Subgroups — C₂×#3546 #62747

Order 256.

4023 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3546	C₂	1	32	yes	maximal, direct product factor
2	C₂×#560	C₂	1	4	yes	maximal, complemented
3	C₂×#556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#553	C₂	1	2	yes	maximal, complemented
5	C₂×#550	C₂	1	2	yes	maximal, complemented
6	C₂×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#547	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#546	C₂	1	2	yes	maximal, complemented
9	C₂×#546	C₂	1	2	yes	maximal, complemented
10	C₂×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#542	C₂	1	2	yes	maximal, complemented
12	C₂×#538	C₂	1	4	yes	maximal, complemented
13	C₂×#537	C₂	1	2	yes	maximal, complemented
14	C₂×#535	C₂	1	2	yes	maximal, complemented
15	C₂×#535	C₂	1	2	yes	maximal, complemented
16	C₂×#532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41	C₂²	1	2	yes	complemented
20	C₂²×#41	C₂²	1	2	yes	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	C₂³×D₄	C₂²	1	2	yes	—
25	#560	C₂²	1	64	yes	complemented
26	#556	C₂²	1	16	yes	complemented
27	#553	C₂²	1	32	yes	complemented
28	#550	C₂²	1	32	yes	complemented
29	#550	C₂²	1	16	yes	complemented
30	#547	C₂²	1	16	yes	complemented
31	#546	C₂²	1	32	yes	complemented
32	#546	C₂²	1	32	yes	complemented
33	D₄²	C₂²	1	16	yes	complemented
34	#542	C₂²	1	32	yes	complemented
35	#538	C₂²	1	64	yes	complemented
36	#537	C₂²	1	32	yes	complemented
37	#535	C₂²	1	32	yes	complemented
38	#535	C₂²	1	32	yes	complemented
39	#532	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	1	yes	characteristic, complemented
43	C₂×#127	C₂²	1	1	yes	characteristic
44	C₂×#127	C₂²	1	1	yes	characteristic
45	C₂×#127	C₂²	1	2	yes	complemented
46	C₂×#127	C₂²	1	4	yes	complemented
47	#529	C₂²	1	16	yes	complemented
48	C₂×#126	C₂²	1	2	yes	complemented
49	C₂×#126	C₂²	1	4	yes	complemented
50	C₂×#126	C₂²	1	4	yes	complemented
51	C₂×#125	C₂²	1	1	yes	characteristic, complemented
52	C₂×#124	C₂²	1	1	yes	characteristic
53	C₂×#124	C₂²	1	2	yes	—
54	C₂×#124	C₂²	1	2	yes	complemented
55	C₂×#124	C₂²	1	2	yes	complemented
56	C₂×#124	C₂²	1	4	yes	complemented
57	C₂×#123	C₂²	1	2	yes	complemented
58	C₂×#123	C₂²	1	4	yes	complemented
59	C₂×#123	C₂²	1	4	yes	complemented
60	C₂×#123	C₂²	1	4	yes	complemented
61	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
65	C₂×#121	C₂²	1	1	yes	characteristic
