Subgroups — C₂×#3519 #62771

Order 256.

4387 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3519	C₂	1	32	yes	maximal, direct product factor
2	C₂×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#553	C₂	1	2	yes	maximal, complemented
5	C₂×#553	C₂	1	2	yes	maximal, complemented
6	C₂×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#546	C₂	1	4	yes	maximal, complemented
8	C₂×#546	C₂	1	2	yes	maximal, complemented
9	C₂×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₄²	C₂	1	2	yes	maximal, complemented
11	C₂×#540	C₂	1	2	yes	maximal, complemented
12	C₂×#538	C₂	1	4	yes	maximal, complemented
13	C₂×#532	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×#121	C₂	1	2	yes	maximal, complemented
17	C₂×#518	C₂	1	2	yes	maximal, complemented
18	C₂²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41	C₂²	1	2	yes	complemented
20	C₂²×#41	C₂²	1	2	yes	complemented
21	C₂³×D₄	C₂²	1	1	yes	characteristic
22	C₂³×D₄	C₂²	1	2	yes	—
23	C₂³×D₄	C₂²	1	2	yes	complemented
24	C₂³×D₄	C₂²	1	4	yes	complemented
25	C₂⁴×C₄	C₂²	1	2	yes	complemented
26	#555	C₂²	1	16	yes	complemented
27	#554	C₂²	1	16	yes	complemented
28	#553	C₂²	1	32	yes	complemented
29	#553	C₂²	1	32	yes	complemented
30	#550	C₂²	1	16	yes	complemented
31	#546	C₂²	1	64	yes	complemented
32	#546	C₂²	1	32	yes	complemented
33	D₄²	C₂²	1	16	yes	complemented
34	D₄²	C₂²	1	32	yes	complemented
35	#540	C₂²	1	32	yes	complemented
36	#538	C₂²	1	64	yes	complemented
37	#532	C₂²	1	16	yes	complemented
38	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×#127	C₂²	1	1	yes	characteristic, complemented
40	C₂×#127	C₂²	1	2	yes	complemented
41	#529	C₂²	1	16	yes	complemented
42	C₂×#126	C₂²	1	2	yes	complemented
43	C₂×#126	C₂²	1	4	yes	complemented
44	C₂×#125	C₂²	1	1	yes	characteristic, complemented
45	C₂×#125	C₂²	1	2	yes	complemented
46	C₂×#124	C₂²	1	1	yes	characteristic, complemented
47	C₂×#124	C₂²	1	2	yes	complemented
48	C₂×#124	C₂²	1	4	yes	complemented
49	#525	C₂²	1	32	yes	complemented
50	C₂×#123	C₂²	1	4	yes	complemented
51	C₂×#123	C₂²	1	2	yes	complemented
52	C₂×#123	C₂²	1	4	yes	complemented
53	C₂×#123	C₂²	1	4	yes	complemented
54	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂×#121	C₂²	1	1	yes	characteristic
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	2	yes	complemented
62	C₂×#121	C₂²	1	2	yes	complemented
63	C₂×#121	C₂²	1	2	yes	complemented
64	C₂×#121	C₂²	1	2	yes	complemented
65	C₂×#121	C₂²	1	4	yes	complemented
66	C₂×#121	C₂²	1	4	yes	complemented
67	C₂×#121	C₂²	1	2	yes	complemented
