Subgroups — C₂×#72213862 #72262856

Order 2048.

At least 7601 conjugacy classes of subgroups; only the 8288 normal subgroups are shown.

The subgroup lattice has 632 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×#359442	C₂	1	2	yes	maximal, complemented
2	C₂×#392699	C₂	1	2	yes	maximal, complemented
3	C₂×#6437621	C₂	1	2	yes	maximal, complemented
4	C₂×#359549	C₂	1	4	yes	maximal, complemented
5	C₂×#394064	C₂	1	8	yes	maximal, complemented
6	C₂×#392109	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#23895	C₂	1	4	yes	maximal, complemented
8	C₂×#6628892	C₂	1	2	yes	maximal, complemented
9	C₂³×#3484	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#7630939	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#394058	C₂	1	4	yes	maximal, complemented
12	#72213862	C₂	1	32	yes	maximal, direct product factor
13	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
14	C₂⁶×D₄	C₂²	1	1	yes	characteristic
15	C₂²×#3484	C₂²	1	4	yes	—
16	C₂²×#3484	C₂²	1	16	yes	complemented
17	C₂²×#3484	C₂²	1	4	yes	complemented
18	C₂²×#3484	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#3484	C₂²	1	2	yes	complemented
20	C₂³×#534	C₂²	1	2	yes	—
21	C₂⁴×#120	C₂²	1	2	yes	complemented
22	C₂³×#518	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#3026	C₂²	1	8	yes	complemented
24	C₂²×#3026	C₂²	1	4	yes	complemented
25	C₂²×#2846	C₂²	1	2	yes	complemented
26	#7630939	C₂²	1	16	yes	complemented
27	C₂×#34980	C₂²	1	2	yes	—
28	C₂×#34980	C₂²	1	4	yes	complemented
29	C₂×#34980	C₂²	1	4	yes	complemented
30	C₂×#34171	C₂²	1	1	yes	characteristic, complemented
31	C₂×#34171	C₂²	1	2	yes	complemented
32	#6628892	C₂²	1	32	yes	complemented
33	C₂×#23895	C₂²	1	64	yes	complemented
34	#6437621	C₂²	1	32	yes	complemented
35	C₂×#23444	C₂²	1	8	yes	complemented
36	C₂²×#2021	C₂²	1	16	yes	complemented
37	C₂²×#1913	C₂²	1	8	yes	complemented
38	C₂²×#1913	C₂²	1	8	yes	complemented
39	C₂²×#1898	C₂²	1	4	yes	complemented
40	C₂×#20960	C₂²	1	4	yes	complemented
41	C₂×#20609	C₂²	1	8	yes	complemented
42	C₂²×#1781	C₂²	1	2	yes	complemented
43	C₂²×#1781	C₂²	1	4	yes	complemented
44	C₂²×#1781	C₂²	1	2	yes	complemented
45	C₂²×#1781	C₂²	1	4	yes	complemented
46	C₂²×#1781	C₂²	1	4	yes	complemented
47	C₂×#14679	C₂²	1	2	yes	complemented
48	#394064	C₂²	1	128	yes	complemented
49	#394058	C₂²	1	64	yes	complemented
50	#392699	C₂²	1	32	yes	complemented
51	#392109	C₂²	1	16	yes	complemented
52	#359549	C₂²	1	64	yes	complemented
53	#359442	C₂²	1	32	yes	complemented
54	C₂×#10991	C₂²	1	16	yes	complemented
55	C₂×#10972	C₂²	1	8	yes	complemented
56	C₂×#10754	C₂²	1	8	yes	complemented
57	C₂×#10735	C₂²	1	4	yes	complemented
58	C₂⁸	D₄	1	1	yes	characteristic, complemented
59	C₂⁸	C₂³	1	1	yes	characteristic
60	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
61	C₂³×H(5,𝔽₂)	C₂³	1	8	yes	complemented
62	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
63	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
64	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
65	C₂⁵×D₄	D₄	1	2	yes	complemented
66	C₂⁵×D₄	D₄	1	2	yes	complemented
67	C₂⁵×D₄	D₄	1	8	yes	complemented
68	C₂⁵×D₄	C₂³	1	1	yes	characteristic
69	C₂⁵×D₄	C₂³	1	2	yes	—
70	C₂⁵×D₄	C₂³	1	2	yes	—
71	C₂⁵×D₄	C₂³	1	1	yes	characteristic
72	C₂⁵×D₄	C₂³	1	2	yes	—
73	C₂⁵×D₄	C₂³	1	8	yes	—
74	C₂⁶×C₄	D₄	1	1	yes	characteristic, complemented
75	C₂×#3484	D₄	1	64	yes	complemented
76	C₂×#3484	C₂³	1	32	yes	—
77	C₂×#3484	C₂³	1	32	yes	complemented
78	C₂×#3484	C₂³	1	8	yes	complemented
79	C₂×#3484	C₂³	1	16	yes	complemented
80	C₂²×#534	D₄	1	8	yes	complemented
81	C₂²×#534	D₄	1	16	yes	complemented
82	C₂²×#534	C₂³	1	4	yes	—
83	C₂²×#534	C₂³	1	16	yes	—
84	C₂²×#534	C₂³	1	4	yes	—
