C₄	C₂⁴	1	4	yes	—
713	C₂²⋊C₄	C₂⁴	1	4	yes	—
714	C₂²⋊C₄	C₂⁴	1	8	yes	—
715	C₂²⋊C₄	C₂⁴	1	4	yes	—
716	C₂²⋊C₄	C₂⁴	1	4	yes	—
717	C₂²⋊C₄	C₂⁴	1	8	yes	—
718	C₂²⋊C₄	C₂⁴	1	8	yes	—
719	C₂²⋊C₄	C₂⁴	1	8	yes	—
720	C₂²⋊C₄	C₂⁴	1	4	yes	—
721	C₂²⋊C₄	C₂⁴	1	4	yes	—
722	C₂²⋊C₄	C₂⁴	1	2	yes	—
723	C₂²⋊C₄	C₂⁴	1	2	yes	—
724	C₂²⋊C₄	C₂⁴	1	2	yes	—
725	C₂²⋊C₄	C₂⁴	1	8	yes	—
726	C₂²⋊C₄	C₂⁴	1	2	yes	—
727	C₂²⋊C₄	C₂⁴	1	4	yes	—
728	C₂²⋊C₄	C₂⁴	1	4	yes	—
729	C₂²⋊C₄	C₂⁴	1	4	yes	—
730	C₂²⋊C₄	C₂⁴	1	4	yes	—
731	C₄²	C₂⁴	1	1	yes	characteristic
732	C₄²	C₂⁴	1	1	yes	characteristic
733	C₄²	C₂⁴	1	1	yes	characteristic
734	C₄²	C₂⁴	1	1	yes	characteristic
735	C₄²	C₂⁴	1	2	yes	—
736	C₄²	C₂⁴	1	4	yes	—
737	C₄²	C₂⁴	1	2	yes	—
738	C₄²	C₂⁴	1	4	yes	—
739	C₄²	C₂⁴	1	4	yes	—
740	C₄²	C₂⁴	1	2	yes	—
741	C₄²	C₂⁴	1	2	yes	—
742	C₄²	C₂⁴	1	2	yes	—
743	C₄²	C₂⁴	1	2	yes	—
744	C₄²	C₂⁴	1	8	yes	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	4	no	—
747	C₂³	—	2	4	no	—
748	C₂³	—	2	8	no	—
749	C₂³	—	2	16	no	—
750	C₂³	—	2	8	no	—
751	C₂³	—	4	2	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	4	2	no	—
754	C₂³	—	4	4	no	—
755	C₂³	—	4	8	no	—
756	C₂³	—	4	4	no	—
757	C₂³	—	4	8	no	—
758	C₂³	—	4	8	no	—
759	C₂³	—	4	4	no	—
760	C₂³	—	4	8	no	—
761	C₂³	—	4	4	no	—
762	C₂³	—	4	8	no	—
763	C₂³	—	4	8	no	—
764	C₂³	—	4	8	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	8	32	no	—
767	C₂³	C₂⁵	1	2	yes	—
768	C₂³	C₂⁵	1	4	yes	—
769	C₂³	C₂⁵	1	2	yes	—
770	C₂³	C₂⁵	1	8	yes	—
771	C₂³	C₂⁵	1	4	yes	—
772	C₂³	C₂⁵	1	2	yes	—
773	C₂³	C₂⁵	1	1	yes	characteristic
774	C₂³	C₂⁵	1	2	yes	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	4	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	4	no	—
779	Q₈	—	4	4	no	—
780	Q₈	—	4	4	no	—
781	Q₈	—	4	2	no	—
782	D₄	—	2	4	no	—
783	D₄	—	2	16	no	—
784	D₄	—	2	8	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	8	no	—
787	D₄	—	2	8	no	—
788	D₄	—	2	4	no	—
789	D₄	—	2	4	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	4	no	—
792	D₄	—	2	8	no	—
793	D₄	—	2	8	no	—
794	D₄	—	2	8	no	—
795	D₄	—	2	4	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	4	no	—
798	D₄	—	2	2	no	—
799	D₄	—	4	8	no	—
800	D₄	—	4	8	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	8	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	8	no	—
809	D₄	—	4	8	no	—
810	D₄	—	4	8	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	4	no	—
814	D₄	—	4	4	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	4	no	—
817	D₄	—	4	4	no	—
818	D₄	—	4	8	no	—
819	D₄	—	4	2	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	8	no	—
823	D₄	—	4	4	no	—
824	D₄	H(5,𝔽₂)	1	4	yes	complemented
