Subgroups — #62919

Order 256.

3541 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3562	C₂	1	6	yes	maximal, complemented
2	#3561	C₂	1	6	yes	maximal, complemented
3	#3551	C₂	1	6	yes	maximal, complemented
4	#3547	C₂	1	6	yes	maximal, complemented
5	#3542	C₂	1	6	yes	maximal, complemented
6	#3538	C₂	1	3	yes	maximal, complemented
7	#3536	C₂	1	3	yes	maximal, complemented
8	#3524	C₂	1	2	yes	maximal, complemented
9	#3516	C₂	1	2	yes	maximal, complemented
10	#3514	C₂	1	6	yes	maximal, complemented
11	#3505	C₂	1	3	yes	maximal, complemented
12	#3500	C₂	1	2	yes	maximal, complemented
13	#3497	C₂	1	2	yes	maximal, complemented
14	#3489	C₂	1	1	yes	maximal, characteristic, complemented
15	#3488	C₂	1	1	yes	maximal, characteristic, complemented
16	#3486	C₂	1	2	yes	maximal, complemented
17	#3482	C₂	1	2	yes	maximal, complemented
18	C₂×#548	C₂	1	1	yes	maximal, characteristic, complemented
19	#3460	C₂	1	3	yes	maximal, complemented
20	C₂×2₋¹⁺⁴	C₂²	1	2	yes	complemented
21	C₂×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
22	C₂×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#41	C₂²	1	1	yes	characteristic
24	C₂³×Q₈	C₂²	1	1	yes	characteristic, complemented
25	#563	C₂²	1	12	yes	complemented
26	#562	C₂²	1	12	yes	complemented
27	#562	C₂²	1	12	yes	complemented
28	#560	C₂²	1	12	yes	complemented
29	#559	C₂²	1	6	yes	complemented
30	#557	C₂²	1	2	yes	complemented
31	#556	C₂²	1	6	yes	complemented
32	#556	C₂²	1	6	yes	complemented
33	#555	C₂²	1	12	yes	complemented
34	#555	C₂²	1	6	yes	complemented
35	#554	C₂²	1	6	yes	complemented
36	#553	C₂²	1	6	yes	complemented
37	#553	C₂²	1	12	yes	complemented
38	#553	C₂²	1	6	yes	complemented
39	#552	C₂²	1	6	yes	complemented
40	#552	C₂²	1	6	yes	complemented
41	#552	C₂²	1	6	yes	complemented
42	#552	C₂²	1	6	yes	complemented
43	#551	C₂²	1	12	yes	complemented
44	#551	C₂²	1	12	yes	complemented
45	#551	C₂²	1	12	yes	complemented
46	#550	C₂²	1	2	yes	complemented
47	#550	C₂²	1	6	yes	complemented
48	D₄×Q₈	C₂²	1	2	yes	complemented
49	D₄×Q₈	C₂²	1	2	yes	complemented
50	D₄×Q₈	C₂²	1	6	yes	complemented
51	D₄×Q₈	C₂²	1	6	yes	complemented
52	D₄×Q₈	C₂²	1	6	yes	complemented
53	#548	C₂²	1	2	yes	—
54	#548	C₂²	1	2	yes	—
55	#548	C₂²	1	2	yes	complemented
56	#548	C₂²	1	6	yes	complemented
57	#548	C₂²	1	6	yes	complemented
58	#548	C₂²	1	2	yes	complemented
59	#548	C₂²	1	2	yes	complemented
60	#548	C₂²	1	6	yes	complemented
61	#548	C₂²	1	6	yes	complemented
62	#548	C₂²	1	2	yes	complemented
63	#548	C₂²	1	6	yes	complemented
64	#548	C₂²	1	6	yes	complemented
