Subgroups — C₂×#72235183 #72314753

Order 2048.

At least 9624 conjugacy classes of subgroups; only the 1736 normal subgroups are shown.

The subgroup lattice has 620 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#106326	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#201462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#185255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#6346594	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#112857	C₂	1	2	yes	maximal, complemented
6	C₂×#111959	C₂	1	2	yes	maximal, complemented
7	C₂×#612425	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#7630944	C₂	1	1	yes	maximal, characteristic, complemented
9	#72235183	C₂	1	16	yes	maximal, direct product factor
10	C₂×#234948	C₂	1	2	yes	maximal, complemented
11	C₂×#184773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#393988	C₂	1	2	yes	maximal, complemented
13	C₂²×#3490	C₂²	1	1	yes	characteristic
14	C₂³×#525	C₂²	1	1	yes	characteristic, complemented
15	C₂⁵×C₂²⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×#60359	C₂²	1	2	yes	complemented
17	C₂×#36614	C₂²	1	2	yes	—
18	#7630944	C₂²	1	8	yes	complemented
19	C₂×#35050	C₂²	1	2	yes	—
20	C₂²×#2404	C₂²	1	1	yes	characteristic
21	C₂²×#2404	C₂²	1	1	yes	characteristic, complemented
22	C₂×#34176	C₂²	1	1	yes	characteristic
23	C₂×#20979	C₂²	1	2	yes	complemented
24	C₂×#20605	C₂²	1	2	yes	complemented
25	C₂×#20579	C₂²	1	2	yes	complemented
26	#6346594	C₂²	1	8	yes	complemented
27	C₂×#17587	C₂²	1	2	yes	complemented
28	C₂×#17587	C₂²	1	2	yes	complemented
29	C₂²×#1462	C₂²	1	1	yes	characteristic
30	C₂²×#1462	C₂²	1	1	yes	characteristic
31	C₂²×#1462	C₂²	1	2	yes	complemented
32	#612425	C₂²	1	8	yes	complemented
33	C₂×#14681	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13868	C₂²	1	1	yes	characteristic
35	C₂×#13868	C₂²	1	1	yes	characteristic, complemented
36	#393988	C₂²	1	16	yes	complemented
37	C₂×#10716	C₂²	1	2	yes	complemented
38	#234948	C₂²	1	16	yes	complemented
39	#201462	C₂²	1	8	yes	complemented
40	#185255	C₂²	1	8	yes	complemented
41	#184773	C₂²	1	8	yes	complemented
42	C₂×#7943	C₂²	1	2	yes	complemented
43	C₂×#7943	C₂²	1	2	yes	complemented
44	#112857	C₂²	1	16	yes	complemented
45	#111959	C₂²	1	16	yes	complemented
46	#106326	C₂²	1	8	yes	complemented
47	C₂⁸	D₄	1	1	yes	characteristic
48	C₂⁴×#41	C₂³	1	1	yes	characteristic
49	C₂⁶×C₄	D₄	1	1	yes	characteristic
50	C₂⁶×C₄	C₂³	1	1	yes	characteristic
51	C₂×#3490	D₄	1	4	yes	complemented
52	C₂×#3490	C₂³	1	4	yes	—
53	C₂²×#538	D₄	1	2	yes	complemented
54	C₂²×#543	D₄	1	1	yes	characteristic, complemented
55	C₂²×#534	D₄	1	1	yes	characteristic, complemented
56	C₂²×#525	D₄	1	4	yes	complemented
57	C₂²×#525	C₂³	1	2	yes	—
58	C₂²×#525	C₂³	1	4	yes	complemented
59	C₂³×#117	C₂³	1	1	yes	characteristic
60	C₂⁴×C₂²⋊C₄	D₄	1	4	yes	—
61	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
62	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
63	C₂⁴×C₂²⋊C₄	C₂³	1	4	yes	—
64	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
65	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
66	#60359	C₂³	1	8	yes	complemented
67	C₂²×#407	C₂³	1	2	yes	—
68	C₂²×#407	C₂³	1	2	yes	—
69	#36614	D₄	1	8	yes	complemented
70	#36614	C₂³	1	8	yes	—
71	#35050	D₄	1	8	yes	complemented
72	#35050	C₂³	1	8	yes	—
73	C₂×#2561	D₄	1	4	yes	complemented
74	C₂×#2539	D₄	1	4	yes	complemented
75	C₂×#2404	D₄	1	4	yes	complemented
