Subgroups — C₂×#72241280 #72319627

Order 2048.

At least 7659 conjugacy classes of subgroups; only the 5192 normal subgroups are shown.

The subgroup lattice has 695 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×#245230	C₂	1	2	yes	maximal, complemented
2	C₂×#201660	C₂	1	2	yes	maximal, complemented
3	C₂×#245228	C₂	1	4	yes	maximal, complemented
4	C₂×#201650	C₂	1	2	yes	maximal, complemented
5	C₂×#7629120	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#7628711	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#245227	C₂	1	4	yes	maximal, complemented
8	C₂×#233538	C₂	1	4	yes	maximal, complemented
9	C₂×#188029	C₂	1	1	yes	maximal, characteristic, complemented
10	#72241280	C₂	1	32	yes	maximal, direct product factor
11	C₂×#245226	C₂	1	2	yes	maximal, complemented
12	C₂×#6628891	C₂	1	2	yes	maximal, complemented
13	C₂×#6629386	C₂	1	2	yes	maximal, complemented
14	C₂×#245229	C₂	1	2	yes	maximal, complemented
15	C₂×#245225	C₂	1	2	yes	maximal, complemented
16	C₂³×#585	C₂²	1	1	yes	characteristic, complemented
17	C₂³×#525	C₂²	1	1	yes	characteristic
18	C₂²×C₄×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
19	#7629120	C₂²	1	16	yes	complemented
20	C₂×#35512	C₂²	1	2	yes	—
21	C₂×#35512	C₂²	1	2	yes	complemented
22	C₂×#35446	C₂²	1	2	yes	complemented
23	#7628711	C₂²	1	16	yes	complemented
24	C₂×#35355	C₂²	1	2	yes	complemented
25	C₂×#35354	C₂²	1	2	yes	complemented
26	C₂×#35351	C₂²	1	1	yes	characteristic, complemented
27	C₂×#35350	C₂²	1	1	yes	characteristic, complemented
28	C₂×#35347	C₂²	1	1	yes	characteristic, complemented
29	C₂×#35346	C₂²	1	2	yes	—
30	C₂×#35346	C₂²	1	1	yes	characteristic, complemented
31	C₂×#34956	C₂²	1	2	yes	complemented
32	C₂×#34736	C₂²	1	2	yes	—
33	C₂×#34736	C₂²	1	2	yes	—
34	C₂×#34736	C₂²	1	2	yes	complemented
35	C₂×#34736	C₂²	1	4	yes	complemented
36	C₂×#34044	C₂²	1	1	yes	characteristic, complemented
37	C₂×#34057	C₂²	1	1	yes	characteristic, complemented
38	#6629386	C₂²	1	32	yes	complemented
39	C₂×#33020	C₂²	1	4	yes	complemented
40	C₂×#33020	C₂²	1	8	yes	complemented
41	#6628891	C₂²	1	32	yes	complemented
42	C₂×#32900	C₂²	1	4	yes	complemented
43	C₂×#32900	C₂²	1	4	yes	complemented
44	C₂×#32898	C₂²	1	4	yes	—
45	C₂×#32898	C₂²	1	4	yes	complemented
46	C₂×#32898	C₂²	1	4	yes	complemented
47	C₂×#20722	C₂²	1	2	yes	complemented
48	C₂×#20722	C₂²	1	4	yes	complemented
49	C₂×#20722	C₂²	1	2	yes	complemented
50	C₂×#20584	C₂²	1	2	yes	complemented
51	C₂×#20584	C₂²	1	4	yes	complemented
52	#245230	C₂²	1	32	yes	complemented
53	#245229	C₂²	1	32	yes	complemented
54	#245228	C₂²	1	64	yes	complemented
55	#245227	C₂²	1	64	yes	complemented
56	#245226	C₂²	1	32	yes	complemented
57	#245225	C₂²	1	32	yes	complemented
58	#233538	C₂²	1	64	yes	complemented
59	C₂×#10338	C₂²	1	8	yes	complemented
60	C₂×#10337	C₂²	1	8	yes	complemented
61	C₂×#10337	C₂²	1	8	yes	complemented
62	C₂×#10336	C₂²	1	8	yes	complemented
63	#201660	C₂²	1	32	yes	complemented
64	C₂×#9501	C₂²	1	4	yes	complemented
65	C₂×#9497	C₂²	1	4	yes	complemented
66	C₂×#9499	C₂²	1	4	yes	complemented
67	#201650	C₂²	1	32	yes	complemented
68	C₂×#9496	C₂²	1	8	yes	complemented
69	C₂×#9495	C₂²	1	4	yes	complemented
70	C₂×#9495	C₂²	1	4	yes	complemented
71	C₂×#9495	C₂²	1	4	yes	complemented
72	#188029	C₂²	1	16	yes	complemented
73	C₂×#8543	C₂²	1	2	yes	complemented
74	C₂×#8542	C₂²	1	2	yes	complemented
75	C₂×#8542	C₂²	1	2	yes	complemented
76	C₂×#8541	C₂²	1	2	yes	complemented
77	C₂×#8100	C₂²	1	4	yes	complemented
78	C₂²×#585	C₂³	1	8	yes	complemented
79	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
80	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
81	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
82	C₂⁴×#41	C₂³	1	1	yes	characteristic
83	C₂⁴×#41	C₂³	1	2	yes	—
84	C₂⁶×C₄	D₄	1	1	yes	characteristic, complemented
85	C₂²×#525	D₄	1	4	yes	complemented
86	C₂²×#525	D₄	1	8	yes	complemented
87	C₂²×#525	C₂³	1	8	yes	—
88	C₂³×#123	D₄	1	1	yes	characteristic, complemented
89	C₂³×#123	C₂³	1	1	yes	characteristic
90	C₂³×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
91	C₂³×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
