Subgroups — C₂×#3505 #62767

Order 256.

4041 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3505	C₂	1	32	yes	maximal, direct product factor
2	C₂×#553	C₂	1	2	yes	maximal, complemented
3	C₂×#553	C₂	1	4	yes	maximal, complemented
4	C₂×#552	C₂	1	2	yes	maximal, complemented
5	C₂×#551	C₂	1	4	yes	maximal, complemented
6	C₂×#548	C₂	1	2	yes	maximal, complemented
7	C₂×#546	C₂	1	2	yes	maximal, complemented
8	C₂×#539	C₂	1	2	yes	maximal, complemented
9	C₂×#538	C₂	1	2	yes	maximal, complemented
10	C₂×#534	C₂	1	2	yes	maximal, complemented
11	C₂×#529	C₂	1	2	yes	maximal, complemented
12	C₂×#525	C₂	1	2	yes	maximal, complemented
13	C₂²×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#121	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#518	C₂	1	2	yes	maximal, complemented
16	C₂²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41	C₂²	1	2	yes	complemented
18	C₂³×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄	C₂²	1	1	yes	characteristic
20	C₂³×D₄	C₂²	1	2	yes	—
21	C₂³×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂⁴×C₄	C₂²	1	1	yes	characteristic
23	C₂⁴×C₄	C₂²	1	1	yes	characteristic, complemented
24	#553	C₂²	1	32	yes	complemented
25	#553	C₂²	1	64	yes	complemented
26	#552	C₂²	1	32	yes	complemented
27	#551	C₂²	1	64	yes	complemented
28	#548	C₂²	1	32	yes	complemented
29	#546	C₂²	1	32	yes	complemented
30	#539	C₂²	1	32	yes	complemented
31	#538	C₂²	1	32	yes	complemented
32	#534	C₂²	1	32	yes	complemented
33	#529	C₂²	1	32	yes	complemented
34	C₂×#126	C₂²	1	4	yes	complemented
35	C₂×#126	C₂²	1	4	yes	complemented
36	C₂×#126	C₂²	1	4	yes	complemented
37	C₂×#125	C₂²	1	2	yes	complemented
38	C₂×#125	C₂²	1	4	yes	complemented
39	C₂×#124	C₂²	1	2	yes	complemented
40	C₂×#124	C₂²	1	4	yes	complemented
41	#525	C₂²	1	32	yes	complemented
42	C₂×#123	C₂²	1	4	yes	—
43	C₂×#123	C₂²	1	4	yes	complemented
44	C₂×#123	C₂²	1	4	yes	complemented
45	C₂×#123	C₂²	1	4	yes	complemented
46	C₂×#123	C₂²	1	4	yes	complemented
47	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
48	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
49	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
50	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
51	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
52	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
53	C₂×C₂²⋊Q₈	C₂²	1	16	yes	complemented
54	C₂×#121	C₂²	1	2	yes	—
55	C₂×#121	C₂²	1	2	yes	—
56	C₂×#121	C₂²	1	2	yes	complemented
57	C₂×#121	C₂²	1	2	yes	complemented
58	C₂×#121	C₂²	1	2	yes	complemented
59	C₂×#121	C₂²	1	4	yes	complemented
60	C₂×#121	C₂²	1	4	yes	complemented
61	C₂×#121	C₂²	1	4	yes	complemented
62	C₂×#121	C₂²	1	16	yes	complemented
63	C₂×#120	C₂²	1	4	yes	—
64	C₂×#120	C₂²	1	4	yes	complemented
65	#518	C₂²	1	32	yes	complemented
