Subgroups — C₂×#72234533 #72260783

Order 2048.

At least 7619 conjugacy classes of subgroups; only the 4168 normal subgroups are shown.

The subgroup lattice has 654 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×#496330	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#508063	C₂	1	2	yes	maximal, complemented
3	C₂×#508062	C₂	1	2	yes	maximal, complemented
4	C₂×#503206	C₂	1	4	yes	maximal, complemented
5	C₂×#503468	C₂	1	4	yes	maximal, complemented
6	C₂×#500781	C₂	1	8	yes	maximal, complemented
7	C₂×#496333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#6491103	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#6491100	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#511776	C₂	1	2	yes	maximal, complemented
11	C₂×#493962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#52031	C₂	1	1	yes	maximal, characteristic, complemented
13	#72234533	C₂	1	32	yes	maximal, direct product factor
14	C₂×#6453841	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#511771	C₂	1	2	yes	maximal, complemented
16	C₂³×#560	C₂²	1	1	yes	characteristic
17	C₂×#62773	C₂²	1	1	yes	characteristic, complemented
18	C₂³×D₄²	C₂²	1	1	yes	characteristic
19	C₂×#52031	C₂²	1	4	yes	—
20	C₂×#52031	C₂²	1	4	yes	—
21	C₂×#52031	C₂²	1	16	yes	complemented
22	C₂²×#2697	C₂²	1	1	yes	characteristic
23	C₂²×#2679	C₂²	1	1	yes	characteristic
24	C₂²×#2534	C₂²	1	1	yes	characteristic
25	C₂²×#2408	C₂²	1	1	yes	characteristic
26	C₂²×#2328	C₂²	1	1	yes	characteristic
27	C₂²×#2200	C₂²	1	8	yes	complemented
28	C₂²×#2196	C₂²	1	8	yes	complemented
29	C₂×#32928	C₂²	1	4	yes	complemented
30	C₂×#32926	C₂²	1	4	yes	complemented
31	#6491103	C₂²	1	16	yes	complemented
32	#6491100	C₂²	1	16	yes	complemented
33	#6453841	C₂²	1	16	yes	complemented
34	C₂×#25949	C₂²	1	2	yes	complemented
35	C₂×#25947	C₂²	1	2	yes	complemented
36	C₂×#24316	C₂²	1	2	yes	complemented
37	C₂×#25773	C₂²	1	2	yes	complemented
38	C₂×#25771	C₂²	1	2	yes	complemented
39	C₂×#24226	C₂²	1	2	yes	complemented
40	C₂×#24018	C₂²	1	2	yes	complemented
41	C₂×#23901	C₂²	1	2	yes	complemented
42	C₂×#23900	C₂²	1	2	yes	—
43	C₂×#23900	C₂²	1	2	yes	—
44	C₂×#23900	C₂²	1	2	yes	complemented
45	C₂×#23906	C₂²	1	2	yes	—
46	C₂×#21473	C₂²	1	4	yes	complemented
47	C₂×#20726	C₂²	1	1	yes	characteristic, complemented
48	C₂×#20722	C₂²	1	1	yes	characteristic, complemented
49	C₂×#20722	C₂²	1	1	yes	characteristic, complemented
50	#511776	C₂²	1	32	yes	complemented
51	#511771	C₂²	1	32	yes	complemented
52	#508063	C₂²	1	32	yes	complemented
53	#508062	C₂²	1	32	yes	complemented
54	#503468	C₂²	1	64	yes	complemented
55	#503206	C₂²	1	64	yes	complemented
56	#500781	C₂²	1	128	yes	complemented
57	C₂×#13420	C₂²	1	8	yes	complemented
58	C₂×#13419	C₂²	1	8	yes	complemented
59	C₂×#13344	C₂²	1	8	yes	complemented
60	C₂×#13343	C₂²	1	8	yes	complemented
61	#496333	C₂²	1	16	yes	complemented
62	#496330	C₂²	1	16	yes	complemented
63	C₂×#13222	C₂²	1	4	yes	complemented
64	C₂×#13221	C₂²	1	4	yes	complemented
65	C₂×#13219	C₂²	1	4	yes	complemented
66	C₂×#13218	C₂²	1	4	yes	complemented
67	#493962	C₂²	1	16	yes	complemented
68	C₂×#12856	C₂²	1	2	yes	complemented
69	C₂×#12799	C₂²	1	4	yes	complemented
70	C₂×#12762	C₂²	1	8	yes	complemented
71	C₂×#12759	C₂²	1	8	yes	complemented
72	C₂×#12693	C₂²	1	2	yes	—
73	C₂×#12688	C₂²	1	2	yes	complemented
74	C₂×#12687	C₂²	1	2	yes	—
75	C₂×#12687	C₂²	1	2	yes	—
76	C₂×#12687	C₂²	1	2	yes	complemented
77	C₂×#12628	C₂²	1	4	yes	complemented
78	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
79	#62773	C₂³	1	8	yes	complemented
80	C₂×#3501	C₂³	1	1	yes	characteristic, complemented
81	C₂×#3496	C₂³	1	1	yes	characteristic, complemented
82	C₂×#3484	C₂³	1	2	yes	—
83	C₂²×D₄²	C₂³	1	4	yes	—
84	C₂²×D₄²	C₂³	1	8	yes	—
85	C₂²×#560	C₂³	1	4	yes	—
86	C₂²×#560	C₂³	1	8	yes	—
87	C₂³×#127	C₂³	1	1	yes	characteristic
88	C₂³×#123	C₂³	1	1	yes	characteristic
