Subgroups — C₂×#72216587 #72275378

Order 2048.

At least 12362 conjugacy classes of subgroups; only the 1648 normal subgroups are shown.

The subgroup lattice has 688 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×#115995	C₂	1	2	yes	maximal, complemented
2	C₂×#647670	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#359501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#6470225	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#115204	C₂	1	2	yes	maximal, complemented
6	C₂×#201664	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#6393523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#106654	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#394058	C₂	1	2	yes	maximal, complemented
10	C₂²×#23900	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#115690	C₂	1	2	yes	maximal, complemented
12	#72216587	C₂	1	16	yes	maximal, direct product factor
13	C₂²×#3484	C₂²	1	1	yes	characteristic
14	C₂⁴×#120	C₂²	1	1	yes	characteristic
15	C₂⁴×#120	C₂²	1	1	yes	characteristic, complemented
16	C₂²×#2846	C₂²	1	2	yes	—
17	C₂×#34980	C₂²	1	2	yes	—
18	C₂²×#2403	C₂²	1	1	yes	characteristic
19	C₂×#34171	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	#6470225	C₂²	1	8	yes	complemented
22	C₂×#23900	C₂²	1	8	yes	complemented
23	#6393523	C₂²	1	8	yes	complemented
24	C₂×#21746	C₂²	1	2	yes	—
25	C₂×#21746	C₂²	1	2	yes	—
26	C₂²×#1898	C₂²	1	2	yes	—
27	C₂²×#1898	C₂²	1	2	yes	—
28	C₂²×#1781	C₂²	1	1	yes	characteristic
29	C₂²×#1781	C₂²	1	1	yes	characteristic
30	C₂²×#1781	C₂²	1	2	yes	complemented
31	#647670	C₂²	1	8	yes	complemented
32	C₂×#14679	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14679	C₂²	1	2	yes	complemented
34	C₂×#13877	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13867	C₂²	1	1	yes	characteristic, complemented
36	#394058	C₂²	1	16	yes	complemented
37	#359501	C₂²	1	8	yes	complemented
38	C₂×#10735	C₂²	1	2	yes	complemented
39	C₂×#10735	C₂²	1	2	yes	complemented
40	#201664	C₂²	1	8	yes	complemented
41	C₂×#8101	C₂²	1	2	yes	complemented
42	C₂×#8101	C₂²	1	2	yes	complemented
43	#115995	C₂²	1	16	yes	complemented
44	#115690	C₂²	1	16	yes	complemented
45	#115204	C₂²	1	16	yes	complemented
46	#106654	C₂²	1	8	yes	complemented
47	C₂⁸	C₂³	1	1	yes	characteristic
48	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
49	C₂⁵×D₄	C₂³	1	1	yes	characteristic
50	C₂⁵×D₄	C₂³	1	1	yes	characteristic
51	C₂×#3484	D₄	1	4	yes	complemented
52	C₂×#3484	C₂³	1	4	yes	—
53	C₂²×#534	D₄	1	2	yes	complemented
54	C₂³×#120	D₄	1	2	yes	complemented
55	C₂³×#120	D₄	1	2	yes	complemented
56	C₂³×#120	D₄	1	4	yes	complemented
57	C₂³×#120	D₄	1	1	yes	characteristic, complemented
58	C₂³×#120	D₄	1	1	yes	characteristic, complemented
59	C₂³×#120	C₂³	1	4	yes	—
60	C₂³×#120	C₂³	1	2	yes	—
61	C₂³×#120	C₂³	1	4	yes	complemented
62	C₂²×#518	D₄	1	1	yes	characteristic, complemented
63	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
64	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
65	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
66	C₂³×#99	D₄	1	4	yes	complemented
67	C₂³×#99	D₄	1	2	yes	complemented
68	C₂³×#99	D₄	1	2	yes	complemented
69	C₂×#2846	C₂³	1	8	yes	—
