Subgroups — C₂×#72218099 #72278556

Order 2048.

At least 14361 conjugacy classes of subgroups; only the 1704 normal subgroups are shown.

The subgroup lattice has 716 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×#147569	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#146593	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#147815	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#7708349	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#494575	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#147567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#394064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#147811	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#12753	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#498927	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#12687	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#33551	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#393975	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#498886	C₂	1	1	yes	maximal, characteristic, complemented
15	#72218099	C₂	1	16	yes	maximal, direct product factor
16	C₂²×#23900	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#3532	C₂²	1	1	yes	characteristic
18	C₂²×#3484	C₂²	1	1	yes	characteristic, complemented
19	C₂⁴×#120	C₂²	1	1	yes	characteristic
20	C₂²×#3026	C₂²	1	1	yes	characteristic, complemented
21	C₂³×B(4,𝔽₂)	C₂²	1	1	yes	characteristic
22	C₂³×B(4,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#3019	C₂²	1	1	yes	characteristic, complemented
24	#7708349	C₂²	1	8	yes	complemented
25	C₂×#36714	C₂²	1	1	yes	characteristic
26	C₂×#36702	C₂²	1	1	yes	characteristic
27	C₂×#35222	C₂²	1	1	yes	characteristic
28	C₂×#34980	C₂²	1	1	yes	characteristic
29	C₂×#34356	C₂²	1	1	yes	characteristic
30	C₂×#33551	C₂²	1	8	yes	complemented
31	C₂²×#2127	C₂²	1	1	yes	characteristic, complemented
32	C₂²×#2127	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#2121	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#2121	C₂²	1	1	yes	characteristic, complemented
35	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
36	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
37	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
38	C₂³×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
39	C₂×#23900	C₂²	1	8	yes	complemented
40	C₂²×#1913	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#1911	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#1889	C₂²	1	1	yes	characteristic
43	C₂²×#1889	C₂²	1	1	yes	characteristic, complemented
44	C₂×#20616	C₂²	1	1	yes	characteristic, complemented
45	C₂×#20609	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#1783	C₂²	1	1	yes	characteristic, complemented
47	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
48	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
49	#498927	C₂²	1	8	yes	complemented
50	#498886	C₂²	1	8	yes	complemented
51	#494575	C₂²	1	8	yes	complemented
52	C₂×#12753	C₂²	1	8	yes	complemented
53	C₂×#12687	C₂²	1	8	yes	complemented
54	C₂×#12582	C₂²	1	1	yes	characteristic, complemented
55	C₂×#12582	C₂²	1	1	yes	characteristic, complemented
56	C₂×#12574	C₂²	1	1	yes	characteristic, complemented
57	C₂×#12574	C₂²	1	1	yes	characteristic, complemented
58	#394064	C₂²	1	8	yes	complemented
59	#393975	C₂²	1	8	yes	complemented
60	C₂×#10754	C₂²	1	1	yes	characteristic, complemented
61	C₂×#10740	C₂²	1	1	yes	characteristic, complemented
62	#147815	C₂²	1	8	yes	complemented
63	#147811	C₂²	1	8	yes	complemented
64	#147569	C₂²	1	8	yes	complemented
65	#147567	C₂²	1	8	yes	complemented
66	#146593	C₂²	1	8	yes	complemented
67	C₂⁸	D₄	1	1	yes	characteristic, complemented
68	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
69	C₂⁵×D₄	C₂³	1	1	yes	characteristic
70	C₂×#3484	C₂³	1	4	yes	complemented
71	C₂×#3532	D₄	1	4	yes	complemented
72	C₂×#3532	C₂³	1	4	yes	—
73	C₂²×#551	D₄	1	1	yes	characteristic, complemented
74	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
75	C₂²×H(3,𝔽₄)	D₄	1	1	yes	characteristic, complemented
76	C₂²×#560	D₄	1	1	yes	characteristic, complemented
77	C₂²×#535	D₄	1	1	yes	characteristic, complemented
