Subgroups — C₂×#3560 #62735

Order 256.

3699 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	#3560	C₂	1	32	yes	maximal, direct product factor
2	C₂×#563	C₂	1	2	yes	maximal, complemented
3	C₂×#560	C₂	1	2	yes	maximal, complemented
4	C₂×#553	C₂	1	2	yes	maximal, complemented
5	C₂×#553	C₂	1	2	yes	maximal, complemented
6	C₂×#551	C₂	1	2	yes	maximal, complemented
7	C₂×#547	C₂	1	2	yes	maximal, complemented
8	C₂×#546	C₂	1	2	yes	maximal, complemented
9	C₂×#546	C₂	1	2	yes	maximal, complemented
10	C₂×#542	C₂	1	2	yes	maximal, complemented
11	C₂×#539	C₂	1	2	yes	maximal, complemented
12	C₂×#539	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#538	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#538	C₂	1	2	yes	maximal, complemented
15	C₂×#538	C₂	1	2	yes	maximal, complemented
16	C₂×#537	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#534	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#532	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#126	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#41	C₂²	1	2	yes	complemented
22	C₂²×#41	C₂²	1	2	yes	complemented
23	C₂³×D₄	C₂²	1	2	yes	—
24	#563	C₂²	1	32	yes	complemented
25	#560	C₂²	1	32	yes	complemented
26	#553	C₂²	1	32	yes	complemented
27	#553	C₂²	1	32	yes	complemented
28	#551	C₂²	1	32	yes	complemented
29	#547	C₂²	1	32	yes	complemented
30	#546	C₂²	1	32	yes	complemented
31	#546	C₂²	1	32	yes	complemented
32	#542	C₂²	1	32	yes	complemented
33	#539	C₂²	1	32	yes	complemented
34	#539	C₂²	1	16	yes	complemented
35	#538	C₂²	1	16	yes	complemented
36	#538	C₂²	1	32	yes	complemented
37	#538	C₂²	1	32	yes	complemented
38	#537	C₂²	1	16	yes	complemented
39	#534	C₂²	1	16	yes	complemented
40	#532	C₂²	1	16	yes	complemented
41	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
43	C₂×#127	C₂²	1	1	yes	characteristic, complemented
44	#529	C₂²	1	16	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×#126	C₂²	1	2	yes	complemented
52	C₂×#126	C₂²	1	2	yes	complemented
53	C₂×#126	C₂²	1	2	yes	complemented
54	C₂×#126	C₂²	1	16	yes	complemented
55	C₂×#125	C₂²	1	1	yes	characteristic, complemented
56	C₂×#125	C₂²	1	2	yes	complemented
57	C₂×#125	C₂²	1	2	yes	complemented
58	C₂×#124	C₂²	1	2	yes	—
59	C₂×#124	C₂²	1	2	yes	—
60	C₂×#124	C₂²	1	1	yes	characteristic, complemented
61	C₂×#124	C₂²	1	2	yes	complemented
62	C₂×#124	C₂²	1	2	yes	complemented
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	complemented
68	C₂×#123	C₂²	1	2	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×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
78	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
79	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
80	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
81	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
82	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
83	C₂×#121	C₂²	1	1	yes	characteristic