92	C₂³×#121	C₂³	1	1	yes	characteristic
93	C₂³×#121	C₂³	1	1	yes	characteristic
94	C₂³×#120	D₄	1	1	yes	characteristic, complemented
95	C₂³×#120	C₂³	1	1	yes	characteristic
96	C₂×C₄×H(5,𝔽₂)	C₂³	1	8	yes	complemented
97	C₂²×#518	C₂³	1	1	yes	characteristic
98	C₂²×#518	C₂³	1	2	yes	—
99	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
100	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
101	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
102	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
103	C₂³×C₄×D₄	C₂³	1	2	yes	—
104	C₂³×#117	D₄	1	1	yes	characteristic, complemented
105	#35512	C₂³	1	16	yes	—
106	#35512	C₂³	1	16	yes	complemented
107	#35446	C₂³	1	16	yes	complemented
108	#35355	C₂³	1	16	yes	complemented
109	#35354	C₂³	1	16	yes	complemented
110	#35351	C₂³	1	8	yes	complemented
111	#35350	C₂³	1	8	yes	complemented
112	#35347	C₂³	1	8	yes	complemented
113	#35346	C₂³	1	16	yes	—
114	#35346	C₂³	1	8	yes	complemented
115	#34956	C₂³	1	16	yes	complemented
116	C₂×#2483	C₂³	1	2	yes	—
117	#34736	D₄	1	16	yes	complemented
118	#34736	D₄	1	16	yes	complemented
119	#34736	C₂³	1	16	yes	—
120	#34736	C₂³	1	16	yes	—
121	#34736	C₂³	1	16	yes	complemented
122	#34736	C₂³	1	32	yes	complemented
123	C₂×#2406	D₄	1	4	yes	complemented
124	C₂×#2404	D₄	1	4	yes	complemented
125	C₂×#2409	D₄	1	4	yes	complemented
126	C₂×#2408	D₄	1	4	yes	complemented
127	C₂×#2405	C₂³	1	4	yes	—
128	C₂×#2405	C₂³	1	2	yes	—
129	C₂×#2405	C₂³	1	2	yes	—
130	C₂×#2405	C₂³	1	2	yes	—
131	C₂×#2405	C₂³	1	4	yes	—
132	C₂×#2405	C₂³	1	2	yes	—
133	C₂×#2405	C₂³	1	8	yes	—
134	C₂×#2403	C₂³	1	2	yes	—
135	C₂×#2403	C₂³	1	4	yes	—
136	C₂×#2403	C₂³	1	2	yes	—
137	C₂×#2403	C₂³	1	4	yes	—
138	C₂×#2403	C₂³	1	2	yes	—
139	C₂×#2403	C₂³	1	8	yes	—
140	#34057	C₂³	1	8	yes	complemented
141	C₂×#2312	C₂³	1	2	yes	—
142	#34044	C₂³	1	8	yes	complemented
143	C₂×#2309	C₂³	1	2	yes	—
144	C₂×#2308	C₂³	1	2	yes	—
145	C₂×#2308	C₂³	1	1	yes	characteristic
146	C₂×#2308	C₂³	1	1	yes	characteristic
147	C₂×C₄×#120	D₄	1	8	yes	complemented
148	C₂×#2297	D₄	1	4	yes	complemented
149	C₂×#2280	C₂³	1	4	yes	—
150	C₂×#2280	C₂³	1	2	yes	—
151	C₂×#2280	C₂³	1	2	yes	—
152	#33020	C₂³	1	32	yes	complemented
153	#33020	C₂³	1	64	yes	complemented
154	#32900	C₂³	1	32	yes	complemented
155	#32900	C₂³	1	32	yes	complemented
156	#32898	C₂³	1	32	yes	—
157	#32898	C₂³	1	32	yes	complemented
158	#32898	C₂³	1	32	yes	complemented
159	#20722	C₂³	1	32	yes	complemented
160	#20722	C₂³	1	16	yes	complemented
161	#20722	C₂³	1	16	yes	complemented
162	C₂×#1819	C₂³	1	8	yes	—
163	C₂×#1819	C₂³	1	4	yes	—
164	C₂×#1819	C₂³	1	4	yes	—
165	#20584	C₂³	1	32	yes	complemented
166	#20584	C₂³	1	16	yes	complemented
167	C₂×#1781	C₂³	1	8	yes	—
168	C₂×#1781	C₂³	1	4	yes	—
169	C₂×#1781	C₂³	1	8	yes	—
170	C₂×#1781	C₂³	1	4	yes	—
171	C₂×#1781	C₂³	1	8	yes	—
172	C₂×#1781	C₂³	1	4	yes	—
173	C₂×#1781	C₂³	1	4	yes	—
174	#10338	C₂³	1	64	yes	complemented
175	#10337	C₂³	1	64	yes	complemented
176	#10337	C₂³	1	64	yes	complemented
177	#10336	C₂³	1	64	yes	complemented
178	#9501	C₂³	1	32	yes	complemented
179	#9499	C₂³	1	32	yes	complemented
180	#9497	C₂³	1	32	yes	complemented
181	#9496	C₂³	1	64	yes	complemented
182	#9495	C₂³	1	32	yes	complemented
183	#9495	C₂³	1	32	yes	complemented
184	#9495	C₂³	1	32	yes	complemented
185	#8543	C₂³	1	16	yes	complemented
186	#8542	C₂³	1	16	yes	complemented
187	#8542	C₂³	1	16	yes	complemented
188	#8541	C₂³	1	16	yes	complemented
189	#8100	C₂³	1	32	yes	complemented
190	C₂×#1304	C₂³	1	8	yes	—
191	C₂×#1304	C₂³	1	8	yes	—
192	C₂⁷	C₂×D₄	1	1	yes	characteristic
193	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
194	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
195	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
196	C₂³×#41	C₂×D₄	1	4	yes	—
197	C₂³×#41	C₂×D₄	1	4	yes	—
198	C₂³×#41	C₂×D₄	1	8	yes	—
199	C₂³×#41	C₂×D₄	1	4	yes	—
200	C₂³×#41	C₂×D₄	1	8	yes	complemented
201	C₂³×#41	C₂⁴	1	4	yes	—
202	C₂³×#41	C₂⁴	1	8	yes	—
203	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
204	C₂⁴×Q₈	C₂×D₄	1	2	yes	complemented
205	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