85	C₂²×#534	C₂³	1	4	yes	—
86	C₂²×#534	C₂³	1	2	yes	complemented
87	C₂²×#534	C₂³	1	8	yes	complemented
88	C₂³×#123	D₄	1	4	yes	complemented
89	C₂³×#120	D₄	1	4	yes	complemented
90	C₂³×#120	C₂³	1	8	yes	—
91	C₂³×#120	C₂³	1	2	yes	—
92	C₂³×#120	C₂³	1	16	yes	complemented
93	C₂³×#120	C₂³	1	4	yes	complemented
94	C₂²×#518	C₂³	1	4	yes	—
95	C₂²×#518	C₂³	1	8	yes	complemented
96	C₂²×#518	C₂³	1	1	yes	characteristic, complemented
97	C₂²×#518	C₂³	1	2	yes	complemented
98	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
99	C₂×#3026	C₂³	1	64	yes	complemented
100	C₂×#3026	C₂³	1	32	yes	complemented
101	C₂³×#99	C₂³	1	8	yes	—
102	C₂³×#99	C₂³	1	8	yes	complemented
103	C₂³×#99	C₂³	1	4	yes	complemented
104	C₂³×#99	C₂³	1	16	yes	complemented
105	C₂³×#99	C₂³	1	4	yes	complemented
106	C₂×#2846	C₂³	1	16	yes	complemented
107	#34980	D₄	1	16	yes	complemented
108	#34980	C₂³	1	16	yes	—
109	#34980	C₂³	1	32	yes	complemented
110	#34980	C₂³	1	32	yes	complemented
111	C₂×#2405	D₄	1	8	yes	complemented
112	C₂×#2403	D₄	1	8	yes	complemented
113	#34171	C₂³	1	16	yes	complemented
114	#34171	C₂³	1	8	yes	complemented
115	C₂×#2308	C₂³	1	4	yes	—
116	C₂×#2308	C₂³	1	2	yes	complemented
117	C₂×#2308	C₂³	1	8	yes	complemented
118	C₂²×#379	C₂³	1	4	yes	—
119	C₂²×#379	C₂³	1	2	yes	—
120	C₂²×#379	C₂³	1	4	yes	complemented
121	C₂²×#379	C₂³	1	8	yes	complemented
122	#23444	C₂³	1	64	yes	complemented
123	C₂×#2021	C₂³	1	128	yes	complemented
124	C₂×#1913	C₂³	1	64	yes	complemented
125	C₂×#1913	C₂³	1	64	yes	complemented
126	C₂×#1898	C₂³	1	32	yes	complemented
127	#20960	C₂³	1	32	yes	complemented
128	#20609	C₂³	1	64	yes	complemented
129	C₂×#1781	C₂³	1	16	yes	complemented
130	C₂×#1781	C₂³	1	32	yes	complemented
131	C₂×#1781	C₂³	1	32	yes	complemented
132	C₂×#1781	C₂³	1	32	yes	complemented
133	C₂×#1781	C₂³	1	16	yes	complemented
134	C₂²×#342	C₂³	1	16	yes	complemented
135	C₂²×#342	C₂³	1	8	yes	complemented
136	#14679	C₂³	1	16	yes	complemented
137	#10991	C₂³	1	128	yes	complemented
138	#10972	C₂³	1	64	yes	complemented
139	#10754	C₂³	1	64	yes	complemented
140	#10735	C₂³	1	32	yes	complemented
141	C₂⁷	C₂×D₄	1	1	yes	characteristic
142	C₂⁷	C₂×D₄	1	1	yes	characteristic
143	C₂⁷	C₂×D₄	1	1	yes	characteristic
144	C₂⁷	C₂×D₄	1	2	yes	—
145	C₂⁷	C₂×D₄	1	4	yes	—
146	C₂⁷	C₂×D₄	1	2	yes	—
147	C₂⁷	C₂×D₄	1	1	yes	characteristic
148	C₂⁷	C₂×D₄	1	2	yes	—
149	C₂⁷	C₂×D₄	1	2	yes	complemented
150	C₂⁷	C₂×D₄	1	8	yes	complemented
151	C₂⁷	C₂⁴	1	2	yes	—
152	C₂⁷	C₂⁴	1	4	yes	—
153	C₂⁷	C₂⁴	1	1	yes	characteristic
154	C₂²×H(5,𝔽₂)	C₂×D₄	1	32	yes	complemented
155	C₂²×H(5,𝔽₂)	C₂⁴	1	16	yes	—
156	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	complemented
157	C₂⁴×D₄	C₂×D₄	1	8	yes	—
158	C₂⁴×D₄	C₂×D₄	1	8	yes	—
159	C₂⁴×D₄	C₂×D₄	1	4	yes	—
160	C₂⁴×D₄	C₂×D₄	1	4	yes	—
161	C₂⁴×D₄	C₂×D₄	1	8	yes	—
162	C₂⁴×D₄	C₂×D₄	1	32	yes	—
163	C₂⁴×D₄	C₂×D₄	1	4	yes	—
164	C₂⁴×D₄	C₂×D₄	1	2	yes	—
165	C₂⁴×D₄	C₂×D₄	1	8	yes	—
166	C₂⁴×D₄	C₂×D₄	1	2	yes	—
167	C₂⁴×D₄	C₂×D₄	1	2	yes	—
168	C₂⁴×D₄	C₂×D₄	1	4	yes	—
169	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
170	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
171	C₂⁴×D₄	C₂×D₄	1	8	yes	—
172	C₂⁴×D₄	C₂×D₄	1	2	yes	—
173	C₂⁴×D₄	C₂×D₄	1	2	yes	—
174	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
175	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
176	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
177	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
178	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
179	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
180	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
181	C₂⁴×D₄	C₂⁴	1	4	yes	—
182	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