76	C₂×#2404	C₂³	1	4	yes	—
77	C₂×#2404	C₂³	1	4	yes	complemented
78	C₂²×#393	D₄	1	2	yes	complemented
79	C₂²×#392	D₄	1	2	yes	complemented
80	#34176	D₄	1	4	yes	complemented
81	#34176	C₂³	1	4	yes	—
82	C₂×#2312	D₄	1	2	yes	complemented
83	C₂×#2280	D₄	1	4	yes	complemented
84	C₂×#2280	C₂³	1	2	yes	—
85	C₂²×#381	C₂³	1	1	yes	characteristic
86	C₂²×#381	C₂³	1	1	yes	characteristic
87	C₂×#2273	D₄	1	2	yes	complemented
88	#20979	C₂³	1	8	yes	complemented
89	#20605	C₂³	1	8	yes	complemented
90	#20579	C₂³	1	8	yes	complemented
91	#17587	C₂³	1	8	yes	complemented
92	#17587	C₂³	1	8	yes	complemented
93	C₂×#1462	D₄	1	4	yes	complemented
94	C₂×#1462	C₂³	1	4	yes	—
95	C₂×#1462	C₂³	1	4	yes	—
96	C₂×#1462	C₂³	1	8	yes	complemented
97	C₂²×#323	D₄	1	4	yes	complemented
98	#14681	C₂³	1	4	yes	complemented
99	#13868	D₄	1	4	yes	complemented
100	#13868	C₂³	1	4	yes	—
101	#13868	C₂³	1	4	yes	complemented
102	C₂×#1437	D₄	1	4	yes	complemented
103	#10716	C₂³	1	8	yes	complemented
104	#7943	C₂³	1	8	yes	complemented
105	#7943	C₂³	1	8	yes	complemented
106	C₂⁷	C₂×D₄	1	1	yes	characteristic
107	C₂⁷	C₂×D₄	1	1	yes	characteristic
108	C₂⁷	C₂×D₄	1	4	yes	—
109	C₂⁷	C₂×D₄	1	1	yes	characteristic
110	C₂³×#41	C₂×D₄	1	2	yes	—
111	C₂³×#41	C₂×D₄	1	2	yes	complemented
112	C₂³×#41	C₂⁴	1	2	yes	—
113	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
114	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
115	C₂⁵×C₄	C₂×D₄	1	4	yes	—
116	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
117	C₂⁵×C₄	C₂×D₄	1	2	yes	—
118	C₂⁵×C₄	C₂×D₄	1	4	yes	—
119	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
120	C₂⁵×C₄	C₂×D₄	1	4	yes	—
121	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
122	C₂⁵×C₄	C₂⁴	1	2	yes	—
123	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
124	C₂×#543	C₂×D₄	1	4	yes	complemented
125	C₂×#538	C₂×D₄	1	8	yes	complemented
126	C₂×#534	C₂×D₄	1	4	yes	complemented
127	C₂×#525	C₂×D₄	1	4	yes	—
128	C₂×#525	C₂×D₄	1	4	yes	—
129	C₂×#525	C₂×D₄	1	4	yes	—
130	C₂×#525	C₂×D₄	1	16	yes	complemented
131	C₂×#525	C₂⁴	1	4	yes	—
132	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
133	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
134	C₂²×#121	C₂×D₄	1	2	yes	—
135	C₂²×#121	C₂×D₄	1	2	yes	—
136	C₂²×#117	C₂×D₄	1	4	yes	—
137	C₂²×#117	C₂×D₄	1	2	yes	—
138	C₂²×#117	C₂×D₄	1	2	yes	complemented
139	C₂²×#117	C₂⁴	1	2	yes	—
140	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
141	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
142	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
143	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
144	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
145	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
146	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
147	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
148	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
149	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
150	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
151	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
152	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
153	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
154	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
155	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
156	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
157	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