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	8	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	4	4	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	8	no	—
844	C₂×C₄	—	4	8	no	—
845	C₂×C₄	—	4	8	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	1	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	H(5,𝔽₂)	1	4	yes	complemented
852	C₂×C₄	C₂⁵	1	1	yes	characteristic
853	C₂×C₄	C₂⁵	1	4	yes	—
854	C₂×C₄	C₂⁵	1	1	yes	characteristic
855	C₂×C₄	C₂⁵	1	2	yes	—
856	C₂×C₄	C₂⁵	1	2	yes	—
857	C₂×C₄	C₂⁵	1	2	yes	—
858	C₂×C₄	C₂⁵	1	2	yes	—
859	C₂×C₄	C₂⁵	1	2	yes	—
860	C₂×C₄	C₂⁵	1	2	yes	—
861	C₂×C₄	C₂⁵	1	4	yes	—
862	C₂×C₄	C₂⁵	1	4	yes	—
863	C₂×C₄	C₂⁵	1	4	yes	—
864	C₂×C₄	C₂⁵	1	2	yes	—
865	C₂×C₄	C₂⁵	1	1	yes	characteristic
866	C₂×C₄	C₂⁵	1	2	yes	—
867	C₂×C₄	C₂⁵	1	1	yes	characteristic
868	C₂×C₄	C₂⁵	1	1	yes	characteristic
869	C₂×C₄	C₂⁵	1	1	yes	characteristic
870	C₂²	—	2	2	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	8	no	—
883	C₂²	—	2	8	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	8	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	4	8	no	—
893	C₂²	—	4	8	no	—
894	C₂²	—	8	8	no	—
895	C₂²	—	8	8	no	—
896	C₂²	—	8	16	no	—
897	C₂²	—	8	16	no	—
898	C₂²	—	16	8	no	—
899	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
900	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
901	C₂²	C₂⁶	1	1	yes	characteristic
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	4	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	4	no	—
916	C₄	—	2	1	no	—
917	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
918	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
919	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
920	C₂	—	2	2	no	—
921	C₂	—	2	4	no	—
922	C₂	—	4	2	no	—
923	C₂	—	4	4	no	—
924	C₂	—	4	2	no	—
925	C₂	—	4	8	no	—
926	C₂	—	4	4	no	—
927	C₂	—	4	2	no	—
928	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
929	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
930	C₂	H(7,𝔽₂)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #3558	C₂	semidirect
2. #3549	C₂	semidirect
3. #3546	C₂	semidirect
4. #3546	C₂	semidirect
5. #3543	C₂	semidirect
6. #3543	C₂	semidirect
7. #3542	C₂	semidirect
8. #3542	C₂	semidirect
9. #3537	C₂	semidirect
10. #3532	C₂	semidirect
11. #3519	C₂	semidirect
12. #3514	C₂	semidirect
13. #3508	C₂	semidirect
14. #3506	C₂	semidirect
15. #3498	C₂	semidirect
16. #3498	C₂	semidirect
17. #3496	C₂	semidirect
18. #3494	C₂	semidirect
19. #3488	C₂	semidirect
20. #3484	C₂	semidirect
21. #3484	C₂	semidirect
22. #3475	C₂	semidirect
23. D₄×#41	C₂	semidirect
24. C₂×D₄²	C₂	semidirect
25. #3460	C₂	semidirect