206	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
207	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
208	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
209	C₂⁴×D₄	C₂⁴	1	2	yes	—
210	C₂⁴×D₄	C₂⁴	1	4	yes	—
211	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
212	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
213	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
214	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
215	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
216	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
217	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
218	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
219	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
220	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
221	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
222	C₂⁵×C₄	C₂×D₄	1	4	yes	complemented
223	C₂⁵×C₄	C₂×D₄	1	2	yes	complemented
224	C₂⁵×C₄	C₂×D₄	1	8	yes	complemented
225	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
226	C₂×#525	C₂×D₄	1	32	yes	complemented
227	C₂²×#123	C₂×D₄	1	4	yes	—
228	C₂²×#123	C₂×D₄	1	4	yes	—
229	C₂²×#123	C₂×D₄	1	4	yes	complemented
230	C₂²×#123	C₂×D₄	1	8	yes	complemented
231	C₂²×#123	C₂⁴	1	4	yes	—
232	C₂²×C₂²⋊Q₈	C₂×D₄	1	8	yes	complemented
233	C₂²×C₂²⋊Q₈	C₂×D₄	1	8	yes	complemented
234	C₂²×#121	C₂×D₄	1	4	yes	—
235	C₂²×#121	C₂×D₄	1	4	yes	—
236	C₂²×#121	C₂⁴	1	4	yes	—
237	C₂²×#121	C₂⁴	1	4	yes	—
238	C₂²×#120	C₂×D₄	1	4	yes	—
239	C₂²×#120	C₂×D₄	1	8	yes	—
240	C₂²×#120	C₂×D₄	1	4	yes	—
241	C₂²×#120	C₂×D₄	1	4	yes	complemented
242	C₂²×#120	C₂×D₄	1	8	yes	complemented
243	C₂²×#120	C₂⁴	1	4	yes	—
244	C₂×#518	C₂⁴	1	4	yes	—
245	C₂×#518	C₂⁴	1	8	yes	—
246	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
247	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
248	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
249	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
250	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
251	C₂²×C₄×D₄	C₂×D₄	1	8	yes	complemented
252	C₂²×C₄×D₄	C₂×D₄	1	8	yes	complemented
253	C₂²×C₄×D₄	C₂×D₄	1	8	yes	complemented
254	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
255	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
256	C₂²×C₄×D₄	C₂⁴	1	8	yes	—
257	C₂²×#117	C₂×D₄	1	4	yes	complemented
258	C₂²×#117	C₂×D₄	1	8	yes	complemented
259	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
260	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
261	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
262	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
263	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
264	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
265	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
266	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
267	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
268	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
269	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
270	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
271	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
272	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
273	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
274	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
275	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
276	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
277	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
278	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
279	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
280	C₂³×C₄²	C₂×D₄	1	2	yes	complemented
281	#2483	C₂⁴	1	8	yes	—
282	#2409	C₂×D₄	1	32	yes	complemented
283	#2408	C₂×D₄	1	32	yes	complemented
284	#2406	C₂×D₄	1	32	yes	complemented
285	#2405	C₂×D₄	1	8	yes	—
286	#2405	C₂×D₄	1	16	yes	complemented
287	#2405	C₂×D₄	1	8	yes	complemented
288	#2405	C₂⁴	1	8	yes	—
289	#2405	C₂⁴	1	8	yes	—
290	#2405	C₂⁴	1	16	yes	—
291	#2405	C₂⁴	1	32	yes	—
292	#2405	C₂⁴	1	16	yes	—
293	#2405	C₂⁴	1	8	yes	—
294	#2405	C₂⁴	1	8	yes	—
295	#2404	C₂×D₄	1	32	yes	complemented