65	#547	C₂²	1	6	yes	complemented
66	#547	C₂²	1	6	yes	complemented
67	#546	C₂²	1	6	yes	complemented
68	#546	C₂²	1	6	yes	complemented
69	#546	C₂²	1	6	yes	complemented
70	#546	C₂²	1	6	yes	complemented
71	#546	C₂²	1	6	yes	complemented
72	#546	C₂²	1	6	yes	complemented
73	#546	C₂²	1	12	yes	complemented
74	D₄²	C₂²	1	6	yes	—
75	#544	C₂²	1	3	yes	complemented
76	#544	C₂²	1	6	yes	complemented
77	#543	C₂²	1	6	yes	complemented
78	#542	C₂²	1	6	yes	complemented
79	#542	C₂²	1	6	yes	complemented
80	#542	C₂²	1	12	yes	complemented
81	#542	C₂²	1	6	yes	complemented
82	#542	C₂²	1	6	yes	complemented
83	#541	C₂²	1	6	yes	complemented
84	#540	C₂²	1	6	yes	complemented
85	#540	C₂²	1	6	yes	complemented
86	#540	C₂²	1	6	yes	complemented
87	#540	C₂²	1	12	yes	complemented
88	#539	C₂²	1	6	yes	complemented
89	#539	C₂²	1	6	yes	complemented
90	#538	C₂²	1	1	yes	characteristic, complemented
91	#538	C₂²	1	3	yes	complemented
92	#538	C₂²	1	6	yes	complemented
93	#538	C₂²	1	12	yes	complemented
94	#538	C₂²	1	6	yes	complemented
95	#538	C₂²	1	12	yes	complemented
96	#537	C₂²	1	3	yes	complemented
97	#537	C₂²	1	3	yes	complemented
98	#537	C₂²	1	3	yes	complemented
99	#537	C₂²	1	6	yes	complemented
100	#537	C₂²	1	6	yes	complemented
101	#536	C₂²	1	6	yes	complemented
102	#536	C₂²	1	6	yes	complemented
103	#536	C₂²	1	3	yes	complemented
104	#536	C₂²	1	6	yes	complemented
105	#535	C₂²	1	6	yes	complemented
106	#535	C₂²	1	3	yes	complemented
107	#535	C₂²	1	6	yes	complemented
108	#534	C₂²	1	6	yes	complemented
109	#533	C₂²	1	6	yes	complemented
110	#532	C₂²	1	6	yes	complemented
111	#532	C₂²	1	6	yes	complemented
112	#532	C₂²	1	6	yes	complemented
113	#529	C₂²	1	6	yes	complemented
114	#529	C₂²	1	6	yes	complemented
115	#529	C₂²	1	6	yes	complemented
116	#529	C₂²	1	6	yes	complemented
117	#529	C₂²	1	6	yes	complemented
118	#529	C₂²	1	6	yes	complemented
119	C₂×#124	C₂²	1	3	yes	complemented
120	C₂×#124	C₂²	1	6	yes	complemented
121	#525	C₂²	1	3	yes	—
122	#525	C₂²	1	6	yes	complemented
123	#525	C₂²	1	3	yes	complemented
124	#525	C₂²	1	6	yes	complemented
125	C₂×C₂²⋊Q₈	C₂²	1	3	yes	complemented
126	C₂×C₂²⋊Q₈	C₂²	1	3	yes	complemented
127	C₂×#121	C₂²	1	3	yes	—
128	C₂×#121	C₂²	1	3	yes	complemented
129	#520	C₂²	1	1	yes	characteristic, complemented
130	#520	C₂²	1	1	yes	characteristic, complemented
131	#519	C₂²	1	2	yes	complemented
132	#518	C₂²	1	6	yes	complemented
133	C₄×#41	C₂²	1	6	yes	complemented
134	C₄×#41	C₂²	1	2	yes	complemented
135	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
137	C₂×C₄×D₄	C₂²	1	3	yes	complemented
138	2₋¹⁺⁴	—	4	8	no	—