66	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
67	C₂×C₄×D₄	C₂²	1	2	yes	—
68	C₂×C₄×D₄	C₂²	1	2	yes	—
69	C₂×C₄×D₄	C₂²	1	2	yes	complemented
70	C₂×C₄×D₄	C₂²	1	2	yes	complemented
71	C₂×C₄×D₄	C₂²	1	4	yes	complemented
72	C₂×C₄×D₄	C₂²	1	4	yes	complemented
73	C₂×C₄×D₄	C₂²	1	4	yes	complemented
74	C₂×C₄×D₄	C₂²	1	4	yes	complemented
75	C₂×C₄×D₄	C₂²	1	4	yes	complemented
76	C₂×C₄×D₄	C₂²	1	2	yes	complemented
77	C₂×C₄×D₄	C₂²	1	16	yes	complemented
78	C₂×#117	C₂²	1	4	yes	complemented
79	C₂×#117	C₂²	1	2	yes	complemented
80	C₂×#117	C₂²	1	4	yes	complemented
81	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
82	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
83	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
84	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
85	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
87	C₂²×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	C₂²×C₂²⋊C₄	C₂²	1	4	yes	complemented
89	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
90	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
91	C₂⁵	C₂³	1	2	yes	—
92	C₂⁵	C₂³	1	1	yes	characteristic
93	C₂⁵	C₂³	1	1	yes	characteristic
94	C₂×#41	—	4	8	no	—
95	C₂×#41	C₂³	1	16	yes	complemented
96	C₂²×Q₈	—	4	4	no	—
97	C₂²×Q₈	C₂³	1	2	yes	—
98	C₂²×Q₈	C₂³	1	2	yes	—
99	C₂²×Q₈	C₂³	1	8	yes	complemented
100	C₂²×D₄	—	2	8	no	—
101	C₂²×D₄	—	2	16	no	—
102	C₂²×D₄	—	4	4	no	—
103	C₂²×D₄	C₂³	1	2	yes	—
104	C₂²×D₄	C₂³	1	4	yes	—
105	C₂²×D₄	C₂³	1	2	yes	—
106	C₂²×D₄	C₂³	1	4	yes	—
107	C₂²×D₄	C₂³	1	8	yes	—
108	C₂²×D₄	C₂³	1	2	yes	—
109	C₂²×D₄	C₂³	1	16	yes	—
110	C₂²×D₄	C₂³	1	4	yes	—
111	C₂²×D₄	C₂³	1	4	yes	—
112	C₂²×D₄	C₂³	1	2	yes	—
113	C₂²×D₄	C₂³	1	8	yes	complemented
114	C₂³×C₄	—	4	4	no	—
115	C₂³×C₄	—	4	4	no	—
116	C₂³×C₄	C₂³	1	2	yes	—
117	C₂³×C₄	C₂³	1	1	yes	characteristic
118	C₂³×C₄	C₂³	1	1	yes	characteristic
119	C₂³×C₄	C₂³	1	1	yes	characteristic
120	C₂³×C₄	C₂³	1	2	yes	—
121	C₂³×C₄	C₂³	1	1	yes	characteristic
122	C₂³×C₄	C₂³	1	1	yes	characteristic
123	C₂³×C₄	C₂³	1	2	yes	—
124	C₂³×C₄	C₂³	1	1	yes	characteristic
125	C₂³×C₄	C₂³	1	2	yes	—
126	C₂³×C₄	C₂³	1	1	yes	characteristic
127	C₂³×C₄	C₂³	1	1	yes	characteristic
128	C₂³×C₄	C₂³	1	4	yes	—
129	C₂³×C₄	C₂³	1	4	yes	—
130	C₂³×C₄	C₂³	1	1	yes	characteristic
131	C₂³×C₄	C₂³	1	2	yes	—
132	C₂³×C₄	C₂³	1	8	yes	—
133	C₂³×C₄	C₂³	1	8	yes	complemented
134	#126	C₂³	1	32	yes	complemented
135	#126	C₂³	1	32	yes	complemented
136	#126	C₂³	1	32	yes	complemented
137	#125	C₂³	1	16	yes	complemented
138	#125	C₂³	1	32	yes	complemented
139	#124	C₂³	1	16	yes	complemented
140	#124	C₂³	1	32	yes	complemented
141	#123	C₂³	1	32	yes	—
142	#123	C₂³	1	32	yes	complemented
143	#123	C₂³	1	32	yes	complemented
144	#123	C₂³	1	32	yes	complemented
145	#123	C₂³	1	32	yes	complemented
146	C₂²⋊Q₈	C₂³	1	16	yes	complemented
147	C₂²⋊Q₈	C₂³	1	16	yes	complemented