296	#2403	C₂×D₄	1	8	yes	—
297	#2403	C₂×D₄	1	16	yes	—
298	#2403	C₂×D₄	1	8	yes	complemented
299	#2403	C₂⁴	1	16	yes	—
300	#2403	C₂⁴	1	8	yes	—
301	#2403	C₂⁴	1	32	yes	—
302	#2403	C₂⁴	1	16	yes	—
303	#2403	C₂⁴	1	8	yes	—
304	#2403	C₂⁴	1	8	yes	—
305	#2312	C₂⁴	1	8	yes	—
306	#2309	C₂⁴	1	8	yes	—
307	#2308	C₂⁴	1	4	yes	—
308	#2308	C₂⁴	1	4	yes	—
309	#2308	C₂⁴	1	8	yes	—
310	C₄×#120	C₂×D₄	1	64	yes	complemented
311	#2297	C₂×D₄	1	32	yes	complemented
312	C₂×#386	C₂×D₄	1	8	yes	—
313	C₂×#386	C₂×D₄	1	4	yes	—
314	C₂×#386	C₂×D₄	1	4	yes	—
315	C₂×#386	C₂×D₄	1	4	yes	complemented
316	C₂×#386	C₂×D₄	1	4	yes	complemented
317	C₂×#385	C₂×D₄	1	8	yes	complemented
318	#2280	C₂×D₄	1	8	yes	complemented
319	#2280	C₂×D₄	1	8	yes	complemented
320	#2280	C₂⁴	1	16	yes	—
321	#2280	C₂⁴	1	8	yes	—
322	#2280	C₂⁴	1	8	yes	—
323	C₂×#381	C₂×D₄	1	4	yes	complemented
324	C₂×#380	C₂×D₄	1	4	yes	complemented
325	C₂×#379	C₂×D₄	1	8	yes	complemented
326	C₂×#379	C₂⁴	1	8	yes	—
327	C₂×#379	C₂⁴	1	4	yes	—
328	C₂×#379	C₂⁴	1	2	yes	—
329	C₂×#379	C₂⁴	1	2	yes	—
330	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
331	#1819	C₂⁴	1	16	yes	—
332	#1819	C₂⁴	1	32	yes	—
333	#1819	C₂⁴	1	16	yes	—
334	#1781	C₂⁴	1	16	yes	—
335	#1781	C₂⁴	1	32	yes	—
336	#1781	C₂⁴	1	32	yes	—
337	#1781	C₂⁴	1	32	yes	—
338	#1781	C₂⁴	1	16	yes	—
339	#1781	C₂⁴	1	16	yes	—
340	#1781	C₂⁴	1	16	yes	—
341	#1304	C₂⁴	1	32	yes	—
342	#1304	C₂⁴	1	32	yes	—
343	C₂⁶	C₂²×D₄	1	1	yes	characteristic
344	C₂⁶	C₂²×D₄	1	1	yes	characteristic
345	C₂⁶	C₂²×D₄	1	1	yes	characteristic
346	C₂⁶	C₂²×D₄	1	4	yes	—
347	C₂⁶	C₂²×D₄	1	2	yes	—
348	C₂⁶	C₂²×D₄	1	4	yes	—
349	C₂⁶	C₂²×D₄	1	1	yes	characteristic
350	C₂⁶	C₂⁵	1	1	yes	characteristic
351	C₂²×#41	#120	1	16	yes	—
352	C₂²×#41	#120	1	16	yes	—
353	C₂²×#41	C₂²×D₄	1	16	yes	—
354	C₂²×#41	C₂²×D₄	1	16	yes	—
355	C₂³×Q₈	#120	1	4	yes	—
356	C₂³×Q₈	#120	1	4	yes	—
357	C₂³×Q₈	C₂²×D₄	1	4	yes	—
358	C₂³×Q₈	C₂²×D₄	1	8	yes	complemented
359	C₂³×D₄	#120	1	4	yes	—
360	C₂³×D₄	#120	1	4	yes	—
361	C₂³×D₄	C₂²×D₄	1	4	yes	—
362	C₂³×D₄	C₂²×D₄	1	4	yes	—
363	C₂³×D₄	C₂²×D₄	1	4	yes	—
364	C₂³×D₄	C₂²×D₄	1	4	yes	—
365	C₂³×D₄	C₂²×D₄	1	4	yes	—
366	C₂³×D₄	C₂²×D₄	1	4	yes	—
367	C₂³×D₄	C₂²×D₄	1	8	yes	—
368	C₂³×D₄	C₂²×D₄	1	4	yes	—
369	C₂³×D₄	C₂²×D₄	1	2	yes	—
370	C₂³×D₄	C₂²×D₄	1	4	yes	—
371	C₂³×D₄	C₂²×D₄	1	4	yes	—
372	C₂³×D₄	C₂²×D₄	1	2	yes	—
373	C₂³×D₄	C₂²×D₄	1	2	yes	—
374	C₂³×D₄	C₂²×D₄	1	2	yes	—
375	C₂³×D₄	C₂²×D₄	1	4	yes	—
376	C₂³×D₄	C₂²×D₄	1	8	yes	complemented
377	C₂³×D₄	C₂⁵	1	8	yes	—
378	C₂³×D₄	C₂⁵	1	4	yes	—
379	C₂³×D₄	C₂⁵	1	2	yes	—
380	C₂³×D₄	C₂⁵	1	2	yes	—
381	C₂³×D₄	C₂⁵	1	2	yes	—
382	C₂³×D₄	C₂⁵	1	2	yes	—
383	C₂⁴×C₄	#120	1	2	yes	—
384	C₂⁴×C₄	#120	1	4	yes	—
385	C₂⁴×C₄	#120	1	2	yes	—
386	C₂⁴×C₄	#120	1	2	yes	—
387	C₂⁴×C₄	#120	1	2	yes	—
388	C₂⁴×C₄	#120	1	2	yes	—
389	C₂⁴×C₄	#120	1	4	yes	—
390	C₂⁴×C₄	#120	1	2	yes	—
391	C₂⁴×C₄	#120	1	4	yes	—
392	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
393	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
394	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
395	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
396	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
397	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
398	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
399	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
400	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
401	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
402	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
403	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
404	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
405	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
406	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
407	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
408	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
409	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
410	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
411	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
412	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