139	2₋¹⁺⁴	—	4	4	no	—
140	H(5,𝔽₂)	—	4	4	no	—
141	C₂×#41	—	4	4	no	—
142	C₂×#41	C₂³	1	2	yes	—
143	C₂×#41	C₂³	1	1	yes	characteristic
144	C₂×#41	C₂³	1	1	yes	characteristic
145	C₂×#41	C₂³	1	6	yes	—
146	C₂×#41	C₂³	1	3	yes	—
147	C₂×#41	C₂³	1	6	yes	—
148	C₂×#41	C₂³	1	3	yes	—
149	C₂×#41	C₂³	1	6	yes	—
150	C₂×#41	C₂³	1	6	yes	—
151	C₂×#41	C₂³	1	6	yes	—
152	C₂×#41	C₂³	1	3	yes	—
153	C₂×#41	C₂³	1	3	yes	—
154	C₂²×Q₈	—	4	4	no	—
155	C₂²×Q₈	C₂³	1	1	yes	characteristic
156	C₂²×Q₈	C₂³	1	2	yes	—
157	C₂²×Q₈	C₂³	1	2	yes	—
158	C₂²×Q₈	C₂³	1	3	yes	—
159	C₂²×Q₈	C₂³	1	3	yes	—
160	C₂²×Q₈	C₂³	1	6	yes	—
161	C₂²×Q₈	C₂³	1	6	yes	—
162	C₂²×D₄	C₂³	1	3	yes	—
163	C₂²×D₄	C₂³	1	6	yes	—
164	C₂²×D₄	C₂³	1	3	yes	—
165	C₂²×D₄	C₂³	1	3	yes	—
166	C₂²×D₄	C₂³	1	6	yes	—
167	C₂³×C₄	C₂³	1	3	yes	—
168	C₂³×C₄	C₂³	1	3	yes	—
169	C₄⋊Q₈	C₂³	1	6	yes	—
170	C₄⋊Q₈	C₂³	1	6	yes	—
171	C₄⋊Q₈	C₂³	1	6	yes	—
172	C₄⋊Q₈	C₂³	1	6	yes	—
173	C₄⋊Q₈	C₂³	1	6	yes	—
174	C₄⋊Q₈	C₂³	1	12	yes	—
175	#127	C₂³	1	6	yes	—
176	#127	C₂³	1	6	yes	—
177	#127	C₂³	1	6	yes	—
178	#126	C₂³	1	2	yes	—
179	#126	C₂³	1	6	yes	—
180	#126	C₂³	1	12	yes	—
181	#126	C₂³	1	6	yes	—
182	#126	C₂³	1	12	yes	—
183	#126	C₂³	1	6	yes	—
184	#126	C₂³	1	12	yes	—
185	#126	C₂³	1	12	yes	—
186	#126	C₂³	1	12	yes	—
187	#125	C₂³	1	6	yes	—
188	#125	C₂³	1	6	yes	—
189	#125	C₂³	1	6	yes	—
190	#125	C₂³	1	6	yes	—
191	#125	C₂³	1	12	yes	—
192	#125	C₂³	1	12	yes	—
193	#124	C₂³	1	6	yes	—
194	#124	C₂³	1	6	yes	—
195	#124	C₂³	1	6	yes	—
196	#124	C₂³	1	6	yes	—
197	#124	C₂³	1	12	yes	—
198	#124	C₂³	1	6	yes	—
199	#124	C₂³	1	6	yes	—
200	#124	C₂³	1	12	yes	—
201	#124	C₂³	1	6	yes	—
202	#124	C₂³	1	6	yes	—
203	#124	C₂³	1	6	yes	—
204	#124	C₂³	1	2	yes	—
205	#124	C₂³	1	6	yes	—
206	#124	C₂³	1	6	yes	—
207	#124	C₂³	1	12	yes	—
208	#124	C₂³	1	12	yes	—
209	#123	C₂³	1	6	yes	—
210	#123	C₂³	1	6	yes	—
211	#123	C₂³	1	6	yes	—
212	#123	C₂³	1	12	yes	—
213	#123	C₂³	1	6	yes	—
214	#123	C₂³	1	6	yes	—
215	#123	C₂³	1	2	yes	—
216	#123	C₂³	1	12	yes	—
217	#123	C₂³	1	12	yes	—
218	#123	C₂³	1	6	yes	—
219	#123	C₂³	1	6	yes	—
220	#123	C₂³	1	12	yes	—
221	#123	C₂³	1	12	yes	—
222	#123	C₂³	1	12	yes	—
223	#123	C₂³	1	12	yes	—
224	#123	C₂³	1	12	yes	—
225	#123	C₂³	1	12	yes	—
226	C₂²⋊Q₈	C₂³	1	3	yes	—
227	C₂²⋊Q₈	C₂³	1	6	yes	—
228	C₂²⋊Q₈	C₂³	1	6	yes	—
229	C₂²⋊Q₈	C₂³	1	6	yes	—
230	C₂²⋊Q₈	C₂³	1	6	yes	—
231	C₂²⋊Q₈	C₂³	1	6	yes	—
232	C₂²⋊Q₈	C₂³	1	6	yes	—
233	C₂²⋊Q₈	C₂³	1	6	yes	—
234	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
235	C₂²⋊Q₈	C₂³	1	3	yes	—
236	C₂²⋊Q₈	C₂³	1	3	yes	—
237	C₂²⋊Q₈	C₂³	1	6	yes	—
238	C₂²⋊Q₈	C₂³	1	6	yes	—
239	C₂²⋊Q₈	C₂³	1	6	yes	—