78	C₂²×#535	C₂³	1	1	yes	characteristic
79	C₂²×#534	D₄	1	1	yes	characteristic, complemented
80	C₂²×#534	C₂³	1	1	yes	characteristic
81	C₂²×#525	D₄	1	1	yes	characteristic, complemented
82	C₂³×#120	D₄	1	1	yes	characteristic, complemented
83	C₂³×#120	D₄	1	1	yes	characteristic, complemented
84	C₂³×#120	D₄	1	1	yes	characteristic, complemented
85	C₂³×#120	D₄	1	4	yes	complemented
86	C₂³×#120	C₂³	1	1	yes	characteristic
87	C₂³×#120	C₂³	1	1	yes	characteristic
88	C₂³×#120	C₂³	1	4	yes	—
89	C₂²×#518	C₂³	1	1	yes	characteristic
90	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
91	C₂×#3026	C₂³	1	4	yes	complemented
92	C₂²×B(4,𝔽₂)	D₄	1	8	yes	complemented
93	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
94	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	complemented
95	C₂×#3019	C₂³	1	4	yes	complemented
96	C₂³×#100	C₂³	1	1	yes	characteristic
97	C₂³×#100	C₂³	1	1	yes	characteristic
98	C₂³×#99	C₂³	1	1	yes	characteristic
99	C₂³×#99	C₂³	1	1	yes	characteristic
100	C₂³×#99	C₂³	1	1	yes	characteristic
101	C₂³×#99	C₂³	1	1	yes	characteristic
102	C₂×#2697	D₄	1	2	yes	complemented
103	C₂×#2684	D₄	1	2	yes	complemented
104	C₂×#2679	D₄	1	2	yes	complemented
105	C₂×#2669	D₄	1	2	yes	complemented
106	#36714	D₄	1	4	yes	complemented
107	#36714	C₂³	1	4	yes	—
108	#36702	D₄	1	4	yes	complemented
109	#36702	C₂³	1	4	yes	—
110	#35222	D₄	1	4	yes	complemented
111	#35222	C₂³	1	4	yes	—
112	#34980	D₄	1	4	yes	complemented
113	#34980	C₂³	1	4	yes	—
114	#34356	D₄	1	4	yes	complemented
115	#34356	C₂³	1	4	yes	—
116	C₂×#2375	D₄	1	2	yes	complemented
117	C₂×#2358	D₄	1	2	yes	complemented
118	C₂×#2309	D₄	1	1	yes	characteristic, complemented
119	C₂×#2309	C₂³	1	1	yes	characteristic
120	C₂×#2308	D₄	1	1	yes	characteristic, complemented
121	C₂×#2308	C₂³	1	1	yes	characteristic
122	C₂×#2280	D₄	1	1	yes	characteristic, complemented
123	C₂²×#379	D₄	1	1	yes	characteristic, complemented
124	C₂×#2127	C₂³	1	4	yes	complemented
125	C₂×#2127	C₂³	1	4	yes	complemented
126	C₂×#2121	C₂³	1	4	yes	complemented
127	C₂×#2121	C₂³	1	4	yes	complemented
128	C₂²×AΣL(1,𝔽₁₆)	D₄	1	8	yes	complemented
129	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	—
130	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	—
131	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
132	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
133	C₂×#1913	C₂³	1	4	yes	complemented
134	C₂×#1911	C₂³	1	4	yes	complemented
135	C₂×#1889	D₄	1	8	yes	complemented
136	C₂×#1889	C₂³	1	4	yes	—
137	C₂×#1889	C₂³	1	4	yes	complemented
138	#20616	C₂³	1	4	yes	complemented
139	#20609	C₂³	1	4	yes	complemented
140	C₂×#1783	C₂³	1	4	yes	complemented
141	C₂×#1781	C₂³	1	4	yes	complemented
142	C₂×#1781	C₂³	1	4	yes	complemented
143	#12582	C₂³	1	4	yes	complemented
144	#12582	C₂³	1	4	yes	complemented
145	#12574	C₂³	1	4	yes	complemented
146	#12574	C₂³	1	4	yes	complemented
147	#10754	C₂³	1	4	yes	complemented
148	#10740	C₂³	1	4	yes	complemented
149	C₂⁷	C₂×D₄	1	1	yes	characteristic
150	C₂⁷	C₂×D₄	1	1	yes	characteristic
151	C₂⁷	C₂×D₄	1	1	yes	characteristic
152	C₂⁷	C₂×D₄	1	1	yes	characteristic
153	C₂⁷	C₂×D₄	1	4	yes	complemented
154	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	complemented
155	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
156	C₂³×#41	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
159	C₂⁴×D₄	C₂×D₄	1	2	yes	—
160	C₂⁴×D₄	C₂×D₄	1	2	yes	—
161	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×D₄	C₂×D₄	1	2	yes	—
164	C₂⁴×D₄	C₂⁴	1	2	yes	—
165	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
166	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
167	C₂×H(3,𝔽₄)	C₂×D₄	1	4	yes	complemented
168	C₂×#560	C₂×D₄	1	4	yes	complemented
169	C₂×#551	C₂×D₄	1	4	yes	complemented
170	C₂×D₄²	C₂×D₄	1	4	yes	complemented
171	C₂×#535	C₂×D₄	1	2	yes	—
172	C₂×#535	C₂×D₄	1	2	yes	—
173	C₂×#535	C₂×D₄	1	2	yes	—
174	C₂×#535	C₂×D₄	1	4	yes	complemented
175	C₂×#535	C₂⁴	1	2	yes	—
176	C₂×#534	C₂×D₄	1	2	yes	—
177	C₂×#534	C₂×D₄	1	2	yes	—
178	C₂×#534	C₂×D₄	1	2	yes	—
179	C₂×#534	C₂×D₄	1	4	yes	complemented
180	C₂×#534	C₂⁴	1	2	yes	—
181	C₂²×#127	C₂×D₄	1	1	yes	characteristic
182	C₂²×#127	C₂×D₄	1	1	yes	characteristic