183	C₂⁴×D₄	C₂⁴	1	4	yes	—
184	C₂⁴×D₄	C₂⁴	1	8	yes	—
185	C₂⁴×D₄	C₂⁴	1	8	yes	—
186	C₂⁴×D₄	C₂⁴	1	4	yes	—
187	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
188	C₂⁴×D₄	C₂⁴	1	2	yes	—
189	C₂⁴×D₄	C₂⁴	1	2	yes	—
190	C₂⁴×D₄	C₂⁴	1	8	yes	—
191	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
192	C₂⁵×C₄	C₂×D₄	1	2	yes	—
193	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
194	C₂⁵×C₄	C₂×D₄	1	2	yes	—
195	C₂⁵×C₄	C₂×D₄	1	2	yes	complemented
196	C₂⁵×C₄	C₂×D₄	1	8	yes	complemented
197	#3484	C₂×D₄	1	256	yes	complemented
198	C₂×#534	C₂×D₄	1	64	yes	—
199	C₂×#534	C₂×D₄	1	16	yes	—
200	C₂×#534	C₂×D₄	1	16	yes	complemented
201	C₂×#534	C₂×D₄	1	64	yes	complemented
202	C₂×#534	C₂×D₄	1	16	yes	complemented
203	C₂×#534	C₂⁴	1	16	yes	—
204	C₂×#534	C₂⁴	1	16	yes	—
205	C₂×#534	C₂⁴	1	16	yes	—
206	C₂×#534	C₂⁴	1	8	yes	complemented
207	C₂×#534	C₂⁴	1	32	yes	complemented
208	C₂²×#123	C₂×D₄	1	8	yes	—
209	C₂²×#123	C₂×D₄	1	8	yes	complemented
210	C₂²×#123	C₂×D₄	1	32	yes	complemented
211	C₂²×#123	C₂×D₄	1	8	yes	complemented
212	C₂²×#120	C₂×D₄	1	8	yes	—
213	C₂²×#120	C₂×D₄	1	64	yes	complemented
214	C₂²×#120	C₂×D₄	1	8	yes	complemented
215	C₂²×#120	C₂×D₄	1	32	yes	complemented
216	C₂²×#120	C₂×D₄	1	8	yes	complemented
217	C₂²×#120	C₂×D₄	1	8	yes	complemented
218	C₂²×#120	C₂⁴	1	32	yes	—
219	C₂²×#120	C₂⁴	1	8	yes	—
220	C₂²×#120	C₂⁴	1	16	yes	complemented
221	C₂×#518	C₂×D₄	1	32	yes	complemented
222	C₂×#518	C₂⁴	1	16	yes	—
223	C₂×#518	C₂⁴	1	8	yes	complemented
224	C₂×#518	C₂⁴	1	4	yes	complemented
225	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
226	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
227	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
228	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
229	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
230	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
231	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
232	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
233	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
234	C₂²×#99	C₂⁴	1	32	yes	—
235	C₂²×#99	C₂⁴	1	16	yes	complemented
236	C₂²×#99	C₂⁴	1	32	yes	complemented
237	C₂²×#99	C₂⁴	1	64	yes	complemented
238	C₂²×#99	C₂⁴	1	16	yes	complemented
239	#2405	C₂×D₄	1	64	yes	complemented
240	#2403	C₂×D₄	1	64	yes	complemented
241	#2308	C₂×D₄	1	16	yes	complemented
242	#2308	C₂⁴	1	16	yes	—
243	#2308	C₂⁴	1	8	yes	complemented
244	#2308	C₂⁴	1	32	yes	complemented
245	C₂×#386	C₂×D₄	1	16	yes	complemented
246	C₂×#379	C₂×D₄	1	8	yes	complemented
247	C₂×#379	C₂×D₄	1	8	yes	complemented
248	C₂×#379	C₂⁴	1	16	yes	—
249	C₂×#379	C₂⁴	1	8	yes	—
250	C₂×#379	C₂⁴	1	16	yes	complemented
251	C₂×#379	C₂⁴	1	32	yes	complemented
252	C₂×#342	C₂⁴	1	32	yes	complemented
253	C₂×#342	C₂⁴	1	64	yes	complemented
254	C₂⁶	#120	1	4	yes	—
255	C₂⁶	#120	1	4	yes	—
256	C₂⁶	#120	1	2	yes	—
257	C₂⁶	#120	1	2	yes	—
258	C₂⁶	#120	1	4	yes	—
259	C₂⁶	#120	1	16	yes	complemented
260	C₂⁶	C₂²×D₄	1	2	yes	—
261	C₂⁶	C₂²×D₄	1	4	yes	—
262	C₂⁶	C₂²×D₄	1	16	yes	—
263	C₂⁶	C₂²×D₄	1	2	yes	—
264	C₂⁶	C₂²×D₄	1	4	yes	—
265	C₂⁶	C₂²×D₄	1	1	yes	characteristic
266	C₂⁶	C₂²×D₄	1	4	yes	—
267	C₂⁶	C₂²×D₄	1	4	yes	—
268	C₂⁶	C₂²×D₄	1	8	yes	—
269	C₂⁶	C₂²×D₄	1	4	yes	—
270	C₂⁶	C₂²×D₄	1	8	yes	—
271	C₂⁶	C₂²×D₄	1	1	yes	characteristic
272	C₂⁶	C₂²×D₄	1	2	yes	—
273	C₂⁶	C₂²×D₄	1	4	yes	—
274	C₂⁶	C₂²×D₄	1	4	yes	—
275	C₂⁶	C₂²×D₄	1	8	yes	—
276	C₂⁶	C₂²×D₄	1	1	yes	characteristic
277	C₂⁶	C₂²×D₄	1	1	yes	characteristic
278	C₂⁶	C₂²×D₄	1	2	yes	—
279	C₂⁶	C₂²×D₄	1	2	yes	—
280	C₂⁶	C₂²×D₄	1	4	yes	—
281	C₂⁶	C₂²×D₄	1	2	yes	—
282	C₂⁶	C₂²×D₄	1	4	yes	—
283	C₂⁶	C₂²×D₄	1	2	yes	complemented
284	C₂⁶	C₂²×D₄	1	8	yes	complemented
285	C₂⁶	H(5,𝔽₂)	1	4	yes	—