68	C₂×#121	C₂²	1	2	yes	complemented
69	C₂×#121	C₂²	1	4	yes	complemented
70	C₂×#121	C₂²	1	32	yes	complemented
71	C₂×#120	C₂²	1	4	yes	complemented
72	C₂×#120	C₂²	1	4	yes	complemented
73	C₂×#120	C₂²	1	4	yes	complemented
74	#518	C₂²	1	32	yes	complemented
75	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
77	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
78	C₂×C₄×D₄	C₂²	1	2	yes	—
79	C₂×C₄×D₄	C₂²	1	2	yes	complemented
80	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×D₄	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×D₄	C₂²	1	4	yes	complemented
84	C₂×C₄×D₄	C₂²	1	2	yes	complemented
85	C₂×C₄×D₄	C₂²	1	4	yes	complemented
86	C₂×C₄×D₄	C₂²	1	2	yes	complemented
87	C₂×C₄×D₄	C₂²	1	4	yes	complemented
88	C₂×C₄×D₄	C₂²	1	2	yes	complemented
89	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄×D₄	C₂²	1	2	yes	complemented
91	C₂×C₄×D₄	C₂²	1	16	yes	complemented
92	C₂×#117	C₂²	1	2	yes	complemented
93	C₂×#117	C₂²	1	2	yes	complemented
94	C₂×#117	C₂²	1	2	yes	complemented
95	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
96	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
97	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
98	C₂²×C₂²⋊C₄	C₂²	1	4	yes	complemented
99	C₂²×C₂²⋊C₄	C₂²	1	4	yes	complemented
100	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵	C₂³	1	2	yes	—
102	C₂⁵	C₂³	1	4	yes	—
103	C₂×#41	—	4	8	no	—
104	C₂×#41	—	4	8	no	—
105	C₂×#41	C₂³	1	16	yes	complemented
106	C₂×#41	C₂³	1	16	yes	complemented
107	C₂²×Q₈	C₂³	1	1	yes	characteristic
108	C₂²×Q₈	C₂³	1	2	yes	—
109	C₂²×D₄	—	2	8	no	—
110	C₂²×D₄	—	2	16	no	—
111	C₂²×D₄	—	4	8	no	—
112	C₂²×D₄	—	4	16	no	—
113	C₂²×D₄	C₂³	1	2	yes	—
114	C₂²×D₄	C₂³	1	4	yes	—
115	C₂²×D₄	C₂³	1	1	yes	characteristic
116	C₂²×D₄	C₂³	1	2	yes	—
117	C₂²×D₄	C₂³	1	8	yes	—
118	C₂²×D₄	C₂³	1	4	yes	—
119	C₂²×D₄	C₂³	1	2	yes	—
120	C₂²×D₄	C₂³	1	1	yes	characteristic
121	C₂²×D₄	C₂³	1	2	yes	—
122	C₂²×D₄	C₂³	1	16	yes	—
123	C₂²×D₄	C₂³	1	4	yes	—
124	C₂²×D₄	C₂³	1	2	yes	—
125	C₂²×D₄	C₂³	1	4	yes	—
126	C₂²×D₄	C₂³	1	4	yes	—
127	C₂²×D₄	C₂³	1	4	yes	—
128	C₂²×D₄	C₂³	1	1	yes	characteristic
129	C₂²×D₄	C₂³	1	16	yes	complemented
130	C₂²×D₄	C₂³	1	32	yes	complemented
131	C₂³×C₄	—	4	8	no	—
132	C₂³×C₄	C₂³	1	1	yes	characteristic
133	C₂³×C₄	C₂³	1	2	yes	—
134	C₂³×C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
139	C₂³×C₄	C₂³	1	4	yes	—
140	C₂³×C₄	C₂³	1	2	yes	—
141	C₂³×C₄	C₂³	1	4	yes	—
142	C₂³×C₄	C₂³	1	4	yes	—
143	C₂³×C₄	C₂³	1	2	yes	—
144	C₂³×C₄	C₂³	1	16	yes	complemented