84	C₂×#121	C₂²	1	1	yes	characteristic
85	C₂×#121	C₂²	1	2	yes	—
86	C₂×#121	C₂²	1	2	yes	—
87	C₂×#121	C₂²	1	2	yes	—
88	C₂×#121	C₂²	1	2	yes	—
89	C₂×#121	C₂²	1	2	yes	—
90	C₂×#121	C₂²	1	1	yes	characteristic, complemented
91	C₂×#121	C₂²	1	2	yes	complemented
92	C₂×#121	C₂²	1	2	yes	complemented
93	C₂×#121	C₂²	1	2	yes	complemented
94	C₂×#121	C₂²	1	2	yes	complemented
95	C₂×#121	C₂²	1	2	yes	complemented
96	C₂×#121	C₂²	1	2	yes	complemented
97	C₂×#121	C₂²	1	2	yes	complemented
98	C₂×#120	C₂²	1	2	yes	—
99	C₂×#120	C₂²	1	2	yes	—
100	C₂×#120	C₂²	1	2	yes	—
101	C₂×#120	C₂²	1	2	yes	complemented
102	C₂×#120	C₂²	1	2	yes	complemented
103	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×D₄	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄	C₂²	1	2	yes	complemented
107	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×D₄	C₂²	1	2	yes	complemented
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×C₄×D₄	C₂²	1	2	yes	complemented
114	C₂×C₄×D₄	C₂²	1	2	yes	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, complemented
118	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
121	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
122	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
123	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
125	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
126	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
127	C₂⁵	C₂³	1	1	yes	characteristic
128	C₂⁵	C₂³	1	2	yes	—
129	C₂×#41	—	4	8	no	—
130	C₂×#41	—	4	8	no	—
131	C₂×#41	C₂³	1	16	yes	complemented
132	C₂×#41	C₂³	1	16	yes	complemented
133	C₂²×Q₈	C₂³	1	1	yes	characteristic
134	C₂²×Q₈	C₂³	1	2	yes	—
135	C₂²×Q₈	C₂³	1	2	yes	—
136	C₂²×D₄	—	4	8	no	—
137	C₂²×D₄	C₂³	1	2	yes	—
138	C₂²×D₄	C₂³	1	2	yes	—
139	C₂²×D₄	C₂³	1	2	yes	—
140	C₂²×D₄	C₂³	1	2	yes	—
141	C₂²×D₄	C₂³	1	1	yes	characteristic
142	C₂²×D₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
148	C₂²×D₄	C₂³	1	2	yes	—
149	C₂²×D₄	C₂³	1	2	yes	—
150	C₂²×D₄	C₂³	1	2	yes	—
151	C₂²×D₄	C₂³	1	2	yes	—
152	C₂²×D₄	C₂³	1	16	yes	—
153	C₂³×C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
167	C₄⋊Q₈	C₂³	1	8	yes	complemented
168	C₄⋊Q₈	C₂³	1	16	yes	complemented
169	#127	C₂³	1	8	yes	complemented
170	#126	C₂³	1	16	yes	complemented
171	#126	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	#126	C₂³	1	16	yes	complemented
179	#125	C₂³	1	8	yes	complemented
180	#125	C₂³	1	16	yes	complemented
181	#125	C₂³	1	16	yes	complemented
182	#124	C₂³	1	16	yes	—
183	#124	C₂³	1	16	yes	—
184	#124	C₂³	1	8	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	complemented
192	#123	C₂³	1	16	yes	complemented
193	#123	C₂³	1	16	yes	complemented
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	C₂²⋊Q₈	C₂³	1	8	yes	complemented
200	C₂²⋊Q₈	C₂³	1	16	yes	complemented
201	C₂²⋊Q₈	C₂³	1	16	yes	complemented
202	C₂²⋊Q₈	C₂³	1	16	yes	complemented