286	C₂⁶	H(5,𝔽₂)	1	4	yes	—
287	C₂⁶	C₂⁵	1	4	yes	—
288	C₂⁶	C₂⁵	1	2	yes	—
289	C₂⁶	C₂⁵	1	1	yes	characteristic
290	C₂×H(5,𝔽₂)	C₂²×D₄	1	64	yes	complemented
291	C₂³×D₄	#120	1	8	yes	—
292	C₂³×D₄	#120	1	8	yes	—
293	C₂³×D₄	#120	1	32	yes	—
294	C₂³×D₄	#120	1	4	yes	—
295	C₂³×D₄	#120	1	4	yes	—
296	C₂³×D₄	#120	1	16	yes	—
297	C₂³×D₄	#120	1	4	yes	—
298	C₂³×D₄	#120	1	4	yes	—
299	C₂³×D₄	#120	1	16	yes	—
300	C₂³×D₄	#120	1	16	yes	complemented
301	C₂³×D₄	#120	1	16	yes	complemented
302	C₂³×D₄	#120	1	64	yes	complemented
303	C₂³×D₄	C₂²×D₄	1	32	yes	—
304	C₂³×D₄	C₂²×D₄	1	4	yes	—
305	C₂³×D₄	C₂²×D₄	1	4	yes	—
306	C₂³×D₄	C₂²×D₄	1	16	yes	—
307	C₂³×D₄	C₂²×D₄	1	16	yes	—
308	C₂³×D₄	C₂²×D₄	1	4	yes	—
309	C₂³×D₄	C₂²×D₄	1	4	yes	—
310	C₂³×D₄	C₂²×D₄	1	16	yes	—
311	C₂³×D₄	C₂²×D₄	1	8	yes	—
312	C₂³×D₄	C₂²×D₄	1	8	yes	—
313	C₂³×D₄	C₂²×D₄	1	16	yes	—
314	C₂³×D₄	C₂²×D₄	1	32	yes	—
315	C₂³×D₄	C₂²×D₄	1	64	yes	—
316	C₂³×D₄	C₂²×D₄	1	2	yes	—
317	C₂³×D₄	C₂²×D₄	1	8	yes	—
318	C₂³×D₄	C₂²×D₄	1	8	yes	—
319	C₂³×D₄	C₂²×D₄	1	8	yes	—
320	C₂³×D₄	C₂²×D₄	1	8	yes	—
321	C₂³×D₄	C₂²×D₄	1	4	yes	—
322	C₂³×D₄	C₂²×D₄	1	4	yes	—
323	C₂³×D₄	C₂²×D₄	1	8	yes	—
324	C₂³×D₄	C₂²×D₄	1	8	yes	—
325	C₂³×D₄	C₂²×D₄	1	2	yes	—
326	C₂³×D₄	C₂²×D₄	1	4	yes	—
327	C₂³×D₄	C₂²×D₄	1	16	yes	complemented
328	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
329	C₂³×D₄	C₂²×D₄	1	16	yes	complemented
330	C₂³×D₄	H(5,𝔽₂)	1	16	yes	—
331	C₂³×D₄	C₂⁵	1	2	yes	—
332	C₂³×D₄	C₂⁵	1	8	yes	—
333	C₂³×D₄	C₂⁵	1	2	yes	—
334	C₂³×D₄	C₂⁵	1	4	yes	—
335	C₂³×D₄	C₂⁵	1	4	yes	—
336	C₂⁴×C₄	#120	1	4	yes	—
337	C₂⁴×C₄	#120	1	4	yes	—
338	C₂⁴×C₄	#120	1	2	yes	—
339	C₂⁴×C₄	#120	1	2	yes	—
340	C₂⁴×C₄	#120	1	4	yes	—
341	C₂⁴×C₄	#120	1	16	yes	complemented
342	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
343	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
344	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
345	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
346	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
347	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
348	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
349	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
350	C₂⁴×C₄	C₂²×D₄	1	2	yes	complemented
351	C₂⁴×C₄	C₂²×D₄	1	8	yes	complemented
352	C₂⁴×C₄	C₂²×D₄	1	4	yes	complemented
353	#534	#120	1	128	yes	complemented
354	#534	C₂²×D₄	1	128	yes	—
355	C₂×#123	#120	1	64	yes	complemented
356	C₂×#123	C₂²×D₄	1	32	yes	—
357	C₂×#123	C₂²×D₄	1	32	yes	complemented
358	C₂×#123	C₂²×D₄	1	32	yes	complemented
359	C₂×#120	#120	1	64	yes	complemented
360	C₂×#120	C₂²×D₄	1	32	yes	—
361	C₂×#120	C₂²×D₄	1	128	yes	complemented
362	C₂×#120	C₂²×D₄	1	32	yes	complemented
363	C₂×#120	C₂²×D₄	1	32	yes	complemented
364	#518	C₂²×D₄	1	64	yes	complemented
365	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
366	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
367	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
368	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
369	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
370	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
371	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
372	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
373	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
374	C₂²×C₂²⋊C₄	C₂⁵	1	16	yes	—
375	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
376	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
377	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
378	#386	C₂²×D₄	1	64	yes	complemented
379	#379	C₂²×D₄	1	32	yes	complemented
380	C₂⁵	C₂×#120	1	1	yes	characteristic
381	C₂⁵	C₂×#120	1	2	yes	—
382	C₂⁵	C₂×#120	1	2	yes	—
383	C₂⁵	C₂×#120	1	8	yes	—
