Subgroups — C₂×#3520 #62772

Order 256.

3955 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3520	C₂	1	32	yes	maximal, direct product factor
2	C₂×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#554	C₂	1	2	yes	maximal, complemented
4	C₂×#552	C₂	1	2	yes	maximal, complemented
5	C₂×#551	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#548	C₂	1	2	yes	maximal, complemented
8	C₂×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#546	C₂	1	2	yes	maximal, complemented
11	C₂×#542	C₂	1	2	yes	maximal, complemented
12	C₂×#539	C₂	1	4	yes	maximal, complemented
13	C₂×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#525	C₂	1	2	yes	maximal, complemented
16	C₂²×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
17	C₂×#520	C₂	1	2	yes	maximal, complemented
18	C₂²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41	C₂²	1	2	yes	—
20	C₂²×#41	C₂²	1	2	yes	complemented
21	C₂³×Q₈	C₂²	1	2	yes	complemented
22	C₂³×D₄	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄	C₂²	1	2	yes	—
24	#556	C₂²	1	16	yes	complemented
25	#554	C₂²	1	32	yes	complemented
26	#552	C₂²	1	32	yes	complemented
27	#551	C₂²	1	64	yes	complemented
28	D₄×Q₈	C₂²	1	16	yes	complemented
29	#548	C₂²	1	32	yes	complemented
30	#547	C₂²	1	16	yes	complemented
31	#547	C₂²	1	16	yes	complemented
32	#546	C₂²	1	32	yes	complemented
33	#542	C₂²	1	32	yes	complemented
34	#539	C₂²	1	64	yes	complemented
35	#533	C₂²	1	16	yes	complemented
36	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
39	#529	C₂²	1	16	yes	complemented
40	C₂×#126	C₂²	1	2	yes	complemented
41	C₂×#126	C₂²	1	4	yes	complemented
42	C₂×#126	C₂²	1	4	yes	complemented
43	C₂×#125	C₂²	1	1	yes	characteristic, complemented
44	C₂×#125	C₂²	1	2	yes	complemented
45	C₂×#125	C₂²	1	4	yes	complemented
46	C₂×#124	C₂²	1	2	yes	—
47	C₂×#124	C₂²	1	1	yes	characteristic, complemented
48	C₂×#124	C₂²	1	4	yes	complemented
49	#525	C₂²	1	32	yes	complemented
50	C₂×#123	C₂²	1	2	yes	—
51	C₂×#123	C₂²	1	4	yes	—
52	C₂×#123	C₂²	1	4	yes	complemented
53	C₂×#123	C₂²	1	4	yes	complemented
54	C₂×#123	C₂²	1	4	yes	complemented
55	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₂×C₂²⋊Q₈	C₂²	1	4	yes	—
58	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
59	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
64	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
65	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₂×C₂²⋊Q₈	C₂²	1	32	yes	complemented
67	C₂×#121	C₂²	1	1	yes	characteristic
68	C₂×#121	C₂²	1	4	yes	—
69	C₂×#121	C₂²	1	2	yes	—
70	C₂×#121	C₂²	1	2	yes	complemented
71	C₂×#120	C₂²	1	4	yes	—
72	#520	C₂²	1	32	yes	complemented