203	C₂²⋊Q₈	C₂³	1	16	yes	complemented
204	C₂²⋊Q₈	C₂³	1	16	yes	complemented
205	C₂²⋊Q₈	C₂³	1	16	yes	complemented
206	C₂²⋊Q₈	C₂³	1	16	yes	complemented
207	#121	C₂³	1	8	yes	—
208	#121	C₂³	1	8	yes	—
209	#121	C₂³	1	16	yes	—
210	#121	C₂³	1	16	yes	—
211	#121	C₂³	1	16	yes	—
212	#121	C₂³	1	16	yes	—
213	#121	C₂³	1	16	yes	—
214	#121	C₂³	1	8	yes	complemented
215	#121	C₂³	1	16	yes	complemented
216	#121	C₂³	1	16	yes	complemented
217	#121	C₂³	1	16	yes	complemented
218	#121	C₂³	1	16	yes	complemented
219	#121	C₂³	1	16	yes	complemented
220	#121	C₂³	1	16	yes	complemented
221	#121	C₂³	1	16	yes	complemented
222	#120	C₂³	1	16	yes	—
223	#120	C₂³	1	16	yes	—
224	#120	C₂³	1	16	yes	—
225	#120	C₂³	1	16	yes	complemented
226	#120	C₂³	1	16	yes	complemented
227	C₄×Q₈	C₂³	1	8	yes	complemented
228	C₄×D₄	C₂³	1	8	yes	complemented
229	C₄×D₄	C₂³	1	16	yes	complemented
230	C₄×D₄	C₂³	1	16	yes	complemented
231	C₄×D₄	C₂³	1	8	yes	complemented
232	C₄×D₄	C₂³	1	8	yes	complemented
233	C₄×D₄	C₂³	1	16	yes	complemented
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	C₄×D₄	C₂³	1	16	yes	complemented
238	C₄×D₄	C₂³	1	16	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	2	yes	—
246	C₂×C₄⋊C₄	C₂³	1	2	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	2	yes	—
253	C₂×C₄⋊C₄	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
259	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
263	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
264	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
265	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
266	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
273	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
274	C₂×C₂²⋊C₄	C₂³	1	8	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	2	yes	—
285	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
287	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
288	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
289	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
290	C₂×C₂²⋊C₄	C₂³	1	2	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	16	yes	complemented
295	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
296	C₂×C₄²	C₂³	1	2	yes	—
297	C₂×C₄²	C₂³	1	1	yes	characteristic
298	C₂×C₄²	C₂³	1	2	yes	—
299	C₂×C₄²	C₂³	1	2	yes	—
300	C₂×C₄²	C₂³	1	1	yes	characteristic
301	C₂×C₄²	C₂³	1	1	yes	characteristic
302	C₂×C₄²	C₂³	1	1	yes	characteristic
303	C₂×C₄²	C₂³	1	8	yes	complemented
304	C₂⁴	—	2	4	no	—
305	C₂⁴	—	4	4	no	—
306	C₂⁴	—	4	2	no	—
307	C₂⁴	—	4	2	no	—
308	C₂⁴	—	4	4	no	—
309	C₂⁴	—	4	4	no	—
310	C₂⁴	C₂⁴	1	2	yes	—
311	C₂⁴	C₂⁴	1	2	yes	—
312	C₂⁴	C₂⁴	1	2	yes	—
313	C₂⁴	C₂⁴	1	2	yes	—
314	C₂⁴	C₂⁴	1	1	yes	characteristic
315	C₂⁴	C₂⁴	1	4	yes	—
316	C₂⁴	C₂⁴	1	8	yes	—
317	#41	—	4	32	no	—
318	#41	—	4	32	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	C₂⁴	1	4	yes	—
323	C₂×Q₈	C₂⁴	1	8	yes	—
324	C₂×Q₈	C₂⁴	1	8	yes	—