145	C₄⋊Q₈	C₂³	1	8	yes	complemented
146	#127	C₂³	1	8	yes	complemented
147	#127	C₂³	1	16	yes	complemented
148	#126	C₂³	1	16	yes	complemented
149	#126	C₂³	1	32	yes	complemented
150	#125	C₂³	1	8	yes	complemented
151	#125	C₂³	1	16	yes	complemented
152	#124	C₂³	1	8	yes	complemented
153	#124	C₂³	1	16	yes	complemented
154	#124	C₂³	1	32	yes	complemented
155	#123	C₂³	1	32	yes	complemented
156	#123	C₂³	1	16	yes	complemented
157	#123	C₂³	1	32	yes	complemented
158	#123	C₂³	1	32	yes	complemented
159	C₂²⋊Q₈	C₂³	1	8	yes	complemented
160	C₂²⋊Q₈	C₂³	1	16	yes	complemented
161	C₂²⋊Q₈	C₂³	1	32	yes	complemented
162	#121	C₂³	1	8	yes	—
163	#121	C₂³	1	16	yes	complemented
164	#121	C₂³	1	32	yes	complemented
165	#121	C₂³	1	32	yes	complemented
166	#121	C₂³	1	16	yes	complemented
167	#121	C₂³	1	16	yes	complemented
168	#121	C₂³	1	16	yes	complemented
169	#121	C₂³	1	16	yes	complemented
170	#121	C₂³	1	32	yes	complemented
171	#121	C₂³	1	32	yes	complemented
172	#121	C₂³	1	16	yes	complemented
173	#121	C₂³	1	16	yes	complemented
174	#121	C₂³	1	32	yes	complemented
175	#120	C₂³	1	32	yes	complemented
176	#120	C₂³	1	32	yes	complemented
177	#120	C₂³	1	32	yes	complemented
178	C₄×Q₈	C₂³	1	8	yes	complemented
179	C₄×D₄	C₂³	1	8	yes	—
180	C₄×D₄	C₂³	1	8	yes	—
181	C₄×D₄	C₂³	1	16	yes	—
182	C₄×D₄	C₂³	1	16	yes	complemented
183	C₄×D₄	C₂³	1	8	yes	complemented
184	C₄×D₄	C₂³	1	16	yes	complemented
185	C₄×D₄	C₂³	1	8	yes	complemented
186	C₄×D₄	C₂³	1	32	yes	complemented
187	C₄×D₄	C₂³	1	16	yes	complemented
188	C₄×D₄	C₂³	1	32	yes	complemented
189	C₄×D₄	C₂³	1	16	yes	complemented
190	C₄×D₄	C₂³	1	32	yes	complemented
191	C₄×D₄	C₂³	1	16	yes	complemented
192	C₄×D₄	C₂³	1	8	yes	complemented
193	C₄×D₄	C₂³	1	16	yes	complemented
194	#117	C₂³	1	16	yes	complemented
195	#117	C₂³	1	16	yes	complemented
196	#117	C₂³	1	16	yes	complemented
197	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄	C₂³	1	4	yes	—
209	C₂×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
211	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
212	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
215	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
218	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
223	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
228	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
229	C₂×C₂²⋊C₄	C₂³	1	32	yes	complemented
230	C₂×C₂²⋊C₄	C₂³	1	32	yes	complemented
231	C₂×C₄²	C₂³	1	1	yes	characteristic
232	C₂×C₄²	C₂³	1	4	yes	—
233	C₂×C₄²	C₂³	1	2	yes	—
234	C₂×C₄²	C₂³	1	1	yes	characteristic
