Subgroups — #62901

Order 256.

3553 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3560	C₂	1	4	yes	maximal, complemented
2	#3559	C₂	1	2	yes	maximal, complemented
3	#3559	C₂	1	4	yes	maximal, complemented
4	#3544	C₂	1	4	yes	maximal, complemented
5	#3542	C₂	1	4	yes	maximal, complemented
6	#3536	C₂	1	2	yes	maximal, complemented
7	#3535	C₂	1	8	yes	maximal, complemented
8	#3533	C₂	1	8	yes	maximal, complemented
9	#3522	C₂	1	2	yes	maximal, complemented
10	#3513	C₂	1	4	yes	maximal, complemented
11	#3505	C₂	1	2	yes	maximal, complemented
12	#3496	C₂	1	1	yes	maximal, characteristic, complemented
13	#3494	C₂	1	2	yes	maximal, complemented
14	#3492	C₂	1	4	yes	maximal, complemented
15	#3491	C₂	1	2	yes	maximal, complemented
16	#3485	C₂	1	4	yes	maximal, complemented
17	C₂×#552	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#547	C₂	1	2	yes	maximal, complemented
19	#3459	C₂	1	1	yes	maximal, characteristic, complemented
20	#3449	C₂	1	2	yes	maximal, complemented
21	C₂×H(5,𝔽₂)	C₂²	1	2	yes	—
22	C₂²×#41	C₂²	1	4	yes	complemented
23	#563	C₂²	1	8	yes	complemented
24	#563	C₂²	1	4	yes	complemented
25	#563	C₂²	1	8	yes	complemented
26	#562	C₂²	1	4	yes	complemented
27	#562	C₂²	1	8	yes	complemented
28	#562	C₂²	1	8	yes	complemented
29	#560	C₂²	1	8	yes	complemented
30	#559	C₂²	1	2	yes	complemented
31	#559	C₂²	1	4	yes	complemented
32	Q₈²	C₂²	1	2	yes	complemented
33	#555	C₂²	1	4	yes	complemented
34	#554	C₂²	1	2	yes	complemented
35	#554	C₂²	1	8	yes	complemented
36	#554	C₂²	1	4	yes	complemented
37	#554	C₂²	1	4	yes	complemented
38	#554	C₂²	1	4	yes	complemented
39	#553	C₂²	1	4	yes	complemented
40	#553	C₂²	1	8	yes	complemented
41	#553	C₂²	1	4	yes	complemented
42	#553	C₂²	1	4	yes	complemented
43	#553	C₂²	1	8	yes	complemented
44	#553	C₂²	1	8	yes	complemented
45	#552	C₂²	1	4	yes	complemented
46	#552	C₂²	1	8	yes	complemented
47	#552	C₂²	1	4	yes	complemented
48	#552	C₂²	1	8	yes	complemented
49	#552	C₂²	1	8	yes	complemented
50	#552	C₂²	1	4	yes	complemented
51	#551	C₂²	1	8	yes	complemented
52	#551	C₂²	1	8	yes	complemented
53	#551	C₂²	1	8	yes	complemented
54	#551	C₂²	1	8	yes	complemented
55	#551	C₂²	1	8	yes	complemented
56	#550	C₂²	1	2	yes	complemented
57	#548	C₂²	1	4	yes	complemented
58	#547	C₂²	1	4	yes	complemented
59	#547	C₂²	1	4	yes	complemented
60	#547	C₂²	1	8	yes	complemented
61	#547	C₂²	1	4	yes	complemented
62	#547	C₂²	1	4	yes	complemented
63	#547	C₂²	1	8	yes	complemented
64	#547	C₂²	1	8	yes	complemented
65	#547	C₂²	1	8	yes	complemented
66	#547	C₂²	1	8	yes	complemented
67	#547	C₂²	1	8	yes	complemented
68	#547	C₂²	1	4	yes	complemented
69	#546	C₂²	1	8	yes	complemented
70	#546	C₂²	1	8	yes	complemented
71	#546	C₂²	1	8	yes	complemented
72	#546	C₂²	1	8	yes	complemented
73	#546	C₂²	1	8	yes	complemented
74	#546	C₂²	1	4	yes	complemented
75	#546	C₂²	1	4	yes	complemented