66	C₂×#121	C₂²	1	1	yes	characteristic
67	C₂×#121	C₂²	1	2	yes	—
68	C₂×#121	C₂²	1	2	yes	—
69	C₂×#121	C₂²	1	2	yes	—
70	C₂×#121	C₂²	1	2	yes	complemented
71	C₂×#121	C₂²	1	1	yes	characteristic, complemented
72	C₂×#121	C₂²	1	2	yes	complemented
73	C₂×#121	C₂²	1	2	yes	complemented
74	C₂×#121	C₂²	1	4	yes	complemented
75	C₂×#121	C₂²	1	2	yes	complemented
76	C₂×#121	C₂²	1	4	yes	complemented
77	C₂×#121	C₂²	1	4	yes	complemented
78	C₂×#121	C₂²	1	4	yes	complemented
79	C₂×#121	C₂²	1	4	yes	complemented
80	C₂×#121	C₂²	1	4	yes	complemented
81	C₂×#120	C₂²	1	4	yes	—
82	C₂×#120	C₂²	1	4	yes	complemented
83	C₂×#120	C₂²	1	4	yes	complemented
84	C₂×#120	C₂²	1	4	yes	complemented
85	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
87	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
88	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
89	C₂×C₄×D₄	C₂²	1	2	yes	complemented
90	C₂×C₄×D₄	C₂²	1	2	yes	complemented
91	C₂×C₄×D₄	C₂²	1	2	yes	complemented
92	C₂×C₄×D₄	C₂²	1	2	yes	complemented
93	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄×D₄	C₂²	1	4	yes	complemented
95	C₂×C₄×D₄	C₂²	1	2	yes	complemented
96	C₂×#117	C₂²	1	2	yes	complemented
97	C₂×#117	C₂²	1	2	yes	complemented
98	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
99	C₂²×C₂²⋊C₄	C₂²	1	4	yes	complemented
100	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵	C₂³	1	4	yes	—
102	C₂×#41	—	4	8	no	—
103	C₂×#41	—	4	8	no	—
104	C₂×#41	—	4	8	no	—
105	C₂×#41	—	4	8	no	—
106	C₂×#41	C₂³	1	16	yes	complemented
107	C₂×#41	C₂³	1	16	yes	complemented
108	C₂×#41	C₂³	1	16	yes	complemented
109	C₂×#41	C₂³	1	16	yes	complemented
110	C₂²×Q₈	C₂³	1	1	yes	characteristic
111	C₂²×Q₈	C₂³	1	2	yes	—
112	C₂²×Q₈	C₂³	1	2	yes	—
113	C₂²×D₄	—	4	8	no	—
114	C₂²×D₄	—	4	8	no	—
115	C₂²×D₄	C₂³	1	1	yes	characteristic
116	C₂²×D₄	C₂³	1	1	yes	characteristic
117	C₂²×D₄	C₂³	1	2	yes	—
118	C₂²×D₄	C₂³	1	2	yes	—
119	C₂²×D₄	C₂³	1	1	yes	characteristic
120	C₂²×D₄	C₂³	1	2	yes	—
121	C₂²×D₄	C₂³	1	2	yes	—
122	C₂²×D₄	C₂³	1	2	yes	—
123	C₂²×D₄	C₂³	1	4	yes	—
124	C₂²×D₄	C₂³	1	4	yes	—
125	C₂²×D₄	C₂³	1	4	yes	—
126	C₂²×D₄	C₂³	1	2	yes	—
127	C₂²×D₄	C₂³	1	4	yes	—
128	C₂²×D₄	C₂³	1	2	yes	—
129	C₂²×D₄	C₂³	1	4	yes	—
130	C₂²×D₄	C₂³	1	4	yes	—
131	C₂²×D₄	C₂³	1	2	yes	—
132	C₂²×D₄	C₂³	1	16	yes	—
133	C₂²×D₄	C₂³	1	16	yes	—
134	C₂³×C₄	C₂³	1	2	yes	—
135	C₂³×C₄	C₂³	1	2	yes	—
136	C₂³×C₄	C₂³	1	2	yes	—
137	C₂³×C₄	C₂³	1	1	yes	characteristic