148	C₂²⋊Q₈	C₂³	1	16	yes	complemented
149	C₂²⋊Q₈	C₂³	1	16	yes	complemented
150	C₂²⋊Q₈	C₂³	1	16	yes	complemented
151	C₂²⋊Q₈	C₂³	1	32	yes	complemented
152	#121	C₂³	1	16	yes	—
153	#121	C₂³	1	16	yes	—
154	#121	C₂³	1	16	yes	complemented
155	#121	C₂³	1	16	yes	complemented
156	#121	C₂³	1	16	yes	complemented
157	#121	C₂³	1	32	yes	complemented
158	#121	C₂³	1	32	yes	complemented
159	#121	C₂³	1	32	yes	complemented
160	#120	C₂³	1	32	yes	—
161	#120	C₂³	1	32	yes	complemented
162	C₄×Q₈	C₂³	1	16	yes	complemented
163	C₄×D₄	C₂³	1	16	yes	—
164	C₄×D₄	C₂³	1	16	yes	—
165	C₄×D₄	C₂³	1	16	yes	complemented
166	C₄×D₄	C₂³	1	16	yes	complemented
167	C₄×D₄	C₂³	1	32	yes	complemented
168	C₄×D₄	C₂³	1	32	yes	complemented
169	C₄×D₄	C₂³	1	32	yes	complemented
170	C₄×D₄	C₂³	1	32	yes	complemented
171	C₄×D₄	C₂³	1	32	yes	complemented
172	C₄×D₄	C₂³	1	16	yes	complemented
173	#117	C₂³	1	32	yes	complemented
174	#117	C₂³	1	16	yes	complemented
175	#117	C₂³	1	32	yes	complemented
176	C₂×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄	C₂³	1	4	yes	—
178	C₂×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄	C₂³	1	4	yes	—
186	C₂×C₄⋊C₄	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
189	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
190	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
191	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
192	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
196	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
197	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
198	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
199	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
202	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
204	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
205	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
206	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
207	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄	C₂³	1	8	yes	complemented
209	C₂×C₂²⋊C₄	C₂³	1	32	yes	complemented
210	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
211	C₂×C₄²	C₂³	1	2	yes	—
212	C₂×C₄²	C₂³	1	4	yes	—
213	C₂×C₄²	C₂³	1	4	yes	—
214	C₂×C₄²	C₂³	1	2	yes	—
215	C₂×C₄²	C₂³	1	8	yes	complemented
216	C₂⁴	—	2	4	no	—
217	C₂⁴	—	2	8	no	—
218	C₂⁴	—	4	2	no	—
219	C₂⁴	—	4	2	no	—
220	C₂⁴	—	4	2	no	—
221	C₂⁴	—	4	2	no	—
222	C₂⁴	—	4	4	no	—
223	C₂⁴	—	4	4	no	—
224	C₂⁴	#41	1	8	yes	complemented
225	C₂⁴	C₂⁴	1	2	yes	—
226	C₂⁴	C₂⁴	1	4	yes	—
227	C₂⁴	C₂⁴	1	1	yes	characteristic
228	C₂⁴	C₂⁴	1	1	yes	characteristic
229	C₂⁴	C₂⁴	1	1	yes	characteristic
230	C₂⁴	C₂⁴	1	8	yes	—
231	C₂⁴	C₂⁴	1	4	yes	—
232	C₂⁴	C₂⁴	1	4	yes	—
233	#41	—	4	32	no	—
234	C₂×Q₈	—	2	8	no	—
235	C₂×Q₈	—	4	4	no	—
236	C₂×Q₈	—	4	16	no	—
237	C₂×Q₈	C₂⁴	1	8	yes	—
238	C₂×Q₈	C₂⁴	1	8	yes	—
239	C₂×D₄	—	2	8	no	—