89	C₂³×#120	C₂³	1	1	yes	characteristic
90	C₂³×#120	C₂³	1	1	yes	characteristic
91	C₂³×#120	C₂³	1	1	yes	characteristic
92	C₂×C₄×H(5,𝔽₂)	C₂³	1	2	yes	complemented
93	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
94	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
95	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
96	C₂²×#458	C₂³	1	4	yes	complemented
97	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
98	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
99	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	complemented
100	C₂²×#453	C₂³	1	4	yes	—
101	C₂×#2697	C₂³	1	4	yes	—
102	C₂×#2697	C₂³	1	8	yes	—
103	C₂×#2679	C₂³	1	4	yes	—
104	C₂×#2679	C₂³	1	8	yes	—
105	#52031	C₂³	1	32	yes	—
106	#52031	C₂³	1	32	yes	—
107	C₂×#2534	D₄	1	2	yes	complemented
108	C₂×#2534	D₄	1	2	yes	complemented
109	C₂×#2534	D₄	1	8	yes	complemented
110	C₂×#2534	C₂³	1	2	yes	—
111	C₂×#2534	C₂³	1	2	yes	—
112	C₂×#2534	C₂³	1	8	yes	—
113	C₂×#2408	D₄	1	2	yes	complemented
114	C₂×#2408	D₄	1	2	yes	complemented
115	C₂×#2408	D₄	1	8	yes	complemented
116	C₂×#2408	C₂³	1	2	yes	—
117	C₂×#2408	C₂³	1	2	yes	—
118	C₂×#2408	C₂³	1	8	yes	—
119	C₂×#2328	D₄	1	8	yes	complemented
120	C₂×#2328	D₄	1	2	yes	complemented
121	C₂×#2328	D₄	1	2	yes	complemented
122	C₂×#2328	C₂³	1	2	yes	—
123	C₂×#2328	C₂³	1	2	yes	—
124	C₂×#2328	C₂³	1	8	yes	—
125	C₂²×#390	D₄	1	1	yes	characteristic, complemented
126	C₂²×#390	C₂³	1	1	yes	characteristic
127	C₂²×#382	D₄	1	1	yes	characteristic, complemented
128	C₂²×#381	D₄	1	1	yes	characteristic, complemented
129	C₂²×#380	D₄	1	1	yes	characteristic, complemented
130	C₂²×#380	D₄	1	1	yes	characteristic, complemented
131	C₂²×#379	D₄	1	1	yes	characteristic, complemented
132	C₂²×#379	D₄	1	1	yes	characteristic, complemented
133	C₂²×#379	D₄	1	1	yes	characteristic, complemented
134	C₂²×#376	D₄	1	1	yes	characteristic, complemented
135	C₂×#2200	C₂³	1	64	yes	complemented
136	C₂×#2196	C₂³	1	64	yes	complemented
137	C₂²×#353	C₂³	1	8	yes	—
138	C₂²×#352	C₂³	1	8	yes	complemented
139	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	8	yes	—
140	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	8	yes	—
141	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	8	yes	complemented
142	#32928	C₂³	1	32	yes	complemented
143	#32926	C₂³	1	32	yes	complemented
144	#25949	C₂³	1	16	yes	complemented
145	#25947	C₂³	1	16	yes	complemented
146	#25773	C₂³	1	16	yes	complemented
147	#25771	C₂³	1	16	yes	complemented
148	#24316	C₂³	1	16	yes	complemented
149	#24226	C₂³	1	16	yes	complemented
150	#24018	C₂³	1	16	yes	complemented
151	#23906	C₂³	1	16	yes	—
152	#23901	C₂³	1	16	yes	complemented
153	#23900	C₂³	1	16	yes	—
154	#23900	C₂³	1	16	yes	—
155	#23900	C₂³	1	16	yes	complemented
156	#21473	C₂³	1	32	yes	complemented
157	C₂×#1890	C₂³	1	4	yes	complemented
158	C₂×#1889	C₂³	1	4	yes	—
159	C₂×#1889	C₂³	1	4	yes	—
160	C₂×#1889	C₂³	1	4	yes	complemented
161	C₂×#1887	C₂³	1	4	yes	—
162	C₂×#1856	C₂³	1	4	yes	complemented
163	#20726	C₂³	1	8	yes	complemented
164	#20722	C₂³	1	8	yes	complemented
165	#20722	C₂³	1	8	yes	complemented
166	C₂×#1800	C₂³	1	2	yes	complemented
167	C₂×#1799	C₂³	1	2	yes	complemented
168	C₂×#1799	C₂³	1	2	yes	complemented
169	C₂×#1792	C₂³	1	4	yes	complemented
170	C₂×#1783	C₂³	1	2	yes	—
171	C₂×#1781	C₂³	1	2	yes	—
172	C₂×#1781	C₂³	1	2	yes	—
173	C₂×C₄×#100	C₂³	1	2	yes	complemented
174	C₂×C₄×#99	C₂³	1	2	yes	complemented
175	C₂×C₄×#99	C₂³	1	2	yes	complemented
176	#13420	C₂³	1	64	yes	complemented
177	#13419	C₂³	1	64	yes	complemented
178	#13344	C₂³	1	64	yes	complemented
179	#13343	C₂³	1	64	yes	complemented
180	#13222	C₂³	1	32	yes	complemented
181	#13221	C₂³	1	32	yes	complemented
182	#13219	C₂³	1	32	yes	complemented
183	#13218	C₂³	1	32	yes	complemented
184	#12856	C₂³	1	16	yes	complemented
185	#12799	C₂³	1	32	yes	complemented
186	#12762	C₂³	1	64	yes	complemented
187	#12759	C₂³	1	64	yes	complemented