158	C₂³×C₂²⋊C₄	#41	1	2	yes	—
159	C₂³×C₂²⋊C₄	#41	1	2	yes	—
160	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
161	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
162	C₂³×C₄²	C₂×D₄	1	2	yes	complemented
163	C₂×#407	C₂×D₄	1	4	yes	complemented
164	C₂×#407	C₂⁴	1	4	yes	—
165	C₂×#407	C₂⁴	1	4	yes	—
166	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	complemented
167	#2561	C₂×D₄	1	16	yes	complemented
168	#2539	C₂×D₄	1	16	yes	complemented
169	C₂×#393	C₂×D₄	1	8	yes	complemented
170	C₂×#392	C₂×D₄	1	8	yes	complemented
171	#2312	C₂×D₄	1	8	yes	complemented
172	#2280	C₂×D₄	1	4	yes	—
173	#2280	C₂×D₄	1	4	yes	—
174	#2280	C₂×D₄	1	4	yes	—
175	#2280	C₂×D₄	1	16	yes	complemented
176	#2280	C₂⁴	1	4	yes	—
177	C₂×#381	C₂×D₄	1	2	yes	complemented
178	C₂×#381	C₂×D₄	1	2	yes	complemented
179	C₂×#381	C₂⁴	1	2	yes	—
180	C₂×#381	C₂⁴	1	2	yes	—
181	#2273	C₂×D₄	1	8	yes	complemented
182	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
183	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
184	C₂²×#95	C₂×D₄	1	2	yes	complemented
185	C₂²×#95	C₂×D₄	1	2	yes	complemented
186	C₂×#323	C₂×D₄	1	16	yes	complemented
187	#1437	C₂×D₄	1	16	yes	complemented
188	C₂⁶	#120	1	2	yes	—
189	C₂⁶	#120	1	1	yes	characteristic
190	C₂⁶	#120	1	2	yes	—
191	C₂⁶	#120	1	2	yes	—
192	C₂⁶	#120	1	2	yes	—
193	C₂⁶	#120	1	2	yes	—
194	C₂⁶	#120	1	1	yes	characteristic
195	C₂⁶	#120	1	2	yes	—
196	C₂⁶	#120	1	2	yes	—
197	C₂⁶	#121	1	2	yes	—
198	C₂⁶	#121	1	2	yes	—
199	C₂⁶	C₂²×D₄	1	2	yes	—
200	C₂⁶	C₂²×D₄	1	1	yes	characteristic
201	C₂⁶	C₂²×D₄	1	2	yes	—
202	C₂⁶	C₂²×D₄	1	2	yes	—
203	C₂²×#41	#120	1	4	yes	complemented
204	C₂²×#41	C₂²×D₄	1	4	yes	—
205	C₂³×Q₈	#120	1	2	yes	complemented
206	C₂³×Q₈	C₂²×D₄	1	2	yes	complemented
207	C₂³×D₄	#120	1	2	yes	complemented
208	C₂³×D₄	C₂²×D₄	1	2	yes	complemented
209	C₂⁴×C₄	#120	1	2	yes	—
210	C₂⁴×C₄	#120	1	8	yes	—
211	C₂⁴×C₄	#120	1	2	yes	—
212	C₂⁴×C₄	#120	1	2	yes	—
213	C₂⁴×C₄	#120	1	2	yes	—
214	C₂⁴×C₄	#120	1	2	yes	—
215	C₂⁴×C₄	#120	1	1	yes	characteristic
216	C₂⁴×C₄	#120	1	1	yes	characteristic
217	C₂⁴×C₄	#120	1	2	yes	—
218	C₂⁴×C₄	#120	1	2	yes	—
219	C₂⁴×C₄	#121	1	2	yes	—
220	C₂⁴×C₄	#121	1	2	yes	—
221	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
222	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
223	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
224	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
225	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
226	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
227	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
228	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
229	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
230	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
231	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
232	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
233	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
234	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
235	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
236	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
237	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
238	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
239	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
240	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
241	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