138	C₂³×C₄	C₂³	1	1	yes	characteristic
139	C₂³×C₄	C₂³	1	4	yes	—
140	C₂³×C₄	C₂³	1	4	yes	—
141	C₂³×C₄	C₂³	1	4	yes	—
142	C₂³×C₄	C₂³	1	1	yes	characteristic
143	C₄⋊Q₈	C₂³	1	8	yes	complemented
144	C₄⋊Q₈	C₂³	1	8	yes	complemented
145	#127	C₂³	1	8	yes	—
146	#127	C₂³	1	8	yes	—
147	#127	C₂³	1	16	yes	complemented
148	#127	C₂³	1	32	yes	complemented
149	#126	C₂³	1	16	yes	complemented
150	#126	C₂³	1	32	yes	complemented
151	#126	C₂³	1	32	yes	complemented
152	#125	C₂³	1	8	yes	complemented
153	#124	C₂³	1	8	yes	—
154	#124	C₂³	1	16	yes	—
155	#124	C₂³	1	16	yes	complemented
156	#124	C₂³	1	16	yes	complemented
157	#124	C₂³	1	32	yes	complemented
158	#123	C₂³	1	16	yes	complemented
159	#123	C₂³	1	32	yes	complemented
160	#123	C₂³	1	32	yes	complemented
161	#123	C₂³	1	32	yes	complemented
162	C₂²⋊Q₈	C₂³	1	8	yes	complemented
163	C₂²⋊Q₈	C₂³	1	32	yes	complemented
164	C₂²⋊Q₈	C₂³	1	16	yes	complemented
165	C₂²⋊Q₈	C₂³	1	16	yes	complemented
166	#121	C₂³	1	8	yes	—
167	#121	C₂³	1	8	yes	—
168	#121	C₂³	1	16	yes	—
169	#121	C₂³	1	16	yes	—
170	#121	C₂³	1	16	yes	—
171	#121	C₂³	1	16	yes	complemented
172	#121	C₂³	1	8	yes	complemented
173	#121	C₂³	1	16	yes	complemented
174	#121	C₂³	1	16	yes	complemented
175	#121	C₂³	1	32	yes	complemented
176	#121	C₂³	1	16	yes	complemented
177	#121	C₂³	1	32	yes	complemented
178	#121	C₂³	1	32	yes	complemented
179	#121	C₂³	1	32	yes	complemented
180	#121	C₂³	1	32	yes	complemented
181	#121	C₂³	1	32	yes	complemented
182	#120	C₂³	1	32	yes	—
183	#120	C₂³	1	32	yes	complemented
184	#120	C₂³	1	32	yes	complemented
185	#120	C₂³	1	32	yes	complemented
186	C₄×Q₈	C₂³	1	8	yes	complemented
187	C₄×Q₈	C₂³	1	16	yes	complemented
188	C₄×D₄	C₂³	1	8	yes	—
189	C₄×D₄	C₂³	1	8	yes	—
190	C₄×D₄	C₂³	1	16	yes	complemented
191	C₄×D₄	C₂³	1	16	yes	complemented
192	C₄×D₄	C₂³	1	16	yes	complemented
193	C₄×D₄	C₂³	1	16	yes	complemented
194	C₄×D₄	C₂³	1	8	yes	complemented
195	C₄×D₄	C₂³	1	32	yes	complemented
196	C₄×D₄	C₂³	1	16	yes	complemented
197	#117	C₂³	1	16	yes	complemented
198	#117	C₂³	1	16	yes	complemented
199	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄	C₂³	1	4	yes	—
202	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₄⋊C₄	C₂³	1	4	yes	—
211	C₂×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
213	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
216	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