188	#12693	C₂³	1	16	yes	—
189	#12688	C₂³	1	16	yes	complemented
190	#12687	C₂³	1	16	yes	—
191	#12687	C₂³	1	16	yes	—
192	#12687	C₂³	1	16	yes	complemented
193	#12628	C₂³	1	32	yes	complemented
194	C₂×#1393	C₂³	1	8	yes	complemented
195	C₂⁷	C₂×D₄	1	1	yes	characteristic
196	C₂⁷	C₂×D₄	1	1	yes	characteristic
197	C₂⁷	C₂×D₄	1	1	yes	characteristic
198	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
199	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
200	C₂⁴×D₄	C₂×D₄	1	2	yes	—
201	C₂⁴×D₄	C₂×D₄	1	2	yes	—
202	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
203	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
204	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
205	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
206	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
207	C₂×#560	C₂⁴	1	16	yes	—
208	#3501	C₂⁴	1	4	yes	complemented
209	#3496	C₂⁴	1	4	yes	complemented
210	#3484	C₂⁴	1	8	yes	—
211	C₂×D₄²	C₂⁴	1	16	yes	—
212	C₂²×#127	C₂×D₄	1	4	yes	—
213	C₂²×#127	C₂×D₄	1	2	yes	—
214	C₂²×#127	C₂⁴	1	4	yes	—
215	C₂²×#127	C₂⁴	1	2	yes	—
216	C₂²×#123	C₂×D₄	1	4	yes	—
217	C₂²×#123	C₂×D₄	1	2	yes	—
218	C₂²×#123	C₂⁴	1	2	yes	—
219	C₂²×#123	C₂⁴	1	4	yes	—
220	C₂²×#120	C₂×D₄	1	4	yes	—
221	C₂²×#120	C₂×D₄	1	2	yes	—
222	C₂²×#120	C₂×D₄	1	4	yes	—
223	C₂²×#120	C₂×D₄	1	4	yes	—
224	C₂²×#120	C₂×D₄	1	2	yes	—
225	C₂²×#120	C₂×D₄	1	2	yes	—
226	C₂²×#120	C₂⁴	1	2	yes	—
227	C₂²×#120	C₂⁴	1	2	yes	—
228	C₂²×#120	C₂⁴	1	2	yes	—
229	C₂²×#120	C₂⁴	1	4	yes	—
230	C₂²×#120	C₂⁴	1	4	yes	—
231	C₂²×#120	C₂⁴	1	4	yes	—
232	C₄×H(5,𝔽₂)	C₂⁴	1	8	yes	complemented
233	C₂×#518	C₂⁴	1	2	yes	—
234	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
235	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
236	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
238	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
241	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
244	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×D₄	C₂×D₄	1	8	yes	complemented
246	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
248	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
249	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
250	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
251	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
252	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
253	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
254	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
255	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
256	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
257	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
258	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
259	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
260	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
261	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
262	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
263	C₂×#458	C₂⁴	1	16	yes	complemented
264	C₂×B(4,𝔽₂)	C₂⁴	1	16	yes	—
265	C₂×B(4,𝔽₂)	C₂⁴	1	16	yes	—
266	C₂×B(4,𝔽₂)	C₂⁴	1	16	yes	complemented
267	C₂×#453	C₂⁴	1	16	yes	—
268	C₂²×#100	C₂⁴	1	4	yes	—
269	C₂²×#99	C₂⁴	1	4	yes	—
270	C₂²×#99	C₂⁴	1	4	yes	—
271	#2697	C₂⁴	1	16	yes	—
272	#2679	C₂⁴	1	16	yes	—
273	#2534	C₂×D₄	1	8	yes	—
274	#2534	C₂×D₄	1	8	yes	—
275	#2534	C₂×D₄	1	16	yes	complemented
276	#2534	C₂×D₄	1	16	yes	complemented
277	#2534	C₂⁴	1	8	yes	—
278	#2534	C₂⁴	1	8	yes	—
279	#2408	C₂×D₄	1	8	yes	—
280	#2408	C₂×D₄	1	8	yes	—
281	#2408	C₂×D₄	1	16	yes	complemented
282	#2408	C₂×D₄	1	16	yes	complemented
283	#2408	C₂⁴	1	8	yes	—
284	#2408	C₂⁴	1	8	yes	—
285	#2328	C₂×D₄	1	8	yes	—
286	#2328	C₂×D₄	1	8	yes	—
287	#2328	C₂×D₄	1	16	yes	complemented
288	#2328	C₂×D₄	1	16	yes	complemented
289	#2328	C₂⁴	1	8	yes	—
290	#2328	C₂⁴	1	8	yes	—
291	C₂×#390	C₂×D₄	1	2	yes	—
292	C₂×#390	C₂×D₄	1	4	yes	—
293	C₂×#390	C₂×D₄	1	2	yes	—