242	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
243	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
244	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
245	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
246	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	#120	1	4	yes	complemented
248	C₂×C₂²⋊Q₈	#120	1	4	yes	complemented
249	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
250	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
251	C₂×#121	#120	1	4	yes	complemented
252	C₂×#121	#120	1	4	yes	complemented
253	C₂×#121	C₂²×D₄	1	4	yes	—
254	C₂×#121	C₂²×D₄	1	4	yes	—
255	C₂×#117	#120	1	4	yes	complemented
256	C₂×#117	#120	1	8	yes	complemented
257	C₂×#117	C₂²×D₄	1	4	yes	—
258	C₂×#117	C₂²×D₄	1	8	yes	—
259	C₂²×C₄⋊C₄	#120	1	2	yes	complemented
260	C₂²×C₄⋊C₄	#120	1	2	yes	complemented
261	C₂²×C₂²⋊C₄	#120	1	8	yes	—
262	C₂²×C₂²⋊C₄	#120	1	2	yes	—
263	C₂²×C₂²⋊C₄	#120	1	2	yes	—
264	C₂²×C₂²⋊C₄	#120	1	4	yes	—
265	C₂²×C₂²⋊C₄	#120	1	2	yes	—
266	C₂²×C₂²⋊C₄	#120	1	2	yes	—
267	C₂²×C₂²⋊C₄	#120	1	4	yes	—
268	C₂²×C₂²⋊C₄	#120	1	2	yes	—
269	C₂²×C₂²⋊C₄	#120	1	2	yes	—
270	C₂²×C₂²⋊C₄	#120	1	2	yes	—
271	C₂²×C₂²⋊C₄	#120	1	4	yes	—
272	C₂²×C₂²⋊C₄	#120	1	2	yes	—
273	C₂²×C₂²⋊C₄	#120	1	4	yes	—
274	C₂²×C₂²⋊C₄	#121	1	2	yes	—
275	C₂²×C₂²⋊C₄	#121	1	2	yes	—
276	C₂²×C₂²⋊C₄	#121	1	4	yes	—
277	C₂²×C₂²⋊C₄	#121	1	2	yes	—
278	C₂²×C₂²⋊C₄	#121	1	2	yes	—
279	C₂²×C₂²⋊C₄	#121	1	4	yes	—
280	C₂²×C₂²⋊C₄	#121	1	2	yes	—
281	C₂²×C₂²⋊C₄	#121	1	2	yes	—
282	C₂²×C₂²⋊C₄	#121	1	4	yes	—
283	C₂²×C₂²⋊C₄	#121	1	2	yes	—
284	C₂²×C₂²⋊C₄	#121	1	2	yes	—
285	C₂²×C₂²⋊C₄	#121	1	4	yes	—
286	C₂²×C₂²⋊C₄	#121	1	4	yes	—
287	C₂²×C₂²⋊C₄	#121	1	4	yes	—
288	C₂²×C₂²⋊C₄	#127	1	2	yes	—
289	C₂²×C₂²⋊C₄	#127	1	2	yes	—
290	C₂²×C₂²⋊C₄	#127	1	2	yes	—
291	C₂²×C₂²⋊C₄	#127	1	4	yes	—
292	C₂²×C₂²⋊C₄	#127	1	2	yes	—
293	C₂²×C₂²⋊C₄	#127	1	4	yes	—
294	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
295	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
296	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
297	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
298	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
299	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
300	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
301	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
302	C₂²×C₂²⋊C₄	C₂×#41	1	4	yes	—
303	C₂²×C₄²	#120	1	8	yes	complemented
304	C₂²×C₄²	C₂²×D₄	1	4	yes	complemented
305	C₂×C₂²⋊C₈	C₂²×D₄	1	8	yes	complemented
306	C₄×C₂²⋊C₄	#120	1	8	yes	complemented
307	C₄×C₂²⋊C₄	#120	1	8	yes	complemented
308	C₄×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
309	C₄×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
310	C₂×#95	C₂²×D₄	1	4	yes	complemented
311	C₂×#95	C₂²×D₄	1	4	yes	complemented
312	C₂⁵	#392	1	2	yes	—
313	C₂⁵	#392	1	2	yes	—
314	C₂⁵	#392	1	4	yes	—
315	C₂⁵	#392	1	2	yes	—
316	C₂⁵	#392	1	4	yes	—
317	C₂⁵	#392	1	2	yes	—
318	C₂⁵	B(4,𝔽₂)	1	8	yes	—
319	C₂⁵	C₂×#120	1	1	yes	characteristic
320	C₂⁵	C₂×#120	1	1	yes	characteristic
321	C₂⁵	C₂×#120	1	1	yes	characteristic
322	C₂⁵	C₂×#120	1	4	yes	—
323	C₂⁵	C₂×#120	1	2	yes	—
324	C₂⁵	C₂×#120	1	4	yes	—
325	C₂⁵	C₂×#120	1	1	yes	characteristic
326	C₂⁵	C₂×#120	1	1	yes	characteristic
327	C₂⁵	C₂×#120	1	1	yes	characteristic
328	C₂⁵	C₂×#120	1	1	yes	characteristic
329	C₂⁵	C₂×#120	1	4	yes	—
330	C₂⁵	C₂×#120	1	2	yes	—