73	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
74	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
75	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
77	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
78	C₂×C₄×D₄	C₂²	1	2	yes	—
79	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
80	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
81	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
82	C₂×C₄×D₄	C₂²	1	2	yes	—
83	C₂×C₄×D₄	C₂²	1	2	yes	—
84	C₂×C₄×D₄	C₂²	1	4	yes	—
85	C₂×C₄×D₄	C₂²	1	2	yes	—
86	C₂×C₄×D₄	C₂²	1	16	yes	complemented
87	C₂×C₄×D₄	C₂²	1	4	yes	complemented
88	C₂×C₄×D₄	C₂²	1	4	yes	complemented
89	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
90	C₂×#117	C₂²	1	2	yes	—
91	C₂×#117	C₂²	1	2	yes	complemented
92	C₂×#117	C₂²	1	4	yes	complemented
93	C₂×#117	C₂²	1	2	yes	complemented
94	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₂²×C₄⋊C₄	C₂²	1	4	yes	complemented
96	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₂²×C₂²⋊C₄	C₂²	1	4	yes	—
100	C₂²×C₄²	C₂²	1	1	yes	characteristic
101	C₂⁵	C₂³	1	2	yes	—
102	C₂×#41	—	2	16	no	—
103	C₂×#41	—	4	8	no	—
104	C₂×#41	C₂³	1	16	yes	—
105	C₂×#41	C₂³	1	16	yes	complemented
106	C₂²×Q₈	—	4	8	no	—
107	C₂²×Q₈	C₂³	1	2	yes	—
108	C₂²×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×Q₈	C₂³	1	2	yes	—
110	C₂²×Q₈	C₂³	1	4	yes	—
111	C₂²×Q₈	C₂³	1	16	yes	complemented
112	C₂²×D₄	—	2	8	no	—
113	C₂²×D₄	C₂³	1	2	yes	—
114	C₂²×D₄	C₂³	1	2	yes	—
115	C₂²×D₄	C₂³	1	1	yes	characteristic
116	C₂²×D₄	C₂³	1	4	yes	—
117	C₂²×D₄	C₂³	1	8	yes	—
118	C₂²×D₄	C₂³	1	1	yes	characteristic
119	C₂²×D₄	C₂³	1	4	yes	—
120	C₂²×D₄	C₂³	1	1	yes	characteristic
121	C₂³×C₄	—	4	8	no	—
122	C₂³×C₄	C₂³	1	1	yes	characteristic
123	C₂³×C₄	C₂³	1	4	yes	—
124	C₂³×C₄	C₂³	1	1	yes	characteristic
125	C₂³×C₄	C₂³	1	2	yes	—
126	C₂³×C₄	C₂³	1	2	yes	—
127	C₂³×C₄	C₂³	1	2	yes	—
128	C₂³×C₄	C₂³	1	1	yes	characteristic
129	C₂³×C₄	C₂³	1	2	yes	—
130	C₂³×C₄	C₂³	1	4	yes	—
131	C₂³×C₄	C₂³	1	2	yes	—
132	C₂³×C₄	C₂³	1	4	yes	—
133	C₂³×C₄	C₂³	1	2	yes	—
134	C₂³×C₄	C₂³	1	16	yes	—
135	C₄⋊Q₈	C₂³	1	8	yes	complemented
136	C₄⋊Q₈	C₂³	1	8	yes	complemented
137	C₄⋊Q₈	C₂³	1	16	yes	complemented
138	#126	C₂³	1	16	yes	complemented
139	#126	C₂³	1	32	yes	complemented
140	#126	C₂³	1	32	yes	complemented
141	#125	C₂³	1	8	yes	complemented
142	#125	C₂³	1	16	yes	complemented
143	#125	C₂³	1	32	yes	complemented
144	#124	C₂³	1	16	yes	—
145	#124	C₂³	1	8	yes	complemented
146	#124	C₂³	1	32	yes	complemented
147	#123	C₂³	1	16	yes	—
148	#123	C₂³	1	32	yes	—
149	#123	C₂³	1	32	yes	complemented
150	#123	C₂³	1	32	yes	complemented
151	#123	C₂³	1	32	yes	complemented
152	C₂²⋊Q₈	C₂³	1	8	yes	—