183	C₂²×#124	C₂×D₄	1	1	yes	characteristic
184	C₂²×#124	C₂×D₄	1	1	yes	characteristic
185	C₂×#525	C₂×D₄	1	4	yes	complemented
186	C₂²×#123	C₂×D₄	1	1	yes	characteristic
187	C₂²×#123	C₂×D₄	1	1	yes	characteristic
188	C₂²×#120	C₂×D₄	1	2	yes	—
189	C₂²×#120	C₂×D₄	1	2	yes	—
190	C₂²×#120	C₂×D₄	1	2	yes	—
191	C₂²×#120	C₂×D₄	1	2	yes	—
192	C₂²×#120	C₂×D₄	1	1	yes	characteristic
193	C₂²×#120	C₂×D₄	1	2	yes	—
194	C₂²×#120	C₂×D₄	1	1	yes	characteristic
195	C₂²×#120	C₂×D₄	1	4	yes	—
196	C₂²×#120	C₂×D₄	1	1	yes	characteristic
197	C₂²×#120	C₂×D₄	1	2	yes	—
198	C₂²×#120	C₂×D₄	1	1	yes	characteristic
199	C₂²×#120	C₂×D₄	1	4	yes	—
200	C₂²×#120	C₂×D₄	1	1	yes	characteristic
201	C₂²×#120	C₂×D₄	1	1	yes	characteristic
202	C₂²×#120	C₂×D₄	1	4	yes	—
203	C₂²×#120	C₂×D₄	1	2	yes	—
204	C₂²×#120	C₂×D₄	1	2	yes	—
205	C₂²×#120	C₂×D₄	1	4	yes	complemented
206	C₂²×#120	C₂×D₄	1	4	yes	complemented
207	C₂²×#120	C₂×D₄	1	4	yes	complemented
208	C₂²×#120	#41	1	4	yes	—
209	C₂²×#120	C₂⁴	1	2	yes	—
210	C₂²×#120	C₂⁴	1	2	yes	—
211	C₂×#518	C₂×D₄	1	4	yes	complemented
212	C₂×#518	C₂⁴	1	2	yes	—
213	C₂²×#117	C₂×D₄	1	1	yes	characteristic
214	C₂²×#117	C₂×D₄	1	1	yes	characteristic
215	C₂²×#117	C₂×D₄	1	1	yes	characteristic
216	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
217	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
222	C₂×B(4,𝔽₂)	C₂×D₄	1	16	yes	complemented
223	C₂²×#100	C₂×D₄	1	4	yes	complemented
224	C₂²×#100	C₂⁴	1	2	yes	—
225	C₂²×#100	C₂⁴	1	2	yes	—
226	C₂²×#99	C₂×D₄	1	4	yes	complemented
227	C₂²×#99	C₂×D₄	1	4	yes	complemented
228	C₂²×#99	C₂×D₄	1	4	yes	complemented
229	C₂²×#99	C₂⁴	1	2	yes	—
230	C₂²×#99	C₂⁴	1	2	yes	—
231	C₂²×#99	C₂⁴	1	2	yes	—
232	C₂²×#99	C₂⁴	1	2	yes	—
233	#2697	C₂×D₄	1	8	yes	complemented
234	#2684	C₂×D₄	1	8	yes	complemented
235	#2679	C₂×D₄	1	8	yes	complemented
236	#2669	C₂×D₄	1	8	yes	complemented
237	#2375	C₂×D₄	1	8	yes	complemented
238	#2358	C₂×D₄	1	8	yes	complemented
239	#2309	C₂×D₄	1	2	yes	—
240	#2309	C₂×D₄	1	2	yes	—
241	#2309	C₂×D₄	1	2	yes	—
242	#2309	C₂×D₄	1	4	yes	complemented
243	#2309	C₂⁴	1	2	yes	—
244	#2308	C₂×D₄	1	2	yes	—
245	#2308	C₂×D₄	1	2	yes	—
246	#2308	C₂×D₄	1	2	yes	—
247	#2308	C₂×D₄	1	4	yes	complemented
248	#2308	C₂⁴	1	2	yes	—
249	C₂×#390	C₂×D₄	1	2	yes	—
250	C₂×#390	C₂×D₄	1	2	yes	—
251	C₂×#386	C₂×D₄	1	2	yes	—
252	C₂×#386	C₂×D₄	1	2	yes	—
253	#2280	C₂×D₄	1	4	yes	complemented
254	C₂×#379	C₂×D₄	1	4	yes	complemented
255	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	16	yes	complemented
256	#1889	C₂×D₄	1	16	yes	complemented
257	C₂⁶	#120	1	1	yes	characteristic
258	C₂⁶	#120	1	1	yes	characteristic
259	C₂⁶	#120	1	1	yes	characteristic
260	C₂⁶	#120	1	2	yes	—
261	C₂⁶	#120	1	2	yes	—
262	C₂⁶	#120	1	2	yes	—
263	C₂⁶	#120	1	2	yes	—
264	C₂⁶	#120	1	1	yes	characteristic
265	C₂⁶	#120	1	1	yes	characteristic
266	C₂⁶	#120	1	2	yes	—
267	C₂⁶	#120	1	4	yes	—
268	C₂⁶	#120	1	1	yes	characteristic, complemented
269	C₂⁶	#121	1	4	yes	—
270	C₂⁶	C₂²×D₄	1	2	yes	—
271	C₂⁶	C₂²×D₄	1	2	yes	—
272	C₂⁶	C₂²×D₄	1	1	yes	characteristic
273	C₂⁶	C₂²×D₄	1	1	yes	characteristic
274	C₂⁶	C₂²×D₄	1	2	yes	—
275	C₂⁶	C₂²×D₄	1	2	yes	—
276	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	complemented
277	C₂²×#41	#120	1	2	yes	complemented
278	C₂²×#41	C₂²×D₄	1	2	yes	—
279	C₂³×Q₈	#120	1	1	yes	characteristic, complemented
280	C₂³×D₄	#120	1	2	yes	—
281	C₂³×D₄	#120	1	2	yes	—
282	C₂³×D₄	#120	1	2	yes	—
283	C₂³×D₄	#120	1	1	yes	characteristic, complemented
284	C₂³×D₄	#120	1	2	yes	complemented
285	C₂³×D₄	C₂²×D₄	1	2	yes	—
286	C₂³×D₄	C₂²×D₄	1	2	yes	—
287	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
288	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
289	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
290	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
291	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
292	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
293	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
294	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
295	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
296	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
297	C₂³×D₄	C₂²×D₄	1	2	yes	—