76	D₄²	C₂²	1	4	yes	complemented
77	#544	C₂²	1	4	yes	complemented
78	#544	C₂²	1	2	yes	complemented
79	#544	C₂²	1	8	yes	complemented
80	#543	C₂²	1	1	yes	characteristic, complemented
81	#543	C₂²	1	4	yes	complemented
82	#542	C₂²	1	4	yes	complemented
83	#542	C₂²	1	4	yes	complemented
84	#542	C₂²	1	8	yes	complemented
85	#542	C₂²	1	4	yes	complemented
86	#542	C₂²	1	8	yes	complemented
87	#540	C₂²	1	4	yes	complemented
88	#540	C₂²	1	4	yes	complemented
89	#540	C₂²	1	8	yes	complemented
90	#539	C₂²	1	4	yes	complemented
91	#539	C₂²	1	2	yes	complemented
92	#539	C₂²	1	4	yes	complemented
93	#539	C₂²	1	4	yes	complemented
94	#539	C₂²	1	8	yes	complemented
95	#539	C₂²	1	8	yes	complemented
96	#539	C₂²	1	4	yes	complemented
97	#539	C₂²	1	8	yes	complemented
98	#539	C₂²	1	8	yes	complemented
99	#538	C₂²	1	4	yes	complemented
100	#538	C₂²	1	2	yes	complemented
101	#538	C₂²	1	4	yes	complemented
102	#538	C₂²	1	8	yes	complemented
103	#538	C₂²	1	4	yes	complemented
104	#538	C₂²	1	8	yes	complemented
105	#537	C₂²	1	4	yes	complemented
106	#537	C₂²	1	4	yes	complemented
107	#537	C₂²	1	4	yes	complemented
108	#537	C₂²	1	2	yes	complemented
109	#536	C₂²	1	8	yes	complemented
110	#536	C₂²	1	8	yes	complemented
111	#535	C₂²	1	8	yes	complemented
112	#535	C₂²	1	2	yes	complemented
113	#534	C₂²	1	2	yes	—
114	#534	C₂²	1	2	yes	—
115	#534	C₂²	1	1	yes	characteristic, complemented
116	#534	C₂²	1	4	yes	complemented
117	#534	C₂²	1	8	yes	complemented
118	#534	C₂²	1	2	yes	complemented
119	#532	C₂²	1	4	yes	complemented
120	#532	C₂²	1	4	yes	complemented
121	#532	C₂²	1	2	yes	complemented
122	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
123	#529	C₂²	1	4	yes	complemented
124	#529	C₂²	1	2	yes	complemented
125	#529	C₂²	1	4	yes	complemented
126	#529	C₂²	1	4	yes	complemented
127	#529	C₂²	1	4	yes	complemented
128	C₂×#126	C₂²	1	2	yes	complemented
129	C₂×#125	C₂²	1	2	yes	complemented
130	C₂×#125	C₂²	1	1	yes	characteristic, complemented
131	#525	C₂²	1	8	yes	complemented
132	#525	C₂²	1	8	yes	complemented
133	#525	C₂²	1	4	yes	complemented
134	#525	C₂²	1	2	yes	complemented
135	#525	C₂²	1	8	yes	complemented
136	#525	C₂²	1	4	yes	complemented
137	C₂×#123	C₂²	1	2	yes	—
138	C₂×#123	C₂²	1	4	yes	complemented
139	C₂×#123	C₂²	1	4	yes	complemented
140	C₂×#123	C₂²	1	8	yes	complemented
141	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
142	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
144	C₂×#121	C₂²	1	2	yes	—
145	C₂×#121	C₂²	1	2	yes	complemented
146	C₂×#121	C₂²	1	2	yes	complemented
147	#520	C₂²	1	2	yes	complemented
148	#520	C₂²	1	4	yes	complemented
149	#518	C₂²	1	4	yes	complemented
150	#518	C₂²	1	2	yes	complemented
151	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
152	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
153	C₂×C₄×D₄	C₂²	1	2	yes	complemented
154	C₂×C₄×D₄	C₂²	1	2	yes	complemented