240	C₂²⋊Q₈	C₂³	1	6	yes	—
241	C₂²⋊Q₈	C₂³	1	6	yes	—
242	C₂²⋊Q₈	C₂³	1	6	yes	—
243	C₂²⋊Q₈	C₂³	1	6	yes	—
244	C₂²⋊Q₈	C₂³	1	6	yes	—
245	C₂²⋊Q₈	C₂³	1	6	yes	—
246	C₂²⋊Q₈	C₂³	1	6	yes	—
247	C₂²⋊Q₈	C₂³	1	12	yes	—
248	C₂²⋊Q₈	C₂³	1	12	yes	—
249	C₂²⋊Q₈	C₂³	1	12	yes	—
250	C₂²⋊Q₈	C₂³	1	12	yes	—
251	C₂²⋊Q₈	C₂³	1	12	yes	—
252	C₂²⋊Q₈	C₂³	1	12	yes	—
253	#121	C₂³	1	3	yes	—
254	#121	C₂³	1	6	yes	—
255	#121	C₂³	1	6	yes	—
256	#121	C₂³	1	6	yes	—
257	#121	C₂³	1	6	yes	—
258	#121	C₂³	1	6	yes	—
259	#121	C₂³	1	12	yes	—
260	#121	C₂³	1	3	yes	—
261	#121	C₂³	1	1	yes	characteristic
262	#121	C₂³	1	6	yes	—
263	#121	C₂³	1	3	yes	—
264	#121	C₂³	1	6	yes	—
265	#121	C₂³	1	6	yes	—
266	#121	C₂³	1	6	yes	—
267	#121	C₂³	1	6	yes	—
268	#121	C₂³	1	6	yes	—
269	#121	C₂³	1	6	yes	—
270	#121	C₂³	1	6	yes	—
271	#121	C₂³	1	6	yes	—
272	#121	C₂³	1	2	yes	—
273	#121	C₂³	1	6	yes	—
274	#121	C₂³	1	6	yes	—
275	#121	C₂³	1	6	yes	—
276	#121	C₂³	1	12	yes	—
277	#121	C₂³	1	6	yes	—
278	#121	C₂³	1	6	yes	—
279	#121	C₂³	1	6	yes	—
280	#121	C₂³	1	12	yes	—
281	#121	C₂³	1	12	yes	—
282	#121	C₂³	1	12	yes	—
283	#121	C₂³	1	12	yes	—
284	#121	C₂³	1	12	yes	—
285	#120	C₂³	1	6	yes	—
286	#120	C₂³	1	6	yes	—
287	#120	C₂³	1	2	yes	—
288	#120	C₂³	1	6	yes	—
289	#120	C₂³	1	12	yes	—
290	#120	C₂³	1	12	yes	—
291	#120	C₂³	1	12	yes	—
292	C₄×Q₈	C₂³	1	2	yes	—
293	C₄×Q₈	C₂³	1	2	yes	—
294	C₄×Q₈	C₂³	1	6	yes	—
295	C₄×Q₈	C₂³	1	6	yes	—
296	C₄×Q₈	C₂³	1	6	yes	—
297	C₄×Q₈	C₂³	1	2	yes	—
298	C₄×Q₈	C₂³	1	6	yes	—
299	C₄×Q₈	C₂³	1	6	yes	—
300	C₄×Q₈	C₂³	1	6	yes	—
301	C₄×Q₈	C₂³	1	6	yes	—
302	C₄×D₄	C₂³	1	6	yes	—
303	C₄×D₄	C₂³	1	6	yes	—
304	C₄×D₄	C₂³	1	6	yes	—
305	C₄×D₄	C₂³	1	6	yes	—
306	C₄×D₄	C₂³	1	2	yes	—
307	C₄×D₄	C₂³	1	6	yes	—
308	C₄×D₄	C₂³	1	6	yes	—
309	C₄×D₄	C₂³	1	6	yes	—
310	C₄×D₄	C₂³	1	6	yes	—
311	C₄×D₄	C₂³	1	6	yes	—
312	C₄×D₄	C₂³	1	6	yes	—
313	C₄×D₄	C₂³	1	6	yes	—
314	C₄×D₄	C₂³	1	12	yes	—
315	C₄×D₄	C₂³	1	12	yes	—
316	C₄×D₄	C₂³	1	12	yes	—
317	C₄×D₄	C₂³	1	6	yes	—
318	C₄×D₄	C₂³	1	6	yes	—
319	C₄×D₄	C₂³	1	6	yes	—
320	C₄×D₄	C₂³	1	6	yes	—
321	C₄×D₄	C₂³	1	6	yes	—
322	C₄×D₄	C₂³	1	6	yes	—
323	C₄×D₄	C₂³	1	12	yes	—
324	C₄×D₄	C₂³	1	12	yes	—
325	C₄×D₄	C₂³	1	12	yes	—
326	#117	C₂³	1	6	yes	—
327	#117	C₂³	1	6	yes	—
328	#117	C₂³	1	6	yes	—
329	#117	C₂³	1	6	yes	—
330	#117	C₂³	1	12	yes	—
331	#117	C₂³	1	6	yes	—
332	#117	C₂³	1	6	yes	—
333	#117	C₂³	1	3	yes	—
334	#117	C₂³	1	3	yes	—
335	#117	C₂³	1	12	yes	—
336	#117	C₂³	1	12	yes	—
337	C₂×C₄⋊C₄	C₂³	1	3	yes	—
338	C₂×C₄⋊C₄	C₂³	1	3	yes	—
339	C₂×C₄⋊C₄	C₂³	1	6	yes	—
340	C₂×C₄⋊C₄	C₂³	1	3	yes	—
341	C₂×C₄⋊C₄	C₂³	1	3	yes	—
342	C₂×C₄⋊C₄	C₂³	1	6	yes	—