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	32	no	—
341	C₂×D₄	C₂⁴	1	8	yes	—
342	C₂×D₄	C₂⁴	1	8	yes	—
343	C₂×D₄	C₂⁴	1	8	yes	—
344	C₂×D₄	C₂⁴	1	8	yes	—
345	C₂×D₄	C₂⁴	1	4	yes	—
346	C₂×D₄	C₂⁴	1	4	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	8	yes	—
351	C₂×D₄	C₂⁴	1	4	yes	—
352	C₂×D₄	C₂⁴	1	8	yes	—
353	C₂×D₄	C₂⁴	1	8	yes	—
354	C₂×D₄	C₂⁴	1	8	yes	—
355	C₂×D₄	C₂⁴	1	8	yes	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	4	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	—	4	4	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	C₂⁴	1	4	yes	—
371	C₂²×C₄	C₂⁴	1	4	yes	—
372	C₂²×C₄	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴	1	2	yes	—
374	C₂²×C₄	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
384	C₂²×C₄	C₂⁴	1	2	yes	—
385	C₂²×C₄	C₂⁴	1	2	yes	—
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	4	yes	—
390	C₂²×C₄	C₂⁴	1	8	yes	—
391	C₂²×C₄	C₂⁴	1	8	yes	—
392	C₂²×C₄	C₂⁴	1	8	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	8	yes	—
397	C₂²×C₄	C₂⁴	1	8	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	8	yes	—
408	C₄⋊C₄	C₂⁴	1	8	yes	—
409	C₄⋊C₄	C₂⁴	1	8	yes	—
410	C₄⋊C₄	C₂⁴	1	8	yes	—
411	C₄⋊C₄	C₂⁴	1	4	yes	—
412	C₄⋊C₄	C₂⁴	1	4	yes	—
413	C₄⋊C₄	C₂⁴	1	8	yes	—
414	C₄⋊C₄	C₂⁴	1	8	yes	—
415	C₄⋊C₄	C₂⁴	1	8	yes	—
416	C₄⋊C₄	C₂⁴	1	4	yes	—
417	C₄⋊C₄	C₂⁴	1	4	yes	—
418	C₄⋊C₄	C₂⁴	1	8	yes	—
419	C₂²⋊C₄	C₂⁴	1	8	yes	—
420	C₂²⋊C₄	C₂⁴	1	8	yes	—
421	C₂²⋊C₄	C₂⁴	1	8	yes	—
422	C₂²⋊C₄	C₂⁴	1	8	yes	—
423	C₂²⋊C₄	C₂⁴	1	8	yes	—
424	C₂²⋊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	C₄²	C₂⁴	1	4	yes	—
445	C₄²	C₂⁴	1	4	yes	—
446	C₄²	C₂⁴	1	4	yes	—
447	C₄²	C₂⁴	1	4	yes	—
448	C₄²	C₂⁴	1	8	yes	—
449	C₄²	C₂⁴	1	8	yes	—
450	C₄²	C₂⁴	1	8	yes	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	8	no	—
466	C₂³	—	4	8	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	8	no	—
470	C₂³	—	4	8	no	—
471	C₂³	—	8	8	no	—
472	C₂³	—	8	16	no	—
473	C₂³	H(5,𝔽₂)	1	4	yes	—
474	C₂³	C₂⁵	1	4	yes	—
475	C₂³	C₂⁵	1	4	yes	—
476	C₂³	C₂⁵	1	4	yes	—
477	C₂³	C₂⁵	1	4	yes	—
478	C₂³	C₂⁵	1	2	yes	—
479	C₂³	C₂⁵	1	1	yes	characteristic
480	Q₈	—	4	4	no	—
481	Q₈	—	4	8	no	—
482	Q₈	—	4	8	no	—
483	D₄	—	2	16	no	—
484	D₄	—	2	16	no	—
485	D₄	—	2	16	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	8	no	—
488	D₄	—	4	8	no	—
489	D₄	—	4	8	no	—
490	D₄	—	4	8	no	—
491	D₄	—	4	8	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	8	no	—
495	D₄	—	4	4	no	—
496	D₄	—	4	8	no	—
497	D₄	—	4	8	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	4	8	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	8	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	4	8	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	C₂⁵	1	2	yes	—
527	C₂×C₄	C₂⁵	1	2	yes	—
528	C₂×C₄	C₂⁵	1	4	yes	—
529	C₂×C₄	C₂⁵	1	2	yes	—
530	C₂×C₄	C₂⁵	1	2	yes	—
531	C₂×C₄	C₂⁵	1	2	yes	—
532	C₂×C₄	C₂⁵	1	2	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	4	yes	—
538	C₂×C₄	C₂⁵	1	4	yes	—