155	C₂×#117	C₂²	1	2	yes	complemented
156	C₂×#117	C₂²	1	1	yes	characteristic, complemented
157	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
159	H(5,𝔽₂)	—	4	8	no	—
160	C₂×#41	—	4	16	no	—
161	C₂×#41	C₂³	1	2	yes	—
162	C₂×#41	C₂³	1	4	yes	—
163	C₂×#41	C₂³	1	8	yes	—
164	C₂×#41	C₂³	1	8	yes	—
165	C₂×#41	C₂³	1	8	yes	—
166	C₂×#41	C₂³	1	4	yes	—
167	C₂×#41	C₂³	1	8	yes	—
168	C₂×#41	C₂³	1	8	yes	—
169	C₂²×Q₈	C₂³	1	1	yes	characteristic
170	C₂²×Q₈	C₂³	1	4	yes	—
171	C₂²×D₄	C₂³	1	1	yes	characteristic
172	C₂²×D₄	C₂³	1	2	yes	—
173	C₂²×D₄	C₂³	1	4	yes	—
174	C₂²×D₄	C₂³	1	2	yes	—
175	C₂²×D₄	C₂³	1	2	yes	—
176	C₂²×D₄	C₂³	1	4	yes	—
177	C₂²×D₄	C₂³	1	4	yes	—
178	C₂²×D₄	C₂³	1	8	yes	—
179	C₂³×C₄	C₂³	1	2	yes	—
180	C₂³×C₄	C₂³	1	1	yes	characteristic
181	C₂³×C₄	C₂³	1	2	yes	—
182	C₂³×C₄	C₂³	1	4	yes	—
183	C₂³×C₄	C₂³	1	1	yes	characteristic
184	C₂³×C₄	C₂³	1	4	yes	—
185	C₄⋊Q₈	C₂³	1	4	yes	—
186	C₄⋊Q₈	C₂³	1	4	yes	—
187	C₄⋊Q₈	C₂³	1	8	yes	—
188	C₄⋊Q₈	C₂³	1	4	yes	—
189	C₄⋊Q₈	C₂³	1	4	yes	—
190	C₄⋊Q₈	C₂³	1	2	yes	—
191	C₄⋊Q₈	C₂³	1	8	yes	—
192	C₄⋊Q₈	C₂³	1	8	yes	—
193	#127	C₂³	1	4	yes	—
194	#127	C₂³	1	4	yes	—
195	#127	C₂³	1	2	yes	—
196	#126	C₂³	1	8	yes	—
197	#126	C₂³	1	8	yes	—
198	#126	C₂³	1	4	yes	—
199	#126	C₂³	1	4	yes	—
200	#126	C₂³	1	8	yes	—
201	#126	C₂³	1	4	yes	—
202	#126	C₂³	1	8	yes	—
203	#126	C₂³	1	8	yes	—
204	#126	C₂³	1	8	yes	—
205	#126	C₂³	1	8	yes	—
206	#126	C₂³	1	8	yes	—
207	#126	C₂³	1	8	yes	—
208	#125	C₂³	1	8	yes	—
209	#125	C₂³	1	4	yes	—
210	#125	C₂³	1	4	yes	—
211	#125	C₂³	1	8	yes	—
212	#125	C₂³	1	4	yes	—
213	#125	C₂³	1	4	yes	—
214	#125	C₂³	1	2	yes	—
215	#125	C₂³	1	4	yes	—
216	#125	C₂³	1	4	yes	—
217	#125	C₂³	1	8	yes	—
218	#125	C₂³	1	8	yes	—
219	#125	C₂³	1	8	yes	—
220	#124	C₂³	1	4	yes	—
221	#124	C₂³	1	4	yes	—
222	#124	C₂³	1	4	yes	—
223	#124	C₂³	1	2	yes	—
224	#124	C₂³	1	4	yes	—
225	#124	C₂³	1	8	yes	—
226	#124	C₂³	1	8	yes	—
227	#124	C₂³	1	4	yes	—
228	#124	C₂³	1	8	yes	—
229	#124	C₂³	1	8	yes	—
230	#124	C₂³	1	8	yes	—
231	#123	C₂³	1	8	yes	—
232	#123	C₂³	1	8	yes	—
233	#123	C₂³	1	8	yes	—
234	#123	C₂³	1	4	yes	—
235	#123	C₂³	1	8	yes	—
236	#123	C₂³	1	8	yes	—
237	#123	C₂³	1	8	yes	—
238	#123	C₂³	1	8	yes	—
239	#123	C₂³	1	8	yes	—
240	#123	C₂³	1	8	yes	—
241	#123	C₂³	1	8	yes	—
242	#123	C₂³	1	8	yes	—
243	#123	C₂³	1	8	yes	—
244	#123	C₂³	1	8	yes	—
245	#123	C₂³	1	8	yes	—
246	#123	C₂³	1	8	yes	—
247	#123	C₂³	1	4	yes	—
248	#123	C₂³	1	8	yes	—
249	#123	C₂³	1	8	yes	—
250	#123	C₂³	1	4	yes	—
251	#123	C₂³	1	4	yes	—
252	#123	C₂³	1	4	yes	—
253	#123	C₂³	1	8	yes	—
254	#123	C₂³	1	4	yes	—
255	#123	C₂³	1	8	yes	—
256	#123	C₂³	1	8	yes	—
257	#123	C₂³	1	8	yes	—
258	#123	C₂³	1	8	yes	—
259	#123	C₂³	1	8	yes	—
260	#123	C₂³	1	8	yes	—
261	#123	C₂³	1	8	yes	—
262	C₂²⋊Q₈	C₂³	1	4	yes	—
263	C₂²⋊Q₈	C₂³	1	4	yes	—
264	C₂²⋊Q₈	C₂³	1	4	yes	—
265	C₂²⋊Q₈	C₂³	1	4	yes	—
266	C₂²⋊Q₈	C₂³	1	8	yes	—
267	C₂²⋊Q₈	C₂³	1	8	yes	—