224	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
225	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
226	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂³	1	32	yes	complemented
230	C₂×C₄²	C₂³	1	1	yes	characteristic
231	C₂×C₄²	C₂³	1	2	yes	—
232	C₂×C₄²	C₂³	1	4	yes	—
233	C₂×C₄²	C₂³	1	1	yes	characteristic
234	C₂×C₄²	C₂³	1	1	yes	characteristic
235	C₂×C₄²	C₂³	1	1	yes	characteristic
236	C₂×C₄²	C₂³	1	8	yes	complemented
237	C₂⁴	—	4	8	no	—
238	C₂⁴	—	4	8	no	—
239	C₂⁴	—	4	8	no	—
240	C₂⁴	C₂⁴	1	2	yes	—
241	C₂⁴	C₂⁴	1	2	yes	—
242	C₂⁴	C₂⁴	1	4	yes	—
243	C₂⁴	C₂⁴	1	1	yes	characteristic
244	C₂⁴	C₂⁴	1	2	yes	—
245	C₂⁴	C₂⁴	1	16	yes	—
246	#41	—	4	32	no	—
247	#41	—	4	32	no	—
248	#41	—	4	32	no	—
249	#41	—	4	32	no	—
250	C₂×Q₈	—	2	4	no	—
251	C₂×Q₈	—	2	8	no	—
252	C₂×Q₈	—	4	4	no	—
253	C₂×Q₈	C₂⁴	1	4	yes	—
254	C₂×Q₈	C₂⁴	1	8	yes	—
255	C₂×Q₈	C₂⁴	1	8	yes	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	2	8	no	—
259	C₂×D₄	—	2	8	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	4	32	no	—
262	C₂×D₄	—	4	32	no	—
263	C₂×D₄	—	4	8	no	—
264	C₂×D₄	—	4	8	no	—
265	C₂×D₄	—	4	4	no	—
266	C₂×D₄	—	4	4	no	—
267	C₂×D₄	—	4	4	no	—
268	C₂×D₄	—	4	8	no	—
269	C₂×D₄	—	4	4	no	—
270	C₂×D₄	—	4	4	no	—
271	C₂×D₄	—	4	4	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	—	4	8	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	C₂⁴	1	4	yes	—
276	C₂×D₄	C₂⁴	1	4	yes	—
277	C₂×D₄	C₂⁴	1	8	yes	—
278	C₂×D₄	C₂⁴	1	8	yes	—
279	C₂×D₄	C₂⁴	1	4	yes	—
280	C₂×D₄	C₂⁴	1	8	yes	—
281	C₂×D₄	C₂⁴	1	8	yes	—
282	C₂×D₄	C₂⁴	1	8	yes	—
283	C₂×D₄	C₂⁴	1	16	yes	—
284	C₂×D₄	C₂⁴	1	16	yes	—
285	C₂×D₄	C₂⁴	1	16	yes	—
286	C₂×D₄	C₂⁴	1	8	yes	—
287	C₂×D₄	C₂⁴	1	16	yes	—
288	C₂×D₄	C₂⁴	1	8	yes	—
289	C₂×D₄	C₂⁴	1	16	yes	—
290	C₂×D₄	C₂⁴	1	16	yes	—
291	C₂×D₄	C₂⁴	1	8	yes	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	8	no	—
299	C₂²×C₄	—	4	8	no	—
300	C₂²×C₄	—	4	8	no	—
301	C₂²×C₄	C₂⁴	1	4	yes	—
302	C₂²×C₄	C₂⁴	1	4	yes	—
303	C₂²×C₄	C₂⁴	1	8	yes	—
304	C₂²×C₄	C₂⁴	1	8	yes	—
305	C₂²×C₄	C₂⁴	1	8	yes	—
306	C₂²×C₄	C₂⁴	1	2	yes	—
307	C₂²×C₄	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴	1	2	yes	—
312	C₂²×C₄	C₂⁴	1	2	yes	—
313	C₂²×C₄	C₂⁴	1	4	yes	—
314	C₂²×C₄	C₂⁴	1	2	yes	—
315	C₂²×C₄	C₂⁴	1	2	yes	—
316	C₂²×C₄	C₂⁴	1	4	yes	—
317	C₂²×C₄	C₂⁴	1	16	yes	—
318	C₂²×C₄	C₂⁴	1	16	yes	—
319	C₂²×C₄	C₂⁴	1	16	yes	—
320	C₂²×C₄	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄	C₂⁴	1	4	yes	—
323	C₄⋊C₄	C₂⁴	1	8	yes	—