331	C₂⁵	C₂×#120	1	1	yes	characteristic
332	C₂⁵	C₂×#121	1	1	yes	characteristic
333	C₂⁵	C₂×#121	1	1	yes	characteristic
334	C₂⁵	C₂×#121	1	4	yes	—
335	C₂⁵	#534	1	1	yes	characteristic
336	C₂⁵	#534	1	1	yes	characteristic
337	C₂⁵	#534	1	1	yes	characteristic
338	C₂⁵	#534	1	1	yes	characteristic
339	C₂⁵	C₂³×D₄	1	1	yes	characteristic
340	C₂²×Q₈	C₂×#120	1	4	yes	complemented
341	C₂²×D₄	C₂×#120	1	4	yes	complemented
342	C₂³×C₄	#392	1	2	yes	—
343	C₂³×C₄	#392	1	2	yes	—
344	C₂³×C₄	#392	1	4	yes	—
345	C₂³×C₄	#392	1	2	yes	—
346	C₂³×C₄	#392	1	2	yes	—
347	C₂³×C₄	#392	1	4	yes	—
348	C₂³×C₄	C₂×#120	1	4	yes	—
349	C₂³×C₄	C₂×#120	1	2	yes	—
350	C₂³×C₄	C₂×#120	1	2	yes	—
351	C₂³×C₄	C₂×#120	1	2	yes	—
352	C₂³×C₄	C₂×#120	1	2	yes	—
353	C₂³×C₄	C₂×#120	1	2	yes	—
354	C₂³×C₄	C₂×#120	1	4	yes	—
355	C₂³×C₄	C₂×#120	1	4	yes	—
356	C₂³×C₄	C₂×#120	1	2	yes	—
357	C₂³×C₄	C₂×#120	1	2	yes	—
358	C₂³×C₄	C₂×#120	1	1	yes	characteristic
359	C₂³×C₄	C₂×#120	1	1	yes	characteristic
360	C₂³×C₄	C₂×#120	1	2	yes	—
361	C₂³×C₄	C₂×#120	1	2	yes	—
362	C₂³×C₄	C₂×#120	1	2	yes	—
363	C₂³×C₄	C₂×#120	1	2	yes	—
364	C₂³×C₄	C₂×#120	1	2	yes	—
365	C₂³×C₄	C₂×#120	1	1	yes	characteristic
366	C₂³×C₄	C₂×#120	1	1	yes	characteristic
367	C₂³×C₄	C₂×#120	1	1	yes	characteristic
368	C₂³×C₄	C₂×#120	1	1	yes	characteristic
369	C₂³×C₄	C₂×#120	1	1	yes	characteristic
370	C₂³×C₄	C₂×#120	1	1	yes	characteristic
371	C₂³×C₄	C₂×#121	1	4	yes	—
372	C₂³×C₄	C₂×#121	1	1	yes	characteristic
373	C₂³×C₄	C₂×#121	1	1	yes	characteristic
374	C₂³×C₄	C₂×#121	1	1	yes	characteristic
375	C₂³×C₄	C₂×#121	1	1	yes	characteristic
376	C₂³×C₄	C₂×#121	1	1	yes	characteristic
377	C₂³×C₄	C₂×#121	1	1	yes	characteristic
378	C₂³×C₄	C₂×#121	1	1	yes	characteristic
379	C₂³×C₄	C₂×#121	1	1	yes	characteristic
380	C₂³×C₄	C₂×#121	1	1	yes	characteristic
381	C₂³×C₄	C₂×#121	1	1	yes	characteristic
382	C₂³×C₄	C₂×#127	1	1	yes	characteristic
383	C₂³×C₄	C₂×#127	1	1	yes	characteristic
384	C₂³×C₄	C₂×#127	1	1	yes	characteristic
385	C₂³×C₄	C₂×#127	1	1	yes	characteristic
386	C₂³×C₄	#534	1	2	yes	—
387	C₂³×C₄	#534	1	2	yes	—
388	C₂³×C₄	#534	1	2	yes	—
389	C₂³×C₄	#534	1	2	yes	—
390	C₂³×C₄	#534	1	2	yes	—
391	C₂³×C₄	#534	1	2	yes	—
392	C₂³×C₄	#535	1	2	yes	—
393	C₂³×C₄	#535	1	2	yes	—
394	C₂³×C₄	#535	1	2	yes	—
395	C₂³×C₄	#535	1	2	yes	—
396	C₂³×C₄	D₄²	1	2	yes	—
397	C₂³×C₄	D₄²	1	2	yes	—
398	C₂³×C₄	D₄²	1	2	yes	—
399	C₂³×C₄	D₄²	1	2	yes	—
400	C₂³×C₄	D₄²	1	2	yes	—
401	C₂³×C₄	D₄²	1	2	yes	—
402	C₂³×C₄	D₄²	1	2	yes	—
403	C₂³×C₄	D₄²	1	2	yes	—
404	C₂³×C₄	D₄²	1	2	yes	—
405	C₂³×C₄	D₄²	1	2	yes	—
406	C₂³×C₄	D₄²	1	2	yes	—
407	C₂³×C₄	D₄²	1	2	yes	—
408	C₂³×C₄	D₄²	1	2	yes	—
409	C₂³×C₄	D₄²	1	2	yes	—
410	C₂³×C₄	D₄²	1	2	yes	—
411	C₂³×C₄	D₄²	1	2	yes	—
412	C₂³×C₄	D₄²	1	2	yes	—
413	C₂³×C₄	D₄²	1	2	yes	—
414	C₂³×C₄	D₄²	1	2	yes	—
415	C₂³×C₄	D₄²	1	2	yes	—
416	C₂³×C₄	D₄²	1	2	yes	—
417	C₂³×C₄	D₄²	1	2	yes	—
418	C₂³×C₄	D₄²	1	2	yes	—
419	C₂³×C₄	D₄²	1	2	yes	—
420	C₂³×C₄	#546	1	2	yes	—
421	C₂³×C₄	#546	1	2	yes	—
422	C₂³×C₄	#546	1	2	yes	—
423	C₂³×C₄	#546	1	2	yes	—
424	C₂³×C₄	#546	1	2	yes	—
425	C₂³×C₄	#546	1	2	yes	—
426	C₂³×C₄	#546	1	2	yes	—
427	C₂³×C₄	#546	1	2	yes	—
428	C₂³×C₄	C₂³×D₄	1	2	yes	—
429	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
430	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
431	C₂³×C₄	C₂³×D₄	1	2	yes	—
432	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
433	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