413	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
414	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
415	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
416	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
417	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
418	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
419	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
420	C₂⁴×C₄	C₂²×D₄	1	16	yes	complemented
421	C₂⁴×C₄	C₂²×D₄	1	8	yes	complemented
422	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
423	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
424	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	—
425	C₂⁴×C₄	C₂⁵	1	2	yes	—
426	C₂×#123	C₂²×D₄	1	16	yes	—
427	C₂×#123	C₂²×D₄	1	16	yes	complemented
428	C₂×#120	C₂²×D₄	1	32	yes	—
429	C₂×#120	C₂²×D₄	1	16	yes	—
430	C₂×#120	C₂²×D₄	1	16	yes	complemented
431	C₂×C₄×D₄	#120	1	16	yes	—
432	C₂×C₄×D₄	#120	1	16	yes	—
433	C₂×C₄×D₄	C₂²×D₄	1	16	yes	—
434	C₂×C₄×D₄	C₂²×D₄	1	16	yes	—
435	C₂×#117	C₂²×D₄	1	16	yes	complemented
436	C₂²×C₄⋊C₄	#120	1	4	yes	—
437	C₂²×C₄⋊C₄	#120	1	4	yes	—
438	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
439	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
440	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
441	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
442	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
443	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
444	C₂²×C₄⋊C₄	C₂²×D₄	1	8	yes	complemented
445	C₂²×C₂²⋊C₄	#120	1	4	yes	—
446	C₂²×C₂²⋊C₄	#120	1	4	yes	—
447	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
448	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
449	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
450	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
451	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
452	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
453	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
454	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
455	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
456	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
457	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
458	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
459	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
460	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
461	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
462	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
463	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
464	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
465	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
466	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
467	C₂²×C₄²	#120	1	2	yes	—
468	C₂²×C₄²	#120	1	2	yes	—
469	C₂²×C₄²	#120	1	4	yes	—
470	C₂²×C₄²	C₂²×D₄	1	4	yes	—
471	C₂²×C₄²	C₂²×D₄	1	4	yes	—
472	C₂²×C₄²	C₂²×D₄	1	8	yes	complemented
473	#386	C₂²×D₄	1	32	yes	—
474	#386	C₂²×D₄	1	16	yes	—
475	#386	C₂²×D₄	1	16	yes	—
476	#386	C₂²×D₄	1	16	yes	complemented
477	#386	C₂²×D₄	1	16	yes	complemented
478	#385	C₂²×D₄	1	32	yes	complemented
479	#381	C₂²×D₄	1	16	yes	complemented
480	#380	C₂²×D₄	1	16	yes	complemented
481	#379	C₂²×D₄	1	8	yes	—
482	#379	C₂²×D₄	1	4	yes	—
483	#379	C₂²×D₄	1	4	yes	—
484	#379	C₂²×D₄	1	32	yes	complemented
485	#379	C₂⁵	1	16	yes	—
486	#379	C₂⁵	1	8	yes	—
487	#379	C₂⁵	1	4	yes	—
488	#379	C₂⁵	1	4	yes	—
489	C₄×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
490	C₂⁵	C₂×#120	1	2	yes	—
491	C₂⁵	C₂×#120	1	2	yes	—
492	C₂⁵	C₂×#120	1	2	yes	—
493	C₂⁵	C₂×#120	1	2	yes	—
494	C₂⁵	C₂×#120	1	2	yes	—
495	C₂⁵	C₂×#120	1	2	yes	—
496	C₂⁵	C₂³×D₄	1	1	yes	characteristic
497	C₂⁵	C₂³×D₄	1	2	yes	—
498	C₂⁵	C₂³×D₄	1	2	yes	—
499	C₂⁵	C₂³×D₄	1	2	yes	—
500	C₂⁵	C₂³×D₄	1	2	yes	—
501	C₂⁵	C₂³×D₄	1	2	yes	—
502	C₂⁵	C₂³×D₄	1	4	yes	—
503	C₂⁵	C₂³×D₄	1	8	yes	—
504	C₂⁵	C₂³×D₄	1	2	yes	—
505	C₂⁵	C₂³×D₄	1	1	yes	characteristic
506	C₂⁵	C₂³×D₄	1	2	yes	—
507	C₂⁵	C₂³×D₄	1	2	yes	—
508	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
509	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
510	C₂⁵	C₂⁶	1	1	yes	characteristic