235	C₂×C₄²	C₂³	1	1	yes	characteristic
236	C₂×C₄²	C₂³	1	1	yes	characteristic
237	C₂×C₄²	C₂³	1	8	yes	complemented
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	2	8	no	—
240	C₂⁴	—	2	16	no	—
241	C₂⁴	—	4	4	no	—
242	C₂⁴	—	4	8	no	—
243	C₂⁴	—	4	8	no	—
244	C₂⁴	C₂⁴	1	2	yes	—
245	C₂⁴	C₂⁴	1	2	yes	—
246	C₂⁴	C₂⁴	1	4	yes	—
247	C₂⁴	C₂⁴	1	8	yes	—
248	C₂⁴	C₂⁴	1	2	yes	—
249	C₂⁴	C₂⁴	1	1	yes	characteristic
250	C₂⁴	C₂⁴	1	16	yes	—
251	#41	—	4	32	no	—
252	#41	—	4	32	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	—	4	4	no	—
255	C₂×Q₈	C₂⁴	1	4	yes	—
256	C₂×Q₈	C₂⁴	1	8	yes	—
257	C₂×D₄	—	2	8	no	—
258	C₂×D₄	—	2	16	no	—
259	C₂×D₄	—	2	8	no	—
260	C₂×D₄	—	2	16	no	—
261	C₂×D₄	—	2	32	no	—
262	C₂×D₄	—	2	64	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	4	32	no	—
268	C₂×D₄	—	4	8	no	—
269	C₂×D₄	—	4	8	no	—
270	C₂×D₄	—	4	8	no	—
271	C₂×D₄	—	4	4	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	—	4	64	no	—
274	C₂×D₄	#41	1	8	yes	complemented
275	C₂×D₄	C₂⁴	1	8	yes	—
276	C₂×D₄	C₂⁴	1	16	yes	—
277	C₂×D₄	C₂⁴	1	4	yes	—
278	C₂×D₄	C₂⁴	1	8	yes	—
279	C₂×D₄	C₂⁴	1	16	yes	—
280	C₂×D₄	C₂⁴	1	8	yes	—
281	C₂×D₄	C₂⁴	1	4	yes	—
282	C₂×D₄	C₂⁴	1	8	yes	—
283	C₂×D₄	C₂⁴	1	16	yes	—
284	C₂×D₄	C₂⁴	1	8	yes	—
285	C₂×D₄	C₂⁴	1	16	yes	—
286	C₂×D₄	C₂⁴	1	16	yes	—
287	C₂×D₄	C₂⁴	1	16	yes	—
288	C₂×D₄	C₂⁴	1	4	yes	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	8	no	—
295	C₂²×C₄	—	4	32	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	8	no	—
300	C₂²×C₄	—	4	8	no	—
301	C₂²×C₄	—	4	8	no	—
302	C₂²×C₄	C₂⁴	1	4	yes	—
303	C₂²×C₄	C₂⁴	1	4	yes	—
304	C₂²×C₄	C₂⁴	1	4	yes	—
305	C₂²×C₄	C₂⁴	1	8	yes	—
306	C₂²×C₄	C₂⁴	1	8	yes	—
307	C₂²×C₄	C₂⁴	1	8	yes	—
308	C₂²×C₄	C₂⁴	1	2	yes	—
309	C₂²×C₄	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄	C₂⁴	1	2	yes	—
313	C₂²×C₄	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴	1	4	yes	—
315	C₂²×C₄	C₂⁴	1	2	yes	—
316	C₂²×C₄	C₂⁴	1	2	yes	—
317	C₂²×C₄	C₂⁴	1	2	yes	—
318	C₂²×C₄	C₂⁴	1	8	yes	—
319	C₂²×C₄	C₂⁴	1	16	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	8	yes	—
324	C₂²×C₄	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄	C₂⁴	1	4	yes	—
327	C₄⋊C₄	C₂⁴	1	4	yes	—
328	C₄⋊C₄	C₂⁴	1	8	yes	—
329	C₄⋊C₄	C₂⁴	1	4	yes	—
330	C₄⋊C₄	C₂⁴	1	8	yes	—
331	C₄⋊C₄	C₂⁴	1	16	yes	—
332	C₄⋊C₄	C₂⁴	1	4	yes	—
333	C₄⋊C₄	C₂⁴	1	8	yes	—
334	C₄⋊C₄	C₂⁴	1	8	yes	—
335	C₄⋊C₄	C₂⁴	1	8	yes	—
336	C₄⋊C₄	C₂⁴	1	8	yes	—
337	C₄⋊C₄	C₂⁴	1	16	yes	—
338	C₄⋊C₄	C₂⁴	1	8	yes	—
339	C₂²⋊C₄	C₂⁴	1	8	yes	—
340	C₂²⋊C₄	C₂⁴	1	8	yes	—
341	C₂²⋊C₄	C₂⁴	1	16	yes	—
342	C₂²⋊C₄	C₂⁴	1	8	yes	—