26. C₂×#535	C₂	semidirect
27. C₂×H(5,𝔽₂)	C₂²	semidirect
28. C₂×H(5,𝔽₂)	C₂²	semidirect
29. C₂²×#41	C₂²	semidirect
30. C₂³×D₄	C₂²	semidirect
31. C₂³×D₄	C₂²	semidirect
32. #562	C₂²	semidirect
33. H(3,𝔽₄)	C₂²	semidirect
34. #560	C₂²	semidirect
35. #560	C₂²	semidirect
36. #560	C₂²	semidirect
37. #560	C₂²	semidirect
38. #559	C₂²	semidirect
39. #559	C₂²	semidirect
40. #559	C₂²	semidirect
41. #556	C₂²	semidirect
42. #556	C₂²	semidirect
43. #555	C₂²	semidirect
44. #555	C₂²	semidirect
45. #555	C₂²	semidirect
46. #555	C₂²	semidirect
47. #554	C₂²	semidirect
48. #553	C₂²	semidirect
49. #553	C₂²	semidirect
50. #553	C₂²	semidirect
51. #553	C₂²	semidirect
52. #553	C₂²	semidirect
53. #552	C₂²	semidirect
54. #552	C₂²	semidirect
55. #551	C₂²	semidirect
56. #551	C₂²	semidirect
57. #551	C₂²	semidirect
58. #550	C₂²	semidirect
59. #550	C₂²	semidirect
60. #550	C₂²	semidirect
61. #550	C₂²	semidirect
62. #550	C₂²	semidirect
63. #550	C₂²	semidirect
64. #550	C₂²	semidirect
65. #550	C₂²	semidirect
66. D₄×Q₈	C₂²	semidirect
67. #548	C₂²	semidirect
68. #548	C₂²	semidirect
69. #547	C₂²	semidirect
70. #547	C₂²	semidirect
71. #547	C₂²	semidirect
72. #547	C₂²	semidirect
73. #547	C₂²	semidirect
74. #546	C₂²	semidirect
75. #546	C₂²	semidirect
76. #546	C₂²	semidirect
77. #546	C₂²	semidirect
78. #546	C₂²	semidirect
79. #546	C₂²	semidirect
80. #546	C₂²	semidirect
81. #546	C₂²	semidirect
82. #546	C₂²	semidirect
83. #546	C₂²	semidirect
84. #546	C₂²	semidirect
85. #546	C₂²	semidirect
86. #546	C₂²	semidirect
87. #546	C₂²	semidirect
88. #546	C₂²	semidirect
89. #546	C₂²	semidirect
90. #546	C₂²	semidirect
91. #546	C₂²	semidirect
92. D₄²	C₂²	semidirect
93. D₄²	C₂²	semidirect
94. D₄²	C₂²	semidirect
95. D₄²	C₂²	semidirect
96. D₄²	C₂²	semidirect
97. D₄²	C₂²	semidirect
98. D₄²	C₂²	semidirect
99. D₄²	C₂²	semidirect
100. D₄²	C₂²	semidirect
101. D₄²	C₂²	semidirect
102. D₄²	C₂²	semidirect
103. D₄²	C₂²	semidirect
104. D₄²	C₂²	semidirect
105. D₄²	C₂²	semidirect
106. D₄²	C₂²	semidirect
107. D₄²	C₂²	semidirect
108. D₄²	C₂²	semidirect
109. D₄²	C₂²	semidirect
110. D₄²	C₂²	semidirect
111. D₄²	C₂²	semidirect
112. D₄²	C₂²	semidirect
113. D₄²	C₂²	semidirect
114. #544	C₂²	semidirect
115. #542	C₂²	semidirect
116. #542	C₂²	semidirect
117. #542	C₂²	semidirect
118. #542	C₂²	semidirect
119. #540	C₂²	semidirect
120. #540	C₂²	semidirect
121. #540	C₂²	semidirect
122. #540	C₂²	semidirect
123. #540	C₂²	semidirect
124. #540	C₂²	semidirect
125. #538	C₂²	semidirect
126. #538	C₂²	semidirect
127. #538	C₂²	semidirect
128. #538	C₂²	semidirect
129. #538	C₂²	semidirect