153	C₂²⋊Q₈	C₂³	1	16	yes	—
154	C₂²⋊Q₈	C₂³	1	32	yes	—
155	C₂²⋊Q₈	C₂³	1	16	yes	—
156	C₂²⋊Q₈	C₂³	1	32	yes	complemented
157	C₂²⋊Q₈	C₂³	1	16	yes	complemented
158	C₂²⋊Q₈	C₂³	1	16	yes	complemented
159	C₂²⋊Q₈	C₂³	1	16	yes	complemented
160	C₂²⋊Q₈	C₂³	1	32	yes	complemented
161	C₂²⋊Q₈	C₂³	1	32	yes	complemented
162	C₂²⋊Q₈	C₂³	1	16	yes	complemented
163	#121	C₂³	1	8	yes	—
164	#121	C₂³	1	32	yes	—
165	#121	C₂³	1	16	yes	—
166	#121	C₂³	1	16	yes	complemented
167	#120	C₂³	1	32	yes	—
168	C₄×Q₈	C₂³	1	16	yes	complemented
169	C₄×Q₈	C₂³	1	16	yes	complemented
170	C₄×Q₈	C₂³	1	8	yes	complemented
171	C₄×Q₈	C₂³	1	16	yes	complemented
172	C₄×D₄	C₂³	1	8	yes	—
173	C₄×D₄	C₂³	1	16	yes	—
174	C₄×D₄	C₂³	1	8	yes	—
175	C₄×D₄	C₂³	1	8	yes	—
176	C₄×D₄	C₂³	1	8	yes	—
177	C₄×D₄	C₂³	1	16	yes	—
178	C₄×D₄	C₂³	1	16	yes	—
179	C₄×D₄	C₂³	1	32	yes	—
180	C₄×D₄	C₂³	1	16	yes	—
181	C₄×D₄	C₂³	1	32	yes	complemented
182	C₄×D₄	C₂³	1	32	yes	complemented
183	C₄×D₄	C₂³	1	8	yes	complemented
184	#117	C₂³	1	16	yes	—
185	#117	C₂³	1	16	yes	complemented
186	#117	C₂³	1	32	yes	complemented
187	#117	C₂³	1	16	yes	complemented
188	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄	C₂³	1	8	yes	—
192	C₂×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₄⋊C₄	C₂³	1	4	yes	—
199	C₂×C₄⋊C₄	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂³	1	4	yes	—
205	C₂×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄	C₂³	1	32	yes	complemented
209	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
210	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
211	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
213	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
218	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
220	C₂×C₂²⋊C₄	C₂³	1	32	yes	—
221	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
225	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₄²	C₂³	1	4	yes	—
229	C₂×C₄²	C₂³	1	1	yes	characteristic
230	C₂×C₄²	C₂³	1	4	yes	—
231	C₂×C₄²	C₂³	1	2	yes	—
232	C₂×C₄²	C₂³	1	1	yes	characteristic
233	C₂×C₄²	C₂³	1	1	yes	characteristic
234	C₂×C₄²	C₂³	1	1	yes	characteristic
235	C₂×C₄²	C₂³	1	8	yes	—
236	C₂⁴	—	2	8	no	—
237	C₂⁴	—	2	8	no	—
238	C₂⁴	—	4	4	no	—
239	C₂⁴	C₂⁴	1	2	yes	—
240	C₂⁴	C₂⁴	1	2	yes	—
241	C₂⁴	C₂⁴	1	8	yes	—
242	C₂⁴	C₂⁴	1	2	yes	—
243	C₂⁴	C₂⁴	1	1	yes	characteristic
244	#41	—	2	64	no	—
245	#41	—	4	32	no	—
246	C₂×Q₈	—	2	8	no	—
247	C₂×Q₈	—	2	4	no	—
248	C₂×Q₈	—	2	8	no	—
249	C₂×Q₈	—	4	8	no	—
250	C₂×Q₈	—	4	32	no	—
251	C₂×Q₈	C₂⁴	1	8	yes	—
252	C₂×Q₈	C₂⁴	1	4	yes	—
253	C₂×Q₈	C₂⁴	1	8	yes	—
254	C₂×Q₈	C₂⁴	1	16	yes	—
255	C₂×D₄	—	2	8	no	—
256	C₂×D₄	—	2	16	no	—
257	C₂×D₄	—	2	8	no	—
258	C₂×D₄	—	2	32	no	—