298	C₂³×D₄	C₂²×D₄	1	2	yes	—
299	C₂³×D₄	C₂²×D₄	1	2	yes	—
300	C₂³×D₄	C₂²×D₄	1	2	yes	—
301	C₂³×D₄	C₂²×D₄	1	2	yes	—
302	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
303	C₂³×D₄	C₂×#41	1	2	yes	—
304	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
305	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
306	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
307	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
308	C₂³×D₄	C₂⁵	1	1	yes	characteristic
309	C₂⁴×C₄	#120	1	1	yes	characteristic
310	C₂⁴×C₄	#120	1	2	yes	—
311	C₂⁴×C₄	#120	1	1	yes	characteristic, complemented
312	C₂⁴×C₄	#120	1	2	yes	complemented
313	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
314	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
315	C₂×#127	#120	1	2	yes	complemented
316	C₂×#127	#120	1	2	yes	complemented
317	C₂×#127	C₂²×D₄	1	2	yes	—
318	C₂×#127	C₂²×D₄	1	2	yes	—
319	C₂×#124	#120	1	2	yes	complemented
320	C₂×#124	#120	1	2	yes	complemented
321	C₂×#124	C₂²×D₄	1	2	yes	—
322	C₂×#124	C₂²×D₄	1	2	yes	—
323	C₂×#123	#120	1	2	yes	complemented
324	C₂×#123	#120	1	2	yes	complemented
325	C₂×#123	C₂²×D₄	1	2	yes	—
326	C₂×#123	C₂²×D₄	1	2	yes	—
327	C₂×#120	#120	1	4	yes	—
328	C₂×#120	#120	1	4	yes	—
329	C₂×#120	#120	1	2	yes	—
330	C₂×#120	#120	1	2	yes	—
331	C₂×#120	#120	1	2	yes	—
332	C₂×#120	#120	1	2	yes	—
333	C₂×#120	#120	1	8	yes	—
334	C₂×#120	#120	1	4	yes	—
335	C₂×#120	#120	1	4	yes	—
336	C₂×#120	#120	1	8	yes	—
337	C₂×#120	#120	1	2	yes	complemented
338	C₂×#120	#120	1	2	yes	complemented
339	C₂×#120	#121	1	8	yes	—
340	C₂×#120	#121	1	4	yes	—
341	C₂×#120	#121	1	4	yes	—
342	C₂×#120	#121	1	4	yes	—
343	C₂×#120	#121	1	4	yes	—
344	C₂×#120	#121	1	8	yes	—
345	C₂×#120	#121	1	8	yes	—
346	C₂×#120	#127	1	4	yes	—
347	C₂×#120	#127	1	4	yes	—
348	C₂×#120	#127	1	8	yes	—
349	C₂×#120	C₂²×D₄	1	4	yes	—
350	C₂×#120	C₂²×D₄	1	4	yes	—
351	C₂×#120	C₂²×D₄	1	2	yes	—
352	C₂×#120	C₂²×D₄	1	2	yes	—
353	C₂×#120	C₂²×D₄	1	4	yes	—
354	C₂×#120	C₂²×D₄	1	2	yes	—
355	C₂×#120	C₂²×D₄	1	2	yes	—
356	C₂×#120	C₂²×D₄	1	4	yes	—
357	C₂×#120	C₂²×D₄	1	2	yes	—
358	C₂×#120	C₂²×D₄	1	2	yes	—
359	C₂×#120	C₂²×D₄	1	4	yes	—
360	C₂×#120	C₂×#41	1	4	yes	—
361	#518	C₂²×D₄	1	4	yes	complemented
362	C₂×#117	#120	1	2	yes	complemented
363	C₂×#117	#120	1	2	yes	complemented
364	C₂×#117	#120	1	2	yes	complemented
365	C₂×#117	C₂²×D₄	1	2	yes	—
366	C₂×#117	C₂²×D₄	1	2	yes	—
367	C₂×#117	C₂²×D₄	1	2	yes	—
368	C₂²×C₄⋊C₄	#120	1	2	yes	complemented
369	C₂²×C₂²⋊C₄	#120	1	2	yes	—
370	C₂²×C₂²⋊C₄	#120	1	2	yes	—
371	C₂²×C₂²⋊C₄	#120	1	2	yes	—
372	C₂²×C₂²⋊C₄	#120	1	4	yes	—
373	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
374	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
376	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
377	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic, complemented
378	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
379	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
380	C₂²×C₂²⋊C₄	#120	1	2	yes	complemented
381	C₂²×C₂²⋊C₄	#121	1	4	yes	—
382	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
383	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
384	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
385	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
386	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
387	C₂²×C₄²	#120	1	1	yes	characteristic, complemented
388	C₂²×C₄²	#120	1	1	yes	characteristic, complemented
389	C₂²×C₄²	#120	1	2	yes	complemented
390	C₂×#100	C₂²×D₄	1	4	yes	complemented
391	C₂×#99	C₂²×D₄	1	4	yes	complemented
392	C₂×#99	C₂²×D₄	1	4	yes	complemented
393	C₂×#99	C₂²×D₄	1	4	yes	complemented
394	#390	#120	1	4	yes	complemented
395	#390	#120	1	4	yes	complemented
396	#390	C₂²×D₄	1	4	yes	—
397	#390	C₂²×D₄	1	4	yes	—
398	#386	#120	1	4	yes	complemented
399	#386	#120	1	4	yes	complemented
400	#386	C₂²×D₄	1	4	yes	—
401	#386	C₂²×D₄	1	4	yes	—
402	C₂⁵	#392	1	4	yes	—
403	C₂⁵	#392	1	4	yes	—
404	C₂⁵	#392	1	8	yes	—
405	C₂⁵	B(4,𝔽₂)	1	2	yes	—
406	C₂⁵	B(4,𝔽₂)	1	4	yes	—
407	C₂⁵	B(4,𝔽₂)	1	2	yes	—
408	C₂⁵	C₂×#120	1	2	yes	—
409	C₂⁵	C₂×#120	1	2	yes	—
410	C₂⁵	C₂×#120	1	2	yes	—
411	C₂⁵	C₂×#120	1	1	yes	characteristic