384	C₂⁵	C₂×#120	1	16	yes	—
385	C₂⁵	C₂×#120	1	2	yes	—
386	C₂⁵	C₂×#120	1	8	yes	—
387	C₂⁵	C₂×#120	1	16	yes	—
388	C₂⁵	C₂×#120	1	8	yes	—
389	C₂⁵	C₂×#120	1	2	yes	—
390	C₂⁵	C₂×#120	1	2	yes	—
391	C₂⁵	C₂×#120	1	4	yes	—
392	C₂⁵	C₂×#120	1	1	yes	characteristic
393	C₂⁵	C₂×#120	1	2	yes	—
394	C₂⁵	C₂×#120	1	2	yes	—
395	C₂⁵	C₂×#120	1	4	yes	—
396	C₂⁵	C₂×#120	1	2	yes	—
397	C₂⁵	C₂×#120	1	8	yes	—
398	C₂⁵	C₂×#120	1	8	yes	—
399	C₂⁵	C₂×#120	1	2	yes	—
400	C₂⁵	C₂×#120	1	8	yes	—
401	C₂⁵	C₂×#120	1	2	yes	—
402	C₂⁵	C₂×#120	1	4	yes	—
403	C₂⁵	C₂×#120	1	8	yes	—
404	C₂⁵	C₂×#120	1	2	yes	—
405	C₂⁵	C₂×#120	1	4	yes	—
406	C₂⁵	C₂×#120	1	16	yes	complemented
407	C₂⁵	C₂×#120	1	32	yes	complemented
408	C₂⁵	#534	1	2	yes	—
409	C₂⁵	#534	1	2	yes	—
410	C₂⁵	#534	1	2	yes	—
411	C₂⁵	#534	1	8	yes	—
412	C₂⁵	#534	1	2	yes	—
413	C₂⁵	#534	1	8	yes	—
414	C₂⁵	D₄²	1	8	yes	—
415	C₂⁵	D₄²	1	8	yes	—
416	C₂⁵	D₄²	1	8	yes	—
417	C₂⁵	D₄²	1	16	yes	—
418	C₂⁵	D₄²	1	16	yes	—
419	C₂⁵	D₄²	1	8	yes	—
420	C₂⁵	C₂³×D₄	1	4	yes	—
421	C₂⁵	C₂³×D₄	1	4	yes	—
422	C₂⁵	C₂³×D₄	1	2	yes	—
423	C₂⁵	C₂³×D₄	1	16	yes	—
424	C₂⁵	C₂³×D₄	1	8	yes	—
425	C₂⁵	C₂³×D₄	1	2	yes	—
426	C₂⁵	C₂³×D₄	1	4	yes	—
427	C₂⁵	C₂³×D₄	1	8	yes	—
428	C₂⁵	C₂³×D₄	1	2	yes	—
429	C₂⁵	C₂³×D₄	1	2	yes	—
430	C₂⁵	C₂³×D₄	1	4	yes	—
431	C₂⁵	C₂³×D₄	1	4	yes	—
432	C₂⁵	C₂³×D₄	1	1	yes	characteristic
433	C₂⁵	C₂³×D₄	1	2	yes	—
434	C₂⁵	C₂³×D₄	1	2	yes	—
435	C₂⁵	C₂³×D₄	1	1	yes	characteristic
436	C₂⁵	C₂³×D₄	1	2	yes	—
437	C₂⁵	C₂³×D₄	1	8	yes	—
438	C₂⁵	C₂³×D₄	1	2	yes	—
439	C₂⁵	C₂³×D₄	1	4	yes	complemented
440	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
441	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
442	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
443	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
444	C₂⁵	C₂⁶	1	1	yes	characteristic
445	C₂²×D₄	C₂×#120	1	32	yes	—
446	C₂²×D₄	C₂×#120	1	32	yes	—
447	C₂²×D₄	C₂×#120	1	8	yes	—
448	C₂²×D₄	C₂×#120	1	32	yes	—
449	C₂²×D₄	C₂×#120	1	16	yes	—
450	C₂²×D₄	C₂×#120	1	16	yes	—
451	C₂²×D₄	C₂×#120	1	8	yes	—
452	C₂²×D₄	C₂×#120	1	16	yes	—
453	C₂²×D₄	C₂×#120	1	16	yes	—
454	C₂²×D₄	C₂×#120	1	16	yes	—
455	C₂²×D₄	C₂×#120	1	32	yes	complemented
456	C₂²×D₄	C₂×#120	1	32	yes	complemented
457	C₂²×D₄	C₂×#120	1	32	yes	complemented
458	C₂²×D₄	#534	1	16	yes	—
459	C₂²×D₄	D₄²	1	64	yes	—
460	C₂²×D₄	D₄²	1	64	yes	—
461	C₂²×D₄	C₂³×D₄	1	8	yes	—
462	C₂²×D₄	C₂³×D₄	1	8	yes	—
463	C₂²×D₄	C₂³×D₄	1	16	yes	—
464	C₂²×D₄	C₂³×D₄	1	16	yes	—
465	C₂²×D₄	C₂³×D₄	1	16	yes	—
466	C₂²×D₄	C₂³×D₄	1	32	yes	—
467	C₂²×D₄	C₂×H(5,𝔽₂)	1	16	yes	—
468	C₂³×C₄	C₂×#120	1	2	yes	—
469	C₂³×C₄	C₂×#120	1	2	yes	—
470	C₂³×C₄	C₂×#120	1	16	yes	—
471	C₂³×C₄	C₂×#120	1	8	yes	—
472	C₂³×C₄	C₂×#120	1	8	yes	—
473	C₂³×C₄	C₂×#120	1	2	yes	—
474	C₂³×C₄	C₂×#120	1	2	yes	—
475	C₂³×C₄	C₂×#120	1	8	yes	—
476	C₂³×C₄	C₂×#120	1	4	yes	—
477	C₂³×C₄	C₂×#120	1	8	yes	—
478	C₂³×C₄	C₂×#120	1	4	yes	—
479	C₂³×C₄	C₂×#120	1	16	yes	complemented
480	C₂³×C₄	C₂×#120	1	32	yes	complemented
481	C₂³×C₄	#534	1	8	yes	—
482	C₂³×C₄	C₂³×D₄	1	2	yes	—
483	C₂³×C₄	C₂³×D₄	1	8	yes	—
484	C₂³×C₄	C₂³×D₄	1	2	yes	—
485	C₂³×C₄	C₂³×D₄	1	4	yes	—
486	C₂³×C₄	C₂³×D₄	1	4	yes	complemented
487	C₂³×C₄	C₂³×D₄	1	8	yes	complemented
488	#123	C₂×#120	1	128	yes	complemented
489	#120	C₂×#120	1	128	yes	complemented
490	C₂×C₂²⋊C₄	C₂×#120	1	32	yes	complemented
491	C₂×C₂²⋊C₄	C₂×#120	1	32	yes	complemented
492	C₂×C₂²⋊C₄	C₂³×D₄	1	32	yes	—
493	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
494	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	complemented
495	C₂⁴	#2403	1	2	yes	—
496	C₂⁴	#2403	1	2	yes	—
497	C₂⁴	#2403	1	4	yes	—
498	C₂⁴	#2403	1	4	yes	—
499	C₂⁴	#2403	1	16	yes	—
500	C₂⁴	#2403	1	4	yes	—
501	C₂⁴	#2403	1	2	yes	—
502	C₂⁴	#2403	1	4	yes	—