240	C₂×D₄	—	2	16	no	—
241	C₂×D₄	—	2	8	no	—
242	C₂×D₄	—	2	16	no	—
243	C₂×D₄	—	2	32	no	—
244	C₂×D₄	—	2	64	no	—
245	C₂×D₄	—	2	8	no	—
246	C₂×D₄	—	4	16	no	—
247	C₂×D₄	—	4	4	no	—
248	C₂×D₄	—	4	8	no	—
249	C₂×D₄	—	4	8	no	—
250	C₂×D₄	C₂⁴	1	8	yes	—
251	C₂×D₄	C₂⁴	1	16	yes	—
252	C₂×D₄	C₂⁴	1	8	yes	—
253	C₂×D₄	C₂⁴	1	16	yes	—
254	C₂×D₄	C₂⁴	1	8	yes	—
255	C₂×D₄	C₂⁴	1	16	yes	—
256	C₂×D₄	C₂⁴	1	16	yes	—
257	C₂×D₄	C₂⁴	1	8	yes	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	4	16	no	—
265	C₂²×C₄	—	4	16	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	4	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	8	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	—	4	8	no	—
276	C₂²×C₄	C₂⁴	1	4	yes	—
277	C₂²×C₄	C₂⁴	1	4	yes	—
278	C₂²×C₄	C₂⁴	1	8	yes	—
279	C₂²×C₄	C₂⁴	1	4	yes	—
280	C₂²×C₄	C₂⁴	1	4	yes	—
281	C₂²×C₄	C₂⁴	1	8	yes	—
282	C₂²×C₄	C₂⁴	1	2	yes	—
283	C₂²×C₄	C₂⁴	1	2	yes	—
284	C₂²×C₄	C₂⁴	1	4	yes	—
285	C₂²×C₄	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄	C₂⁴	1	2	yes	—
287	C₂²×C₄	C₂⁴	1	4	yes	—
288	C₂²×C₄	C₂⁴	1	4	yes	—
289	C₂²×C₄	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴	1	4	yes	—
292	C₂²×C₄	C₂⁴	1	8	yes	—
293	C₂²×C₄	C₂⁴	1	4	yes	—
294	C₂²×C₄	C₂⁴	1	8	yes	—
295	C₂²×C₄	C₂⁴	1	4	yes	—
296	C₂²×C₄	C₂⁴	1	4	yes	—
297	C₂²×C₄	C₂⁴	1	16	yes	—
298	C₂²×C₄	C₂⁴	1	16	yes	—
299	C₂²×C₄	C₂⁴	1	4	yes	—
300	C₂²×C₄	C₂⁴	1	8	yes	—
301	C₂²×C₄	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄	C₂⁴	1	8	yes	—
303	C₄⋊C₄	C₂⁴	1	16	yes	—
304	C₄⋊C₄	C₂⁴	1	8	yes	—
305	C₄⋊C₄	C₂⁴	1	8	yes	—
306	C₄⋊C₄	C₂⁴	1	8	yes	—
307	C₄⋊C₄	C₂⁴	1	8	yes	—
308	C₄⋊C₄	C₂⁴	1	16	yes	—
309	C₄⋊C₄	C₂⁴	1	8	yes	—
310	C₄⋊C₄	C₂⁴	1	16	yes	—
311	C₄⋊C₄	C₂⁴	1	16	yes	—
312	C₄⋊C₄	C₂⁴	1	16	yes	—
313	C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₂²⋊C₄	C₂⁴	1	8	yes	—
315	C₂²⋊C₄	C₂⁴	1	16	yes	—
316	C₂²⋊C₄	C₂⁴	1	8	yes	—
317	C₂²⋊C₄	C₂⁴	1	16	yes	—
318	C₂²⋊C₄	C₂⁴	1	16	yes	—
319	C₂²⋊C₄	C₂⁴	1	8	yes	—
320	C₂²⋊C₄	C₂⁴	1	8	yes	—
321	C₂²⋊C₄	C₂⁴	1	16	yes	—
322	C₂²⋊C₄	C₂⁴	1	16	yes	—
323	C₂²⋊C₄	C₂⁴	1	16	yes	—
324	C₂²⋊C₄	C₂⁴	1	16	yes	—
325	C₂²⋊C₄	C₂⁴	1	16	yes	—
326	C₂²⋊C₄	C₂⁴	1	16	yes	—
327	C₂²⋊C₄	C₂⁴	1	16	yes	—
328	C₄²	C₂⁴	1	8	yes	—
329	C₄²	C₂⁴	1	8	yes	—
330	C₄²	C₂⁴	1	16	yes	—
331	C₄²	C₂⁴	1	16	yes	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	2	8	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	16	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	16	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	4	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	4	16	no	—
354	C₂³	—	8	16	no	—
355	C₂³	C₂×#41	1	4	yes	—
356	C₂³	C₂×#41	1	4	yes	—
357	C₂³	C₂×#41	1	4	yes	—
358	C₂³	C₂×#41	1	16	yes	complemented
359	C₂³	C₂⁵	1	4	yes	—
360	C₂³	C₂⁵	1	8	yes	—
361	C₂³	C₂⁵	1	2	yes	—
362	C₂³	C₂⁵	1	2	yes	—
363	C₂³	C₂⁵	1	2	yes	—
364	C₂³	C₂⁵	1	1	yes	characteristic