412	C₂⁵	C₂×#120	1	1	yes	characteristic
413	C₂⁵	C₂×#120	1	1	yes	characteristic
414	C₂⁵	C₂×#120	1	1	yes	characteristic
415	C₂⁵	C₂×#120	1	1	yes	characteristic
416	C₂⁵	C₂×#120	1	1	yes	characteristic
417	C₂⁵	C₂×#120	1	1	yes	characteristic
418	C₂⁵	C₂×#120	1	1	yes	characteristic
419	C₂⁵	C₂×#120	1	1	yes	characteristic
420	C₂⁵	C₂×#120	1	1	yes	characteristic
421	C₂⁵	C₂×#120	1	2	yes	—
422	C₂⁵	C₂×#120	1	4	yes	—
423	C₂⁵	C₂×#120	1	2	yes	—
424	C₂⁵	C₂×#120	1	2	yes	—
425	C₂⁵	C₂×#120	1	4	yes	—
426	C₂⁵	C₂×#120	1	1	yes	characteristic
427	C₂⁵	C₂×#120	1	2	yes	complemented
428	C₂⁵	C₂×#121	1	2	yes	—
429	C₂⁵	C₂×#121	1	4	yes	—
430	C₂⁵	#534	1	2	yes	—
431	C₂⁵	#534	1	2	yes	—
432	C₂⁵	D₄²	1	2	yes	—
433	C₂⁵	D₄²	1	2	yes	—
434	C₂⁵	D₄²	1	2	yes	—
435	C₂⁵	#546	1	2	yes	—
436	C₂⁵	C₂³×D₄	1	1	yes	characteristic
437	C₂⁵	C₂³×D₄	1	1	yes	characteristic
438	C₂²×Q₈	C₂×#120	1	2	yes	complemented
439	C₂²×D₄	C₂×#120	1	1	yes	characteristic
440	C₂²×D₄	C₂×#120	1	1	yes	characteristic
441	C₂²×D₄	C₂×#120	1	1	yes	characteristic
442	C₂²×D₄	C₂×#120	1	1	yes	characteristic
443	C₂²×D₄	C₂×#120	1	1	yes	characteristic
444	C₂²×D₄	C₂×#120	1	1	yes	characteristic
445	C₂²×D₄	C₂×#120	1	1	yes	characteristic
446	C₂²×D₄	C₂×#120	1	1	yes	characteristic
447	C₂²×D₄	C₂×#120	1	2	yes	—
448	C₂²×D₄	C₂×#120	1	2	yes	—
449	C₂²×D₄	C₂×#120	1	2	yes	—
450	C₂²×D₄	C₂×#120	1	1	yes	characteristic
451	C₂²×D₄	C₂×#120	1	1	yes	characteristic
452	C₂²×D₄	C₂×#120	1	1	yes	characteristic
453	C₂²×D₄	C₂×#120	1	1	yes	characteristic
454	C₂²×D₄	C₂×#120	1	2	yes	complemented
455	C₂²×D₄	C₂×#121	1	2	yes	—
456	C₂²×D₄	C₂×#121	1	2	yes	—
457	C₂²×D₄	C₂×#121	1	2	yes	—
458	C₂²×D₄	C₂×#121	1	2	yes	—
459	C₂²×D₄	C₂×#121	1	2	yes	—
460	C₂²×D₄	C₂×#127	1	2	yes	—
461	C₂²×D₄	C₂×#127	1	2	yes	—
462	C₂²×D₄	#534	1	2	yes	—
463	C₂²×D₄	#534	1	2	yes	—
464	C₂²×D₄	#534	1	2	yes	—
465	C₂²×D₄	#534	1	2	yes	—
466	C₂²×D₄	#534	1	2	yes	—
467	C₂²×D₄	#534	1	2	yes	—
468	C₂²×D₄	#535	1	2	yes	—
469	C₂²×D₄	#535	1	2	yes	—
470	C₂²×D₄	#535	1	2	yes	—
471	C₂²×D₄	#535	1	2	yes	—
472	C₂²×D₄	D₄²	1	2	yes	—
473	C₂²×D₄	D₄²	1	2	yes	—
474	C₂²×D₄	D₄²	1	2	yes	—
475	C₂²×D₄	D₄²	1	2	yes	—
476	C₂²×D₄	D₄²	1	2	yes	—
477	C₂²×D₄	D₄²	1	2	yes	—
478	C₂²×D₄	D₄²	1	2	yes	—
479	C₂²×D₄	D₄²	1	2	yes	—
480	C₂²×D₄	D₄²	1	2	yes	—
481	C₂²×D₄	D₄²	1	2	yes	—
482	C₂²×D₄	D₄²	1	2	yes	—
483	C₂²×D₄	D₄²	1	2	yes	—
484	C₂²×D₄	D₄²	1	2	yes	—
485	C₂²×D₄	D₄²	1	2	yes	—
486	C₂²×D₄	D₄²	1	2	yes	—
487	C₂²×D₄	D₄²	1	2	yes	—
488	C₂²×D₄	D₄²	1	2	yes	—
489	C₂²×D₄	D₄²	1	2	yes	—
490	C₂²×D₄	#546	1	2	yes	—
491	C₂²×D₄	#546	1	2	yes	—
492	C₂²×D₄	#546	1	2	yes	—
493	C₂²×D₄	#546	1	2	yes	—
494	C₂²×D₄	#546	1	2	yes	—
495	C₂²×D₄	#546	1	2	yes	—
496	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
497	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
498	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
499	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
500	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
501	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
502	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
503	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
504	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
506	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂³×C₄	C₂×#120	1	2	yes	—
509	C₂³×C₄	C₂×#120	1	1	yes	characteristic
510	C₂³×C₄	C₂×#120	1	1	yes	characteristic
511	C₂³×C₄	C₂×#120	1	1	yes	characteristic
512	C₂³×C₄	C₂×#120	1	1	yes	characteristic
513	C₂³×C₄	C₂×#120	1	1	yes	characteristic
514	C₂³×C₄	C₂×#120	1	2	yes	complemented
515	C₂³×C₄	C₂×#120	1	4	yes	complemented
516	C₂³×C₄	D₄²	1	2	yes	—
517	C₂³×C₄	D₄²	1	2	yes	—
518	C₂³×C₄	D₄²	1	2	yes	—
519	C₂³×C₄	#546	1	2	yes	—
520	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
521	#120	#392	1	8	yes	—
522	#120	#392	1	8	yes	—
523	#120	#392	1	8	yes	—
524	#120	#392	1	8	yes	—
525	#120	C₂×#120	1	4	yes	—
526	#120	C₂×#120	1	4	yes	—
527	#120	C₂×#121	1	4	yes	—
528	#120	C₂×#121	1	4	yes	—
529	#120	C₂×#121	1	4	yes	—
530	#120	C₂×#121	1	4	yes	—
531	#120	C₂×#127	1	4	yes	—
532	#120	C₂×#127	1	4	yes	—
533	C₂×C₄⋊C₄	C₂×#120	1	4	yes	complemented
534	C₂×C₂²⋊C₄	#392	1	4	yes	—
535	C₂×C₂²⋊C₄	#392	1	4	yes	—
536	C₂×C₂²⋊C₄	#392	1	8	yes	—