324	C₄⋊C₄	C₂⁴	1	16	yes	—
325	C₄⋊C₄	C₂⁴	1	4	yes	—
326	C₄⋊C₄	C₂⁴	1	8	yes	—
327	C₄⋊C₄	C₂⁴	1	8	yes	—
328	C₄⋊C₄	C₂⁴	1	4	yes	—
329	C₄⋊C₄	C₂⁴	1	4	yes	—
330	C₄⋊C₄	C₂⁴	1	8	yes	—
331	C₄⋊C₄	C₂⁴	1	8	yes	—
332	C₄⋊C₄	C₂⁴	1	8	yes	—
333	C₄⋊C₄	C₂⁴	1	16	yes	—
334	C₄⋊C₄	C₂⁴	1	8	yes	—
335	C₂²⋊C₄	C₂⁴	1	8	yes	—
336	C₂²⋊C₄	C₂⁴	1	8	yes	—
337	C₂²⋊C₄	C₂⁴	1	16	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	C₂²⋊C₄	C₂⁴	1	8	yes	—
343	C₂²⋊C₄	C₂⁴	1	8	yes	—
344	C₂²⋊C₄	C₂⁴	1	8	yes	—
345	C₂²⋊C₄	C₂⁴	1	16	yes	—
346	C₂²⋊C₄	C₂⁴	1	16	yes	—
347	C₂²⋊C₄	C₂⁴	1	16	yes	—
348	C₂²⋊C₄	C₂⁴	1	16	yes	—
349	C₂²⋊C₄	C₂⁴	1	8	yes	—
350	C₂²⋊C₄	C₂⁴	1	8	yes	—
351	C₄²	C₂⁴	1	4	yes	—
352	C₄²	C₂⁴	1	4	yes	—
353	C₄²	C₂⁴	1	4	yes	—
354	C₄²	C₂⁴	1	4	yes	—
355	C₄²	C₂⁴	1	8	yes	—
356	C₄²	C₂⁴	1	16	yes	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	2	8	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	4	16	no	—
373	C₂³	—	4	16	no	—
374	C₂³	—	4	16	no	—
375	C₂³	—	8	32	no	—
376	C₂³	C₂⁵	1	4	yes	—
377	C₂³	C₂⁵	1	4	yes	—
378	C₂³	C₂⁵	1	8	yes	—
379	C₂³	C₂⁵	1	2	yes	—
380	C₂³	C₂⁵	1	4	yes	—
381	C₂³	C₂⁵	1	1	yes	characteristic
382	Q₈	—	2	8	no	—
383	Q₈	—	2	16	no	—
384	Q₈	—	4	8	no	—
385	D₄	—	2	8	no	—
386	D₄	—	2	8	no	—
387	D₄	—	2	16	no	—
388	D₄	—	2	16	no	—
389	D₄	—	2	8	no	—
390	D₄	—	4	16	no	—
391	D₄	—	4	16	no	—
392	D₄	—	4	8	no	—
393	D₄	—	4	8	no	—
394	D₄	—	4	8	no	—
395	D₄	—	4	16	no	—
396	D₄	—	4	8	no	—
397	D₄	—	4	8	no	—
398	D₄	—	4	8	no	—
399	D₄	—	4	16	no	—
400	D₄	—	4	16	no	—
401	D₄	—	4	16	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	8	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	16	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	16	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	16	no	—
419	C₂×C₄	—	4	16	no	—
420	C₂×C₄	—	4	16	no	—
421	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
422	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
423	C₂×C₄	C₂⁵	1	4	yes	—
424	C₂×C₄	C₂⁵	1	2	yes	—
425	C₂×C₄	C₂⁵	1	2	yes	—
426	C₂×C₄	C₂⁵	1	2	yes	—
427	C₂×C₄	C₂⁵	1	2	yes	—
428	C₂×C₄	C₂⁵	1	4	yes	—
429	C₂×C₄	C₂⁵	1	4	yes	—
430	C₂×C₄	C₂⁵	1	8	yes	—
431	C₂×C₄	C₂⁵	1	4	yes	—
432	C₂×C₄	C₂⁵	1	4	yes	—
433	C₂×C₄	C₂⁵	1	2	yes	—
434	C₂×C₄	C₂⁵	1	2	yes	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	8	no	—
442	C₂²	—	2	8	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	8	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	8	no	—
452	C₂²	—	4	16	no	—