343	C₂²⋊C₄	C₂⁴	1	8	yes	—
344	C₂²⋊C₄	C₂⁴	1	16	yes	—
345	C₂²⋊C₄	C₂⁴	1	16	yes	—
346	C₂²⋊C₄	C₂⁴	1	8	yes	—
347	C₂²⋊C₄	C₂⁴	1	16	yes	—
348	C₂²⋊C₄	C₂⁴	1	8	yes	—
349	C₂²⋊C₄	C₂⁴	1	16	yes	—
350	C₂²⋊C₄	C₂⁴	1	8	yes	—
351	C₂²⋊C₄	C₂⁴	1	8	yes	—
352	C₂²⋊C₄	C₂⁴	1	8	yes	—
353	C₂²⋊C₄	C₂⁴	1	16	yes	—
354	C₂²⋊C₄	C₂⁴	1	16	yes	—
355	C₄²	C₂⁴	1	4	yes	—
356	C₄²	C₂⁴	1	4	yes	—
357	C₄²	C₂⁴	1	4	yes	—
358	C₄²	C₂⁴	1	4	yes	—
359	C₄²	C₂⁴	1	16	yes	—
360	C₄²	C₂⁴	1	8	yes	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	16	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	8	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	2	16	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	32	no	—
377	C₂³	—	4	8	no	—
378	C₂³	—	4	16	no	—
379	C₂³	—	4	16	no	—
380	C₂³	—	4	32	no	—
381	C₂³	—	8	32	no	—
382	C₂³	C₂×#41	1	8	yes	—
383	C₂³	H(5,𝔽₂)	1	4	yes	—
384	C₂³	C₂⁵	1	4	yes	—
385	C₂³	C₂⁵	1	4	yes	—
386	C₂³	C₂⁵	1	8	yes	—
387	C₂³	C₂⁵	1	4	yes	—
388	C₂³	C₂⁵	1	2	yes	—
389	C₂³	C₂⁵	1	1	yes	characteristic
390	Q₈	—	2	8	no	—
391	Q₈	—	4	8	no	—
392	D₄	—	2	16	no	—
393	D₄	—	2	32	no	—
394	D₄	—	2	16	no	—
395	D₄	—	2	32	no	—
396	D₄	—	2	8	no	—
397	D₄	—	2	16	no	—
398	D₄	—	2	8	no	—
399	D₄	—	2	16	no	—
400	D₄	—	4	16	no	—
401	D₄	—	4	16	no	—
402	D₄	—	4	16	no	—
403	D₄	—	4	8	no	—
404	D₄	—	4	16	no	—
405	D₄	C₂×#41	1	16	yes	complemented
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	16	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	16	no	—
421	C₂×C₄	—	2	16	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	4	16	no	—
426	C₂×C₄	—	4	16	no	—
427	C₂×C₄	—	4	16	no	—
428	C₂×C₄	C₂×#41	1	4	yes	—
429	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
430	C₂×C₄	C₂⁵	1	2	yes	—
431	C₂×C₄	C₂⁵	1	4	yes	—
432	C₂×C₄	C₂⁵	1	2	yes	—
433	C₂×C₄	C₂⁵	1	2	yes	—
434	C₂×C₄	C₂⁵	1	4	yes	—
435	C₂×C₄	C₂⁵	1	2	yes	—
436	C₂×C₄	C₂⁵	1	8	yes	—
437	C₂×C₄	C₂⁵	1	4	yes	—
438	C₂×C₄	C₂⁵	1	4	yes	—
439	C₂×C₄	C₂⁵	1	4	yes	—
440	C₂×C₄	C₂⁵	1	2	yes	—
441	C₂×C₄	C₂⁵	1	2	yes	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	2	16	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	8	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	8	no	—
453	C₂²	—	2	8	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	4	32	no	—
458	C₂²	—	4	8	no	—
459	C₂²	—	4	16	no	—
460	C₂²	—	4	8	no	—
461	C₂²	—	8	32	no	—
462	C₂²	C₂²×#41	1	8	yes	—
463	C₂²	C₂²×#41	1	2	yes	—
464	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
465	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
466	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