343	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₂³	1	3	yes	—
345	C₂×C₂²⋊C₄	C₂³	1	6	yes	—
346	C₂×C₂²⋊C₄	C₂³	1	12	yes	—
347	C₂×C₂²⋊C₄	C₂³	1	6	yes	—
348	C₂×C₂²⋊C₄	C₂³	1	6	yes	—
349	C₂×C₂²⋊C₄	C₂³	1	12	yes	—
350	C₂×C₄²	C₂³	1	3	yes	—
351	C₂×C₄²	C₂³	1	6	yes	—
352	C₂×C₄²	C₂³	1	6	yes	—
353	C₂⁴	C₂⁴	1	3	yes	—
354	C₂⁴	C₂⁴	1	1	yes	characteristic
355	C₂⁴	C₂⁴	1	6	yes	—
356	#41	—	2	4	no	—
357	#41	—	2	4	no	—
358	#41	—	2	8	no	—
359	#41	—	4	6	no	—
360	#41	—	4	12	no	—
361	#41	—	4	6	no	—
362	#41	—	4	12	no	—
363	#41	—	4	6	no	—
364	#41	—	4	6	no	—
365	#41	—	4	12	no	—
366	#41	—	4	12	no	—
367	#41	—	4	12	no	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	8	no	—
370	C₂×Q₈	—	2	8	no	—
371	C₂×Q₈	—	4	6	no	—
372	C₂×Q₈	—	4	12	no	—
373	C₂×Q₈	—	4	6	no	—
374	C₂×Q₈	—	4	12	no	—
375	C₂×Q₈	C₂⁴	1	6	yes	—
376	C₂×Q₈	C₂⁴	1	3	yes	—
377	C₂×Q₈	C₂⁴	1	6	yes	—
378	C₂×Q₈	C₂⁴	1	6	yes	—
379	C₂×Q₈	C₂⁴	1	3	yes	—
380	C₂×Q₈	C₂⁴	1	6	yes	—
381	C₂×Q₈	C₂⁴	1	6	yes	—
382	C₂×Q₈	C₂⁴	1	1	yes	characteristic
383	C₂×Q₈	C₂⁴	1	1	yes	characteristic
384	C₂×D₄	—	4	6	no	—
385	C₂×D₄	—	4	6	no	—
386	C₂×D₄	—	4	12	no	—
387	C₂×D₄	—	4	6	no	—
388	C₂×D₄	—	4	12	no	—
389	C₂×D₄	C₂⁴	1	2	yes	—
390	C₂×D₄	C₂⁴	1	6	yes	—
391	C₂×D₄	C₂⁴	1	3	yes	—
392	C₂×D₄	C₂⁴	1	6	yes	—
393	C₂×D₄	C₂⁴	1	3	yes	—
394	C₂×D₄	C₂⁴	1	6	yes	—
395	C₂×D₄	C₂⁴	1	6	yes	—
396	C₂×D₄	C₂⁴	1	6	yes	—
397	C₂×D₄	C₂⁴	1	2	yes	—
398	C₂×D₄	C₂⁴	1	6	yes	—
399	C₂×D₄	C₂⁴	1	6	yes	—
400	C₂×D₄	C₂⁴	1	12	yes	—
401	C₂×D₄	C₂⁴	1	6	yes	—
402	C₂×D₄	C₂⁴	1	6	yes	—
403	C₂×D₄	C₂⁴	1	6	yes	—
404	C₂×D₄	C₂⁴	1	6	yes	—
405	C₂×D₄	C₂⁴	1	6	yes	—
406	C₂×D₄	C₂⁴	1	6	yes	—
407	C₂×D₄	C₂⁴	1	2	yes	—
408	C₂×D₄	C₂⁴	1	1	yes	characteristic
409	C₂×D₄	C₂⁴	1	3	yes	—
410	C₂²×C₄	—	4	6	no	—
411	C₂²×C₄	—	4	6	no	—
412	C₂²×C₄	C₂⁴	1	3	yes	—
413	C₂²×C₄	C₂⁴	1	3	yes	—
414	C₂²×C₄	C₂⁴	1	6	yes	—
415	C₂²×C₄	C₂⁴	1	6	yes	—
416	C₂²×C₄	C₂⁴	1	3	yes	—
417	C₂²×C₄	C₂⁴	1	3	yes	—
418	C₂²×C₄	C₂⁴	1	6	yes	—
419	C₂²×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴	1	2	yes	—
421	C₂²×C₄	C₂⁴	1	6	yes	—
422	C₂²×C₄	C₂⁴	1	6	yes	—
423	C₂²×C₄	C₂⁴	1	6	yes	—
424	C₂²×C₄	C₂⁴	1	3	yes	—
425	C₂²×C₄	C₂⁴	1	12	yes	—
426	C₂²×C₄	C₂⁴	1	3	yes	—
427	C₂²×C₄	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴	1	6	yes	—
429	C₂²×C₄	C₂⁴	1	6	yes	—
430	C₂²×C₄	C₂⁴	1	6	yes	—
431	C₂²×C₄	C₂⁴	1	3	yes	—
432	C₂²×C₄	C₂⁴	1	6	yes	—
433	C₄⋊C₄	C₂⁴	1	6	yes	—
434	C₄⋊C₄	C₂⁴	1	6	yes	—
435	C₄⋊C₄	C₂⁴	1	3	yes	—
436	C₄⋊C₄	C₂⁴	1	3	yes	—
437	C₄⋊C₄	C₂⁴	1	6	yes	—
438	C₄⋊C₄	C₂⁴	1	6	yes	—
439	C₄⋊C₄	C₂⁴	1	12	yes	—
440	C₄⋊C₄	C₂⁴	1	6	yes	—
441	C₄⋊C₄	C₂⁴	1	6	yes	—
442	C₄⋊C₄	C₂⁴	1	6	yes	—