453	C₂²	—	4	8	no	—
454	C₂²	—	4	8	no	—
455	C₂²	—	8	32	no	—
456	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
457	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
458	C₂²	#585	1	2	yes	—
459	C₂²	C₂⁶	1	1	yes	characteristic
460	C₄	—	2	2	no	—
461	C₄	—	2	4	no	—
462	C₄	—	2	4	no	—
463	C₄	—	2	4	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	8	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	4	no	—
470	C₄	C₂×H(5,𝔽₂)	1	4	yes	—
471	C₄	C₂×H(5,𝔽₂)	1	4	yes	—
472	C₂	—	4	2	no	—
473	C₂	—	4	4	no	—
474	C₂	—	4	8	no	—
475	C₂	—	4	4	no	—
476	C₂	—	4	4	no	—
477	C₂	#3546	1	4	yes	direct product factor
478	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
479	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
480	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. #3546	C₂	direct (N × H)
2. C₂×#560	C₂	semidirect
3. C₂×#556	C₂	semidirect
4. C₂×#553	C₂	semidirect
5. C₂×#550	C₂	semidirect
6. C₂×#550	C₂	semidirect
7. C₂×#547	C₂	semidirect
8. C₂×#546	C₂	semidirect
9. C₂×#546	C₂	semidirect
10. C₂×D₄²	C₂	semidirect
11. C₂×#542	C₂	semidirect
12. C₂×#538	C₂	semidirect
13. C₂×#537	C₂	semidirect
14. C₂×#535	C₂	semidirect
15. C₂×#535	C₂	semidirect
16. C₂×#532	C₂	semidirect
17. C₂×#532	C₂	semidirect
18. C₂×#529	C₂	semidirect
19. C₂²×#41	C₂²	semidirect
20. C₂²×#41	C₂²	semidirect
21. C₂²×#41	C₂²	semidirect
22. C₂²×#41	C₂²	semidirect
25. #560	C₂²	semidirect
26. #556	C₂²	semidirect
27. #553	C₂²	semidirect
28. #550	C₂²	semidirect
29. #550	C₂²	semidirect
30. #547	C₂²	semidirect
31. #546	C₂²	semidirect
32. #546	C₂²	semidirect
33. D₄²	C₂²	semidirect
34. #542	C₂²	semidirect
35. #538	C₂²	semidirect
36. #537	C₂²	semidirect
37. #535	C₂²	semidirect
38. #535	C₂²	semidirect
39. #532	C₂²	semidirect
40. #532	C₂²	semidirect
41. C₂×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₄⋊Q₈	C₂²	semidirect
45. C₂×#127	C₂²	semidirect
46. C₂×#127	C₂²	semidirect
47. #529	C₂²	semidirect
48. C₂×#126	C₂²	semidirect
49. C₂×#126	C₂²	semidirect
50. C₂×#126	C₂²	semidirect
51. C₂×#125	C₂²	semidirect
54. C₂×#124	C₂²	semidirect
55. C₂×#124	C₂²	semidirect
56. C₂×#124	C₂²	semidirect
57. C₂×#123	C₂²	semidirect
58. C₂×#123	C₂²	semidirect
59. C₂×#123	C₂²	semidirect
60. C₂×#123	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
70. C₂×#121	C₂²	semidirect
71. C₂×#121	C₂²	semidirect
72. C₂×#121	C₂²	semidirect
73. C₂×#121	C₂²	semidirect