268	C₂²⋊Q₈	C₂³	1	8	yes	—
269	C₂²⋊Q₈	C₂³	1	8	yes	—
270	C₂²⋊Q₈	C₂³	1	2	yes	—
271	C₂²⋊Q₈	C₂³	1	8	yes	—
272	C₂²⋊Q₈	C₂³	1	8	yes	—
273	C₂²⋊Q₈	C₂³	1	8	yes	—
274	C₂²⋊Q₈	C₂³	1	8	yes	—
275	C₂²⋊Q₈	C₂³	1	4	yes	—
276	C₂²⋊Q₈	C₂³	1	2	yes	—
277	C₂²⋊Q₈	C₂³	1	4	yes	—
278	C₂²⋊Q₈	C₂³	1	8	yes	—
279	C₂²⋊Q₈	C₂³	1	4	yes	—
280	C₂²⋊Q₈	C₂³	1	8	yes	—
281	C₂²⋊Q₈	C₂³	1	2	yes	—
282	C₂²⋊Q₈	C₂³	1	4	yes	—
283	C₂²⋊Q₈	C₂³	1	8	yes	—
284	C₂²⋊Q₈	C₂³	1	8	yes	—
285	C₂²⋊Q₈	C₂³	1	8	yes	—
286	C₂²⋊Q₈	C₂³	1	8	yes	—
287	C₂²⋊Q₈	C₂³	1	8	yes	—
288	C₂²⋊Q₈	C₂³	1	8	yes	—
289	C₂²⋊Q₈	C₂³	1	8	yes	—
290	C₂²⋊Q₈	C₂³	1	8	yes	—
291	#121	C₂³	1	4	yes	—
292	#121	C₂³	1	4	yes	—
293	#121	C₂³	1	4	yes	—
294	#121	C₂³	1	4	yes	—
295	#121	C₂³	1	4	yes	—
296	#121	C₂³	1	4	yes	—
297	#121	C₂³	1	4	yes	—
298	#121	C₂³	1	4	yes	—
299	#121	C₂³	1	8	yes	—
300	#121	C₂³	1	4	yes	—
301	#121	C₂³	1	2	yes	—
302	#121	C₂³	1	4	yes	—
303	#121	C₂³	1	8	yes	—
304	#121	C₂³	1	8	yes	—
305	#121	C₂³	1	8	yes	—
306	#121	C₂³	1	8	yes	—
307	#121	C₂³	1	4	yes	—
308	#121	C₂³	1	8	yes	—
309	#121	C₂³	1	2	yes	—
310	#121	C₂³	1	4	yes	—
311	#121	C₂³	1	8	yes	—
312	#121	C₂³	1	4	yes	—
313	#121	C₂³	1	2	yes	—
314	#121	C₂³	1	4	yes	—
315	#121	C₂³	1	8	yes	—
316	#121	C₂³	1	8	yes	—
317	#121	C₂³	1	8	yes	—
318	#121	C₂³	1	8	yes	—
319	#121	C₂³	1	8	yes	—
320	#121	C₂³	1	8	yes	—
321	#121	C₂³	1	8	yes	—
322	#121	C₂³	1	8	yes	—
323	#120	C₂³	1	4	yes	—
324	#120	C₂³	1	8	yes	—
325	#120	C₂³	1	4	yes	—
326	#120	C₂³	1	8	yes	—
327	#120	C₂³	1	4	yes	—
328	#120	C₂³	1	8	yes	—
329	#120	C₂³	1	8	yes	—
330	#120	C₂³	1	8	yes	—
331	#120	C₂³	1	8	yes	—
332	C₄×Q₈	C₂³	1	2	yes	—
333	C₄×Q₈	C₂³	1	2	yes	—
334	C₄×Q₈	C₂³	1	4	yes	—
335	C₄×Q₈	C₂³	1	4	yes	—
336	C₄×Q₈	C₂³	1	4	yes	—
337	C₄×Q₈	C₂³	1	2	yes	—
338	C₄×Q₈	C₂³	1	4	yes	—
339	C₄×D₄	C₂³	1	4	yes	—
340	C₄×D₄	C₂³	1	4	yes	—
341	C₄×D₄	C₂³	1	4	yes	—
342	C₄×D₄	C₂³	1	4	yes	—
343	C₄×D₄	C₂³	1	4	yes	—
344	C₄×D₄	C₂³	1	4	yes	—
345	C₄×D₄	C₂³	1	8	yes	—
346	C₄×D₄	C₂³	1	4	yes	—
347	C₄×D₄	C₂³	1	4	yes	—
348	C₄×D₄	C₂³	1	4	yes	—
349	C₄×D₄	C₂³	1	8	yes	—
350	C₄×D₄	C₂³	1	8	yes	—
351	C₄×D₄	C₂³	1	8	yes	—
352	C₄×D₄	C₂³	1	8	yes	—
353	C₄×D₄	C₂³	1	4	yes	—
354	C₄×D₄	C₂³	1	4	yes	—
355	C₄×D₄	C₂³	1	8	yes	—
356	C₄×D₄	C₂³	1	4	yes	—
357	C₄×D₄	C₂³	1	8	yes	—
358	C₄×D₄	C₂³	1	8	yes	—
359	C₄×D₄	C₂³	1	4	yes	—
360	C₄×D₄	C₂³	1	4	yes	—
361	C₄×D₄	C₂³	1	2	yes	—
362	C₄×D₄	C₂³	1	4	yes	—
363	C₄×D₄	C₂³	1	8	yes	—
364	C₄×D₄	C₂³	1	4	yes	—
365	C₄×D₄	C₂³	1	8	yes	—
366	C₄×D₄	C₂³	1	8	yes	—
367	C₄×D₄	C₂³	1	8	yes	—
368	C₄×D₄	C₂³	1	4	yes	—
369	C₄×D₄	C₂³	1	4	yes	—
370	#117	C₂³	1	2	yes	—
371	#117	C₂³	1	8	yes	—
372	#117	C₂³	1	8	yes	—
373	#117	C₂³	1	2	yes	—
374	#117	C₂³	1	4	yes	—
375	#117	C₂³	1	2	yes	—
376	#117	C₂³	1	8	yes	—
377	#117	C₂³	1	4	yes	—
378	#117	C₂³	1	4	yes	—
379	#117	C₂³	1	8	yes	—
380	#117	C₂³	1	8	yes	—
381	#117	C₂³	1	8	yes	—
382	C₂×C₄⋊C₄	C₂³	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³	1	8	yes	—