539	C₂×C₄	C₂⁵	1	4	yes	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	8	no	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	2	4	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	4	8	no	—
556	C₂²	—	4	8	no	—
557	C₂²	—	4	8	no	—
558	C₂²	—	4	8	no	—
559	C₂²	—	8	8	no	—
560	C₂²	—	8	16	no	—
561	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
562	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
563	C₂²	#585	1	2	yes	—
564	C₂²	#585	1	2	yes	—
565	C₂²	C₂⁶	1	1	yes	characteristic
566	C₄	—	2	2	no	—
567	C₄	—	2	4	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	4	no	—
570	C₄	—	2	4	no	—
571	C₄	—	2	4	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	4	no	—
574	C₄	—	2	4	no	—
575	C₄	—	2	4	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	4	no	—
579	C₄	—	2	2	no	—
580	C₂	—	2	4	no	—
581	C₂	—	4	4	no	—
582	C₂	—	4	4	no	—
583	C₂	—	4	4	no	—
584	C₂	—	4	4	no	—
585	C₂	#3560	1	4	yes	direct product factor
586	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂	C₂×#585	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. #3560	C₂	direct (N × H)
2. C₂×#563	C₂	semidirect
3. C₂×#560	C₂	semidirect
4. C₂×#553	C₂	semidirect
5. C₂×#553	C₂	semidirect
6. C₂×#551	C₂	semidirect
7. C₂×#547	C₂	semidirect
8. C₂×#546	C₂	semidirect
9. C₂×#546	C₂	semidirect
10. C₂×#542	C₂	semidirect
11. C₂×#539	C₂	semidirect
12. C₂×#539	C₂	semidirect
13. C₂×#538	C₂	semidirect
14. C₂×#538	C₂	semidirect
15. C₂×#538	C₂	semidirect
16. C₂×#537	C₂	semidirect
17. C₂×#534	C₂	semidirect
18. C₂×#532	C₂	semidirect
19. C₂×#529	C₂	semidirect
20. C₂²×#126	C₂	semidirect
21. C₂²×#41	C₂²	semidirect
22. C₂²×#41	C₂²	semidirect
24. #563	C₂²	semidirect
25. #560	C₂²	semidirect
26. #553	C₂²	semidirect
27. #553	C₂²	semidirect
28. #551	C₂²	semidirect
29. #547	C₂²	semidirect
30. #546	C₂²	semidirect
31. #546	C₂²	semidirect
32. #542	C₂²	semidirect
33. #539	C₂²	semidirect
34. #539	C₂²	semidirect
35. #538	C₂²	semidirect
36. #538	C₂²	semidirect
37. #538	C₂²	semidirect
38. #537	C₂²	semidirect
39. #534	C₂²	semidirect
40. #532	C₂²	semidirect
41. C₂×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₄⋊Q₈	C₂²	semidirect
43. C₂×#127	C₂²	semidirect
44. #529	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×#126	C₂²	semidirect
52. C₂×#126	C₂²	semidirect
53. C₂×#126	C₂²	semidirect
54. C₂×#126	C₂²	semidirect
55. C₂×#125	C₂²	semidirect
56. C₂×#125	C₂²	semidirect
57. C₂×#125	C₂²	semidirect
60. C₂×#124	C₂²	semidirect
61. C₂×#124	C₂²	semidirect
62. C₂×#124	C₂²	semidirect
67. C₂×#123	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×C₂²⋊Q₈	C₂²	semidirect
76. C₂×C₂²⋊Q₈	C₂²	semidirect
77. C₂×C₂²⋊Q₈	C₂²	semidirect
78. C₂×C₂²⋊Q₈	C₂²	semidirect
79. C₂×C₂²⋊Q₈	C₂²	semidirect
80. C₂×C₂²⋊Q₈	C₂²	semidirect
81. C₂×C₂²⋊Q₈	C₂²	semidirect
82. C₂×C₂²⋊Q₈	C₂²	semidirect
90. C₂×#121	C₂²	semidirect
91. C₂×#121	C₂²	semidirect