365	Q₈	—	2	16	no	—
366	Q₈	—	4	8	no	—
367	D₄	—	2	16	no	—
368	D₄	—	2	32	no	—
369	D₄	—	2	16	no	—
370	D₄	—	2	32	no	—
371	D₄	—	2	16	no	—
372	D₄	—	4	8	no	—
373	D₄	—	4	16	no	—
374	D₄	—	4	16	no	—
375	C₂×C₄	—	2	16	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	16	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	16	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	16	no	—
400	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
401	C₂×C₄	C₂⁵	1	4	yes	—
402	C₂×C₄	C₂⁵	1	4	yes	—
403	C₂×C₄	C₂⁵	1	8	yes	—
404	C₂×C₄	C₂⁵	1	2	yes	—
405	C₂×C₄	C₂⁵	1	4	yes	—
406	C₂×C₄	C₂⁵	1	8	yes	—
407	C₂×C₄	C₂⁵	1	8	yes	—
408	C₂×C₄	C₂⁵	1	2	yes	—
409	C₂×C₄	C₂⁵	1	2	yes	—
410	C₂×C₄	C₂⁵	1	2	yes	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	8	no	—
418	C₂²	—	2	8	no	—
419	C₂²	—	2	8	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	8	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	4	16	no	—
427	C₂²	—	4	16	no	—
428	C₂²	—	4	8	no	—
429	C₂²	—	4	16	no	—
430	C₂²	—	8	16	no	—
431	C₂²	C₂²×#41	1	4	yes	—
432	C₂²	C₂²×#41	1	4	yes	—
433	C₂²	C₂²×#41	1	4	yes	—
434	C₂²	C₂²×#41	1	2	yes	—
435	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
436	C₂²	#585	1	2	yes	—
437	C₂²	C₂⁶	1	1	yes	characteristic
438	C₄	—	2	8	no	—
439	C₄	—	2	4	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	8	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	8	no	—
447	C₄	C₂×H(5,𝔽₂)	1	4	yes	—
448	C₂	—	2	4	no	—
449	C₂	—	2	4	no	—
450	C₂	—	2	4	no	—
451	C₂	—	4	4	no	—
452	C₂	—	4	8	no	—
453	C₂	#3505	1	4	yes	direct product factor
454	C₂	C₂³×#41	1	1	yes	characteristic
455	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
456	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. #3505	C₂	direct (N × H)
2. C₂×#553	C₂	semidirect
3. C₂×#553	C₂	semidirect
4. C₂×#552	C₂	semidirect
5. C₂×#551	C₂	semidirect
6. C₂×#548	C₂	semidirect
7. C₂×#546	C₂	semidirect
8. C₂×#539	C₂	semidirect
9. C₂×#538	C₂	semidirect
10. C₂×#534	C₂	semidirect
11. C₂×#529	C₂	semidirect
12. C₂×#525	C₂	semidirect
13. C₂²×C₂²⋊Q₈	C₂	semidirect
14. C₂²×#121	C₂	semidirect
15. C₂×#518	C₂	semidirect
16. C₂²×C₄×D₄	C₂	semidirect
17. C₂²×#41	C₂²	semidirect
18. C₂³×Q₈	C₂²	semidirect
21. C₂³×D₄	C₂²	semidirect
23. C₂⁴×C₄	C₂²	semidirect
24. #553	C₂²	semidirect
25. #553	C₂²	semidirect
26. #552	C₂²	semidirect
27. #551	C₂²	semidirect
28. #548	C₂²	semidirect
29. #546	C₂²	semidirect
30. #539	C₂²	semidirect
31. #538	C₂²	semidirect
32. #534	C₂²	semidirect
33. #529	C₂²	semidirect
34. C₂×#126	C₂²	semidirect
35. C₂×#126	C₂²	semidirect
36. C₂×#126	C₂²	semidirect
37. C₂×#125	C₂²	semidirect
38. C₂×#125	C₂²	semidirect
39. C₂×#124	C₂²	semidirect
40. C₂×#124	C₂²	semidirect
41. #525	C₂²	semidirect
43. C₂×#123	C₂²	semidirect
44. C₂×#123	C₂²	semidirect
45. C₂×#123	C₂²	semidirect
46. C₂×#123	C₂²	semidirect