294	C₂×#390	C₂×D₄	1	2	yes	—
295	C₂×#390	C₂×D₄	1	8	yes	complemented
296	C₂×#390	C₂⁴	1	2	yes	—
297	C₂×#390	C₂⁴	1	4	yes	—
298	C₂×#382	C₂×D₄	1	2	yes	—
299	C₂×#382	C₂×D₄	1	2	yes	—
300	C₂×#382	C₂×D₄	1	8	yes	complemented
301	C₂×#381	C₂×D₄	1	2	yes	—
302	C₂×#381	C₂×D₄	1	2	yes	—
303	C₂×#381	C₂×D₄	1	8	yes	complemented
304	C₂×#380	C₂×D₄	1	2	yes	—
305	C₂×#380	C₂×D₄	1	2	yes	—
306	C₂×#380	C₂×D₄	1	2	yes	—
307	C₂×#380	C₂×D₄	1	2	yes	—
308	C₂×#380	C₂×D₄	1	8	yes	complemented
309	C₂×#380	C₂×D₄	1	8	yes	complemented
310	C₂×#379	C₂×D₄	1	2	yes	—
311	C₂×#379	C₂×D₄	1	2	yes	—
312	C₂×#379	C₂×D₄	1	2	yes	—
313	C₂×#379	C₂×D₄	1	2	yes	—
314	C₂×#379	C₂×D₄	1	2	yes	—
315	C₂×#379	C₂×D₄	1	2	yes	—
316	C₂×#379	C₂×D₄	1	8	yes	complemented
317	C₂×#379	C₂×D₄	1	8	yes	complemented
318	C₂×#379	C₂×D₄	1	8	yes	complemented
319	C₂×#376	C₂×D₄	1	2	yes	—
320	C₂×#376	C₂×D₄	1	2	yes	—
321	C₂×#376	C₂×D₄	1	8	yes	complemented
322	C₂×#353	C₂⁴	1	32	yes	—
323	C₂×#352	C₂⁴	1	32	yes	complemented
324	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	32	yes	—
325	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	32	yes	—
326	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	32	yes	complemented
327	#1890	C₂⁴	1	16	yes	complemented
328	#1889	C₂⁴	1	16	yes	—
329	#1889	C₂⁴	1	16	yes	—
330	#1889	C₂⁴	1	16	yes	complemented
331	#1887	C₂⁴	1	16	yes	—
332	#1856	C₂⁴	1	16	yes	complemented
333	#1800	C₂⁴	1	8	yes	complemented
334	#1799	C₂⁴	1	8	yes	complemented
335	#1799	C₂⁴	1	8	yes	complemented
336	#1792	C₂⁴	1	16	yes	complemented
337	#1783	C₂⁴	1	8	yes	—
338	#1781	C₂⁴	1	8	yes	—
339	#1781	C₂⁴	1	8	yes	—
340	C₄×#100	C₂⁴	1	8	yes	complemented
341	C₄×#99	C₂⁴	1	8	yes	complemented
342	C₄×#99	C₂⁴	1	8	yes	complemented
343	#1393	C₂⁴	1	32	yes	complemented
344	C₂⁶	C₂²×D₄	1	1	yes	characteristic
345	C₂⁶	C₂²×D₄	1	1	yes	characteristic
346	C₂⁶	C₂²×D₄	1	2	yes	—
347	C₂⁶	C₂²×D₄	1	2	yes	—
348	C₂⁶	C₂²×D₄	1	2	yes	—
349	C₂⁶	C₂²×D₄	1	4	yes	—
350	C₂⁶	C₂²×D₄	1	4	yes	—
351	C₂⁶	C₂²×D₄	1	4	yes	—
352	C₂×H(5,𝔽₂)	C₂⁵	1	4	yes	—
353	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
354	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
355	C₂³×D₄	C₂²×D₄	1	2	yes	—
356	C₂³×D₄	C₂²×D₄	1	2	yes	—
357	C₂³×D₄	C₂²×D₄	1	4	yes	—
358	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
359	C₂³×D₄	C₂²×D₄	1	2	yes	—
360	C₂³×D₄	C₂²×D₄	1	2	yes	—
361	C₂³×D₄	C₂²×D₄	1	8	yes	—
362	C₂³×D₄	C₂²×D₄	1	8	yes	—
363	C₂³×D₄	C₂⁵	1	2	yes	—
364	C₂³×D₄	C₂⁵	1	1	yes	characteristic
365	C₂⁴×C₄	#120	1	1	yes	characteristic
366	C₂⁴×C₄	#120	1	1	yes	characteristic
367	C₂⁴×C₄	#120	1	1	yes	characteristic
368	C₂⁴×C₄	#120	1	1	yes	characteristic
369	C₂⁴×C₄	#120	1	1	yes	characteristic
370	C₂⁴×C₄	#120	1	4	yes	—
371	C₂⁴×C₄	#120	1	1	yes	characteristic
372	C₂⁴×C₄	#120	1	1	yes	characteristic
373	C₂⁴×C₄	#120	1	4	yes	—
374	C₂⁴×C₄	#120	1	1	yes	characteristic
375	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
376	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
377	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
378	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
379	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
380	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
381	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
382	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
383	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
384	C₂×#127	C₂²×D₄	1	8	yes	—
385	C₂×#127	C₂²×D₄	1	4	yes	—
386	C₂×#127	H(5,𝔽₂)	1	16	yes	—
387	C₂×#127	C₂⁵	1	4	yes	—
388	C₂×#123	C₂²×D₄	1	4	yes	—
389	C₂×#123	C₂²×D₄	1	8	yes	—
390	C₂×#123	C₂⁵	1	4	yes	—
391	C₂×#120	C₂²×D₄	1	4	yes	—
392	C₂×#120	C₂²×D₄	1	4	yes	—
393	C₂×#120	C₂²×D₄	1	4	yes	—
394	C₂×#120	C₂²×D₄	1	8	yes	—
395	C₂×#120	C₂²×D₄	1	8	yes	—
396	C₂×#120	C₂²×D₄	1	8	yes	—
397	C₂×#120	C₂⁵	1	4	yes	—
398	C₂×#120	C₂⁵	1	4	yes	—
399	C₂×#120	C₂⁵	1	4	yes	—
400	#518	C₂⁵	1	4	yes	—
401	C₂×C₄×D₄	#120	1	4	yes	—
