Subgroups — C₂×#3562 #62740

Order 256.

3677 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂³	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶
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. #3562	C₂	direct (N × H)
2. C₂×#562	C₂	semidirect
3. C₂×#560	C₂	semidirect
4. C₂×#559	C₂	semidirect
5. C₂×#556	C₂	semidirect
6. C₂×#553	C₂	semidirect
7. C₂×#551	C₂	semidirect
8. C₂×#550	C₂	semidirect
9. C₂×#548	C₂	semidirect
10. C₂×#548	C₂	semidirect
11. C₂×#547	C₂	semidirect
12. C₂×#546	C₂	semidirect
13. C₂×#546	C₂	semidirect
14. C₂×#541	C₂	semidirect
15. C₂×#540	C₂	semidirect
16. C₂×#540	C₂	semidirect
17. C₂×#539	C₂	semidirect
18. C₂×#538	C₂	semidirect
19. C₂×#538	C₂	semidirect
20. C₂×#536	C₂	semidirect
21. C₂×#535	C₂	semidirect
22. C₂×#532	C₂	semidirect
23. C₂×#529	C₂	semidirect
24. C₂×#529	C₂	semidirect
28. C₂²×#41	C₂²	semidirect
29. C₂³×Q₈	C₂²	semidirect
31. #562	C₂²	semidirect
32. #560	C₂²	semidirect
33. #559	C₂²	semidirect
34. #556	C₂²	semidirect
35. #553	C₂²	semidirect
36. #551	C₂²	semidirect
37. #550	C₂²	semidirect
38. #548	C₂²	semidirect
39. #548	C₂²	semidirect
40. #547	C₂²	semidirect
41. #546	C₂²	semidirect
42. #546	C₂²	semidirect
43. #541	C₂²	semidirect
44. #540	C₂²	semidirect
45. #540	C₂²	semidirect
46. #539	C₂²	semidirect
47. #538	C₂²	semidirect
48. #538	C₂²	semidirect
49. #536	C₂²	semidirect
50. #535	C₂²	semidirect
51. #532	C₂²	semidirect
52. C₂×C₄⋊Q₈	C₂²	semidirect
53. C₂×C₄⋊Q₈	C₂²	semidirect
56. C₂×#127	C₂²	semidirect
57. #529	C₂²	semidirect
58. #529	C₂²	semidirect
62. C₂×#126	C₂²	semidirect
63. C₂×#126	C₂²	semidirect
64. C₂×#126	C₂²	semidirect
65. C₂×#126	C₂²	semidirect
66. C₂×#125	C₂²	semidirect
67. C₂×#125	C₂²	semidirect
68. C₂×#125	C₂²	semidirect
69. C₂×#125	C₂²	semidirect
76. C₂×#124	C₂²	semidirect
77. C₂×#124	C₂²	semidirect
78. C₂×#124	C₂²	semidirect
83. C₂×#123	C₂²	semidirect
84. C₂×#123	C₂²	semidirect
85. C₂×#123	C₂²	semidirect
86. C₂×#123	C₂²	semidirect
87. C₂×#123	C₂²	semidirect
88. C₂×#123	C₂²	semidirect
89. C₂×#123	C₂²	semidirect
90. C₂×#123	C₂²	semidirect
91. C₂×#123	C₂²	semidirect
94. C₂×C₂²⋊Q₈	C₂²	semidirect
95. C₂×C₂²⋊Q₈	C₂²	semidirect
96. C₂×C₂²⋊Q₈	C₂²	semidirect
97. C₂×C₂²⋊Q₈	C₂²	semidirect
98. C₂×C₂²⋊Q₈	C₂²	semidirect
99. C₂×C₂²⋊Q₈	C₂²	semidirect
100. C₂×C₂²⋊Q₈	C₂²	semidirect
110. C₂×#121	C₂²	semidirect
111. C₂×#121	C₂²	semidirect
112. C₂×#121	C₂²	semidirect
113. C₂×#121	C₂²	semidirect
114. C₂×#121	C₂²	semidirect
115. C₂×#121	C₂²	semidirect
116. C₂×#121	C₂²	semidirect