47. C₂×C₂²⋊Q₈	C₂²	semidirect
48. C₂×C₂²⋊Q₈	C₂²	semidirect
49. C₂×C₂²⋊Q₈	C₂²	semidirect
50. C₂×C₂²⋊Q₈	C₂²	semidirect
51. C₂×C₂²⋊Q₈	C₂²	semidirect
52. C₂×C₂²⋊Q₈	C₂²	semidirect
53. C₂×C₂²⋊Q₈	C₂²	semidirect
56. C₂×#121	C₂²	semidirect
57. C₂×#121	C₂²	semidirect
58. C₂×#121	C₂²	semidirect
59. C₂×#121	C₂²	semidirect
60. C₂×#121	C₂²	semidirect
61. C₂×#121	C₂²	semidirect
62. C₂×#121	C₂²	semidirect
64. C₂×#120	C₂²	semidirect
65. #518	C₂²	semidirect
66. C₂×C₄×Q₈	C₂²	semidirect
69. C₂×C₄×D₄	C₂²	semidirect
70. C₂×C₄×D₄	C₂²	semidirect
71. C₂×C₄×D₄	C₂²	semidirect
72. C₂×C₄×D₄	C₂²	semidirect
73. C₂×C₄×D₄	C₂²	semidirect
74. C₂×C₄×D₄	C₂²	semidirect
75. C₂×C₄×D₄	C₂²	semidirect
76. C₂×C₄×D₄	C₂²	semidirect
77. C₂×C₄×D₄	C₂²	semidirect
78. C₂×#117	C₂²	semidirect
79. C₂×#117	C₂²	semidirect
80. C₂×#117	C₂²	semidirect
81. C₂²×C₄⋊C₄	C₂²	semidirect
82. C₂²×C₄⋊C₄	C₂²	semidirect
83. C₂²×C₄⋊C₄	C₂²	semidirect
84. C₂²×C₄⋊C₄	C₂²	semidirect
87. C₂²×C₂²⋊C₄	C₂²	semidirect
88. C₂²×C₂²⋊C₄	C₂²	semidirect
89. C₂²×C₂²⋊C₄	C₂²	semidirect
90. C₂²×C₄²	C₂²	semidirect
95. C₂×#41	C₂³	semidirect
99. C₂²×Q₈	C₂³	semidirect
113. C₂²×D₄	C₂³	semidirect
133. C₂³×C₄	C₂³	semidirect
134. #126	C₂³	semidirect
135. #126	C₂³	semidirect
136. #126	C₂³	semidirect
137. #125	C₂³	semidirect
138. #125	C₂³	semidirect
139. #124	C₂³	semidirect
140. #124	C₂³	semidirect
142. #123	C₂³	semidirect
143. #123	C₂³	semidirect
144. #123	C₂³	semidirect
145. #123	C₂³	semidirect
146. C₂²⋊Q₈	C₂³	semidirect
147. C₂²⋊Q₈	C₂³	semidirect
148. C₂²⋊Q₈	C₂³	semidirect
149. C₂²⋊Q₈	C₂³	semidirect
150. C₂²⋊Q₈	C₂³	semidirect
151. C₂²⋊Q₈	C₂³	semidirect
154. #121	C₂³	semidirect
155. #121	C₂³	semidirect
156. #121	C₂³	semidirect
157. #121	C₂³	semidirect
158. #121	C₂³	semidirect
159. #121	C₂³	semidirect
161. #120	C₂³	semidirect
162. C₄×Q₈	C₂³	semidirect
165. C₄×D₄	C₂³	semidirect
166. C₄×D₄	C₂³	semidirect
167. C₄×D₄	C₂³	semidirect
168. C₄×D₄	C₂³	semidirect
169. C₄×D₄	C₂³	semidirect
170. C₄×D₄	C₂³	semidirect
171. C₄×D₄	C₂³	semidirect
172. C₄×D₄	C₂³	semidirect
173. #117	C₂³	semidirect
174. #117	C₂³	semidirect
175. #117	C₂³	semidirect
188. C₂×C₄⋊C₄	C₂³	semidirect
189. C₂×C₄⋊C₄	C₂³	semidirect
190. C₂×C₄⋊C₄	C₂³	semidirect
191. C₂×C₄⋊C₄	C₂³	semidirect
208. C₂×C₂²⋊C₄	C₂³	semidirect
209. C₂×C₂²⋊C₄	C₂³	semidirect
210. C₂×C₂²⋊C₄	C₂³	semidirect
215. C₂×C₄²	C₂³	semidirect
224. C₂⁴	#41	semidirect
358. C₂³	C₂×#41	semidirect
453. C₂	#3505	direct (N × H)

Maximal subgroups

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

subgroup	index
#3505	2
C₂×#553	2
C₂×#552	2
C₂×#551	2
C₂×#548	2
C₂×#546	2
C₂×#539	2
C₂×#538	2
C₂×#534	2
C₂×#529	2
C₂×#525	2
C₂²×C₂²⋊Q₈	2
C₂²×#121	2
C₂×#518	2
C₂²×C₄×D₄	2

Subgroups — C2×#3505 #62767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3505 #62767