70	#34980	C₂³	1	8	yes	—
71	C₂×#2403	D₄	1	4	yes	complemented
72	C₂×#2403	C₂³	1	4	yes	—
73	#34171	C₂³	1	4	yes	—
74	C₂×D₄×C₂²⋊C₄	D₄	1	4	yes	complemented
75	C₂×D₄×C₂²⋊C₄	C₂³	1	4	yes	—
76	C₂²×#386	D₄	1	1	yes	characteristic, complemented
77	C₂²×#386	D₄	1	1	yes	characteristic, complemented
78	C₂²×#380	D₄	1	1	yes	characteristic, complemented
79	C₂²×#379	D₄	1	1	yes	characteristic, complemented
80	C₂²×#379	C₂³	1	2	yes	—
81	C₂²×#379	C₂³	1	1	yes	characteristic
82	C₂²×#379	C₂³	1	1	yes	characteristic
83	C₂²×#379	C₂³	1	2	yes	—
84	C₂²×#379	C₂³	1	2	yes	—
85	C₂²×C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
86	#21746	C₂³	1	8	yes	—
87	#21746	C₂³	1	8	yes	—
88	C₂×#1898	D₄	1	8	yes	complemented
89	C₂×#1898	C₂³	1	8	yes	—
90	C₂×#1898	C₂³	1	8	yes	—
91	C₂×#1781	D₄	1	2	yes	complemented
92	C₂×#1781	D₄	1	2	yes	complemented
93	C₂×#1781	D₄	1	4	yes	complemented
94	C₂×#1781	D₄	1	4	yes	complemented
95	C₂×#1781	C₂³	1	4	yes	—
96	C₂×#1781	C₂³	1	4	yes	—
97	C₂×#1781	C₂³	1	8	yes	complemented
98	C₂²×#342	D₄	1	4	yes	complemented
99	#14679	C₂³	1	4	yes	complemented
100	#14679	C₂³	1	8	yes	complemented
101	#13877	C₂³	1	4	yes	complemented
102	#13867	C₂³	1	4	yes	complemented
103	#10735	C₂³	1	8	yes	complemented
104	#10735	C₂³	1	8	yes	complemented
105	#8101	C₂³	1	8	yes	complemented
106	#8101	C₂³	1	8	yes	complemented
107	C₂⁷	C₂×D₄	1	1	yes	characteristic
108	C₂⁷	C₂×D₄	1	2	yes	—
109	C₂⁷	C₂×D₄	1	2	yes	—
110	C₂⁷	C₂×D₄	1	1	yes	characteristic
111	C₂⁷	C₂⁴	1	2	yes	—
112	C₂⁷	C₂⁴	1	1	yes	characteristic
113	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	complemented
114	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
115	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
116	C₂⁴×D₄	C₂×D₄	1	2	yes	—
117	C₂⁴×D₄	C₂×D₄	1	2	yes	—
118	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
121	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
122	C₂⁴×D₄	C₂×D₄	1	2	yes	—
123	C₂⁴×D₄	C₂×D₄	1	2	yes	—
124	C₂⁴×D₄	C₂×D₄	1	2	yes	—
125	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
126	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
127	C₂⁴×D₄	C₂×D₄	1	2	yes	—
128	C₂⁴×D₄	C₂×D₄	1	2	yes	—
129	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
130	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
131	C₂⁴×D₄	C₂×D₄	1	2	yes	—
132	C₂⁴×D₄	C₂×D₄	1	2	yes	—
133	C₂⁴×D₄	#41	1	2	yes	—
134	C₂⁴×D₄	#41	1	1	yes	characteristic
135	C₂⁴×D₄	#41	1	1	yes	characteristic
136	C₂⁴×D₄	#41	1	2	yes	—
137	C₂⁴×D₄	C₂⁴	1	2	yes	—
138	C₂⁴×D₄	C₂⁴	1	2	yes	—
139	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
140	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
141	C₂×#534	C₂×D₄	1	8	yes	complemented
142	C₂²×#120	C₂×D₄	1	4	yes	—
143	C₂²×#120	C₂×D₄	1	4	yes	—
144	C₂²×#120	C₂×D₄	1	4	yes	complemented
145	C₂²×#120	C₂×D₄	1	8	yes	complemented
146	C₂²×#120	C₂×D₄	1	8	yes	complemented
147	C₂²×#120	C₂×D₄	1	4	yes	complemented
148	C₂²×#120	#41	1	4	yes	—
149	C₂²×#120	C₂⁴	1	4	yes	—
150	C₂×#518	C₂×D₄	1	4	yes	complemented
151	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
152	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
153	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
154	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