537	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	complemented
542	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	complemented
543	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	complemented
544	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
545	C₂×C₄²	C₂×#120	1	2	yes	complemented
546	C₂×C₄²	C₂×#120	1	2	yes	complemented
547	C₂×C₄²	C₂×#120	1	4	yes	complemented
548	C₂⁴	C₂×#392	1	2	yes	—
549	C₂⁴	C₂×#392	1	2	yes	—
550	C₂⁴	C₂×#392	1	4	yes	—
551	C₂⁴	C₂×#392	1	4	yes	—
552	C₂⁴	#2403	1	2	yes	—
553	C₂⁴	#2403	1	2	yes	—
554	C₂⁴	#2403	1	2	yes	—
555	C₂⁴	#2403	1	2	yes	—
556	C₂⁴	#2403	1	2	yes	—
557	C₂⁴	#2403	1	2	yes	—
558	C₂⁴	#2403	1	2	yes	—
559	C₂⁴	#2408	1	2	yes	—
560	C₂⁴	#2408	1	2	yes	—
561	C₂⁴	#2410	1	2	yes	—
562	C₂⁴	#2410	1	2	yes	—
563	C₂⁴	#2410	1	2	yes	—
564	C₂⁴	#2410	1	2	yes	—
565	C₂⁴	#2410	1	2	yes	—
566	C₂⁴	#2410	1	2	yes	—
567	C₂⁴	#2410	1	2	yes	—
568	C₂⁴	#2433	1	2	yes	—
569	C₂⁴	#2433	1	2	yes	—
570	C₂⁴	#2613	1	2	yes	—
571	C₂⁴	#2613	1	2	yes	—
572	C₂⁴	#2846	1	1	yes	characteristic
573	C₂⁴	#2846	1	1	yes	characteristic
574	C₂⁴	#2846	1	1	yes	characteristic
575	C₂⁴	#2846	1	1	yes	characteristic
576	C₂⁴	#2846	1	1	yes	characteristic
577	C₂⁴	#2846	1	1	yes	characteristic
578	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
579	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
580	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
581	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
582	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
583	C₂⁴	#3026	1	1	yes	characteristic
584	C₂⁴	#3026	1	2	yes	—
585	C₂⁴	#3026	1	1	yes	characteristic
586	C₂⁴	C₂²×#120	1	1	yes	characteristic
587	C₂⁴	C₂²×#120	1	1	yes	characteristic
588	C₂⁴	C₂²×#120	1	1	yes	characteristic
589	C₂⁴	C₂²×#120	1	1	yes	characteristic
590	C₂⁴	C₂²×#120	1	1	yes	characteristic
591	C₂⁴	C₂²×#120	1	1	yes	characteristic
592	C₂⁴	C₂²×#121	1	1	yes	characteristic
593	C₂⁴	C₂×#534	1	1	yes	characteristic
594	C₂⁴	C₂×#534	1	1	yes	characteristic
595	C₂⁴	C₂×D₄²	1	1	yes	characteristic
596	C₂⁴	C₂×D₄²	1	1	yes	characteristic
597	C₂⁴	C₂×D₄²	1	1	yes	characteristic
598	C₂⁴	C₂×#546	1	1	yes	characteristic
599	C₂×D₄	C₂×#392	1	2	yes	—
600	C₂×D₄	C₂×#392	1	2	yes	—
601	C₂×D₄	#2403	1	2	yes	—
602	C₂×D₄	#2403	1	2	yes	—
603	C₂×D₄	#2403	1	2	yes	—
604	C₂×D₄	#2403	1	2	yes	—
605	C₂×D₄	#2403	1	2	yes	—
606	C₂×D₄	#2403	1	2	yes	—
607	C₂×D₄	#2408	1	2	yes	—
608	C₂×D₄	#2408	1	2	yes	—
609	C₂×D₄	#2408	1	2	yes	—
610	C₂×D₄	#2408	1	2	yes	—
611	C₂×D₄	#2410	1	2	yes	—
612	C₂×D₄	#2410	1	2	yes	—
613	C₂×D₄	#2410	1	2	yes	—
614	C₂×D₄	#2410	1	2	yes	—
615	C₂×D₄	#2410	1	2	yes	—
616	C₂×D₄	#2410	1	2	yes	—
617	C₂×D₄	#2433	1	2	yes	—
618	C₂×D₄	#2433	1	2	yes	—
619	C₂×D₄	#2433	1	2	yes	—
620	C₂×D₄	#2433	1	2	yes	—
621	C₂×D₄	#2613	1	2	yes	—
622	C₂×D₄	#2613	1	2	yes	—
623	C₂×D₄	C₂²×#120	1	1	yes	characteristic
624	C₂×D₄	C₂²×#121	1	1	yes	characteristic
625	C₂×D₄	C₂²×#121	1	1	yes	characteristic
626	C₂×D₄	C₂²×#127	1	1	yes	characteristic
627	C₂×D₄	C₂×#534	1	1	yes	characteristic
628	C₂×D₄	C₂×#534	1	1	yes	characteristic
629	C₂×D₄	C₂×#535	1	1	yes	characteristic
630	C₂×D₄	C₂×#535	1	1	yes	characteristic
631	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
632	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
633	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
634	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
635	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
636	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
637	C₂×D₄	C₂×#546	1	1	yes	characteristic
638	C₂×D₄	C₂×#546	1	1	yes	characteristic
639	C₂²×C₄	#2403	1	2	yes	—
640	C₂²×C₄	#2403	1	2	yes	—
641	C₂²×C₄	#2403	1	2	yes	—
642	C₂²×C₄	#2408	1	2	yes	—
643	C₂²×C₄	#2408	1	2	yes	—
644	C₂²×C₄	#2410	1	2	yes	—
645	C₂²×C₄	#2410	1	2	yes	—
646	C₂²×C₄	#2410	1	2	yes	—
647	C₂²×C₄	#2433	1	2	yes	—
648	C₂²×C₄	#2433	1	2	yes	—
649	C₂²×C₄	#2846	1	1	yes	characteristic
650	C₂²×C₄	#2846	1	1	yes	characteristic
651	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
652	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
656	C₂²×C₄	C₂×#546	1	1	yes	characteristic
657	C₂²⋊C₄	C₂×#392	1	4	yes	—
658	C₂²⋊C₄	C₂×#392	1	4	yes	—
659	C₂³	#14715	1	2	yes	—