74. C₂×#121	C₂²	semidirect
75. C₂×#121	C₂²	semidirect
76. C₂×#121	C₂²	semidirect
77. C₂×#121	C₂²	semidirect
78. C₂×#121	C₂²	semidirect
79. C₂×#121	C₂²	semidirect
80. C₂×#121	C₂²	semidirect
82. C₂×#120	C₂²	semidirect
83. C₂×#120	C₂²	semidirect
84. C₂×#120	C₂²	semidirect
85. C₂×C₄×Q₈	C₂²	semidirect
86. C₂×C₄×Q₈	C₂²	semidirect
89. C₂×C₄×D₄	C₂²	semidirect
90. C₂×C₄×D₄	C₂²	semidirect
91. C₂×C₄×D₄	C₂²	semidirect
92. C₂×C₄×D₄	C₂²	semidirect
93. C₂×C₄×D₄	C₂²	semidirect
94. C₂×C₄×D₄	C₂²	semidirect
95. C₂×C₄×D₄	C₂²	semidirect
96. C₂×#117	C₂²	semidirect
97. C₂×#117	C₂²	semidirect
98. C₂²×C₄⋊C₄	C₂²	semidirect
99. C₂²×C₂²⋊C₄	C₂²	semidirect
100. C₂²×C₄²	C₂²	semidirect
106. C₂×#41	C₂³	semidirect
107. C₂×#41	C₂³	semidirect
108. C₂×#41	C₂³	semidirect
109. C₂×#41	C₂³	semidirect
143. C₄⋊Q₈	C₂³	semidirect
144. C₄⋊Q₈	C₂³	semidirect
147. #127	C₂³	semidirect
148. #127	C₂³	semidirect
149. #126	C₂³	semidirect
150. #126	C₂³	semidirect
151. #126	C₂³	semidirect
152. #125	C₂³	semidirect
155. #124	C₂³	semidirect
156. #124	C₂³	semidirect
157. #124	C₂³	semidirect
158. #123	C₂³	semidirect
159. #123	C₂³	semidirect
160. #123	C₂³	semidirect
161. #123	C₂³	semidirect
162. C₂²⋊Q₈	C₂³	semidirect
163. C₂²⋊Q₈	C₂³	semidirect
164. C₂²⋊Q₈	C₂³	semidirect
165. C₂²⋊Q₈	C₂³	semidirect
171. #121	C₂³	semidirect
172. #121	C₂³	semidirect
173. #121	C₂³	semidirect
174. #121	C₂³	semidirect
175. #121	C₂³	semidirect
176. #121	C₂³	semidirect
177. #121	C₂³	semidirect
178. #121	C₂³	semidirect
179. #121	C₂³	semidirect
180. #121	C₂³	semidirect
181. #121	C₂³	semidirect
183. #120	C₂³	semidirect
184. #120	C₂³	semidirect
185. #120	C₂³	semidirect
186. C₄×Q₈	C₂³	semidirect
187. C₄×Q₈	C₂³	semidirect
190. C₄×D₄	C₂³	semidirect
191. C₄×D₄	C₂³	semidirect
192. C₄×D₄	C₂³	semidirect
193. C₄×D₄	C₂³	semidirect
194. C₄×D₄	C₂³	semidirect
195. C₄×D₄	C₂³	semidirect
196. C₄×D₄	C₂³	semidirect
197. #117	C₂³	semidirect
198. #117	C₂³	semidirect
212. C₂×C₄⋊C₄	C₂³	semidirect
229. C₂×C₂²⋊C₄	C₂³	semidirect
236. C₂×C₄²	C₂³	semidirect
477. C₂	#3546	direct (N × H)

Maximal subgroups

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

subgroup	index
#3546	2
C₂×#560	2
C₂×#556	2
C₂×#553	2
C₂×#550	2
C₂×#547	2
C₂×#546	2
C₂×D₄²	2
C₂×#542	2
C₂×#538	2
C₂×#537	2
C₂×#535	2
C₂×#532	2
C₂×#529	2

Subgroups — C2×#3546 #62747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3546 #62747