434	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
435	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
436	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
437	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
438	C₂×C₄⋊C₄	C₂×#120	1	4	yes	complemented
439	C₂×C₄⋊C₄	C₂×#120	1	4	yes	complemented
440	C₂×C₂²⋊C₄	#392	1	4	yes	—
441	C₂×C₂²⋊C₄	#392	1	4	yes	—
442	C₂×C₂²⋊C₄	#392	1	4	yes	—
443	C₂×C₂²⋊C₄	#392	1	4	yes	—
444	C₂×C₂²⋊C₄	#392	1	4	yes	—
445	C₂×C₂²⋊C₄	#392	1	4	yes	—
446	C₂×C₂²⋊C₄	#392	1	4	yes	—
447	C₂×C₂²⋊C₄	#392	1	4	yes	—
448	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂×#127	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂×#127	1	4	yes	—
456	C₂×C₄²	C₂×#120	1	16	yes	complemented
457	C₂⁴	#2010	1	8	yes	complemented
458	C₂⁴	C₂×#392	1	1	yes	characteristic
459	C₂⁴	C₂×#392	1	1	yes	characteristic
460	C₂⁴	C₂×#392	1	1	yes	characteristic
461	C₂⁴	C₂×#392	1	1	yes	characteristic
462	C₂⁴	C₂×#392	1	4	yes	—
463	C₂⁴	C₂×#392	1	4	yes	—
464	C₂⁴	#2403	1	1	yes	characteristic
465	C₂⁴	#2403	1	1	yes	characteristic
466	C₂⁴	#2403	1	1	yes	characteristic
467	C₂⁴	#2403	1	1	yes	characteristic
468	C₂⁴	#2403	1	1	yes	characteristic
469	C₂⁴	#2403	1	1	yes	characteristic
470	C₂⁴	#2403	1	1	yes	characteristic
471	C₂⁴	#2403	1	1	yes	characteristic
472	C₂⁴	#2410	1	1	yes	characteristic
473	C₂⁴	#2410	1	1	yes	characteristic
474	C₂⁴	#2410	1	1	yes	characteristic
475	C₂⁴	#2410	1	1	yes	characteristic
476	C₂⁴	#2410	1	1	yes	characteristic
477	C₂⁴	#2410	1	1	yes	characteristic
478	C₂⁴	#2410	1	1	yes	characteristic
479	C₂⁴	#2410	1	1	yes	characteristic
480	C₂⁴	#2613	1	1	yes	characteristic
481	C₂⁴	#2613	1	1	yes	characteristic
482	C₂⁴	#2613	1	1	yes	characteristic
483	C₂⁴	#2613	1	1	yes	characteristic
484	C₂⁴	#2846	1	1	yes	characteristic
485	C₂⁴	#2846	1	1	yes	characteristic
486	C₂⁴	#2846	1	1	yes	characteristic
487	C₂⁴	#2846	1	1	yes	characteristic
488	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
489	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
490	C₂⁴	#3026	1	4	yes	—
491	C₂⁴	C₂²×#120	1	1	yes	characteristic
492	C₂⁴	C₂²×#120	1	1	yes	characteristic
493	C₂⁴	C₂²×#120	1	1	yes	characteristic
494	C₂⁴	C₂²×#120	1	1	yes	characteristic
495	C₂⁴	C₂²×#121	1	1	yes	characteristic
496	C₂⁴	C₂×#534	1	1	yes	characteristic
497	C₂⁴	C₂×#534	1	1	yes	characteristic
498	C₂²×C₄	C₂×#392	1	4	yes	—
499	C₂²×C₄	C₂×#392	1	4	yes	—
500	C₂²×C₄	C₂×#392	1	1	yes	characteristic
501	C₂²×C₄	C₂×#392	1	1	yes	characteristic
502	C₂²×C₄	C₂×#392	1	1	yes	characteristic
503	C₂²×C₄	C₂×#392	1	1	yes	characteristic
504	C₂²×C₄	#2403	1	2	yes	—
505	C₂²×C₄	#2403	1	2	yes	—
506	C₂²×C₄	#2403	1	2	yes	—
507	C₂²×C₄	#2403	1	2	yes	—
508	C₂²×C₄	#2403	1	2	yes	—
509	C₂²×C₄	#2403	1	2	yes	—
510	C₂²×C₄	#2403	1	2	yes	—
511	C₂²×C₄	#2403	1	2	yes	—
512	C₂²×C₄	#2403	1	2	yes	—
513	C₂²×C₄	#2403	1	2	yes	—
514	C₂²×C₄	#2403	1	2	yes	—
515	C₂²×C₄	#2403	1	2	yes	—
516	C₂²×C₄	#2408	1	2	yes	—
517	C₂²×C₄	#2408	1	2	yes	—
518	C₂²×C₄	#2408	1	2	yes	—
519	C₂²×C₄	#2408	1	2	yes	—
520	C₂²×C₄	#2408	1	2	yes	—
521	C₂²×C₄	#2408	1	2	yes	—
522	C₂²×C₄	#2408	1	2	yes	—
523	C₂²×C₄	#2408	1	2	yes	—
524	C₂²×C₄	#2410	1	2	yes	—
525	C₂²×C₄	#2410	1	2	yes	—
526	C₂²×C₄	#2410	1	2	yes	—
527	C₂²×C₄	#2410	1	2	yes	—
528	C₂²×C₄	#2410	1	2	yes	—
529	C₂²×C₄	#2410	1	2	yes	—
530	C₂²×C₄	#2410	1	2	yes	—
531	C₂²×C₄	#2410	1	2	yes	—
532	C₂²×C₄	#2410	1	2	yes	—
533	C₂²×C₄	#2410	1	2	yes	—
534	C₂²×C₄	#2410	1	2	yes	—