443	C₄⋊C₄	C₂⁴	1	12	yes	—
444	C₄⋊C₄	C₂⁴	1	6	yes	—
445	C₄⋊C₄	C₂⁴	1	2	yes	—
446	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄	C₂⁴	1	6	yes	—
449	C₄⋊C₄	C₂⁴	1	12	yes	—
450	C₄⋊C₄	C₂⁴	1	12	yes	—
451	C₄⋊C₄	C₂⁴	1	6	yes	—
452	C₄⋊C₄	C₂⁴	1	6	yes	—
453	C₄⋊C₄	C₂⁴	1	6	yes	—
454	C₄⋊C₄	C₂⁴	1	6	yes	—
455	C₄⋊C₄	C₂⁴	1	6	yes	—
456	C₄⋊C₄	C₂⁴	1	6	yes	—
457	C₄⋊C₄	C₂⁴	1	6	yes	—
458	C₄⋊C₄	C₂⁴	1	2	yes	—
459	C₂²⋊C₄	C₂⁴	1	6	yes	—
460	C₂²⋊C₄	C₂⁴	1	6	yes	—
461	C₂²⋊C₄	C₂⁴	1	6	yes	—
462	C₂²⋊C₄	C₂⁴	1	12	yes	—
463	C₂²⋊C₄	C₂⁴	1	12	yes	—
464	C₂²⋊C₄	C₂⁴	1	6	yes	—
465	C₂²⋊C₄	C₂⁴	1	6	yes	—
466	C₂²⋊C₄	C₂⁴	1	6	yes	—
467	C₂²⋊C₄	C₂⁴	1	12	yes	—
468	C₂²⋊C₄	C₂⁴	1	12	yes	—
469	C₂²⋊C₄	C₂⁴	1	12	yes	—
470	C₂²⋊C₄	C₂⁴	1	2	yes	—
471	C₂²⋊C₄	C₂⁴	1	2	yes	—
472	C₂²⋊C₄	C₂⁴	1	6	yes	—
473	C₂²⋊C₄	C₂⁴	1	12	yes	—
474	C₂²⋊C₄	C₂⁴	1	2	yes	—
475	C₂²⋊C₄	C₂⁴	1	2	yes	—
476	C₂²⋊C₄	C₂⁴	1	6	yes	—
477	C₂²⋊C₄	C₂⁴	1	2	yes	—
478	C₂²⋊C₄	C₂⁴	1	6	yes	—
479	C₂²⋊C₄	C₂⁴	1	6	yes	—
480	C₂²⋊C₄	C₂⁴	1	6	yes	—
481	C₂²⋊C₄	C₂⁴	1	12	yes	—
482	C₂²⋊C₄	C₂⁴	1	6	yes	—
483	C₂²⋊C₄	C₂⁴	1	6	yes	—
484	C₂²⋊C₄	C₂⁴	1	6	yes	—
485	C₂²⋊C₄	C₂⁴	1	2	yes	—
486	C₂²⋊C₄	C₂⁴	1	2	yes	—
487	C₂²⋊C₄	C₂⁴	1	6	yes	—
488	C₄²	C₂⁴	1	6	yes	—
489	C₄²	C₂⁴	1	2	yes	—
490	C₄²	C₂⁴	1	6	yes	—
491	C₄²	C₂⁴	1	6	yes	—
492	C₄²	C₂⁴	1	6	yes	—
493	C₄²	C₂⁴	1	6	yes	—
494	C₄²	C₂⁴	1	6	yes	—
495	C₄²	C₂⁴	1	6	yes	—
496	C₄²	C₂⁴	1	12	yes	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	6	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	3	no	—
502	C₂³	—	4	3	no	—
503	C₂³	—	4	6	no	—
504	C₂³	—	4	6	no	—
505	C₂³	—	4	6	no	—
506	C₂³	C₂⁵	1	3	yes	—
507	C₂³	C₂⁵	1	6	yes	—
508	C₂³	C₂⁵	1	2	yes	—
509	C₂³	C₂⁵	1	3	yes	—
510	C₂³	C₂⁵	1	2	yes	—
511	C₂³	C₂⁵	1	1	yes	characteristic
512	Q₈	—	2	12	no	—
513	Q₈	—	2	6	no	—
514	Q₈	—	2	12	no	—
515	Q₈	—	4	6	no	—
516	Q₈	—	4	3	no	—
517	Q₈	—	4	6	no	—
518	Q₈	—	4	6	no	—
519	Q₈	—	4	1	no	—
520	Q₈	H(5,𝔽₂)	1	4	yes	—
521	D₄	—	2	12	no	—
522	D₄	—	2	4	no	—
523	D₄	—	2	6	no	—
524	D₄	—	2	12	no	—
525	D₄	—	2	6	no	—
526	D₄	—	4	3	no	—
527	D₄	—	4	6	no	—
528	D₄	—	4	6	no	—
529	D₄	—	4	6	no	—
530	D₄	—	4	12	no	—
531	D₄	—	4	6	no	—
532	D₄	—	4	6	no	—
533	D₄	—	4	6	no	—
534	D₄	—	4	6	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	6	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	6	no	—
540	D₄	—	4	6	no	—
541	D₄	—	4	6	no	—
542	C₂×C₄	—	2	6	no	—
543	C₂×C₄	—	2	6	no	—
544	C₂×C₄	—	2	6	no	—
545	C₂×C₄	—	2	12	no	—
546	C₂×C₄	—	2	6	no	—
547	C₂×C₄	—	2	12	no	—
548	C₂×C₄	—	2	12	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	6	no	—
551	C₂×C₄	—	4	3	no	—
552	C₂×C₄	—	4	3	no	—
