Subgroups — C₂×#3535 #62722

Order 256.

3651 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

Maximal subgroups

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

subgroup	index
#3535	2
C₂×#563	2
C₂×#562	2
C₂×#554	2
C₂×#552	2
C₂×#551	2
C₂×#547	2
C₂×#546	2
C₂×#544	2
C₂×#543	2
C₂×#542	2
C₂×#539	2
C₂×#538	2
C₂×#536	2
C₂×#525	2
C₂²×#123	2
C₂²×C₂²⋊Q₈	2

Subgroups — C2×#3535 #62722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3535 #62722