535	C₂²×C₄	#2410	1	2	yes	—
536	C₂²×C₄	#2433	1	2	yes	—
537	C₂²×C₄	#2433	1	2	yes	—
538	C₂²×C₄	#2433	1	2	yes	—
539	C₂²×C₄	#2433	1	2	yes	—
540	C₂²×C₄	#2433	1	2	yes	—
541	C₂²×C₄	#2433	1	2	yes	—
542	C₂²×C₄	#2433	1	2	yes	—
543	C₂²×C₄	#2433	1	2	yes	—
544	C₂²×C₄	#2613	1	2	yes	—
545	C₂²×C₄	#2613	1	2	yes	—
546	C₂²×C₄	#2846	1	2	yes	—
547	C₂²×C₄	#2846	1	2	yes	—
548	C₂²×C₄	C₂²×#120	1	2	yes	—
549	C₂²×C₄	C₂²×#120	1	2	yes	—
550	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
551	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
552	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
553	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
554	C₂²×C₄	C₂×#534	1	2	yes	—
555	C₂²×C₄	C₂×#535	1	2	yes	—
556	C₂²×C₄	C₂×D₄²	1	2	yes	—
557	C₂²×C₄	C₂×D₄²	1	2	yes	—
558	C₂²×C₄	C₂×D₄²	1	2	yes	—
559	C₂²×C₄	C₂×D₄²	1	2	yes	—
560	C₂²×C₄	C₂×D₄²	1	2	yes	—
561	C₂²×C₄	C₂×D₄²	1	2	yes	—
562	C₂²×C₄	C₂×#546	1	2	yes	—
563	C₂²×C₄	C₂×#546	1	2	yes	—
564	C₂³	#14715	1	1	yes	characteristic
565	C₂³	#14715	1	1	yes	characteristic
566	C₂³	#14715	1	1	yes	characteristic
567	C₂³	#14715	1	1	yes	characteristic
568	C₂³	#14715	1	1	yes	characteristic
569	C₂³	#14715	1	1	yes	characteristic
570	C₂³	#14715	1	1	yes	characteristic
571	C₂³	#14715	1	1	yes	characteristic
572	C₂³	C₂×#2010	1	4	yes	—
573	C₂³	C₂×#2010	1	8	yes	complemented
574	C₂³	#23897	1	4	yes	—
575	C₂³	#23900	1	2	yes	—
576	C₂³	#23900	1	2	yes	—
577	C₂³	#23903	1	2	yes	—
578	C₂³	#23903	1	2	yes	—
579	C₂³	#24404	1	4	yes	—
580	C₂³	#24404	1	4	yes	—
581	C₂³	#32898	1	4	yes	—
582	C₂³	#32898	1	4	yes	—
583	C₂³	C₂²×#392	1	1	yes	characteristic
584	C₂³	C₂×#2613	1	1	yes	characteristic
585	C₂³	C₂×#2403	1	1	yes	characteristic
586	C₂³	C₂×#2403	1	1	yes	characteristic
587	C₂³	C₂×#2410	1	1	yes	characteristic
588	C₂³	C₂×#2410	1	1	yes	characteristic
589	C₂³	C₂×#2846	1	1	yes	characteristic
590	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
591	C₂³	C₂×#3026	1	2	yes	—
592	C₂×C₄	#14715	1	2	yes	—
593	C₂×C₄	#14715	1	2	yes	—
594	C₂×C₄	#14715	1	2	yes	—
595	C₂×C₄	#14715	1	2	yes	—
596	C₂×C₄	C₂×#2403	1	2	yes	—
597	C₂×C₄	C₂×#2410	1	2	yes	—
598	C₂×C₄	C₂×#2408	1	2	yes	—
599	C₂×C₄	C₂×#2433	1	2	yes	—
600	C₂²	#393975	1	2	yes	—
601	C₂²	#393975	1	2	yes	—
602	C₂²	#393988	1	2	yes	—
603	C₂²	#393988	1	2	yes	—
604	C₂²	#394066	1	2	yes	—
605	C₂²	#394066	1	2	yes	—
606	C₂²	#394066	1	2	yes	—
607	C₂²	#394066	1	2	yes	—
608	C₂²	C₂×#14715	1	1	yes	characteristic
609	C₂²	C₂²×#2010	1	2	yes	—
610	C₂²	C₂×#23897	1	2	yes	—
611	C₂²	C₂×#23900	1	1	yes	characteristic
612	C₂²	C₂×#23903	1	1	yes	characteristic
613	C₂²	C₂×#24404	1	2	yes	—
614	C₂²	C₂×#32898	1	2	yes	—
615	C₂	C₂×#393988	1	1	yes	characteristic
616	C₂	C₂×#393975	1	1	yes	characteristic
617	C₂	C₂×#394066	1	1	yes	characteristic
618	C₂	#72235183	1	4	yes	direct product factor

	subgroup	G/H
center, socle	C₂³	#14715
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#106326	C₂	semidirect
2. C₂×#201462	C₂	semidirect
3. C₂×#185255	C₂	semidirect
4. C₂×#6346594	C₂	semidirect
5. C₂×#112857	C₂	semidirect
6. C₂×#111959	C₂	semidirect
7. C₂×#612425	C₂	semidirect
8. C₂×#7630944	C₂	semidirect
9. #72235183	C₂	direct (N × H)
10. C₂×#234948	C₂	semidirect
11. C₂×#184773	C₂	semidirect
12. C₂×#393988	C₂	semidirect
14. C₂³×#525	C₂²	semidirect
16. C₂×#60359	C₂²	semidirect
18. #7630944	C₂²	semidirect
21. C₂²×#2404	C₂²	semidirect
23. C₂×#20979	C₂²	semidirect