393	C₂×C₄⋊C₄	C₂³	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³	1	8	yes	—
401	C₂×C₄⋊C₄	C₂³	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³	1	8	yes	—
405	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
413	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
414	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
419	C₂×C₄²	C₂³	1	2	yes	—
420	C₂×C₄²	C₂³	1	2	yes	—
421	C₂×C₄²	C₂³	1	1	yes	characteristic
422	C₂×C₄²	C₂³	1	2	yes	—
423	C₂⁴	C₂⁴	1	4	yes	—
424	C₂⁴	C₂⁴	1	1	yes	characteristic
425	C₂⁴	C₂⁴	1	2	yes	—
426	C₂⁴	C₂⁴	1	4	yes	—
427	C₂⁴	C₂⁴	1	1	yes	characteristic
428	#41	—	4	4	no	—
429	#41	—	4	16	no	—
430	#41	—	4	16	no	—
431	#41	—	4	16	no	—
432	#41	—	4	16	no	—
433	#41	—	4	16	no	—
434	#41	—	4	8	no	—
435	#41	—	4	8	no	—
436	C₂×Q₈	—	4	8	no	—
437	C₂×Q₈	—	4	2	no	—
438	C₂×Q₈	C₂⁴	1	2	yes	—
439	C₂×Q₈	C₂⁴	1	2	yes	—
440	C₂×Q₈	C₂⁴	1	2	yes	—
441	C₂×Q₈	C₂⁴	1	2	yes	—
442	C₂×Q₈	C₂⁴	1	8	yes	—
443	C₂×Q₈	C₂⁴	1	4	yes	—
444	C₂×Q₈	C₂⁴	1	8	yes	—
445	C₂×D₄	—	2	8	no	—
446	C₂×D₄	—	2	16	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	4	4	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	8	no	—
451	C₂×D₄	—	4	16	no	—
452	C₂×D₄	—	4	8	no	—
453	C₂×D₄	C₂⁴	1	4	yes	—
454	C₂×D₄	C₂⁴	1	4	yes	—
455	C₂×D₄	C₂⁴	1	8	yes	—
456	C₂×D₄	C₂⁴	1	4	yes	—
457	C₂×D₄	C₂⁴	1	4	yes	—
458	C₂×D₄	C₂⁴	1	8	yes	—
459	C₂×D₄	C₂⁴	1	4	yes	—
460	C₂×D₄	C₂⁴	1	4	yes	—
461	C₂×D₄	C₂⁴	1	8	yes	—
462	C₂×D₄	C₂⁴	1	2	yes	—
463	C₂×D₄	C₂⁴	1	4	yes	—
464	C₂×D₄	C₂⁴	1	8	yes	—
465	C₂×D₄	C₂⁴	1	4	yes	—
466	C₂×D₄	C₂⁴	1	4	yes	—
467	C₂×D₄	C₂⁴	1	2	yes	—
468	C₂×D₄	C₂⁴	1	8	yes	—
469	C₂×D₄	C₂⁴	1	8	yes	—
470	C₂×D₄	C₂⁴	1	8	yes	—
471	C₂×D₄	C₂⁴	1	4	yes	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	8	no	—
477	C₂²×C₄	—	4	8	no	—
478	C₂²×C₄	C₂⁴	1	2	yes	—
479	C₂²×C₄	C₂⁴	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴	1	2	yes	—
482	C₂²×C₄	C₂⁴	1	2	yes	—
483	C₂²×C₄	C₂⁴	1	2	yes	—
484	C₂²×C₄	C₂⁴	1	4	yes	—
485	C₂²×C₄	C₂⁴	1	4	yes	—
486	C₂²×C₄	C₂⁴	1	4	yes	—
487	C₂²×C₄	C₂⁴	1	4	yes	—
488	C₂²×C₄	C₂⁴	1	2	yes	—
489	C₂²×C₄	C₂⁴	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴	1	2	yes	—
492	C₂²×C₄	C₂⁴	1	2	yes	—
493	C₂²×C₄	C₂⁴	1	2	yes	—
494	C₂²×C₄	C₂⁴	1	2	yes	—
495	C₂²×C₄	C₂⁴	1	2	yes	—
496	C₂²×C₄	C₂⁴	1	8	yes	—
497	C₂²×C₄	C₂⁴	1	8	yes	—
498	C₂²×C₄	C₂⁴	1	2	yes	—
499	C₂²×C₄	C₂⁴	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴	1	8	yes	—
501	C₂²×C₄	C₂⁴	1	4	yes	—
502	C₂²×C₄	C₂⁴	1	8	yes	—
503	C₂²×C₄	C₂⁴	1	8	yes	—
504	C₂²×C₄	C₂⁴	1	4	yes	—
505	C₂²×C₄	C₂⁴	1	8	yes	—
506	C₂²×C₄	C₂⁴	1	8	yes	—
507	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
508	C₄⋊C₄	C₂⁴	1	2	yes	—
509	C₄⋊C₄	C₂⁴	1	4	yes	—
510	C₄⋊C₄	C₂⁴	1	4	yes	—
511	C₄⋊C₄	C₂⁴	1	8	yes	—
512	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
513	C₄⋊C₄	C₂⁴	1	2	yes	—
514	C₄⋊C₄	C₂⁴	1	4	yes	—
515	C₄⋊C₄	C₂⁴	1	4	yes	—
516	C₄⋊C₄	C₂⁴	1	4	yes	—
517	C₄⋊C₄	C₂⁴	1	8	yes	—