660	C₂³	#14715	1	2	yes	—
661	C₂³	#14715	1	2	yes	—
662	C₂³	#14715	1	2	yes	—
663	C₂³	#14715	1	2	yes	—
664	C₂³	#14715	1	2	yes	—
665	C₂³	#23900	1	2	yes	—
666	C₂³	#23900	1	2	yes	—
667	C₂³	#23903	1	2	yes	—
668	C₂³	#23903	1	2	yes	—
669	C₂³	#24404	1	2	yes	—
670	C₂³	#24404	1	2	yes	—
671	C₂³	#24404	1	2	yes	—
672	C₂³	#24404	1	2	yes	—
673	C₂³	#32898	1	1	yes	characteristic
674	C₂³	#32898	1	1	yes	characteristic
675	C₂³	#32898	1	1	yes	characteristic
676	C₂³	#32898	1	2	yes	—
677	C₂³	#32898	1	2	yes	—
678	C₂³	#32898	1	1	yes	characteristic
679	C₂³	C₂²×#392	1	1	yes	characteristic
680	C₂³	C₂×#2613	1	1	yes	characteristic
681	C₂³	C₂×#2403	1	1	yes	characteristic
682	C₂³	C₂×#2403	1	1	yes	characteristic
683	C₂³	C₂×#2403	1	1	yes	characteristic
684	C₂³	C₂×#2410	1	1	yes	characteristic
685	C₂³	C₂×#2410	1	1	yes	characteristic
686	C₂³	C₂×#2410	1	1	yes	characteristic
687	C₂³	C₂×#2408	1	1	yes	characteristic
688	C₂³	C₂×#2433	1	1	yes	characteristic
689	C₂³	C₂×#2846	1	1	yes	characteristic
690	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
691	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
692	C₂³	C₂×#3026	1	1	yes	characteristic
693	C₂³	C₂×#3026	1	1	yes	characteristic
694	C₂×C₄	#14715	1	2	yes	—
695	C₂×C₄	#14715	1	2	yes	—
696	C₂×C₄	C₂×#2403	1	1	yes	characteristic
697	C₂×C₄	C₂×#2410	1	1	yes	characteristic
698	C₂×C₄	C₂×#2408	1	1	yes	characteristic
699	C₂×C₄	C₂×#2433	1	1	yes	characteristic
700	C₂²	#394066	1	2	yes	—
701	C₂²	#394066	1	2	yes	—
702	C₂²	#394066	1	2	yes	—
703	C₂²	#394066	1	2	yes	—
704	C₂²	#511790	1	4	yes	—
705	C₂²	C₂×#14715	1	1	yes	characteristic
706	C₂²	C₂×#23900	1	1	yes	characteristic
707	C₂²	C₂×#23903	1	1	yes	characteristic
708	C₂²	C₂×#24404	1	1	yes	characteristic
709	C₂²	C₂×#24404	1	1	yes	characteristic
710	C₂²	C₂×#32898	1	1	yes	characteristic
711	C₂²	C₂×#32898	1	1	yes	characteristic
712	C₂	C₂×#511790	1	2	yes	—
713	C₂	#72218099	1	4	yes	direct product factor
714	C₂	C₂×#394066	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	#32898
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#147569	C₂	semidirect
2. C₂×#146593	C₂	semidirect
3. C₂×#147815	C₂	semidirect
4. C₂×#7708349	C₂	semidirect
5. C₂×#494575	C₂	semidirect
6. C₂×#147567	C₂	semidirect
7. C₂×#394064	C₂	semidirect
8. C₂×#147811	C₂	semidirect
9. C₂²×#12753	C₂	semidirect
10. C₂×#498927	C₂	semidirect
11. C₂²×#12687	C₂	semidirect
12. C₂²×#33551	C₂	semidirect
13. C₂×#393975	C₂	semidirect
14. C₂×#498886	C₂	semidirect
15. #72218099	C₂	direct (N × H)
16. C₂²×#23900	C₂	semidirect
18. C₂²×#3484	C₂²	semidirect
20. C₂²×#3026	C₂²	semidirect
22. C₂³×B(4,𝔽₂)	C₂²	semidirect
23. C₂²×#3019	C₂²	semidirect
24. #7708349	C₂²	semidirect
30. C₂×#33551	C₂²	semidirect
31. C₂²×#2127	C₂²	semidirect
32. C₂²×#2127	C₂²	semidirect
33. C₂²×#2121	C₂²	semidirect
34. C₂²×#2121	C₂²	semidirect
37. C₂³×AΣL(1,𝔽₁₆)	C₂²	semidirect
38. C₂³×AΣL(1,𝔽₁₆)	C₂²	semidirect
39. C₂×#23900	C₂²	semidirect
40. C₂²×#1913	C₂²	semidirect
41. C₂²×#1911	C₂²	semidirect
43. C₂²×#1889	C₂²	semidirect
44. C₂×#20616	C₂²	semidirect
45. C₂×#20609	C₂²	semidirect
46. C₂²×#1783	C₂²	semidirect
47. C₂²×#1781	C₂²	semidirect
48. C₂²×#1781	C₂²	semidirect
49. #498927	C₂²	semidirect
50. #498886	C₂²	semidirect
51. #494575	C₂²	semidirect
52. C₂×#12753	C₂²	semidirect
53. C₂×#12687	C₂²	semidirect
54. C₂×#12582	C₂²	semidirect
55. C₂×#12582	C₂²	semidirect
56. C₂×#12574	C₂²	semidirect
57. C₂×#12574	C₂²	semidirect
58. #394064	C₂²	semidirect
59. #393975	C₂²	semidirect
60. C₂×#10754	C₂²	semidirect
61. C₂×#10740	C₂²	semidirect
62. #147815	C₂²	semidirect
63. #147811	C₂²	semidirect
64. #147569	C₂²	semidirect
65. #147567	C₂²	semidirect
66. #146593	C₂²	semidirect
67. C₂⁸	D₄	semidirect
70. C₂×#3484	C₂³	semidirect
71. C₂×#3532	D₄	semidirect
73. C₂²×#551	D₄	semidirect
74. C₂²×D₄²	D₄	semidirect
75. C₂²×H(3,𝔽₄)	D₄	semidirect
76. C₂²×#560	D₄	semidirect
77. C₂²×#535	D₄	semidirect
79. C₂²×#534	D₄	semidirect
81. C₂²×#525	D₄	semidirect
82. C₂³×#120	D₄	semidirect
83. C₂³×#120	D₄	semidirect
84. C₂³×#120	D₄	semidirect
85. C₂³×#120	D₄	semidirect
90. C₂⁴×C₂²⋊C₄	D₄	semidirect
91. C₂×#3026	C₂³	semidirect
92. C₂²×B(4,𝔽₂)	D₄	semidirect