467	C₂²	C₂⁶	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	4	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	4	no	—
473	C₄	—	2	4	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	4	no	—
476	C₄	—	2	8	no	—
477	C₄	—	2	4	no	—
478	C₄	C₂²×#41	1	4	yes	—
479	C₄	C₂×H(5,𝔽₂)	1	4	yes	—
480	C₂	—	2	4	no	—
481	C₂	—	2	8	no	—
482	C₂	—	4	4	no	—
483	C₂	—	4	8	no	—
484	C₂	—	4	4	no	—
485	C₂	#3519	1	4	yes	direct product factor
486	C₂	C₂³×#41	1	1	yes	characteristic
487	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂	C₂²×H(5,𝔽₂)	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. #3519	C₂	direct (N × H)
2. C₂×#555	C₂	semidirect
3. C₂×#554	C₂	semidirect
4. C₂×#553	C₂	semidirect
5. C₂×#553	C₂	semidirect
6. C₂×#550	C₂	semidirect
7. C₂×#546	C₂	semidirect
8. C₂×#546	C₂	semidirect
9. C₂×D₄²	C₂	semidirect
10. C₂×D₄²	C₂	semidirect
11. C₂×#540	C₂	semidirect
12. C₂×#538	C₂	semidirect
13. C₂×#532	C₂	semidirect
14. C₂×#529	C₂	semidirect
15. C₂×#525	C₂	semidirect
16. C₂²×#121	C₂	semidirect
17. C₂×#518	C₂	semidirect
18. C₂²×C₄×D₄	C₂	semidirect
19. C₂²×#41	C₂²	semidirect
20. C₂²×#41	C₂²	semidirect
23. C₂³×D₄	C₂²	semidirect
24. C₂³×D₄	C₂²	semidirect
25. C₂⁴×C₄	C₂²	semidirect
26. #555	C₂²	semidirect
27. #554	C₂²	semidirect
28. #553	C₂²	semidirect
29. #553	C₂²	semidirect
30. #550	C₂²	semidirect
31. #546	C₂²	semidirect
32. #546	C₂²	semidirect
33. D₄²	C₂²	semidirect
34. D₄²	C₂²	semidirect
35. #540	C₂²	semidirect
36. #538	C₂²	semidirect
37. #532	C₂²	semidirect
38. C₂×C₄⋊Q₈	C₂²	semidirect
39. C₂×#127	C₂²	semidirect
40. C₂×#127	C₂²	semidirect
41. #529	C₂²	semidirect
42. C₂×#126	C₂²	semidirect
43. C₂×#126	C₂²	semidirect
44. C₂×#125	C₂²	semidirect
45. C₂×#125	C₂²	semidirect
46. C₂×#124	C₂²	semidirect
47. C₂×#124	C₂²	semidirect
48. C₂×#124	C₂²	semidirect
49. #525	C₂²	semidirect
50. C₂×#123	C₂²	semidirect
51. C₂×#123	C₂²	semidirect
52. C₂×#123	C₂²	semidirect
53. C₂×#123	C₂²	semidirect
54. C₂×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₂²⋊Q₈	C₂²	semidirect
56. C₂×C₂²⋊Q₈	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
63. C₂×#121	C₂²	semidirect
64. C₂×#121	C₂²	semidirect
65. C₂×#121	C₂²	semidirect
66. C₂×#121	C₂²	semidirect
67. C₂×#121	C₂²	semidirect
68. C₂×#121	C₂²	semidirect
69. C₂×#121	C₂²	semidirect
70. C₂×#121	C₂²	semidirect
71. C₂×#120	C₂²	semidirect
72. C₂×#120	C₂²	semidirect
73. C₂×#120	C₂²	semidirect
74. #518	C₂²	semidirect
75. C₂×C₄×Q₈	C₂²	semidirect
79. C₂×C₄×D₄	C₂²	semidirect