553	C₂×C₄	—	4	3	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	6	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	6	no	—
558	C₂×C₄	—	4	6	no	—
559	C₂×C₄	—	4	6	no	—
560	C₂×C₄	—	4	12	no	—
561	C₂×C₄	—	4	6	no	—
562	C₂×C₄	—	4	6	no	—
563	C₂×C₄	C₂⁵	1	2	yes	—
564	C₂×C₄	C₂⁵	1	2	yes	—
565	C₂×C₄	C₂⁵	1	2	yes	—
566	C₂×C₄	C₂⁵	1	6	yes	—
567	C₂×C₄	C₂⁵	1	6	yes	—
568	C₂×C₄	C₂⁵	1	6	yes	—
569	C₂×C₄	C₂⁵	1	2	yes	—
570	C₂×C₄	C₂⁵	1	6	yes	—
571	C₂×C₄	C₂⁵	1	3	yes	—
572	C₂×C₄	C₂⁵	1	6	yes	—
573	C₂×C₄	C₂⁵	1	1	yes	characteristic
574	C₂×C₄	C₂⁵	1	1	yes	characteristic
575	C₂×C₄	C₂⁵	1	3	yes	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	3	no	—
581	C₂²	—	2	6	no	—
582	C₂²	—	2	3	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	3	no	—
585	C₂²	—	2	6	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	3	no	—
588	C₂²	—	2	3	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	6	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	3	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	8	6	no	—
595	C₂²	—	16	6	no	—
596	C₂²	#585	1	2	yes	—
597	C₂²	C₂⁶	1	1	yes	characteristic
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	3	no	—
602	C₄	—	2	6	no	—
603	C₄	—	2	6	no	—
604	C₄	—	2	6	no	—
605	C₄	—	2	6	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	6	no	—
609	C₄	—	2	2	no	—
610	C₄	C₂×H(5,𝔽₂)	1	6	yes	—
611	C₂	—	2	2	no	—
612	C₂	—	4	2	no	—
613	C₂	—	4	2	no	—
614	C₂	—	4	3	no	—
615	C₂	—	4	3	no	—
616	C₂	—	4	6	no	—
617	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
618	C₂	C₂×#585	1	1	yes	characteristic
619	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. #3562	C₂	semidirect
2. #3561	C₂	semidirect
3. #3551	C₂	semidirect
4. #3547	C₂	semidirect
5. #3542	C₂	semidirect
6. #3538	C₂	semidirect
7. #3536	C₂	semidirect
8. #3524	C₂	semidirect
9. #3516	C₂	semidirect
10. #3514	C₂	semidirect
11. #3505	C₂	semidirect
12. #3500	C₂	semidirect
13. #3497	C₂	semidirect
14. #3489	C₂	semidirect
15. #3488	C₂	semidirect
16. #3486	C₂	semidirect
17. #3482	C₂	semidirect
18. C₂×#548	C₂	semidirect
19. #3460	C₂	semidirect
20. C₂×2₋¹⁺⁴	C₂²	semidirect
21. C₂×2₋¹⁺⁴	C₂²	semidirect
22. C₂×H(5,𝔽₂)	C₂²	semidirect
24. C₂³×Q₈	C₂²	semidirect
25. #563	C₂²	semidirect
26. #562	C₂²	semidirect
27. #562	C₂²	semidirect
28. #560	C₂²	semidirect
29. #559	C₂²	semidirect
30. #557	C₂²	semidirect
31. #556	C₂²	semidirect
32. #556	C₂²	semidirect
33. #555	C₂²	semidirect
34. #555	C₂²	semidirect
35. #554	C₂²	semidirect
36. #553	C₂²	semidirect
37. #553	C₂²	semidirect
38. #553	C₂²	semidirect
39. #552	C₂²	semidirect