518	C₄⋊C₄	C₂⁴	1	2	yes	—
519	C₄⋊C₄	C₂⁴	1	4	yes	—
520	C₄⋊C₄	C₂⁴	1	8	yes	—
521	C₄⋊C₄	C₂⁴	1	8	yes	—
522	C₄⋊C₄	C₂⁴	1	4	yes	—
523	C₄⋊C₄	C₂⁴	1	2	yes	—
524	C₄⋊C₄	C₂⁴	1	8	yes	—
525	C₄⋊C₄	C₂⁴	1	8	yes	—
526	C₄⋊C₄	C₂⁴	1	2	yes	—
527	C₄⋊C₄	C₂⁴	1	8	yes	—
528	C₄⋊C₄	C₂⁴	1	8	yes	—
529	C₄⋊C₄	C₂⁴	1	8	yes	—
530	C₄⋊C₄	C₂⁴	1	4	yes	—
531	C₄⋊C₄	C₂⁴	1	4	yes	—
532	C₄⋊C₄	C₂⁴	1	4	yes	—
533	C₄⋊C₄	C₂⁴	1	4	yes	—
534	C₄⋊C₄	C₂⁴	1	8	yes	—
535	C₄⋊C₄	C₂⁴	1	4	yes	—
536	C₄⋊C₄	C₂⁴	1	4	yes	—
537	C₄⋊C₄	C₂⁴	1	4	yes	—
538	C₄⋊C₄	C₂⁴	1	8	yes	—
539	C₄⋊C₄	C₂⁴	1	2	yes	—
540	C₄⋊C₄	C₂⁴	1	8	yes	—
541	C₄⋊C₄	C₂⁴	1	2	yes	—
542	C₄⋊C₄	C₂⁴	1	2	yes	—
543	C₄⋊C₄	C₂⁴	1	2	yes	—
544	C₄⋊C₄	C₂⁴	1	4	yes	—
545	C₂²⋊C₄	C₂⁴	1	4	yes	—
546	C₂²⋊C₄	C₂⁴	1	4	yes	—
547	C₂²⋊C₄	C₂⁴	1	8	yes	—
548	C₂²⋊C₄	C₂⁴	1	8	yes	—
549	C₂²⋊C₄	C₂⁴	1	4	yes	—
550	C₂²⋊C₄	C₂⁴	1	8	yes	—
551	C₂²⋊C₄	C₂⁴	1	4	yes	—
552	C₂²⋊C₄	C₂⁴	1	8	yes	—
553	C₂²⋊C₄	C₂⁴	1	8	yes	—
554	C₂²⋊C₄	C₂⁴	1	4	yes	—
555	C₂²⋊C₄	C₂⁴	1	4	yes	—
556	C₂²⋊C₄	C₂⁴	1	8	yes	—
557	C₂²⋊C₄	C₂⁴	1	8	yes	—
558	C₂²⋊C₄	C₂⁴	1	8	yes	—
559	C₂²⋊C₄	C₂⁴	1	8	yes	—
560	C₂²⋊C₄	C₂⁴	1	4	yes	—
561	C₂²⋊C₄	C₂⁴	1	4	yes	—
562	C₂²⋊C₄	C₂⁴	1	8	yes	—
563	C₂²⋊C₄	C₂⁴	1	8	yes	—
564	C₂²⋊C₄	C₂⁴	1	8	yes	—
565	C₂²⋊C₄	C₂⁴	1	8	yes	—
566	C₂²⋊C₄	C₂⁴	1	4	yes	—
567	C₂²⋊C₄	C₂⁴	1	4	yes	—
568	C₂²⋊C₄	C₂⁴	1	8	yes	—
569	C₂²⋊C₄	C₂⁴	1	4	yes	—
570	C₂²⋊C₄	C₂⁴	1	8	yes	—
571	C₂²⋊C₄	C₂⁴	1	4	yes	—
572	C₂²⋊C₄	C₂⁴	1	4	yes	—
573	C₂²⋊C₄	C₂⁴	1	8	yes	—
574	C₂²⋊C₄	C₂⁴	1	4	yes	—
575	C₄²	C₂⁴	1	4	yes	—
576	C₄²	C₂⁴	1	4	yes	—
577	C₄²	C₂⁴	1	4	yes	—
578	C₄²	C₂⁴	1	4	yes	—
579	C₄²	C₂⁴	1	2	yes	—
580	C₄²	C₂⁴	1	4	yes	—
581	C₄²	C₂⁴	1	4	yes	—
582	C₄²	C₂⁴	1	2	yes	—
583	C₄²	C₂⁴	1	8	yes	—
584	C₄²	C₂⁴	1	8	yes	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	8	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	2	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	4	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	4	no	—
596	C₂³	—	4	4	no	—
597	C₂³	—	4	4	no	—
598	C₂³	—	4	4	no	—
599	C₂³	H(5,𝔽₂)	1	4	yes	—
600	C₂³	C₂⁵	1	2	yes	—
601	C₂³	C₂⁵	1	8	yes	—
602	C₂³	C₂⁵	1	4	yes	—
603	C₂³	C₂⁵	1	2	yes	—
604	C₂³	C₂⁵	1	1	yes	characteristic
605	Q₈	—	2	4	no	—
606	Q₈	—	4	2	no	—
607	Q₈	—	4	8	no	—
608	Q₈	—	4	8	no	—
609	Q₈	—	4	2	no	—
610	Q₈	—	4	2	no	—
611	Q₈	—	4	4	no	—
612	D₄	—	2	8	no	—
613	D₄	—	2	16	no	—
614	D₄	—	2	16	no	—
615	D₄	—	2	8	no	—
616	D₄	—	2	8	no	—
617	D₄	—	2	8	no	—
618	D₄	—	4	4	no	—
619	D₄	—	4	8	no	—
620	D₄	—	4	4	no	—
621	D₄	—	4	4	no	—
622	D₄	—	4	8	no	—
623	D₄	—	4	8	no	—
624	D₄	—	4	8	no	—
625	D₄	—	4	4	no	—
626	D₄	—	4	4	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	4	no	—
629	D₄	—	4	2	no	—
630	D₄	—	4	8	no	—
631	C₂×C₄	—	2	8	no	—
632	C₂×C₄	—	2	8	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	8	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	8	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	2	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	8	no	—