80. C₂×C₄×D₄	C₂²	semidirect
81. C₂×C₄×D₄	C₂²	semidirect
82. C₂×C₄×D₄	C₂²	semidirect
83. C₂×C₄×D₄	C₂²	semidirect
84. C₂×C₄×D₄	C₂²	semidirect
85. C₂×C₄×D₄	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
90. C₂×C₄×D₄	C₂²	semidirect
91. C₂×C₄×D₄	C₂²	semidirect
92. C₂×#117	C₂²	semidirect
93. C₂×#117	C₂²	semidirect
94. C₂×#117	C₂²	semidirect
95. C₂²×C₄⋊C₄	C₂²	semidirect
96. C₂²×C₄⋊C₄	C₂²	semidirect
97. C₂²×C₂²⋊C₄	C₂²	semidirect
98. C₂²×C₂²⋊C₄	C₂²	semidirect
99. C₂²×C₂²⋊C₄	C₂²	semidirect
100. C₂²×C₄²	C₂²	semidirect
105. C₂×#41	C₂³	semidirect
106. C₂×#41	C₂³	semidirect
129. C₂²×D₄	C₂³	semidirect
130. C₂²×D₄	C₂³	semidirect
144. C₂³×C₄	C₂³	semidirect
145. C₄⋊Q₈	C₂³	semidirect
146. #127	C₂³	semidirect
147. #127	C₂³	semidirect
148. #126	C₂³	semidirect
149. #126	C₂³	semidirect
150. #125	C₂³	semidirect
151. #125	C₂³	semidirect
152. #124	C₂³	semidirect
153. #124	C₂³	semidirect
154. #124	C₂³	semidirect
155. #123	C₂³	semidirect
156. #123	C₂³	semidirect
157. #123	C₂³	semidirect
158. #123	C₂³	semidirect
159. C₂²⋊Q₈	C₂³	semidirect
160. C₂²⋊Q₈	C₂³	semidirect
161. C₂²⋊Q₈	C₂³	semidirect
163. #121	C₂³	semidirect
164. #121	C₂³	semidirect
165. #121	C₂³	semidirect
166. #121	C₂³	semidirect
167. #121	C₂³	semidirect
168. #121	C₂³	semidirect
169. #121	C₂³	semidirect
170. #121	C₂³	semidirect
171. #121	C₂³	semidirect
172. #121	C₂³	semidirect
173. #121	C₂³	semidirect
174. #121	C₂³	semidirect
175. #120	C₂³	semidirect
176. #120	C₂³	semidirect
177. #120	C₂³	semidirect
178. C₄×Q₈	C₂³	semidirect
182. C₄×D₄	C₂³	semidirect
183. C₄×D₄	C₂³	semidirect
184. C₄×D₄	C₂³	semidirect
185. C₄×D₄	C₂³	semidirect
186. C₄×D₄	C₂³	semidirect
187. C₄×D₄	C₂³	semidirect
188. C₄×D₄	C₂³	semidirect
189. C₄×D₄	C₂³	semidirect
190. C₄×D₄	C₂³	semidirect
191. C₄×D₄	C₂³	semidirect
192. C₄×D₄	C₂³	semidirect
193. C₄×D₄	C₂³	semidirect
194. #117	C₂³	semidirect
195. #117	C₂³	semidirect
196. #117	C₂³	semidirect
210. C₂×C₄⋊C₄	C₂³	semidirect
211. C₂×C₄⋊C₄	C₂³	semidirect
228. C₂×C₂²⋊C₄	C₂³	semidirect
229. C₂×C₂²⋊C₄	C₂³	semidirect
230. C₂×C₂²⋊C₄	C₂³	semidirect
237. C₂×C₄²	C₂³	semidirect
274. C₂×D₄	#41	semidirect
405. D₄	C₂×#41	semidirect
485. C₂	#3519	direct (N × H)

Maximal subgroups

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

subgroup	index
#3519	2
C₂×#555	2
C₂×#554	2
C₂×#553	2
C₂×#550	2
C₂×#546	2
C₂×D₄²	2
C₂×#540	2
C₂×#538	2
C₂×#532	2
C₂×#529	2
C₂×#525	2
C₂²×#121	2
C₂×#518	2
C₂²×C₄×D₄	2

Subgroups — C2×#3519 #62771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3519 #62771