402	C₂×C₄×D₄	#120	1	4	yes	—
403	C₂×C₄×D₄	#120	1	4	yes	—
404	C₂×C₄×D₄	#120	1	4	yes	—
405	C₂×C₄×D₄	#120	1	4	yes	—
406	C₂×C₄×D₄	#120	1	4	yes	—
407	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
408	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
409	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
410	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
411	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
412	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
413	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
414	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
415	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
416	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
417	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
418	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
419	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
420	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
421	C₂×C₄×D₄	C₂⁵	1	2	yes	—
422	C₂×C₄×D₄	C₂⁵	1	2	yes	—
423	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	#120	1	4	yes	—
426	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
427	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
428	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
429	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
431	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
432	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
433	C₂²×C₂²⋊C₄	#120	1	4	yes	—
434	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
435	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
436	C₂²×C₂²⋊C₄	#120	1	4	yes	—
437	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
438	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
439	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
440	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
441	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
442	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
443	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
444	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
445	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
446	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
447	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
448	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
449	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
450	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
451	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
452	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
453	C₂²×C₄²	#120	1	1	yes	characteristic
454	C₂²×C₄²	#120	1	1	yes	characteristic
455	C₂²×C₄²	#120	1	4	yes	—
456	C₂²×C₄²	C₂²×D₄	1	4	yes	—
457	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
458	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
459	C₂²×C₄²	C₂²×D₄	1	4	yes	—
460	C₂²×C₄²	C₂²×D₄	1	2	yes	—
461	C₂²×C₄²	C₂²×D₄	1	2	yes	—
462	C₂²×C₄²	C₂²×D₄	1	4	yes	—
463	C₂×#100	C₂⁵	1	8	yes	—
464	C₂×#99	C₂⁵	1	8	yes	—
465	C₂×#99	C₂⁵	1	8	yes	—
466	#390	C₂²×D₄	1	4	yes	—
467	#390	C₂²×D₄	1	8	yes	—
468	#390	C₂²×D₄	1	8	yes	—
469	#390	C₂²×D₄	1	8	yes	—
470	#390	C₂⁵	1	4	yes	—
471	#382	C₂²×D₄	1	8	yes	—
472	#382	C₂²×D₄	1	8	yes	—
473	#381	C₂²×D₄	1	8	yes	—
474	#381	C₂²×D₄	1	8	yes	—
475	#380	C₂²×D₄	1	8	yes	—
476	#380	C₂²×D₄	1	8	yes	—
477	#380	C₂²×D₄	1	8	yes	—
478	#380	C₂²×D₄	1	8	yes	—
479	#379	C₂²×D₄	1	8	yes	—
480	#379	C₂²×D₄	1	8	yes	—
481	#379	C₂²×D₄	1	8	yes	—
482	#379	C₂²×D₄	1	8	yes	—
483	#379	C₂²×D₄	1	8	yes	—
484	#379	C₂²×D₄	1	8	yes	—
485	#376	C₂²×D₄	1	8	yes	—
486	#376	C₂²×D₄	1	8	yes	—
487	C₂⁵	C₂×#120	1	1	yes	characteristic
488	C₂⁵	C₂×#120	1	1	yes	characteristic
489	C₂⁵	C₂×#120	1	1	yes	characteristic
490	C₂⁵	C₂×#120	1	2	yes	—
491	C₂⁵	C₂×#120	1	2	yes	—
492	C₂⁵	C₂³×D₄	1	2	yes	—
493	C₂⁵	C₂³×D₄	1	2	yes	—
494	C₂⁵	C₂³×D₄	1	1	yes	characteristic