511	C₂²×Q₈	C₂×#120	1	16	yes	—
512	C₂²×D₄	C₂×#120	1	8	yes	—
513	C₂²×D₄	C₂×#120	1	8	yes	—
514	C₂²×D₄	C₂×#120	1	16	yes	—
515	C₂²×D₄	C₂×#120	1	8	yes	—
516	C₂²×D₄	C₂³×D₄	1	8	yes	—
517	C₂²×D₄	C₂³×D₄	1	8	yes	—
518	C₂²×D₄	C₂³×D₄	1	8	yes	—
519	C₂³×C₄	B(4,𝔽₂)	1	16	yes	complemented
520	C₂³×C₄	C₂×#120	1	2	yes	—
521	C₂³×C₄	C₂×#120	1	2	yes	—
522	C₂³×C₄	C₂×#120	1	2	yes	—
523	C₂³×C₄	C₂×#120	1	8	yes	—
524	C₂³×C₄	C₂×#120	1	8	yes	—
525	C₂³×C₄	C₂×#120	1	2	yes	—
526	C₂³×C₄	C₂×#120	1	1	yes	characteristic
527	C₂³×C₄	C₂×#120	1	1	yes	characteristic
528	C₂³×C₄	C₂×#120	1	2	yes	—
529	C₂³×C₄	C₂×#120	1	4	yes	—
530	C₂³×C₄	C₂×#120	1	2	yes	—
531	C₂³×C₄	C₂×#120	1	1	yes	characteristic
532	C₂³×C₄	C₂×#120	1	2	yes	—
533	C₂³×C₄	C₂×#120	1	8	yes	—
534	C₂³×C₄	C₂×#120	1	2	yes	—
535	C₂³×C₄	C₂×#120	1	2	yes	—
536	C₂³×C₄	C₂×#120	1	2	yes	—
537	C₂³×C₄	C₂×#120	1	2	yes	—
538	C₂³×C₄	C₂×#120	1	2	yes	—
539	C₂³×C₄	C₂×#120	1	8	yes	—
540	C₂³×C₄	C₂×#120	1	8	yes	—
541	C₂³×C₄	C₂×#120	1	8	yes	—
542	C₂³×C₄	C₂×#120	1	2	yes	—
543	C₂³×C₄	C₂×#120	1	2	yes	—
544	C₂³×C₄	C₂×#120	1	2	yes	—
545	C₂³×C₄	C₂×#120	1	2	yes	—
546	C₂³×C₄	C₂×#120	1	4	yes	—
547	C₂³×C₄	C₂×#120	1	4	yes	—
548	C₂³×C₄	C₂×#120	1	4	yes	—
549	C₂³×C₄	C₂×#120	1	1	yes	characteristic
550	C₂³×C₄	#534	1	1	yes	characteristic
551	C₂³×C₄	#534	1	2	yes	—
552	C₂³×C₄	#534	1	1	yes	characteristic
553	C₂³×C₄	#534	1	2	yes	—
554	C₂³×C₄	#534	1	2	yes	—
555	C₂³×C₄	#534	1	4	yes	—
556	C₂³×C₄	#534	1	4	yes	—
557	C₂³×C₄	D₄²	1	4	yes	—
558	C₂³×C₄	D₄²	1	8	yes	—
559	C₂³×C₄	D₄²	1	4	yes	—
560	C₂³×C₄	D₄²	1	4	yes	—
561	C₂³×C₄	D₄²	1	4	yes	—
562	C₂³×C₄	D₄²	1	8	yes	—
563	C₂³×C₄	D₄²	1	8	yes	—
564	C₂³×C₄	D₄²	1	8	yes	—
565	C₂³×C₄	D₄²	1	8	yes	—
566	C₂³×C₄	D₄²	1	8	yes	—
567	C₂³×C₄	C₂³×D₄	1	2	yes	—
568	C₂³×C₄	C₂³×D₄	1	2	yes	—
569	C₂³×C₄	C₂³×D₄	1	4	yes	—
570	C₂³×C₄	C₂³×D₄	1	2	yes	—
571	C₂³×C₄	C₂³×D₄	1	2	yes	—
572	C₂³×C₄	C₂³×D₄	1	4	yes	—
573	C₂³×C₄	C₂³×D₄	1	4	yes	—
574	C₂³×C₄	C₂³×D₄	1	8	yes	—
575	C₂³×C₄	C₂³×D₄	1	2	yes	—
576	C₂³×C₄	C₂³×D₄	1	4	yes	—
577	C₂³×C₄	C₂³×D₄	1	2	yes	—
578	C₂³×C₄	C₂³×D₄	1	2	yes	—
579	C₂³×C₄	C₂³×D₄	1	2	yes	—
580	C₂³×C₄	C₂³×D₄	1	2	yes	—
581	C₂³×C₄	C₂³×D₄	1	2	yes	—
582	C₂³×C₄	C₂³×D₄	1	4	yes	—
583	C₂³×C₄	C₂³×D₄	1	4	yes	—
584	C₂³×C₄	C₂³×D₄	1	4	yes	—
585	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
586	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
587	C₂×C₄⋊C₄	C₂×#120	1	16	yes	—
588	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
589	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
590	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
591	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
592	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
593	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
594	C₂×C₄²	C₂×#120	1	8	yes	—
595	C₂×C₄²	C₂×#120	1	8	yes	—
596	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
597	C₂⁴	#3025	1	8	yes	complemented
598	C₂⁴	C₂²×#120	1	1	yes	characteristic
599	C₂⁴	C₂²×#120	1	1	yes	characteristic
600	C₂⁴	C₂²×#120	1	1	yes	characteristic
601	C₂⁴	C₂²×#120	1	1	yes	characteristic
602	C₂⁴	C₂²×#120	1	4	yes	—
603	C₂⁴	C₂²×#120	1	2	yes	—
604	C₂⁴	C₂²×#120	1	2	yes	—
605	C₂⁴	C₂²×#120	1	4	yes	—
606	C₂⁴	C₂²×#120	1	4	yes	—
607	C₂⁴	C₂×#534	1	1	yes	characteristic
608	C₂⁴	C₂×#534	1	1	yes	characteristic
609	C₂⁴	C₂×#534	1	2	yes	—
610	C₂⁴	C₂×D₄²	1	4	yes	—
611	C₂⁴	C₂×D₄²	1	4	yes	—
612	C₂⁴	C₂×D₄²	1	4	yes	—
613	C₂⁴	C₂×D₄²	1	4	yes	—
614	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
615	C₂⁴	C₂⁴×D₄	1	2	yes	—
616	C₂⁴	C₂⁴×D₄	1	2	yes	—
617	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
618	C₂²×C₄	#2403	1	1	yes	characteristic
619	C₂²×C₄	#2403	1	1	yes	characteristic
620	C₂²×C₄	#2403	1	2	yes	—
621	C₂²×C₄	#2403	1	2	yes	—
622	C₂²×C₄	#2403	1	2	yes	—
623	C₂²×C₄	#2403	1	2	yes	—
624	C₂²×C₄	#2403	1	2	yes	—
625	C₂²×C₄	#2403	1	4	yes	—
626	C₂²×C₄	#2403	1	4	yes	—
627	C₂²×C₄	#2403	1	8	yes	—
628	C₂²×C₄	#2403	1	8	yes	—
629	C₂²×C₄	#2403	1	4	yes	—
630	C₂²×C₄	#2403	1	4	yes	—
631	C₂²×C₄	#2403	1	8	yes	—
632	C₂²×C₄	#2403	1	8	yes	—
633	C₂²×C₄	#2403	1	1	yes	characteristic
634	C₂²×C₄	#2403	1	2	yes	—
635	C₂²×C₄	#2403	1	1	yes	characteristic