130. #538	C₂²	semidirect
131. #538	C₂²	semidirect
132. #537	C₂²	semidirect
133. #537	C₂²	semidirect
134. #537	C₂²	semidirect
135. #535	C₂²	semidirect
136. #535	C₂²	semidirect
137. #535	C₂²	semidirect
138. #535	C₂²	semidirect
139. #535	C₂²	semidirect
140. #535	C₂²	semidirect
141. #535	C₂²	semidirect
142. #535	C₂²	semidirect
143. #535	C₂²	semidirect
144. #535	C₂²	semidirect
145. #535	C₂²	semidirect
146. #535	C₂²	semidirect
147. #535	C₂²	semidirect
148. #535	C₂²	semidirect
149. #535	C₂²	semidirect
150. #535	C₂²	semidirect
151. #535	C₂²	semidirect
152. #534	C₂²	semidirect
153. #534	C₂²	semidirect
154. #534	C₂²	semidirect
155. #534	C₂²	semidirect
156. #534	C₂²	semidirect
157. #533	C₂²	semidirect
158. #532	C₂²	semidirect
159. #532	C₂²	semidirect
160. #532	C₂²	semidirect
161. #532	C₂²	semidirect
162. #532	C₂²	semidirect
163. #532	C₂²	semidirect
164. #532	C₂²	semidirect
165. #532	C₂²	semidirect
166. C₂×#127	C₂²	semidirect
167. C₂×#127	C₂²	semidirect
168. C₂×#127	C₂²	semidirect
169. #529	C₂²	semidirect
170. #529	C₂²	semidirect
171. #529	C₂²	semidirect
172. #529	C₂²	semidirect
173. #529	C₂²	semidirect
174. C₂×#124	C₂²	semidirect
175. #525	C₂²	semidirect
176. #525	C₂²	semidirect
177. #525	C₂²	semidirect
178. #525	C₂²	semidirect
179. #525	C₂²	semidirect
180. #525	C₂²	semidirect
181. C₂×#121	C₂²	semidirect
182. C₂×#121	C₂²	semidirect
183. C₂×#121	C₂²	semidirect
184. C₂×#121	C₂²	semidirect
185. C₂×#121	C₂²	semidirect
186. C₂×#120	C₂²	semidirect
187. C₂×#120	C₂²	semidirect
188. C₂×#120	C₂²	semidirect
189. #520	C₂²	semidirect
190. #518	C₂²	semidirect
191. #518	C₂²	semidirect
192. C₄×#41	C₂²	semidirect
193. C₄×#41	C₂²	semidirect
194. C₄×#41	C₂²	semidirect
195. C₂×C₄×D₄	C₂²	semidirect
196. C₂×C₄×D₄	C₂²	semidirect
197. C₂×C₄×D₄	C₂²	semidirect
198. C₂×#117	C₂²	semidirect
208. C₂×#41	C₂³	semidirect
209. C₂×#41	C₂³	semidirect
210. C₂×#41	C₂³	semidirect
211. C₂×#41	C₂³	semidirect
212. C₂×#41	C₂³	semidirect
213. C₂×#41	C₂³	semidirect
214. C₂×#41	C₂³	semidirect
215. C₂×#41	C₂³	semidirect
216. C₂×#41	C₂³	semidirect
217. C₂×#41	C₂³	semidirect
218. C₂²×Q₈	C₂³	semidirect
238. C₂²×D₄	C₂³	semidirect
239. C₂²×D₄	C₂³	semidirect
240. C₂²×D₄	C₂³	semidirect
241. C₂²×D₄	C₂³	semidirect
242. C₂²×D₄	C₂³	semidirect
243. C₂²×D₄	C₂³	semidirect
244. C₂²×D₄	C₂³	semidirect
245. C₂²×D₄	C₂³	semidirect
246. C₂²×D₄	C₂³	semidirect
247. C₂²×D₄	C₂³	semidirect
250. C₂³×C₄	C₂³	semidirect
251. C₄⋊Q₈	C₂³	semidirect
252. C₄⋊Q₈	C₂³	semidirect
253. C₄⋊Q₈	C₂³	semidirect
254. C₄⋊Q₈	C₂³	semidirect
255. C₄⋊Q₈	C₂³	semidirect
256. C₄⋊Q₈	C₂³	semidirect