495	C₂⁵	C₂³×D₄	1	1	yes	characteristic
496	C₂⁵	C₂³×D₄	1	4	yes	—
497	C₂⁵	C₂³×D₄	1	4	yes	—
498	C₂⁵	C₂³×D₄	1	4	yes	—
499	C₂²×D₄	C₂×#120	1	2	yes	—
500	C₂²×D₄	C₂×#120	1	2	yes	—
501	C₂²×D₄	C₂×#120	1	2	yes	—
502	C₂²×D₄	#535	1	8	yes	complemented
503	C₂²×D₄	C₂³×D₄	1	2	yes	—
504	C₂²×D₄	C₂³×D₄	1	4	yes	—
505	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
506	C₂²×D₄	C₂³×D₄	1	2	yes	—
507	C₂²×D₄	C₂³×D₄	1	2	yes	—
508	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
509	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
510	C₂²×D₄	C₂×H(5,𝔽₂)	1	8	yes	—
511	C₂²×D₄	C₂⁶	1	1	yes	characteristic
512	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
513	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
514	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
515	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
516	C₂³×C₄	B(4,𝔽₂)	1	4	yes	—
517	C₂³×C₄	C₂×#120	1	1	yes	characteristic
518	C₂³×C₄	C₂×#120	1	2	yes	—
519	C₂³×C₄	C₂×#120	1	1	yes	characteristic
520	C₂³×C₄	C₂×#120	1	1	yes	characteristic
521	C₂³×C₄	C₂×#120	1	4	yes	—
522	C₂³×C₄	C₂×#120	1	1	yes	characteristic
523	C₂³×C₄	C₂×#120	1	1	yes	characteristic
524	C₂³×C₄	C₂×#120	1	4	yes	—
525	C₂³×C₄	C₂×#120	1	1	yes	characteristic
526	C₂³×C₄	C₂×#120	1	1	yes	characteristic
527	C₂³×C₄	C₂×#120	1	4	yes	—
528	C₂³×C₄	C₂×#120	1	2	yes	—
529	C₂³×C₄	C₂×#120	1	2	yes	—
530	C₂³×C₄	C₂×#120	1	4	yes	—
531	C₂³×C₄	C₂×#120	1	4	yes	—
532	C₂³×C₄	C₂×#120	1	2	yes	—
533	C₂³×C₄	C₂×#120	1	2	yes	—
534	C₂³×C₄	C₂×#120	1	4	yes	—
535	C₂³×C₄	C₂×#120	1	4	yes	—
536	C₂³×C₄	C₂×#120	1	1	yes	characteristic
537	C₂³×C₄	C₂×#120	1	1	yes	characteristic
538	C₂³×C₄	C₂×#120	1	4	yes	—
539	C₂³×C₄	C₂³×D₄	1	2	yes	—
540	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
541	C₂³×C₄	C₂³×D₄	1	4	yes	—
542	C₂³×C₄	C₂³×D₄	1	2	yes	—
543	C₂³×C₄	C₂³×D₄	1	2	yes	—
544	C₂³×C₄	C₂³×D₄	1	2	yes	—
545	C₂³×C₄	C₂³×D₄	1	2	yes	—
546	#127	#535	1	16	yes	complemented
547	#127	C₂×H(5,𝔽₂)	1	16	yes	—
548	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
549	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
550	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
551	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
552	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
553	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
561	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
564	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
565	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
566	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
567	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
571	C₂×C₄²	C₂×#120	1	2	yes	—
572	C₂×C₄²	C₂×#120	1	4	yes	—
573	C₂×C₄²	C₂×#120	1	4	yes	—
574	C₂×C₄²	C₂×#120	1	2	yes	—
575	C₂×C₄²	#535	1	8	yes	complemented
576	C₂×C₄²	C₂³×D₄	1	2	yes	—
577	C₂×C₄²	C₂³×D₄	1	2	yes	—
578	C₂×C₄²	C₂³×D₄	1	4	yes	—
579	C₂×C₄²	C₂³×D₄	1	4	yes	—
580	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
581	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
582	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
583	C₂⁴	C₂²×#120	1	2	yes	—
584	C₂⁴	C₂²×#120	1	1	yes	characteristic
585	C₂⁴	C₂²×#120	1	2	yes	—
586	C₂⁴	C₂²×#120	1	2	yes	—
587	C₂⁴	C₂²×#120	1	1	yes	characteristic
588	C₂⁴	C₂²×#120	1	1	yes	characteristic
589	C₂⁴	#3484	1	4	yes	—
590	C₂⁴	#3484	1	4	yes	—
591	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
592	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
593	C₂×D₄	C₂×#535	1	4	yes	—
594	C₂×D₄	C₂×#535	1	8	yes	complemented
595	C₂×D₄	#3484	1	4	yes	—
596	C₂×D₄	#3484	1	4	yes	—
597	C₂×D₄	C₂²×H(5,𝔽₂)	1	4	yes	—
598	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
599	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
600	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
601	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
602	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