636	C₂²×C₄	C₂×B(4,𝔽₂)	1	8	yes	—
637	C₂²×C₄	C₂×B(4,𝔽₂)	1	8	yes	—
638	C₂²×C₄	C₂×B(4,𝔽₂)	1	32	yes	complemented
639	C₂²×C₄	C₂²×#120	1	4	yes	—
640	C₂²×C₄	C₂²×#120	1	4	yes	—
641	C₂²×C₄	C₂²×#120	1	2	yes	—
642	C₂²×C₄	C₂²×#120	1	4	yes	—
643	C₂²×C₄	C₂²×#120	1	2	yes	—
644	C₂²×C₄	C₂²×#120	1	2	yes	—
645	C₂²×C₄	C₂²×#120	1	4	yes	—
646	C₂²×C₄	C₂²×#120	1	4	yes	—
647	C₂²×C₄	C₂²×#120	1	4	yes	—
648	C₂²×C₄	C₂²×#120	1	4	yes	—
649	C₂²×C₄	C₂²×#120	1	2	yes	—
650	C₂²×C₄	C₂×#534	1	2	yes	—
651	C₂²×C₄	C₂×#534	1	2	yes	—
652	C₂²×C₄	C₂×#534	1	4	yes	—
653	C₂²×C₄	C₂×D₄²	1	8	yes	—
654	C₂²×C₄	C₂×D₄²	1	8	yes	—
655	C₂²×C₄	C₂×D₄²	1	8	yes	—
656	C₂²×C₄	C₂×D₄²	1	8	yes	—
657	C₂³	C₂×#2403	1	4	yes	—
658	C₂³	C₂×#2403	1	1	yes	characteristic
659	C₂³	C₂×#2403	1	1	yes	characteristic
660	C₂³	C₂×#2403	1	1	yes	characteristic
661	C₂³	C₂×#2403	1	1	yes	characteristic
662	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
663	C₂³	C₂²×B(4,𝔽₂)	1	8	yes	—
664	C₂³	C₂×#3025	1	4	yes	—
665	C₂³	C₂×#3025	1	8	yes	complemented
666	C₂³	C₂³×#120	1	1	yes	characteristic
667	C₂³	C₂³×#120	1	1	yes	characteristic
668	C₂³	C₂²×#534	1	1	yes	characteristic
669	C₂³	C₂²×D₄²	1	4	yes	—
670	C₂×C₄	#23900	1	4	yes	—
671	C₂×C₄	#23900	1	4	yes	—
672	C₂×C₄	#23900	1	8	yes	—
673	C₂×C₄	C₂×#2403	1	2	yes	—
674	C₂×C₄	C₂×#2403	1	2	yes	—
675	C₂×C₄	C₂×#2403	1	8	yes	—
676	C₂×C₄	C₂×#2403	1	2	yes	—
677	C₂×C₄	C₂×#2403	1	2	yes	—
678	C₂×C₄	C₂²×B(4,𝔽₂)	1	8	yes	—
679	C₂×C₄	C₂²×B(4,𝔽₂)	1	8	yes	—
680	C₂²	C₂×#23900	1	2	yes	—
681	C₂²	C₂×#23900	1	2	yes	—
682	C₂²	#6437616	1	2	yes	—
683	C₂²	#6437616	1	2	yes	—
684	C₂²	#6437628	1	2	yes	—
685	C₂²	C₂²×#2403	1	1	yes	characteristic
686	C₂²	C₂³×B(4,𝔽₂)	1	2	yes	—
687	C₂²	C₂²×#3025	1	2	yes	—
688	C₄	C₂×#23900	1	4	yes	—
689	C₄	C₂×#23900	1	4	yes	—
690	C₂	C₂²×#23900	1	1	yes	characteristic
691	C₂	C₂×#6437616	1	1	yes	characteristic
692	C₂	C₂×#6437628	1	1	yes	characteristic
693	C₂	#72241280	1	4	yes	direct product factor

	subgroup	G/H
center	C₂²×C₄	#2403
commutator, Frattini, cosocle	C₂⁵	C₂⁶
socle	C₂³	C₂×#2403
LCS	G ▷ C₂⁵ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#245230	C₂	semidirect
2. C₂×#201660	C₂	semidirect
3. C₂×#245228	C₂	semidirect
4. C₂×#201650	C₂	semidirect
5. C₂×#7629120	C₂	semidirect
6. C₂×#7628711	C₂	semidirect
7. C₂×#245227	C₂	semidirect
8. C₂×#233538	C₂	semidirect
9. C₂×#188029	C₂	semidirect
10. #72241280	C₂	direct (N × H)
11. C₂×#245226	C₂	semidirect
12. C₂×#6628891	C₂	semidirect
13. C₂×#6629386	C₂	semidirect
14. C₂×#245229	C₂	semidirect
15. C₂×#245225	C₂	semidirect
16. C₂³×#585	C₂²	semidirect
18. C₂²×C₄×H(5,𝔽₂)	C₂²	semidirect
19. #7629120	C₂²	semidirect
21. C₂×#35512	C₂²	semidirect
22. C₂×#35446	C₂²	semidirect
23. #7628711	C₂²	semidirect
24. C₂×#35355	C₂²	semidirect
25. C₂×#35354	C₂²	semidirect
26. C₂×#35351	C₂²	semidirect
27. C₂×#35350	C₂²	semidirect
28. C₂×#35347	C₂²	semidirect
30. C₂×#35346	C₂²	semidirect
31. C₂×#34956	C₂²	semidirect
34. C₂×#34736	C₂²	semidirect
35. C₂×#34736	C₂²	semidirect
36. C₂×#34044	C₂²	semidirect
37. C₂×#34057	C₂²	semidirect
38. #6629386	C₂²	semidirect
39. C₂×#33020	C₂²	semidirect
40. C₂×#33020	C₂²	semidirect
41. #6628891	C₂²	semidirect
42. C₂×#32900	C₂²	semidirect
43. C₂×#32900	C₂²	semidirect
45. C₂×#32898	C₂²	semidirect
46. C₂×#32898	C₂²	semidirect
47. C₂×#20722	C₂²	semidirect
48. C₂×#20722	C₂²	semidirect
49. C₂×#20722	C₂²	semidirect
50. C₂×#20584	C₂²	semidirect
51. C₂×#20584	C₂²	semidirect
52. #245230	C₂²	semidirect
53. #245229	C₂²	semidirect
54. #245228	C₂²	semidirect
55. #245227	C₂²	semidirect
56. #245226	C₂²	semidirect
57. #245225	C₂²	semidirect
58. #233538	C₂²	semidirect
59. C₂×#10338	C₂²	semidirect
60. C₂×#10337	C₂²	semidirect
61. C₂×#10337	C₂²	semidirect
62. C₂×#10336	C₂²	semidirect
63. #201660	C₂²	semidirect
64. C₂×#9501	C₂²	semidirect
65. C₂×#9497	C₂²	semidirect
66. C₂×#9499	C₂²	semidirect
67. #201650	C₂²	semidirect
68. C₂×#9496	C₂²	semidirect
69. C₂×#9495	C₂²	semidirect
70. C₂×#9495	C₂²	semidirect
71. C₂×#9495	C₂²	semidirect
72. #188029	C₂²	semidirect
73. C₂×#8543	C₂²	semidirect
74. C₂×#8542	C₂²	semidirect
75. C₂×#8542	C₂²	semidirect