265. #127	C₂³	semidirect
266. #127	C₂³	semidirect
267. #127	C₂³	semidirect
268. #127	C₂³	semidirect
269. #127	C₂³	semidirect
270. #127	C₂³	semidirect
271. #127	C₂³	semidirect
272. #127	C₂³	semidirect
273. #126	C₂³	semidirect
274. #126	C₂³	semidirect
275. #126	C₂³	semidirect
276. #126	C₂³	semidirect
277. #126	C₂³	semidirect
278. #126	C₂³	semidirect
279. #126	C₂³	semidirect
280. #126	C₂³	semidirect
281. #125	C₂³	semidirect
282. #125	C₂³	semidirect
283. #125	C₂³	semidirect
284. #125	C₂³	semidirect
285. #125	C₂³	semidirect
290. #124	C₂³	semidirect
291. #124	C₂³	semidirect
292. #124	C₂³	semidirect
293. #124	C₂³	semidirect
294. #124	C₂³	semidirect
295. #124	C₂³	semidirect
296. #124	C₂³	semidirect
297. #124	C₂³	semidirect
298. #124	C₂³	semidirect
299. #124	C₂³	semidirect
300. #124	C₂³	semidirect
301. #124	C₂³	semidirect
302. #124	C₂³	semidirect
303. #124	C₂³	semidirect
304. #124	C₂³	semidirect
308. #123	C₂³	semidirect
309. #123	C₂³	semidirect
310. #123	C₂³	semidirect
311. #123	C₂³	semidirect
312. #123	C₂³	semidirect
313. #123	C₂³	semidirect
314. #123	C₂³	semidirect
315. #123	C₂³	semidirect
316. #123	C₂³	semidirect
317. #123	C₂³	semidirect
318. #123	C₂³	semidirect
319. #123	C₂³	semidirect
320. #123	C₂³	semidirect
321. #123	C₂³	semidirect
322. #123	C₂³	semidirect
323. #123	C₂³	semidirect
324. #123	C₂³	semidirect
325. #123	C₂³	semidirect
326. #123	C₂³	semidirect
330. C₂²⋊Q₈	C₂³	semidirect
331. C₂²⋊Q₈	C₂³	semidirect
332. C₂²⋊Q₈	C₂³	semidirect
333. C₂²⋊Q₈	C₂³	semidirect
334. C₂²⋊Q₈	C₂³	semidirect
335. C₂²⋊Q₈	C₂³	semidirect
336. C₂²⋊Q₈	C₂³	semidirect
337. C₂²⋊Q₈	C₂³	semidirect
338. C₂²⋊Q₈	C₂³	semidirect
339. C₂²⋊Q₈	C₂³	semidirect
340. C₂²⋊Q₈	C₂³	semidirect
341. C₂²⋊Q₈	C₂³	semidirect
342. C₂²⋊Q₈	C₂³	semidirect
343. C₂²⋊Q₈	C₂³	semidirect
364. #121	C₂³	semidirect
365. #121	C₂³	semidirect
366. #121	C₂³	semidirect
367. #121	C₂³	semidirect
368. #121	C₂³	semidirect
369. #121	C₂³	semidirect
370. #121	C₂³	semidirect
371. #121	C₂³	semidirect
372. #121	C₂³	semidirect
373. #121	C₂³	semidirect
374. #121	C₂³	semidirect
375. #121	C₂³	semidirect
376. #121	C₂³	semidirect
377. #121	C₂³	semidirect
378. #121	C₂³	semidirect
379. #121	C₂³	semidirect
380. #121	C₂³	semidirect
381. #121	C₂³	semidirect
382. #121	C₂³	semidirect
383. #121	C₂³	semidirect
384. #121	C₂³	semidirect
385. #121	C₂³	semidirect
386. #121	C₂³	semidirect
387. #121	C₂³	semidirect
388. #121	C₂³	semidirect
389. #121	C₂³	semidirect
390. #121	C₂³	semidirect
391. #121	C₂³	semidirect
392. #121	C₂³	semidirect
393. #121	C₂³	semidirect
394. #121	C₂³	semidirect
395. #121	C₂³	semidirect