603	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
604	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
605	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
606	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
607	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
608	C₂²×C₄	C₂²×#120	1	2	yes	—
609	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
610	C₂²×C₄	C₂²×#120	1	2	yes	—
611	C₂²×C₄	C₂²×#120	1	2	yes	—
612	C₂²×C₄	C₂²×#120	1	2	yes	—
613	C₂²×C₄	C₂²×#120	1	2	yes	—
614	C₂²×C₄	C₂²×#120	1	2	yes	—
615	C₂²×C₄	C₂²×#120	1	2	yes	—
616	C₂²×C₄	C₂²×#120	1	2	yes	—
617	C₂²×C₄	C₂²×#120	1	2	yes	—
618	C₂²×C₄	C₂×#535	1	4	yes	—
619	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
620	C₄²	C₂×#535	1	8	yes	complemented
621	C₂³	#33551	1	4	yes	—
622	C₂³	#33553	1	4	yes	—
623	C₂³	#35222	1	2	yes	—
624	C₂³	#35222	1	2	yes	—
625	C₂³	#35222	1	2	yes	—
626	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
627	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
628	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
629	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
630	C₂³	#60398	1	2	yes	—
631	C₂³	C₂³×#120	1	1	yes	characteristic
632	C₂³	C₂×#3484	1	2	yes	—
633	C₂³	C₂×#3484	1	2	yes	—
634	C₂×C₄	#35222	1	2	yes	—
635	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
636	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
637	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
638	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
639	C₂×C₄	C₂²×#535	1	2	yes	—
640	C₂²	#6487644	1	2	yes	—
641	C₂²	#6487644	1	2	yes	—
642	C₂²	C₂×#33551	1	4	yes	—
643	C₂²	C₂×#33551	1	2	yes	—
644	C₂²	C₂×#33553	1	4	yes	—
645	C₂²	C₂×#33553	1	2	yes	—
646	C₂²	C₂×#35222	1	1	yes	characteristic
647	C₂²	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
648	C₂²	C₂×#60398	1	1	yes	characteristic
649	C₂	C₂²×#33551	1	1	yes	characteristic
650	C₂	#72234533	1	4	yes	direct product factor
651	C₂	C₂²×#33553	1	1	yes	characteristic
652	C₂	C₂×#6487644	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂²×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂⁶
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂³×C₄×D₄ ◁ G
LECS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#496330	C₂	semidirect
2. C₂×#508063	C₂	semidirect
3. C₂×#508062	C₂	semidirect
4. C₂×#503206	C₂	semidirect
5. C₂×#503468	C₂	semidirect
6. C₂×#500781	C₂	semidirect
7. C₂×#496333	C₂	semidirect
8. C₂×#6491103	C₂	semidirect
9. C₂×#6491100	C₂	semidirect
10. C₂×#511776	C₂	semidirect
11. C₂×#493962	C₂	semidirect
12. C₂²×#52031	C₂	semidirect
13. #72234533	C₂	direct (N × H)
14. C₂×#6453841	C₂	semidirect
15. C₂×#511771	C₂	semidirect
17. C₂×#62773	C₂²	semidirect
21. C₂×#52031	C₂²	semidirect
27. C₂²×#2200	C₂²	semidirect
28. C₂²×#2196	C₂²	semidirect
29. C₂×#32928	C₂²	semidirect
30. C₂×#32926	C₂²	semidirect
31. #6491103	C₂²	semidirect
32. #6491100	C₂²	semidirect
33. #6453841	C₂²	semidirect
34. C₂×#25949	C₂²	semidirect
35. C₂×#25947	C₂²	semidirect
36. C₂×#24316	C₂²	semidirect
37. C₂×#25773	C₂²	semidirect
38. C₂×#25771	C₂²	semidirect
39. C₂×#24226	C₂²	semidirect
40. C₂×#24018	C₂²	semidirect
41. C₂×#23901	C₂²	semidirect
44. C₂×#23900	C₂²	semidirect
46. C₂×#21473	C₂²	semidirect
47. C₂×#20726	C₂²	semidirect
48. C₂×#20722	C₂²	semidirect
49. C₂×#20722	C₂²	semidirect
50. #511776	C₂²	semidirect
51. #511771	C₂²	semidirect
52. #508063	C₂²	semidirect
53. #508062	C₂²	semidirect
54. #503468	C₂²	semidirect
55. #503206	C₂²	semidirect
56. #500781	C₂²	semidirect
57. C₂×#13420	C₂²	semidirect
58. C₂×#13419	C₂²	semidirect
59. C₂×#13344	C₂²	semidirect
60. C₂×#13343	C₂²	semidirect
61. #496333	C₂²	semidirect
62. #496330	C₂²	semidirect
63. C₂×#13222	C₂²	semidirect
64. C₂×#13221	C₂²	semidirect
65. C₂×#13219	C₂²	semidirect
66. C₂×#13218	C₂²	semidirect
67. #493962	C₂²	semidirect
68. C₂×#12856	C₂²	semidirect