24. C₂×#20605	C₂²	semidirect
25. C₂×#20579	C₂²	semidirect
26. #6346594	C₂²	semidirect
27. C₂×#17587	C₂²	semidirect
28. C₂×#17587	C₂²	semidirect
31. C₂²×#1462	C₂²	semidirect
32. #612425	C₂²	semidirect
33. C₂×#14681	C₂²	semidirect
35. C₂×#13868	C₂²	semidirect
36. #393988	C₂²	semidirect
37. C₂×#10716	C₂²	semidirect
38. #234948	C₂²	semidirect
39. #201462	C₂²	semidirect
40. #185255	C₂²	semidirect
41. #184773	C₂²	semidirect
42. C₂×#7943	C₂²	semidirect
43. C₂×#7943	C₂²	semidirect
44. #112857	C₂²	semidirect
45. #111959	C₂²	semidirect
46. #106326	C₂²	semidirect
51. C₂×#3490	D₄	semidirect
53. C₂²×#538	D₄	semidirect
54. C₂²×#543	D₄	semidirect
55. C₂²×#534	D₄	semidirect
56. C₂²×#525	D₄	semidirect
58. C₂²×#525	C₂³	semidirect
66. #60359	C₂³	semidirect
69. #36614	D₄	semidirect
71. #35050	D₄	semidirect
73. C₂×#2561	D₄	semidirect
74. C₂×#2539	D₄	semidirect
75. C₂×#2404	D₄	semidirect
77. C₂×#2404	C₂³	semidirect
78. C₂²×#393	D₄	semidirect
79. C₂²×#392	D₄	semidirect
80. #34176	D₄	semidirect
82. C₂×#2312	D₄	semidirect
83. C₂×#2280	D₄	semidirect
87. C₂×#2273	D₄	semidirect
88. #20979	C₂³	semidirect
89. #20605	C₂³	semidirect
90. #20579	C₂³	semidirect
91. #17587	C₂³	semidirect
92. #17587	C₂³	semidirect
93. C₂×#1462	D₄	semidirect
96. C₂×#1462	C₂³	semidirect
97. C₂²×#323	D₄	semidirect
98. #14681	C₂³	semidirect
99. #13868	D₄	semidirect
101. #13868	C₂³	semidirect
102. C₂×#1437	D₄	semidirect
103. #10716	C₂³	semidirect
104. #7943	C₂³	semidirect
105. #7943	C₂³	semidirect
111. C₂³×#41	C₂×D₄	semidirect
113. C₂⁴×Q₈	C₂×D₄	semidirect
114. C₂⁴×D₄	C₂×D₄	semidirect
124. C₂×#543	C₂×D₄	semidirect
125. C₂×#538	C₂×D₄	semidirect
126. C₂×#534	C₂×D₄	semidirect
130. C₂×#525	C₂×D₄	semidirect
138. C₂²×#117	C₂×D₄	semidirect
162. C₂³×C₄²	C₂×D₄	semidirect
163. C₂×#407	C₂×D₄	semidirect
166. C₂²×C₂²⋊C₈	C₂×D₄	semidirect
167. #2561	C₂×D₄	semidirect
168. #2539	C₂×D₄	semidirect
169. C₂×#393	C₂×D₄	semidirect
170. C₂×#392	C₂×D₄	semidirect
171. #2312	C₂×D₄	semidirect
175. #2280	C₂×D₄	semidirect
177. C₂×#381	C₂×D₄	semidirect
178. C₂×#381	C₂×D₄	semidirect
181. #2273	C₂×D₄	semidirect
184. C₂²×#95	C₂×D₄	semidirect
185. C₂²×#95	C₂×D₄	semidirect
186. C₂×#323	C₂×D₄	semidirect
187. #1437	C₂×D₄	semidirect
203. C₂²×#41	#120	semidirect
205. C₂³×Q₈	#120	semidirect
206. C₂³×Q₈	C₂²×D₄	semidirect
207. C₂³×D₄	#120	semidirect
208. C₂³×D₄	C₂²×D₄	semidirect
247. C₂×C₂²⋊Q₈	#120	semidirect
248. C₂×C₂²⋊Q₈	#120	semidirect
251. C₂×#121	#120	semidirect
252. C₂×#121	#120	semidirect
255. C₂×#117	#120	semidirect
256. C₂×#117	#120	semidirect
259. C₂²×C₄⋊C₄	#120	semidirect
260. C₂²×C₄⋊C₄	#120	semidirect
303. C₂²×C₄²	#120	semidirect
304. C₂²×C₄²	C₂²×D₄	semidirect
305. C₂×C₂²⋊C₈	C₂²×D₄	semidirect
306. C₄×C₂²⋊C₄	#120	semidirect
307. C₄×C₂²⋊C₄	#120	semidirect
310. C₂×#95	C₂²×D₄	semidirect
311. C₂×#95	C₂²×D₄	semidirect
340. C₂²×Q₈	C₂×#120	semidirect
341. C₂²×D₄	C₂×#120	semidirect
438. C₂×C₄⋊C₄	C₂×#120	semidirect
439. C₂×C₄⋊C₄	C₂×#120	semidirect
456. C₂×C₄²	C₂×#120	semidirect
457. C₂⁴	#2010	semidirect
573. C₂³	C₂×#2010	semidirect
618. C₂	#72235183	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#106326	2
C₂×#201462	2
C₂×#185255	2
C₂×#6346594	2
C₂×#112857	2
C₂×#111959	2
C₂×#612425	2
C₂×#7630944	2
#72235183	2
C₂×#234948	2
C₂×#184773	2
C₂×#393988	2

Subgroups — C2×#72235183 #72314753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72235183 #72314753