76. C₂×#8541	C₂²	semidirect
77. C₂×#8100	C₂²	semidirect
78. C₂²×#585	C₂³	semidirect
84. C₂⁶×C₄	D₄	semidirect
85. C₂²×#525	D₄	semidirect
86. C₂²×#525	D₄	semidirect
88. C₂³×#123	D₄	semidirect
90. C₂³×C₂²⋊Q₈	D₄	semidirect
91. C₂³×C₂²⋊Q₈	D₄	semidirect
94. C₂³×#120	D₄	semidirect
96. C₂×C₄×H(5,𝔽₂)	C₂³	semidirect
99. C₂³×C₄×D₄	D₄	semidirect
100. C₂³×C₄×D₄	D₄	semidirect
104. C₂³×#117	D₄	semidirect
106. #35512	C₂³	semidirect
107. #35446	C₂³	semidirect
108. #35355	C₂³	semidirect
109. #35354	C₂³	semidirect
110. #35351	C₂³	semidirect
111. #35350	C₂³	semidirect
112. #35347	C₂³	semidirect
114. #35346	C₂³	semidirect
115. #34956	C₂³	semidirect
117. #34736	D₄	semidirect
118. #34736	D₄	semidirect
121. #34736	C₂³	semidirect
122. #34736	C₂³	semidirect
123. C₂×#2406	D₄	semidirect
124. C₂×#2404	D₄	semidirect
125. C₂×#2409	D₄	semidirect
126. C₂×#2408	D₄	semidirect
140. #34057	C₂³	semidirect
142. #34044	C₂³	semidirect
147. C₂×C₄×#120	D₄	semidirect
148. C₂×#2297	D₄	semidirect
152. #33020	C₂³	semidirect
153. #33020	C₂³	semidirect
154. #32900	C₂³	semidirect
155. #32900	C₂³	semidirect
157. #32898	C₂³	semidirect
158. #32898	C₂³	semidirect
159. #20722	C₂³	semidirect
160. #20722	C₂³	semidirect
161. #20722	C₂³	semidirect
165. #20584	C₂³	semidirect
166. #20584	C₂³	semidirect
174. #10338	C₂³	semidirect
175. #10337	C₂³	semidirect
176. #10337	C₂³	semidirect
177. #10336	C₂³	semidirect
178. #9501	C₂³	semidirect
179. #9499	C₂³	semidirect
180. #9497	C₂³	semidirect
181. #9496	C₂³	semidirect
182. #9495	C₂³	semidirect
183. #9495	C₂³	semidirect
184. #9495	C₂³	semidirect
185. #8543	C₂³	semidirect
186. #8542	C₂³	semidirect
187. #8542	C₂³	semidirect
188. #8541	C₂³	semidirect
189. #8100	C₂³	semidirect
200. C₂³×#41	C₂×D₄	semidirect
204. C₂⁴×Q₈	C₂×D₄	semidirect
208. C₂⁴×D₄	C₂×D₄	semidirect
222. C₂⁵×C₄	C₂×D₄	semidirect
223. C₂⁵×C₄	C₂×D₄	semidirect
224. C₂⁵×C₄	C₂×D₄	semidirect
226. C₂×#525	C₂×D₄	semidirect
229. C₂²×#123	C₂×D₄	semidirect
230. C₂²×#123	C₂×D₄	semidirect
232. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
233. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
241. C₂²×#120	C₂×D₄	semidirect
242. C₂²×#120	C₂×D₄	semidirect
251. C₂²×C₄×D₄	C₂×D₄	semidirect
252. C₂²×C₄×D₄	C₂×D₄	semidirect
253. C₂²×C₄×D₄	C₂×D₄	semidirect
257. C₂²×#117	C₂×D₄	semidirect
258. C₂²×#117	C₂×D₄	semidirect
265. C₂³×C₄⋊C₄	C₂×D₄	semidirect
274. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
280. C₂³×C₄²	C₂×D₄	semidirect
282. #2409	C₂×D₄	semidirect
283. #2408	C₂×D₄	semidirect
284. #2406	C₂×D₄	semidirect
286. #2405	C₂×D₄	semidirect
287. #2405	C₂×D₄	semidirect
295. #2404	C₂×D₄	semidirect
298. #2403	C₂×D₄	semidirect
310. C₄×#120	C₂×D₄	semidirect
311. #2297	C₂×D₄	semidirect
315. C₂×#386	C₂×D₄	semidirect
316. C₂×#386	C₂×D₄	semidirect
317. C₂×#385	C₂×D₄	semidirect
318. #2280	C₂×D₄	semidirect
319. #2280	C₂×D₄	semidirect
323. C₂×#381	C₂×D₄	semidirect
324. C₂×#380	C₂×D₄	semidirect
325. C₂×#379	C₂×D₄	semidirect
330. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
358. C₂³×Q₈	C₂²×D₄	semidirect
376. C₂³×D₄	C₂²×D₄	semidirect
420. C₂⁴×C₄	C₂²×D₄	semidirect
421. C₂⁴×C₄	C₂²×D₄	semidirect
427. C₂×#123	C₂²×D₄	semidirect
430. C₂×#120	C₂²×D₄	semidirect
435. C₂×#117	C₂²×D₄	semidirect
444. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
463. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
472. C₂²×C₄²	C₂²×D₄	semidirect
476. #386	C₂²×D₄	semidirect
477. #386	C₂²×D₄	semidirect
478. #385	C₂²×D₄	semidirect
479. #381	C₂²×D₄	semidirect
480. #380	C₂²×D₄	semidirect
484. #379	C₂²×D₄	semidirect
489. C₄×C₂²⋊C₄	C₂²×D₄	semidirect
519. C₂³×C₄	B(4,𝔽₂)	semidirect
597. C₂⁴	#3025	semidirect
638. C₂²×C₄	C₂×B(4,𝔽₂)	semidirect
665. C₂³	C₂×#3025	semidirect
693. C₂	#72241280	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×#245230	2
C₂×#201660	2
C₂×#245228	2
C₂×#201650	2
C₂×#7629120	2
C₂×#7628711	2
C₂×#245227	2
C₂×#233538	2
C₂×#188029	2
#72241280	2
C₂×#245226	2
C₂×#6628891	2
C₂×#6629386	2
C₂×#245229	2
C₂×#245225	2

Subgroups — C2×#72241280 #72319627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72241280 #72319627