259	C₂×D₄	—	2	4	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	4	8	no	—
262	C₂×D₄	#41	1	8	yes	complemented
263	C₂×D₄	C₂⁴	1	8	yes	—
264	C₂×D₄	C₂⁴	1	8	yes	—
265	C₂×D₄	C₂⁴	1	4	yes	—
266	C₂×D₄	C₂⁴	1	16	yes	—
267	C₂×D₄	C₂⁴	1	4	yes	—
268	C₂×D₄	C₂⁴	1	16	yes	—
269	C₂×D₄	C₂⁴	1	4	yes	—
270	C₂²×C₄	—	2	16	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	4	32	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	—	4	4	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	8	no	—
282	C₂²×C₄	—	4	8	no	—
283	C₂²×C₄	C₂⁴	1	4	yes	—
284	C₂²×C₄	C₂⁴	1	4	yes	—
285	C₂²×C₄	C₂⁴	1	4	yes	—
286	C₂²×C₄	C₂⁴	1	16	yes	—
287	C₂²×C₄	C₂⁴	1	8	yes	—
288	C₂²×C₄	C₂⁴	1	8	yes	—
289	C₂²×C₄	C₂⁴	1	8	yes	—
290	C₂²×C₄	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴	1	2	yes	—
292	C₂²×C₄	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄	C₂⁴	1	4	yes	—
294	C₂²×C₄	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴	1	2	yes	—
297	C₂²×C₄	C₂⁴	1	2	yes	—
298	C₂²×C₄	C₂⁴	1	4	yes	—
299	C₂²×C₄	C₂⁴	1	2	yes	—
300	C₂²×C₄	C₂⁴	1	2	yes	—
301	C₂²×C₄	C₂⁴	1	8	yes	—
302	C₂²×C₄	C₂⁴	1	16	yes	—
303	C₂²×C₄	C₂⁴	1	8	yes	—
304	C₂²×C₄	C₂⁴	1	16	yes	—
305	C₂²×C₄	C₂⁴	1	8	yes	—
306	C₂²×C₄	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴	1	1	yes	characteristic
308	C₄⋊C₄	C₂⁴	1	4	yes	—
309	C₄⋊C₄	C₂⁴	1	8	yes	—
310	C₄⋊C₄	C₂⁴	1	4	yes	—
311	C₄⋊C₄	C₂⁴	1	8	yes	—
312	C₄⋊C₄	C₂⁴	1	16	yes	—
313	C₄⋊C₄	C₂⁴	1	4	yes	—
314	C₄⋊C₄	C₂⁴	1	8	yes	—
315	C₄⋊C₄	C₂⁴	1	8	yes	—
316	C₄⋊C₄	C₂⁴	1	16	yes	—
317	C₄⋊C₄	C₂⁴	1	16	yes	—
318	C₄⋊C₄	C₂⁴	1	16	yes	—
319	C₄⋊C₄	C₂⁴	1	8	yes	—
320	C₄⋊C₄	C₂⁴	1	8	yes	—
321	C₄⋊C₄	C₂⁴	1	8	yes	—
322	C₄⋊C₄	C₂⁴	1	4	yes	—
323	C₄⋊C₄	C₂⁴	1	16	yes	—
324	C₄⋊C₄	C₂⁴	1	8	yes	—
325	C₄⋊C₄	C₂⁴	1	16	yes	—
326	C₄⋊C₄	C₂⁴	1	8	yes	—
327	C₂²⋊C₄	C₂⁴	1	8	yes	—
328	C₂²⋊C₄	C₂⁴	1	16	yes	—
329	C₂²⋊C₄	C₂⁴	1	8	yes	—
330	C₂²⋊C₄	C₂⁴	1	8	yes	—
331	C₂²⋊C₄	C₂⁴	1	8	yes	—
332	C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₂²⋊C₄	C₂⁴	1	16	yes	—
334	C₂²⋊C₄	C₂⁴	1	16	yes	—
335	C₂²⋊C₄	C₂⁴	1	16	yes	—
336	C₂²⋊C₄	C₂⁴	1	8	yes	—
337	C₂²⋊C₄	C₂⁴	1	8	yes	—
338	C₂²⋊C₄	C₂⁴	1	16	yes	—
339	C₂²⋊C₄	C₂⁴	1	8	yes	—
340	C₂²⋊C₄	C₂⁴	1	16	yes	—
341	C₂²⋊C₄	C₂⁴	1	8	yes	—
342	C₄²	C₂⁴	1	4	yes	—
343	C₄²	C₂⁴	1	4	yes	—
344	C₄²	C₂⁴	1	4	yes	—
345	C₄²	C₂⁴	1	4	yes	—
346	C₄²	C₂⁴	1	16	yes	—
347	C₄²	C₂⁴	1	16	yes	—
348	C₄²	C₂⁴	1	8	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	2	16	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	16	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	32	no	—
363	C₂³	C₂×#41	1	8	yes	—
364	C₂³	2₋¹⁺⁴	1	4	yes	—
365	C₂³	C₂⁵	1	4	yes	—
366	C₂³	C₂⁵	1	4	yes	—
367	C₂³	C₂⁵	1	4	yes	—
368	C₂³	C₂⁵	1	2	yes	—
369	C₂³	C₂⁵	1	1	yes	characteristic