649	C₂×C₄	—	4	8	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	4	8	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	8	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	8	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	8	no	—
660	C₂×C₄	C₂⁵	1	2	yes	—
661	C₂×C₄	C₂⁵	1	4	yes	—
662	C₂×C₄	C₂⁵	1	4	yes	—
663	C₂×C₄	C₂⁵	1	4	yes	—
664	C₂×C₄	C₂⁵	1	2	yes	—
665	C₂×C₄	C₂⁵	1	2	yes	—
666	C₂×C₄	C₂⁵	1	2	yes	—
667	C₂×C₄	C₂⁵	1	1	yes	characteristic
668	C₂×C₄	C₂⁵	1	4	yes	—
669	C₂×C₄	C₂⁵	1	2	yes	—
670	C₂×C₄	C₂⁵	1	4	yes	—
671	C₂×C₄	C₂⁵	1	8	yes	—
672	C₂×C₄	C₂⁵	1	2	yes	—
673	C₂×C₄	C₂⁵	1	4	yes	—
674	C₂×C₄	C₂⁵	1	1	yes	characteristic
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	8	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	8	no	—
685	C₂²	—	2	8	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	4	4	no	—
689	C₂²	—	4	8	no	—
690	C₂²	—	8	8	no	—
691	C₂²	—	8	2	no	—
692	C₂²	—	16	4	no	—
693	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
694	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
695	C₂²	C₂⁶	1	1	yes	characteristic
696	C₄	—	2	2	no	—
697	C₄	—	2	4	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	8	no	—
701	C₄	—	2	4	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	4	no	—
704	C₄	—	2	1	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	2	no	—
710	C₄	#585	1	2	yes	—
711	C₂	—	2	4	no	—
712	C₂	—	2	2	no	—
713	C₂	—	4	4	no	—
714	C₂	—	4	8	no	—
715	C₂	—	4	2	no	—
716	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
717	C₂	C₂×#585	1	1	yes	characteristic
718	C₂	2₋¹⁺⁶	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. #3560	C₂	semidirect
2. #3559	C₂	semidirect
3. #3559	C₂	semidirect
4. #3544	C₂	semidirect
5. #3542	C₂	semidirect
6. #3536	C₂	semidirect
7. #3535	C₂	semidirect
8. #3533	C₂	semidirect
9. #3522	C₂	semidirect
10. #3513	C₂	semidirect
11. #3505	C₂	semidirect
12. #3496	C₂	semidirect
13. #3494	C₂	semidirect
14. #3492	C₂	semidirect
15. #3491	C₂	semidirect
16. #3485	C₂	semidirect
17. C₂×#552	C₂	semidirect
18. C₂×#547	C₂	semidirect
19. #3459	C₂	semidirect
20. #3449	C₂	semidirect
22. C₂²×#41	C₂²	semidirect
23. #563	C₂²	semidirect
24. #563	C₂²	semidirect
25. #563	C₂²	semidirect
26. #562	C₂²	semidirect
27. #562	C₂²	semidirect
28. #562	C₂²	semidirect
29. #560	C₂²	semidirect
30. #559	C₂²	semidirect
31. #559	C₂²	semidirect
32. Q₈²	C₂²	semidirect
33. #555	C₂²	semidirect
34. #554	C₂²	semidirect
35. #554	C₂²	semidirect
36. #554	C₂²	semidirect
37. #554	C₂²	semidirect
38. #554	C₂²	semidirect
39. #553	C₂²	semidirect
40. #553	C₂²	semidirect
41. #553	C₂²	semidirect
42. #553	C₂²	semidirect
43. #553	C₂²	semidirect
44. #553	C₂²	semidirect
45. #552	C₂²	semidirect
46. #552	C₂²	semidirect
47. #552	C₂²	semidirect
48. #552	C₂²	semidirect
49. #552	C₂²	semidirect
50. #552	C₂²	semidirect