69. C₂×#12799	C₂²	semidirect
70. C₂×#12762	C₂²	semidirect
71. C₂×#12759	C₂²	semidirect
73. C₂×#12688	C₂²	semidirect
76. C₂×#12687	C₂²	semidirect
77. C₂×#12628	C₂²	semidirect
78. C₂⁵×D₄	D₄	semidirect
79. #62773	C₂³	semidirect
80. C₂×#3501	C₂³	semidirect
81. C₂×#3496	C₂³	semidirect
92. C₂×C₄×H(5,𝔽₂)	C₂³	semidirect
93. C₂³×C₄×D₄	D₄	semidirect
95. C₂⁴×C₂²⋊C₄	D₄	semidirect
96. C₂²×#458	C₂³	semidirect
99. C₂²×B(4,𝔽₂)	C₂³	semidirect
107. C₂×#2534	D₄	semidirect
108. C₂×#2534	D₄	semidirect
109. C₂×#2534	D₄	semidirect
113. C₂×#2408	D₄	semidirect
114. C₂×#2408	D₄	semidirect
115. C₂×#2408	D₄	semidirect
119. C₂×#2328	D₄	semidirect
120. C₂×#2328	D₄	semidirect
121. C₂×#2328	D₄	semidirect
125. C₂²×#390	D₄	semidirect
127. C₂²×#382	D₄	semidirect
128. C₂²×#381	D₄	semidirect
129. C₂²×#380	D₄	semidirect
130. C₂²×#380	D₄	semidirect
131. C₂²×#379	D₄	semidirect
132. C₂²×#379	D₄	semidirect
133. C₂²×#379	D₄	semidirect
134. C₂²×#376	D₄	semidirect
135. C₂×#2200	C₂³	semidirect
136. C₂×#2196	C₂³	semidirect
138. C₂²×#352	C₂³	semidirect
141. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
142. #32928	C₂³	semidirect
143. #32926	C₂³	semidirect
144. #25949	C₂³	semidirect
145. #25947	C₂³	semidirect
146. #25773	C₂³	semidirect
147. #25771	C₂³	semidirect
148. #24316	C₂³	semidirect
149. #24226	C₂³	semidirect
150. #24018	C₂³	semidirect
152. #23901	C₂³	semidirect
155. #23900	C₂³	semidirect
156. #21473	C₂³	semidirect
157. C₂×#1890	C₂³	semidirect
160. C₂×#1889	C₂³	semidirect
162. C₂×#1856	C₂³	semidirect
163. #20726	C₂³	semidirect
164. #20722	C₂³	semidirect
165. #20722	C₂³	semidirect
166. C₂×#1800	C₂³	semidirect
167. C₂×#1799	C₂³	semidirect
168. C₂×#1799	C₂³	semidirect
169. C₂×#1792	C₂³	semidirect
173. C₂×C₄×#100	C₂³	semidirect
174. C₂×C₄×#99	C₂³	semidirect
175. C₂×C₄×#99	C₂³	semidirect
176. #13420	C₂³	semidirect
177. #13419	C₂³	semidirect
178. #13344	C₂³	semidirect
179. #13343	C₂³	semidirect
180. #13222	C₂³	semidirect
181. #13221	C₂³	semidirect
182. #13219	C₂³	semidirect
183. #13218	C₂³	semidirect
184. #12856	C₂³	semidirect
185. #12799	C₂³	semidirect
186. #12762	C₂³	semidirect
187. #12759	C₂³	semidirect
189. #12688	C₂³	semidirect
192. #12687	C₂³	semidirect
193. #12628	C₂³	semidirect
194. C₂×#1393	C₂³	semidirect
202. C₂⁴×D₄	C₂×D₄	semidirect
208. #3501	C₂⁴	semidirect
209. #3496	C₂⁴	semidirect
232. C₄×H(5,𝔽₂)	C₂⁴	semidirect
245. C₂²×C₄×D₄	C₂×D₄	semidirect
259. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
263. C₂×#458	C₂⁴	semidirect
266. C₂×B(4,𝔽₂)	C₂⁴	semidirect
275. #2534	C₂×D₄	semidirect
276. #2534	C₂×D₄	semidirect
281. #2408	C₂×D₄	semidirect
282. #2408	C₂×D₄	semidirect
287. #2328	C₂×D₄	semidirect
288. #2328	C₂×D₄	semidirect
295. C₂×#390	C₂×D₄	semidirect
300. C₂×#382	C₂×D₄	semidirect
303. C₂×#381	C₂×D₄	semidirect
308. C₂×#380	C₂×D₄	semidirect
309. C₂×#380	C₂×D₄	semidirect
316. C₂×#379	C₂×D₄	semidirect
317. C₂×#379	C₂×D₄	semidirect
318. C₂×#379	C₂×D₄	semidirect
321. C₂×#376	C₂×D₄	semidirect
323. C₂×#352	C₂⁴	semidirect
326. C₂×AΣL(1,𝔽₁₆)	C₂⁴	semidirect
327. #1890	C₂⁴	semidirect
330. #1889	C₂⁴	semidirect
332. #1856	C₂⁴	semidirect
333. #1800	C₂⁴	semidirect
334. #1799	C₂⁴	semidirect
335. #1799	C₂⁴	semidirect
336. #1792	C₂⁴	semidirect
340. C₄×#100	C₂⁴	semidirect
341. C₄×#99	C₂⁴	semidirect
342. C₄×#99	C₂⁴	semidirect
343. #1393	C₂⁴	semidirect
502. C₂²×D₄	#535	semidirect
546. #127	#535	semidirect
575. C₂×C₄²	#535	semidirect
594. C₂×D₄	C₂×#535	semidirect
620. C₄²	C₂×#535	semidirect
650. C₂	#72234533	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×#496330	2
C₂×#508063	2
C₂×#508062	2
C₂×#503206	2
C₂×#503468	2
C₂×#500781	2
C₂×#496333	2
C₂×#6491103	2
C₂×#6491100	2
C₂×#511776	2
C₂×#493962	2
C₂²×#52031	2
#72234533	2
C₂×#6453841	2
C₂×#511771	2

Subgroups — C2×#72234533 #72260783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72234533 #72260783