370	Q₈	—	2	16	no	—
371	Q₈	—	2	8	no	—
372	Q₈	—	2	16	no	—
373	Q₈	—	4	16	no	—
374	D₄	—	2	16	no	—
375	D₄	—	2	32	no	—
376	D₄	—	2	16	no	—
377	D₄	—	2	8	no	—
378	D₄	—	2	8	no	—
379	D₄	—	4	16	no	—
380	D₄	C₂×#41	1	16	yes	complemented
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	32	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	16	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	16	no	—
398	C₂×C₄	—	2	16	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	16	no	—
403	C₂×C₄	—	4	16	no	—
404	C₂×C₄	C₂×#41	1	4	yes	—
405	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
406	C₂×C₄	C₂⁵	1	2	yes	—
407	C₂×C₄	C₂⁵	1	4	yes	—
408	C₂×C₄	C₂⁵	1	2	yes	—
409	C₂×C₄	C₂⁵	1	8	yes	—
410	C₂×C₄	C₂⁵	1	2	yes	—
411	C₂×C₄	C₂⁵	1	2	yes	—
412	C₂×C₄	C₂⁵	1	4	yes	—
413	C₂×C₄	C₂⁵	1	4	yes	—
414	C₂×C₄	C₂⁵	1	8	yes	—
415	C₂×C₄	C₂⁵	1	4	yes	—
416	C₂×C₄	C₂⁵	1	4	yes	—
417	C₂×C₄	C₂⁵	1	2	yes	—
418	C₂×C₄	C₂⁵	1	2	yes	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	16	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	32	no	—
432	C₂²	—	4	8	no	—
433	C₂²	—	4	8	no	—
434	C₂²	C₂²×#41	1	8	yes	—
435	C₂²	C₂²×#41	1	2	yes	—
436	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
437	C₂²	C₂×2₋¹⁺⁴	1	4	yes	—
438	C₂²	C₂×2₋¹⁺⁴	1	2	yes	—
439	C₂²	C₂⁶	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	8	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	8	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	4	no	—
451	C₄	C₂²×#41	1	4	yes	—
452	C₄	C₂×H(5,𝔽₂)	1	4	yes	—
453	C₂	—	2	4	no	—
454	C₂	—	2	8	no	—
455	C₂	—	4	4	no	—
456	C₂	—	4	4	no	—
457	C₂	#3520	1	4	yes	direct product factor
458	C₂	C₂³×#41	1	1	yes	characteristic
459	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂	C₂²×2₋¹⁺⁴	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. #3520	C₂	direct (N × H)
2. C₂×#556	C₂	semidirect
3. C₂×#554	C₂	semidirect
4. C₂×#552	C₂	semidirect
5. C₂×#551	C₂	semidirect
6. C₂×D₄×Q₈	C₂	semidirect
7. C₂×#548	C₂	semidirect
8. C₂×#547	C₂	semidirect
9. C₂×#547	C₂	semidirect
10. C₂×#546	C₂	semidirect
11. C₂×#542	C₂	semidirect
12. C₂×#539	C₂	semidirect
13. C₂×#533	C₂	semidirect
14. C₂×#529	C₂	semidirect
15. C₂×#525	C₂	semidirect
16. C₂²×C₂²⋊Q₈	C₂	semidirect
17. C₂×#520	C₂	semidirect
18. C₂²×C₄×D₄	C₂	semidirect
20. C₂²×#41	C₂²	semidirect
21. C₂³×Q₈	C₂²	semidirect
24. #556	C₂²	semidirect
25. #554	C₂²	semidirect
26. #552	C₂²	semidirect
27. #551	C₂²	semidirect
28. D₄×Q₈	C₂²	semidirect
29. #548	C₂²	semidirect
30. #547	C₂²	semidirect
31. #547	C₂²	semidirect
32. #546	C₂²	semidirect
33. #542	C₂²	semidirect
34. #539	C₂²	semidirect
35. #533	C₂²	semidirect