396. #121	C₂³	semidirect
397. #121	C₂³	semidirect
398. #121	C₂³	semidirect
399. #121	C₂³	semidirect
400. #121	C₂³	semidirect
401. #121	C₂³	semidirect
402. #121	C₂³	semidirect
403. #121	C₂³	semidirect
404. #121	C₂³	semidirect
405. #121	C₂³	semidirect
418. #120	C₂³	semidirect
419. #120	C₂³	semidirect
420. #120	C₂³	semidirect
421. #120	C₂³	semidirect
422. #120	C₂³	semidirect
423. #120	C₂³	semidirect
424. #120	C₂³	semidirect
425. #120	C₂³	semidirect
426. #120	C₂³	semidirect
427. #120	C₂³	semidirect
428. #120	C₂³	semidirect
429. #120	C₂³	semidirect
430. #120	C₂³	semidirect
431. #120	C₂³	semidirect
432. #120	C₂³	semidirect
433. #120	C₂³	semidirect
434. C₄×Q₈	C₂³	semidirect
435. C₄×Q₈	C₂³	semidirect
436. C₄×Q₈	C₂³	semidirect
437. C₄×Q₈	C₂³	semidirect
438. C₄×Q₈	C₂³	semidirect
439. C₄×Q₈	C₂³	semidirect
440. C₄×Q₈	C₂³	semidirect
441. C₄×Q₈	C₂³	semidirect
459. C₄×D₄	C₂³	semidirect
460. C₄×D₄	C₂³	semidirect
461. C₄×D₄	C₂³	semidirect
462. C₄×D₄	C₂³	semidirect
463. C₄×D₄	C₂³	semidirect
464. C₄×D₄	C₂³	semidirect
465. C₄×D₄	C₂³	semidirect
466. C₄×D₄	C₂³	semidirect
467. C₄×D₄	C₂³	semidirect
468. C₄×D₄	C₂³	semidirect
469. C₄×D₄	C₂³	semidirect
470. C₄×D₄	C₂³	semidirect
471. C₄×D₄	C₂³	semidirect
472. C₄×D₄	C₂³	semidirect
473. C₄×D₄	C₂³	semidirect
474. C₄×D₄	C₂³	semidirect
475. C₄×D₄	C₂³	semidirect
476. C₄×D₄	C₂³	semidirect
477. C₄×D₄	C₂³	semidirect
478. C₄×D₄	C₂³	semidirect
479. C₄×D₄	C₂³	semidirect
480. C₄×D₄	C₂³	semidirect
481. C₄×D₄	C₂³	semidirect
482. C₄×D₄	C₂³	semidirect
483. C₄×D₄	C₂³	semidirect
484. C₄×D₄	C₂³	semidirect
485. C₄×D₄	C₂³	semidirect
486. C₄×D₄	C₂³	semidirect
487. C₄×D₄	C₂³	semidirect
492. #117	C₂³	semidirect
493. #117	C₂³	semidirect
494. #117	C₂³	semidirect
495. #117	C₂³	semidirect
496. #117	C₂³	semidirect
497. #117	C₂³	semidirect
498. #117	C₂³	semidirect
499. #117	C₂³	semidirect
500. #117	C₂³	semidirect
501. #117	C₂³	semidirect
502. #117	C₂³	semidirect
505. C₂×C₄⋊C₄	C₂³	semidirect
506. C₂×C₄⋊C₄	C₂³	semidirect
507. C₂×C₄⋊C₄	C₂³	semidirect
508. C₂×C₄⋊C₄	C₂³	semidirect
514. C₂×C₂²⋊C₄	C₂³	semidirect
515. C₂×C₂²⋊C₄	C₂³	semidirect
516. C₂×C₂²⋊C₄	C₂³	semidirect
517. C₂×C₂²⋊C₄	C₂³	semidirect
518. C₂×C₂²⋊C₄	C₂³	semidirect
519. C₂×C₂²⋊C₄	C₂³	semidirect
521. C₂×C₄²	C₂³	semidirect
522. C₂×C₄²	C₂³	semidirect
523. C₂×C₄²	C₂³	semidirect
824. D₄	H(5,𝔽₂)	semidirect
851. C₂×C₄	H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#3558	2
#3549	2
#3546	2
#3543	2
#3542	2
#3537	2
#3532	2
#3519	2
#3514	2
#3508	2
#3506	2
#3498	2
#3496	2
#3494	2
#3488	2
#3484	2
#3475	2
D₄×#41	2
C₂×D₄²	2
#3460	2
C₂×#535	2