94. C₂²×B(4,𝔽₂)	C₂³	semidirect
95. C₂×#3019	C₂³	semidirect
102. C₂×#2697	D₄	semidirect
103. C₂×#2684	D₄	semidirect
104. C₂×#2679	D₄	semidirect
105. C₂×#2669	D₄	semidirect
106. #36714	D₄	semidirect
108. #36702	D₄	semidirect
110. #35222	D₄	semidirect
112. #34980	D₄	semidirect
114. #34356	D₄	semidirect
116. C₂×#2375	D₄	semidirect
117. C₂×#2358	D₄	semidirect
118. C₂×#2309	D₄	semidirect
120. C₂×#2308	D₄	semidirect
122. C₂×#2280	D₄	semidirect
123. C₂²×#379	D₄	semidirect
124. C₂×#2127	C₂³	semidirect
125. C₂×#2127	C₂³	semidirect
126. C₂×#2121	C₂³	semidirect
127. C₂×#2121	C₂³	semidirect
128. C₂²×AΣL(1,𝔽₁₆)	D₄	semidirect
131. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
132. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
133. C₂×#1913	C₂³	semidirect
134. C₂×#1911	C₂³	semidirect
135. C₂×#1889	D₄	semidirect
137. C₂×#1889	C₂³	semidirect
138. #20616	C₂³	semidirect
139. #20609	C₂³	semidirect
140. C₂×#1783	C₂³	semidirect
141. C₂×#1781	C₂³	semidirect
142. C₂×#1781	C₂³	semidirect
143. #12582	C₂³	semidirect
144. #12582	C₂³	semidirect
145. #12574	C₂³	semidirect
146. #12574	C₂³	semidirect
147. #10754	C₂³	semidirect
148. #10740	C₂³	semidirect
153. C₂⁷	C₂×D₄	semidirect
154. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
167. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
168. C₂×#560	C₂×D₄	semidirect
169. C₂×#551	C₂×D₄	semidirect
170. C₂×D₄²	C₂×D₄	semidirect
174. C₂×#535	C₂×D₄	semidirect
179. C₂×#534	C₂×D₄	semidirect
185. C₂×#525	C₂×D₄	semidirect
205. C₂²×#120	C₂×D₄	semidirect
206. C₂²×#120	C₂×D₄	semidirect
207. C₂²×#120	C₂×D₄	semidirect
211. C₂×#518	C₂×D₄	semidirect
221. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
222. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
223. C₂²×#100	C₂×D₄	semidirect
226. C₂²×#99	C₂×D₄	semidirect
227. C₂²×#99	C₂×D₄	semidirect
228. C₂²×#99	C₂×D₄	semidirect
233. #2697	C₂×D₄	semidirect
234. #2684	C₂×D₄	semidirect
235. #2679	C₂×D₄	semidirect
236. #2669	C₂×D₄	semidirect
237. #2375	C₂×D₄	semidirect
238. #2358	C₂×D₄	semidirect
242. #2309	C₂×D₄	semidirect
247. #2308	C₂×D₄	semidirect
253. #2280	C₂×D₄	semidirect
254. C₂×#379	C₂×D₄	semidirect
255. C₂×AΣL(1,𝔽₁₆)	C₂×D₄	semidirect
256. #1889	C₂×D₄	semidirect
268. C₂⁶	#120	semidirect
276. C₂×H(5,𝔽₂)	C₂²×D₄	semidirect
277. C₂²×#41	#120	semidirect
279. C₂³×Q₈	#120	semidirect
283. C₂³×D₄	#120	semidirect
284. C₂³×D₄	#120	semidirect
311. C₂⁴×C₄	#120	semidirect
312. C₂⁴×C₄	#120	semidirect
315. C₂×#127	#120	semidirect
316. C₂×#127	#120	semidirect
319. C₂×#124	#120	semidirect
320. C₂×#124	#120	semidirect
323. C₂×#123	#120	semidirect
324. C₂×#123	#120	semidirect
337. C₂×#120	#120	semidirect
338. C₂×#120	#120	semidirect
361. #518	C₂²×D₄	semidirect
362. C₂×#117	#120	semidirect
363. C₂×#117	#120	semidirect
364. C₂×#117	#120	semidirect
368. C₂²×C₄⋊C₄	#120	semidirect
375. C₂²×C₂²⋊C₄	#120	semidirect
376. C₂²×C₂²⋊C₄	#120	semidirect
377. C₂²×C₂²⋊C₄	#120	semidirect
378. C₂²×C₂²⋊C₄	#120	semidirect
379. C₂²×C₂²⋊C₄	#120	semidirect
380. C₂²×C₂²⋊C₄	#120	semidirect
387. C₂²×C₄²	#120	semidirect
388. C₂²×C₄²	#120	semidirect
389. C₂²×C₄²	#120	semidirect
390. C₂×#100	C₂²×D₄	semidirect
391. C₂×#99	C₂²×D₄	semidirect
392. C₂×#99	C₂²×D₄	semidirect
393. C₂×#99	C₂²×D₄	semidirect
394. #390	#120	semidirect
395. #390	#120	semidirect
398. #386	#120	semidirect
399. #386	#120	semidirect
427. C₂⁵	C₂×#120	semidirect
438. C₂²×Q₈	C₂×#120	semidirect
454. C₂²×D₄	C₂×#120	semidirect
514. C₂³×C₄	C₂×#120	semidirect
515. C₂³×C₄	C₂×#120	semidirect
533. C₂×C₄⋊C₄	C₂×#120	semidirect
541. C₂×C₂²⋊C₄	C₂×#120	semidirect
542. C₂×C₂²⋊C₄	C₂×#120	semidirect
543. C₂×C₂²⋊C₄	C₂×#120	semidirect
545. C₂×C₄²	C₂×#120	semidirect
546. C₂×C₄²	C₂×#120	semidirect
547. C₂×C₄²	C₂×#120	semidirect
713. C₂	#72218099	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×#147569	2
C₂×#146593	2
C₂×#147815	2
C₂×#7708349	2
C₂×#494575	2
C₂×#147567	2
C₂×#394064	2
C₂×#147811	2
C₂²×#12753	2
C₂×#498927	2
C₂²×#12687	2
C₂²×#33551	2
C₂×#393975	2
C₂×#498886	2
#72218099	2
C₂²×#23900	2

Subgroups — C2×#72218099 #72278556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72218099 #72278556