92. C₂×#121	C₂²	semidirect
93. C₂×#121	C₂²	semidirect
94. C₂×#121	C₂²	semidirect
95. C₂×#121	C₂²	semidirect
96. C₂×#121	C₂²	semidirect
97. C₂×#121	C₂²	semidirect
101. C₂×#120	C₂²	semidirect
102. C₂×#120	C₂²	semidirect
103. C₂×C₄×Q₈	C₂²	semidirect
104. C₂×C₄×D₄	C₂²	semidirect
105. C₂×C₄×D₄	C₂²	semidirect
106. C₂×C₄×D₄	C₂²	semidirect
107. C₂×C₄×D₄	C₂²	semidirect
108. C₂×C₄×D₄	C₂²	semidirect
109. C₂×C₄×D₄	C₂²	semidirect
110. C₂×C₄×D₄	C₂²	semidirect
111. C₂×C₄×D₄	C₂²	semidirect
112. C₂×C₄×D₄	C₂²	semidirect
113. C₂×C₄×D₄	C₂²	semidirect
114. C₂×C₄×D₄	C₂²	semidirect
115. C₂×#117	C₂²	semidirect
116. C₂×#117	C₂²	semidirect
117. C₂²×C₄⋊C₄	C₂²	semidirect
118. C₂²×C₄⋊C₄	C₂²	semidirect
119. C₂²×C₄⋊C₄	C₂²	semidirect
120. C₂²×C₄⋊C₄	C₂²	semidirect
124. C₂²×C₂²⋊C₄	C₂²	semidirect
125. C₂²×C₂²⋊C₄	C₂²	semidirect
126. C₂²×C₄²	C₂²	semidirect
131. C₂×#41	C₂³	semidirect
132. C₂×#41	C₂³	semidirect
167. C₄⋊Q₈	C₂³	semidirect
168. C₄⋊Q₈	C₂³	semidirect
169. #127	C₂³	semidirect
170. #126	C₂³	semidirect
171. #126	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. #126	C₂³	semidirect
179. #125	C₂³	semidirect
180. #125	C₂³	semidirect
181. #125	C₂³	semidirect
184. #124	C₂³	semidirect
185. #124	C₂³	semidirect
186. #124	C₂³	semidirect
191. #123	C₂³	semidirect
192. #123	C₂³	semidirect
193. #123	C₂³	semidirect
194. #123	C₂³	semidirect
195. #123	C₂³	semidirect
196. #123	C₂³	semidirect
197. #123	C₂³	semidirect
198. #123	C₂³	semidirect
199. C₂²⋊Q₈	C₂³	semidirect
200. C₂²⋊Q₈	C₂³	semidirect
201. C₂²⋊Q₈	C₂³	semidirect
202. C₂²⋊Q₈	C₂³	semidirect
203. C₂²⋊Q₈	C₂³	semidirect
204. C₂²⋊Q₈	C₂³	semidirect
205. C₂²⋊Q₈	C₂³	semidirect
206. C₂²⋊Q₈	C₂³	semidirect
214. #121	C₂³	semidirect
215. #121	C₂³	semidirect
216. #121	C₂³	semidirect
217. #121	C₂³	semidirect
218. #121	C₂³	semidirect
219. #121	C₂³	semidirect
220. #121	C₂³	semidirect
221. #121	C₂³	semidirect
225. #120	C₂³	semidirect
226. #120	C₂³	semidirect
227. C₄×Q₈	C₂³	semidirect
228. C₄×D₄	C₂³	semidirect
229. C₄×D₄	C₂³	semidirect
230. C₄×D₄	C₂³	semidirect
231. C₄×D₄	C₂³	semidirect
232. C₄×D₄	C₂³	semidirect
233. C₄×D₄	C₂³	semidirect
234. C₄×D₄	C₂³	semidirect
235. C₄×D₄	C₂³	semidirect
236. C₄×D₄	C₂³	semidirect
237. C₄×D₄	C₂³	semidirect
238. C₄×D₄	C₂³	semidirect
239. #117	C₂³	semidirect
240. #117	C₂³	semidirect
262. C₂×C₄⋊C₄	C₂³	semidirect
263. C₂×C₄⋊C₄	C₂³	semidirect
264. C₂×C₄⋊C₄	C₂³	semidirect
265. C₂×C₄⋊C₄	C₂³	semidirect
294. C₂×C₂²⋊C₄	C₂³	semidirect
295. C₂×C₂²⋊C₄	C₂³	semidirect
303. C₂×C₄²	C₂³	semidirect
585. C₂	#3560	direct (N × H)

Maximal subgroups

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

subgroup	index
#3560	2
C₂×#563	2
C₂×#560	2
C₂×#553	2
C₂×#551	2
C₂×#547	2
C₂×#546	2
C₂×#542	2
C₂×#539	2
C₂×#538	2
C₂×#537	2
C₂×#534	2
C₂×#532	2
C₂×#529	2
C₂²×#126	2

Subgroups — C2×#3560 #62735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3560 #62735