36. C₂×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₄⋊Q₈	C₂²	semidirect
38. C₂×C₄⋊Q₈	C₂²	semidirect
39. #529	C₂²	semidirect
40. C₂×#126	C₂²	semidirect
41. C₂×#126	C₂²	semidirect
42. C₂×#126	C₂²	semidirect
43. C₂×#125	C₂²	semidirect
44. C₂×#125	C₂²	semidirect
45. C₂×#125	C₂²	semidirect
47. C₂×#124	C₂²	semidirect
48. C₂×#124	C₂²	semidirect
49. #525	C₂²	semidirect
52. C₂×#123	C₂²	semidirect
53. C₂×#123	C₂²	semidirect
54. C₂×#123	C₂²	semidirect
59. C₂×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₂²⋊Q₈	C₂²	semidirect
61. C₂×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₂²⋊Q₈	C₂²	semidirect
63. C₂×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₂²⋊Q₈	C₂²	semidirect
65. C₂×C₂²⋊Q₈	C₂²	semidirect
66. C₂×C₂²⋊Q₈	C₂²	semidirect
70. C₂×#121	C₂²	semidirect
72. #520	C₂²	semidirect
73. C₂×C₄×Q₈	C₂²	semidirect
74. C₂×C₄×Q₈	C₂²	semidirect
75. C₂×C₄×Q₈	C₂²	semidirect
76. C₂×C₄×Q₈	C₂²	semidirect
86. C₂×C₄×D₄	C₂²	semidirect
87. C₂×C₄×D₄	C₂²	semidirect
88. C₂×C₄×D₄	C₂²	semidirect
89. C₂×C₄×D₄	C₂²	semidirect
91. C₂×#117	C₂²	semidirect
92. C₂×#117	C₂²	semidirect
93. C₂×#117	C₂²	semidirect
95. C₂²×C₄⋊C₄	C₂²	semidirect
96. C₂²×C₄⋊C₄	C₂²	semidirect
97. C₂²×C₄⋊C₄	C₂²	semidirect
105. C₂×#41	C₂³	semidirect
111. C₂²×Q₈	C₂³	semidirect
135. C₄⋊Q₈	C₂³	semidirect
136. C₄⋊Q₈	C₂³	semidirect
137. C₄⋊Q₈	C₂³	semidirect
138. #126	C₂³	semidirect
139. #126	C₂³	semidirect
140. #126	C₂³	semidirect
141. #125	C₂³	semidirect
142. #125	C₂³	semidirect
143. #125	C₂³	semidirect
145. #124	C₂³	semidirect
146. #124	C₂³	semidirect
149. #123	C₂³	semidirect
150. #123	C₂³	semidirect
151. #123	C₂³	semidirect
156. C₂²⋊Q₈	C₂³	semidirect
157. C₂²⋊Q₈	C₂³	semidirect
158. C₂²⋊Q₈	C₂³	semidirect
159. C₂²⋊Q₈	C₂³	semidirect
160. C₂²⋊Q₈	C₂³	semidirect
161. C₂²⋊Q₈	C₂³	semidirect
162. C₂²⋊Q₈	C₂³	semidirect
166. #121	C₂³	semidirect
168. C₄×Q₈	C₂³	semidirect
169. C₄×Q₈	C₂³	semidirect
170. C₄×Q₈	C₂³	semidirect
171. C₄×Q₈	C₂³	semidirect
181. C₄×D₄	C₂³	semidirect
182. C₄×D₄	C₂³	semidirect
183. C₄×D₄	C₂³	semidirect
185. #117	C₂³	semidirect
186. #117	C₂³	semidirect
187. #117	C₂³	semidirect
208. C₂×C₄⋊C₄	C₂³	semidirect
209. C₂×C₄⋊C₄	C₂³	semidirect
210. C₂×C₄⋊C₄	C₂³	semidirect
262. C₂×D₄	#41	semidirect
380. D₄	C₂×#41	semidirect
457. C₂	#3520	direct (N × H)

Maximal subgroups

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

subgroup	index
#3520	2
C₂×#556	2
C₂×#554	2
C₂×#552	2
C₂×#551	2
C₂×D₄×Q₈	2
C₂×#548	2
C₂×#547	2
C₂×#546	2
C₂×#542	2
C₂×#539	2
C₂×#533	2
C₂×#529	2
C₂×#525	2
C₂²×C₂²⋊Q₈	2
C₂×#520	2
C₂²×C₄×D₄	2

Subgroups — C2×#3520 #62772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3520 #62772