503	C₂⁴	#2403	1	16	yes	—
504	C₂⁴	#2403	1	16	yes	—
505	C₂⁴	#2403	1	2	yes	—
506	C₂⁴	#2403	1	4	yes	—
507	C₂⁴	#2403	1	4	yes	—
508	C₂⁴	#2403	1	16	yes	—
509	C₂⁴	#2846	1	8	yes	—
510	C₂⁴	#2846	1	8	yes	—
511	C₂⁴	C₂²×#120	1	2	yes	—
512	C₂⁴	C₂²×#120	1	4	yes	—
513	C₂⁴	C₂²×#120	1	1	yes	characteristic
514	C₂⁴	C₂²×#120	1	1	yes	characteristic
515	C₂⁴	C₂²×#120	1	4	yes	—
516	C₂⁴	C₂²×#120	1	8	yes	—
517	C₂⁴	C₂²×#120	1	8	yes	—
518	C₂⁴	C₂²×#120	1	4	yes	—
519	C₂⁴	C₂²×#120	1	4	yes	—
520	C₂⁴	C₂²×#120	1	8	yes	—
521	C₂⁴	C₂²×#120	1	2	yes	—
522	C₂⁴	C₂²×#120	1	4	yes	—
523	C₂⁴	C₂²×#120	1	8	yes	—
524	C₂⁴	C₂²×#120	1	8	yes	—
525	C₂⁴	C₂²×#120	1	4	yes	—
526	C₂⁴	C₂²×#120	1	1	yes	characteristic
527	C₂⁴	C₂²×#120	1	2	yes	—
528	C₂⁴	C₂²×#120	1	8	yes	—
529	C₂⁴	C₂²×#120	1	1	yes	characteristic
530	C₂⁴	C₂²×#120	1	2	yes	—
531	C₂⁴	C₂²×#120	1	4	yes	—
532	C₂⁴	C₂²×#120	1	8	yes	—
533	C₂⁴	C₂²×#120	1	16	yes	complemented
534	C₂⁴	C₂×#534	1	4	yes	—
535	C₂⁴	C₂×#534	1	1	yes	characteristic
536	C₂⁴	C₂×#534	1	4	yes	—
537	C₂⁴	C₂×#534	1	8	yes	—
538	C₂⁴	C₂×#534	1	1	yes	characteristic
539	C₂⁴	C₂×#534	1	4	yes	—
540	C₂⁴	C₂×#534	1	2	yes	—
541	C₂⁴	C₂×#534	1	4	yes	—
542	C₂⁴	C₂×D₄²	1	16	yes	—
543	C₂⁴	C₂×D₄²	1	4	yes	—
544	C₂⁴	C₂×D₄²	1	16	yes	—
545	C₂⁴	C₂×D₄²	1	4	yes	—
546	C₂⁴	C₂×D₄²	1	16	yes	—
547	C₂⁴	C₂×D₄²	1	4	yes	—
548	C₂⁴	C₂×D₄²	1	4	yes	—
549	C₂⁴	C₂×D₄²	1	16	yes	—
550	C₂⁴	#3484	1	8	yes	—
551	C₂⁴	#3484	1	16	yes	—
552	C₂⁴	#3484	1	8	yes	—
553	C₂⁴	#3484	1	16	yes	—
554	C₂⁴	C₂⁴×D₄	1	2	yes	—
555	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
556	C₂⁴	C₂⁴×D₄	1	2	yes	—
557	C₂⁴	C₂⁴×D₄	1	4	yes	—
558	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
559	C₂⁴	C₂²×H(5,𝔽₂)	1	4	yes	—
560	C₂×D₄	#2403	1	64	yes	—
561	C₂×D₄	#2846	1	32	yes	—
562	C₂×D₄	C₂²×#120	1	32	yes	—
563	C₂×D₄	C₂×D₄²	1	64	yes	—
564	C₂²×C₄	#2403	1	16	yes	—
565	C₂²×C₄	#2403	1	16	yes	—
566	C₂²×C₄	#2846	1	8	yes	—
567	C₂²×C₄	#2846	1	8	yes	—
568	C₂²×C₄	C₂²×#120	1	4	yes	—
569	C₂²×C₄	C₂²×#120	1	4	yes	—
570	C₂²×C₄	C₂²×#120	1	8	yes	—
571	C₂²×C₄	C₂²×#120	1	8	yes	—
572	C₂²×C₄	C₂²×#120	1	8	yes	—
573	C₂²×C₄	C₂²×#120	1	16	yes	complemented
574	C₂²×C₄	C₂×#534	1	8	yes	—
575	C₂²⋊C₄	C₂²×#120	1	32	yes	complemented
576	C₂³	#23895	1	8	yes	complemented
577	C₂³	C₂×#2403	1	4	yes	—
578	C₂³	C₂×#2403	1	8	yes	—
579	C₂³	C₂×#2403	1	1	yes	characteristic
580	C₂³	C₂×#2403	1	1	yes	characteristic
581	C₂³	C₂×#2403	1	4	yes	—
582	C₂³	C₂×#2403	1	1	yes	characteristic
583	C₂³	C₂×#2403	1	4	yes	—
584	C₂³	C₂×#2403	1	4	yes	—
585	C₂³	C₂×#2403	1	16	yes	—
586	C₂³	C₂×#2403	1	4	yes	—
587	C₂³	C₂×#2403	1	8	yes	—
588	C₂³	C₂×#2403	1	1	yes	characteristic
589	C₂³	#34980	1	2	yes	—
590	C₂³	#34980	1	4	yes	—
591	C₂³	#34980	1	2	yes	—
592	C₂³	#34980	1	4	yes	—
593	C₂³	#34980	1	4	yes	—
594	C₂³	#34980	1	8	yes	—
595	C₂³	D₄×#120	1	16	yes	—
596	C₂³	D₄×#120	1	16	yes	—
597	C₂³	D₄×#120	1	16	yes	—
598	C₂³	D₄×#120	1	16	yes	—
599	C₂³	C₂×#2846	1	2	yes	—
600	C₂³	C₂×#2846	1	8	yes	—
601	C₂³	C₂×#2846	1	2	yes	—
602	C₂³	C₂×#2846	1	4	yes	—
603	C₂³	C₂³×#120	1	1	yes	characteristic
604	C₂³	C₂³×#120	1	1	yes	characteristic
605	C₂³	C₂³×#120	1	2	yes	—
606	C₂³	C₂³×#120	1	4	yes	—
607	C₂³	C₂²×#534	1	1	yes	characteristic
608	C₂³	C₂²×#534	1	2	yes	—
609	C₂³	C₂²×D₄²	1	4	yes	—
610	C₂³	C₂²×D₄²	1	8	yes	—
611	C₂³	C₂×#3484	1	4	yes	—
612	C₂³	C₂×#3484	1	8	yes	—
613	C₂×C₄	C₂×#2403	1	16	yes	—
614	C₂×C₄	C₂×#2846	1	8	yes	—
615	C₂²	#612424	1	2	yes	—
616	C₂²	#612424	1	2	yes	—
617	C₂²	#612424	1	2	yes	—
618	C₂²	#612424	1	8	yes	—
619	C₂²	#612424	1	2	yes	—
620	C₂²	C₂×#23895	1	4	yes	—
621	C₂²	C₂×#23895	1	8	yes	complemented
622	C₂²	C₂²×#2403	1	2	yes	—
623	C₂²	C₂²×#2403	1	1	yes	characteristic
624	C₂²	C₂×#34980	1	1	yes	characteristic
625	C₂²	C₂×#34980	1	2	yes	—