51. #551	C₂²	semidirect
52. #551	C₂²	semidirect
53. #551	C₂²	semidirect
54. #551	C₂²	semidirect
55. #551	C₂²	semidirect
56. #550	C₂²	semidirect
57. #548	C₂²	semidirect
58. #547	C₂²	semidirect
59. #547	C₂²	semidirect
60. #547	C₂²	semidirect
61. #547	C₂²	semidirect
62. #547	C₂²	semidirect
63. #547	C₂²	semidirect
64. #547	C₂²	semidirect
65. #547	C₂²	semidirect
66. #547	C₂²	semidirect
67. #547	C₂²	semidirect
68. #547	C₂²	semidirect
69. #546	C₂²	semidirect
70. #546	C₂²	semidirect
71. #546	C₂²	semidirect
72. #546	C₂²	semidirect
73. #546	C₂²	semidirect
74. #546	C₂²	semidirect
75. #546	C₂²	semidirect
76. D₄²	C₂²	semidirect
77. #544	C₂²	semidirect
78. #544	C₂²	semidirect
79. #544	C₂²	semidirect
80. #543	C₂²	semidirect
81. #543	C₂²	semidirect
82. #542	C₂²	semidirect
83. #542	C₂²	semidirect
84. #542	C₂²	semidirect
85. #542	C₂²	semidirect
86. #542	C₂²	semidirect
87. #540	C₂²	semidirect
88. #540	C₂²	semidirect
89. #540	C₂²	semidirect
90. #539	C₂²	semidirect
91. #539	C₂²	semidirect
92. #539	C₂²	semidirect
93. #539	C₂²	semidirect
94. #539	C₂²	semidirect
95. #539	C₂²	semidirect
96. #539	C₂²	semidirect
97. #539	C₂²	semidirect
98. #539	C₂²	semidirect
99. #538	C₂²	semidirect
100. #538	C₂²	semidirect
101. #538	C₂²	semidirect
102. #538	C₂²	semidirect
103. #538	C₂²	semidirect
104. #538	C₂²	semidirect
105. #537	C₂²	semidirect
106. #537	C₂²	semidirect
107. #537	C₂²	semidirect
108. #537	C₂²	semidirect
109. #536	C₂²	semidirect
110. #536	C₂²	semidirect
111. #535	C₂²	semidirect
112. #535	C₂²	semidirect
115. #534	C₂²	semidirect
116. #534	C₂²	semidirect
117. #534	C₂²	semidirect
118. #534	C₂²	semidirect
119. #532	C₂²	semidirect
120. #532	C₂²	semidirect
121. #532	C₂²	semidirect
122. C₂×C₄⋊Q₈	C₂²	semidirect
123. #529	C₂²	semidirect
124. #529	C₂²	semidirect
125. #529	C₂²	semidirect
126. #529	C₂²	semidirect
127. #529	C₂²	semidirect
128. C₂×#126	C₂²	semidirect
129. C₂×#125	C₂²	semidirect
130. C₂×#125	C₂²	semidirect
131. #525	C₂²	semidirect
132. #525	C₂²	semidirect
133. #525	C₂²	semidirect
134. #525	C₂²	semidirect
135. #525	C₂²	semidirect
136. #525	C₂²	semidirect
138. C₂×#123	C₂²	semidirect
139. C₂×#123	C₂²	semidirect
140. C₂×#123	C₂²	semidirect
141. C₂×C₂²⋊Q₈	C₂²	semidirect
142. C₂×C₂²⋊Q₈	C₂²	semidirect
143. C₂×C₂²⋊Q₈	C₂²	semidirect
145. C₂×#121	C₂²	semidirect
146. C₂×#121	C₂²	semidirect
147. #520	C₂²	semidirect
148. #520	C₂²	semidirect
149. #518	C₂²	semidirect
150. #518	C₂²	semidirect
151. C₂×C₄×Q₈	C₂²	semidirect
153. C₂×C₄×D₄	C₂²	semidirect
154. C₂×C₄×D₄	C₂²	semidirect
155. C₂×#117	C₂²	semidirect
156. C₂×#117	C₂²	semidirect
157. C₂²×C₄⋊C₄	C₂²	semidirect
158. C₂²×C₄⋊C₄	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3560	2
#3559	2
#3544	2
#3542	2
#3536	2
#3535	2
#3533	2
#3522	2
#3513	2
#3505	2
#3496	2
#3494	2
#3492	2
#3491	2
#3485	2
C₂×#552	2
C₂×#547	2
#3459	2
#3449	2