40. #552	C₂²	semidirect
41. #552	C₂²	semidirect
42. #552	C₂²	semidirect
43. #551	C₂²	semidirect
44. #551	C₂²	semidirect
45. #551	C₂²	semidirect
46. #550	C₂²	semidirect
47. #550	C₂²	semidirect
48. D₄×Q₈	C₂²	semidirect
49. D₄×Q₈	C₂²	semidirect
50. D₄×Q₈	C₂²	semidirect
51. D₄×Q₈	C₂²	semidirect
52. D₄×Q₈	C₂²	semidirect
55. #548	C₂²	semidirect
56. #548	C₂²	semidirect
57. #548	C₂²	semidirect
58. #548	C₂²	semidirect
59. #548	C₂²	semidirect
60. #548	C₂²	semidirect
61. #548	C₂²	semidirect
62. #548	C₂²	semidirect
63. #548	C₂²	semidirect
64. #548	C₂²	semidirect
65. #547	C₂²	semidirect
66. #547	C₂²	semidirect
67. #546	C₂²	semidirect
68. #546	C₂²	semidirect
69. #546	C₂²	semidirect
70. #546	C₂²	semidirect
71. #546	C₂²	semidirect
72. #546	C₂²	semidirect
73. #546	C₂²	semidirect
75. #544	C₂²	semidirect
76. #544	C₂²	semidirect
77. #543	C₂²	semidirect
78. #542	C₂²	semidirect
79. #542	C₂²	semidirect
80. #542	C₂²	semidirect
81. #542	C₂²	semidirect
82. #542	C₂²	semidirect
83. #541	C₂²	semidirect
84. #540	C₂²	semidirect
85. #540	C₂²	semidirect
86. #540	C₂²	semidirect
87. #540	C₂²	semidirect
88. #539	C₂²	semidirect
89. #539	C₂²	semidirect
90. #538	C₂²	semidirect
91. #538	C₂²	semidirect
92. #538	C₂²	semidirect
93. #538	C₂²	semidirect
94. #538	C₂²	semidirect
95. #538	C₂²	semidirect
96. #537	C₂²	semidirect
97. #537	C₂²	semidirect
98. #537	C₂²	semidirect
99. #537	C₂²	semidirect
100. #537	C₂²	semidirect
101. #536	C₂²	semidirect
102. #536	C₂²	semidirect
103. #536	C₂²	semidirect
104. #536	C₂²	semidirect
105. #535	C₂²	semidirect
106. #535	C₂²	semidirect
107. #535	C₂²	semidirect
108. #534	C₂²	semidirect
109. #533	C₂²	semidirect
110. #532	C₂²	semidirect
111. #532	C₂²	semidirect
112. #532	C₂²	semidirect
113. #529	C₂²	semidirect
114. #529	C₂²	semidirect
115. #529	C₂²	semidirect
116. #529	C₂²	semidirect
117. #529	C₂²	semidirect
118. #529	C₂²	semidirect
119. C₂×#124	C₂²	semidirect
120. C₂×#124	C₂²	semidirect
122. #525	C₂²	semidirect
123. #525	C₂²	semidirect
124. #525	C₂²	semidirect
125. C₂×C₂²⋊Q₈	C₂²	semidirect
126. C₂×C₂²⋊Q₈	C₂²	semidirect
128. C₂×#121	C₂²	semidirect
129. #520	C₂²	semidirect
130. #520	C₂²	semidirect
131. #519	C₂²	semidirect
132. #518	C₂²	semidirect
133. C₄×#41	C₂²	semidirect
134. C₄×#41	C₂²	semidirect
135. C₂×C₄×Q₈	C₂²	semidirect
136. C₂×C₄×Q₈	C₂²	semidirect
137. C₂×C₄×D₄	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3562	2
#3561	2
#3551	2
#3547	2
#3542	2
#3538	2
#3536	2
#3524	2
#3516	2
#3514	2
#3505	2
#3500	2
#3497	2
#3489	2
#3488	2
#3486	2
#3482	2
C₂×#548	2
#3460	2