626	C₂²	C₂×D₄×#120	1	8	yes	—
627	C₂²	C₂²×#2846	1	1	yes	characteristic
628	C₂	#72213862	1	4	yes	direct product factor
629	C₂	C₂×#612424	1	1	yes	characteristic
630	C₂	C₂²×#23895	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator, Frattini, cosocle	C₂⁵	C₂⁶
LCS	G ▷ C₂⁵ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#359442	C₂	semidirect
2. C₂×#392699	C₂	semidirect
3. C₂×#6437621	C₂	semidirect
4. C₂×#359549	C₂	semidirect
5. C₂×#394064	C₂	semidirect
6. C₂×#392109	C₂	semidirect
7. C₂²×#23895	C₂	semidirect
8. C₂×#6628892	C₂	semidirect
9. C₂³×#3484	C₂	semidirect
10. C₂×#7630939	C₂	semidirect
11. C₂×#394058	C₂	semidirect
12. #72213862	C₂	direct (N × H)
13. C₂⁴×H(5,𝔽₂)	C₂²	semidirect
16. C₂²×#3484	C₂²	semidirect
17. C₂²×#3484	C₂²	semidirect
18. C₂²×#3484	C₂²	semidirect
19. C₂²×#3484	C₂²	semidirect
21. C₂⁴×#120	C₂²	semidirect
22. C₂³×#518	C₂²	semidirect
23. C₂²×#3026	C₂²	semidirect
24. C₂²×#3026	C₂²	semidirect
25. C₂²×#2846	C₂²	semidirect
26. #7630939	C₂²	semidirect
28. C₂×#34980	C₂²	semidirect
29. C₂×#34980	C₂²	semidirect
30. C₂×#34171	C₂²	semidirect
31. C₂×#34171	C₂²	semidirect
32. #6628892	C₂²	semidirect
33. C₂×#23895	C₂²	semidirect
34. #6437621	C₂²	semidirect
35. C₂×#23444	C₂²	semidirect
36. C₂²×#2021	C₂²	semidirect
37. C₂²×#1913	C₂²	semidirect
38. C₂²×#1913	C₂²	semidirect
39. C₂²×#1898	C₂²	semidirect
40. C₂×#20960	C₂²	semidirect
41. C₂×#20609	C₂²	semidirect
42. C₂²×#1781	C₂²	semidirect
43. C₂²×#1781	C₂²	semidirect
44. C₂²×#1781	C₂²	semidirect
45. C₂²×#1781	C₂²	semidirect
46. C₂²×#1781	C₂²	semidirect
47. C₂×#14679	C₂²	semidirect
48. #394064	C₂²	semidirect
49. #394058	C₂²	semidirect
50. #392699	C₂²	semidirect
51. #392109	C₂²	semidirect
52. #359549	C₂²	semidirect
53. #359442	C₂²	semidirect
54. C₂×#10991	C₂²	semidirect
55. C₂×#10972	C₂²	semidirect
56. C₂×#10754	C₂²	semidirect
57. C₂×#10735	C₂²	semidirect
58. C₂⁸	D₄	semidirect
61. C₂³×H(5,𝔽₂)	C₂³	semidirect
62. C₂³×H(5,𝔽₂)	C₂³	semidirect
63. C₂⁵×D₄	D₄	semidirect
64. C₂⁵×D₄	D₄	semidirect
65. C₂⁵×D₄	D₄	semidirect
66. C₂⁵×D₄	D₄	semidirect
67. C₂⁵×D₄	D₄	semidirect
74. C₂⁶×C₄	D₄	semidirect
75. C₂×#3484	D₄	semidirect
77. C₂×#3484	C₂³	semidirect
78. C₂×#3484	C₂³	semidirect
79. C₂×#3484	C₂³	semidirect
80. C₂²×#534	D₄	semidirect
81. C₂²×#534	D₄	semidirect
86. C₂²×#534	C₂³	semidirect
87. C₂²×#534	C₂³	semidirect
88. C₂³×#123	D₄	semidirect
89. C₂³×#120	D₄	semidirect
92. C₂³×#120	C₂³	semidirect
93. C₂³×#120	C₂³	semidirect
95. C₂²×#518	C₂³	semidirect
96. C₂²×#518	C₂³	semidirect
97. C₂²×#518	C₂³	semidirect
99. C₂×#3026	C₂³	semidirect
100. C₂×#3026	C₂³	semidirect
102. C₂³×#99	C₂³	semidirect
103. C₂³×#99	C₂³	semidirect
104. C₂³×#99	C₂³	semidirect
105. C₂³×#99	C₂³	semidirect
106. C₂×#2846	C₂³	semidirect
107. #34980	D₄	semidirect
109. #34980	C₂³	semidirect
110. #34980	C₂³	semidirect
111. C₂×#2405	D₄	semidirect
112. C₂×#2403	D₄	semidirect
113. #34171	C₂³	semidirect
114. #34171	C₂³	semidirect
116. C₂×#2308	C₂³	semidirect
117. C₂×#2308	C₂³	semidirect
120. C₂²×#379	C₂³	semidirect
121. C₂²×#379	C₂³	semidirect
122. #23444	C₂³	semidirect
123. C₂×#2021	C₂³	semidirect
124. C₂×#1913	C₂³	semidirect
125. C₂×#1913	C₂³	semidirect
126. C₂×#1898	C₂³	semidirect
127. #20960	C₂³	semidirect
128. #20609	C₂³	semidirect
129. C₂×#1781	C₂³	semidirect
130. C₂×#1781	C₂³	semidirect
131. C₂×#1781	C₂³	semidirect
132. C₂×#1781	C₂³	semidirect
133. C₂×#1781	C₂³	semidirect
134. C₂²×#342	C₂³	semidirect
135. C₂²×#342	C₂³	semidirect
136. #14679	C₂³	semidirect
137. #10991	C₂³	semidirect
138. #10972	C₂³	semidirect
139. #10754	C₂³	semidirect
140. #10735	C₂³	semidirect
149. C₂⁷	C₂×D₄	semidirect
150. C₂⁷	C₂×D₄	semidirect
154. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
156. C₂²×H(5,𝔽₂)	C₂⁴	semidirect
174. C₂⁴×D₄	C₂×D₄	semidirect
175. C₂⁴×D₄	C₂×D₄	semidirect
176. C₂⁴×D₄	C₂×D₄	semidirect
177. C₂⁴×D₄	C₂×D₄	semidirect
178. C₂⁴×D₄	C₂×D₄	semidirect
179. C₂⁴×D₄	C₂×D₄	semidirect
180. C₂⁴×D₄	C₂×D₄	semidirect
195. C₂⁵×C₄	C₂×D₄	semidirect
196. C₂⁵×C₄	C₂×D₄	semidirect
197. #3484	C₂×D₄	semidirect
200. C₂×#534	C₂×D₄	semidirect
201. C₂×#534	C₂×D₄	semidirect
202. C₂×#534	C₂×D₄	semidirect
206. C₂×#534	C₂⁴	semidirect
207. C₂×#534	C₂⁴	semidirect
209. C₂²×#123	C₂×D₄	semidirect
210. C₂²×#123	C₂×D₄	semidirect
211. C₂²×#123	C₂×D₄	semidirect
213. C₂²×#120	C₂×D₄	semidirect
214. C₂²×#120	C₂×D₄	semidirect
215. C₂²×#120	C₂×D₄	semidirect
216. C₂²×#120	C₂×D₄	semidirect
217. C₂²×#120	C₂×D₄	semidirect
220. C₂²×#120	C₂⁴	semidirect
221. C₂×#518	C₂×D₄	semidirect
223. C₂×#518	C₂⁴	semidirect
224. C₂×#518	C₂⁴	semidirect
225. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
226. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
227. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
228. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
235. C₂²×#99	C₂⁴	semidirect
236. C₂²×#99	C₂⁴	semidirect
237. C₂²×#99	C₂⁴	semidirect
238. C₂²×#99	C₂⁴	semidirect
239. #2405	C₂×D₄	semidirect
240. #2403	C₂×D₄	semidirect
241. #2308	C₂×D₄	semidirect
243. #2308	C₂⁴	semidirect
244. #2308	C₂⁴	semidirect
245. C₂×#386	C₂×D₄	semidirect
246. C₂×#379	C₂×D₄	semidirect
247. C₂×#379	C₂×D₄	semidirect
250. C₂×#379	C₂⁴	semidirect
251. C₂×#379	C₂⁴	semidirect
252. C₂×#342	C₂⁴	semidirect
253. C₂×#342	C₂⁴	semidirect
259. C₂⁶	#120	semidirect
283. C₂⁶	C₂²×D₄	semidirect
284. C₂⁶	C₂²×D₄	semidirect
290. C₂×H(5,𝔽₂)	C₂²×D₄	semidirect
300. C₂³×D₄	#120	semidirect
301. C₂³×D₄	#120	semidirect
302. C₂³×D₄	#120	semidirect
327. C₂³×D₄	C₂²×D₄	semidirect
328. C₂³×D₄	C₂²×D₄	semidirect
329. C₂³×D₄	C₂²×D₄	semidirect
341. C₂⁴×C₄	#120	semidirect
350. C₂⁴×C₄	C₂²×D₄	semidirect
351. C₂⁴×C₄	C₂²×D₄	semidirect
352. C₂⁴×C₄	C₂²×D₄	semidirect
353. #534	#120	semidirect
355. C₂×#123	#120	semidirect
357. C₂×#123	C₂²×D₄	semidirect
358. C₂×#123	C₂²×D₄	semidirect
359. C₂×#120	#120	semidirect
361. C₂×#120	C₂²×D₄	semidirect
362. C₂×#120	C₂²×D₄	semidirect
363. C₂×#120	C₂²×D₄	semidirect
364. #518	C₂²×D₄	semidirect
368. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
369. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
370. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
371. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
372. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
373. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
378. #386	C₂²×D₄	semidirect
379. #379	C₂²×D₄	semidirect
406. C₂⁵	C₂×#120	semidirect
407. C₂⁵	C₂×#120	semidirect
439. C₂⁵	C₂³×D₄	semidirect
455. C₂²×D₄	C₂×#120	semidirect
456. C₂²×D₄	C₂×#120	semidirect
457. C₂²×D₄	C₂×#120	semidirect
479. C₂³×C₄	C₂×#120	semidirect
480. C₂³×C₄	C₂×#120	semidirect
486. C₂³×C₄	C₂³×D₄	semidirect
487. C₂³×C₄	C₂³×D₄	semidirect
488. #123	C₂×#120	semidirect
489. #120	C₂×#120	semidirect
490. C₂×C₂²⋊C₄	C₂×#120	semidirect
491. C₂×C₂²⋊C₄	C₂×#120	semidirect
494. C₂×C₂²⋊C₄	C₂³×D₄	semidirect
533. C₂⁴	C₂²×#120	semidirect
573. C₂²×C₄	C₂²×#120	semidirect
575. C₂²⋊C₄	C₂²×#120	semidirect
576. C₂³	#23895	semidirect
621. C₂²	C₂×#23895	semidirect
628. C₂	#72213862	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×#359442	2
C₂×#392699	2
C₂×#6437621	2
C₂×#359549	2
C₂×#394064	2
C₂×#392109	2
C₂²×#23895	2
C₂×#6628892	2
C₂³×#3484	2
C₂×#7630939	2
C₂×#394058	2
#72213862	2

Subgroups — C2×#72213862 #72262856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72213862 #72262856