117. C₂×#121	C₂²	semidirect
122. C₂×C₄×Q₈	C₂²	semidirect
123. C₂×C₄×Q₈	C₂²	semidirect
124. C₂×C₄×Q₈	C₂²	semidirect
125. C₂×C₄×Q₈	C₂²	semidirect
130. C₂×C₄×D₄	C₂²	semidirect
131. C₂×C₄×D₄	C₂²	semidirect
132. C₂×C₄×D₄	C₂²	semidirect
133. C₂×C₄×D₄	C₂²	semidirect
134. C₂×C₄×D₄	C₂²	semidirect
135. C₂×C₄×D₄	C₂²	semidirect
136. C₂×C₄×D₄	C₂²	semidirect
137. C₂×C₄×D₄	C₂²	semidirect
138. C₂×C₄×D₄	C₂²	semidirect
140. C₂×#117	C₂²	semidirect
141. C₂×#117	C₂²	semidirect
142. C₂×#117	C₂²	semidirect
143. C₂²×C₄⋊C₄	C₂²	semidirect
146. C₂²×C₄²	C₂²	semidirect
155. C₂×#41	C₂³	semidirect
162. C₂²×Q₈	C₂³	semidirect
196. C₄⋊Q₈	C₂³	semidirect
197. C₄⋊Q₈	C₂³	semidirect
200. #127	C₂³	semidirect
204. #126	C₂³	semidirect
205. #126	C₂³	semidirect
206. #126	C₂³	semidirect
207. #126	C₂³	semidirect
208. #125	C₂³	semidirect
209. #125	C₂³	semidirect
210. #125	C₂³	semidirect
211. #125	C₂³	semidirect
218. #124	C₂³	semidirect
219. #124	C₂³	semidirect
220. #124	C₂³	semidirect
225. #123	C₂³	semidirect
226. #123	C₂³	semidirect
227. #123	C₂³	semidirect
228. #123	C₂³	semidirect
229. #123	C₂³	semidirect
230. #123	C₂³	semidirect
231. #123	C₂³	semidirect
232. #123	C₂³	semidirect
233. #123	C₂³	semidirect
236. C₂²⋊Q₈	C₂³	semidirect
237. C₂²⋊Q₈	C₂³	semidirect
238. C₂²⋊Q₈	C₂³	semidirect
239. C₂²⋊Q₈	C₂³	semidirect
240. C₂²⋊Q₈	C₂³	semidirect
241. C₂²⋊Q₈	C₂³	semidirect
242. C₂²⋊Q₈	C₂³	semidirect
252. #121	C₂³	semidirect
253. #121	C₂³	semidirect
254. #121	C₂³	semidirect
255. #121	C₂³	semidirect
256. #121	C₂³	semidirect
257. #121	C₂³	semidirect
258. #121	C₂³	semidirect
259. #121	C₂³	semidirect
264. C₄×Q₈	C₂³	semidirect
265. C₄×Q₈	C₂³	semidirect
266. C₄×Q₈	C₂³	semidirect
267. C₄×Q₈	C₂³	semidirect
272. C₄×D₄	C₂³	semidirect
273. C₄×D₄	C₂³	semidirect
274. C₄×D₄	C₂³	semidirect
275. C₄×D₄	C₂³	semidirect
276. C₄×D₄	C₂³	semidirect
277. C₄×D₄	C₂³	semidirect
278. C₄×D₄	C₂³	semidirect
279. C₄×D₄	C₂³	semidirect
280. C₄×D₄	C₂³	semidirect
282. #117	C₂³	semidirect
283. #117	C₂³	semidirect
284. #117	C₂³	semidirect
309. C₂×C₄⋊C₄	C₂³	semidirect
350. C₂×C₄²	C₂³	semidirect
669. C₂	#3562	direct (N × H)

Maximal subgroups

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

subgroup	index
#3562	2
C₂×#562	2
C₂×#560	2
C₂×#559	2
C₂×#556	2
C₂×#553	2
C₂×#551	2
C₂×#550	2
C₂×#548	2
C₂×#547	2
C₂×#546	2
C₂×#541	2
C₂×#540	2
C₂×#539	2
C₂×#538	2
C₂×#536	2
C₂×#535	2
C₂×#532	2
C₂×#529	2

Subgroups — C2×#3562 #62740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3562 #62740