155	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
156	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
157	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
158	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
159	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
160	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
161	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
162	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
163	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
164	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
165	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
166	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
167	C₂³×C₂²⋊C₄	#41	1	2	yes	—
168	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
169	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
170	C₂²×#99	C₂×D₄	1	8	yes	complemented
171	C₂²×#99	C₂×D₄	1	16	yes	complemented
172	C₂²×#99	C₂×D₄	1	8	yes	complemented
173	C₂×#386	C₂×D₄	1	4	yes	complemented
174	C₂×#386	C₂×D₄	1	4	yes	complemented
175	C₂×#380	C₂×D₄	1	4	yes	complemented
176	C₂×#379	C₂×D₄	1	4	yes	—
177	C₂×#379	C₂×D₄	1	4	yes	—
178	C₂×#379	C₂×D₄	1	2	yes	—
179	C₂×#379	C₂×D₄	1	2	yes	—
180	C₂×#379	C₂×D₄	1	4	yes	—
181	C₂×#379	C₂×D₄	1	4	yes	—
182	C₂×#379	C₂×D₄	1	4	yes	complemented
183	C₂×#379	C₂⁴	1	4	yes	—
184	C₂×#379	C₂⁴	1	2	yes	—
185	C₂×#379	C₂⁴	1	2	yes	—
186	C₂×#379	C₂⁴	1	4	yes	—
187	C₂×#379	C₂⁴	1	4	yes	—
188	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
189	#1781	C₂×D₄	1	8	yes	complemented
190	#1781	C₂×D₄	1	8	yes	complemented
191	C₂×#342	C₂×D₄	1	16	yes	complemented
192	C₂⁶	#120	1	1	yes	characteristic
193	C₂⁶	#120	1	1	yes	characteristic
194	C₂⁶	#120	1	2	yes	—
195	C₂⁶	#121	1	1	yes	characteristic
196	C₂⁶	#121	1	1	yes	characteristic
197	C₂⁶	#121	1	2	yes	—
198	C₂⁶	#121	1	2	yes	complemented
199	C₂⁶	#127	1	1	yes	characteristic
200	C₂⁶	#127	1	1	yes	characteristic
201	C₂⁶	#127	1	2	yes	—
202	C₂⁶	C₂²×D₄	1	1	yes	characteristic
203	C₂⁶	C₂²×D₄	1	1	yes	characteristic
204	C₂⁶	C₂²×D₄	1	1	yes	characteristic
205	C₂⁶	C₂²×D₄	1	2	yes	—
206	C₂⁶	C₂²×D₄	1	1	yes	characteristic
207	C₂⁶	C₂²×D₄	1	2	yes	—
208	C₂⁶	C₂²×D₄	1	4	yes	—
209	C₂⁶	C₂²×D₄	1	2	yes	—
210	C₂⁶	C₂²×D₄	1	1	yes	characteristic
211	C₂⁶	C₂²×D₄	1	1	yes	characteristic
212	C₂⁶	C₂²×D₄	1	1	yes	characteristic
213	C₂⁶	C₂²×D₄	1	1	yes	characteristic
214	C₂⁶	C₂²×D₄	1	1	yes	characteristic
215	C₂⁶	C₂²×D₄	1	2	yes	—
216	C₂⁶	C₂²×D₄	1	1	yes	characteristic
217	C₂⁶	C₂²×D₄	1	1	yes	characteristic
218	C₂⁶	C₂²×D₄	1	1	yes	characteristic
219	C₂⁶	C₂×#41	1	2	yes	—
220	C₂⁶	C₂×#41	1	1	yes	characteristic
221	C₂⁶	C₂×#41	1	1	yes	characteristic
222	C₂⁶	C₂×#41	1	2	yes	—
223	C₂⁶	H(5,𝔽₂)	1	2	yes	—
224	C₂⁶	H(5,𝔽₂)	1	2	yes	—
225	C₂⁶	H(5,𝔽₂)	1	2	yes	—
226	C₂⁶	H(5,𝔽₂)	1	2	yes	—
227	C₂⁶	C₂⁵	1	1	yes	characteristic
228	C₂³×D₄	#120	1	2	yes	—
229	C₂³×D₄	#120	1	2	yes	—
230	C₂³×D₄	#120	1	2	yes	—
231	C₂³×D₄	#120	1	2	yes	—
232	C₂³×D₄	#120	1	1	yes	characteristic
233	C₂³×D₄	#120	1	1	yes	characteristic
234	C₂³×D₄	#120	1	1	yes	characteristic
235	C₂³×D₄	#120	1	1	yes	characteristic
236	C₂³×D₄	#120	1	1	yes	characteristic
237	C₂³×D₄	#120	1	2	yes	—
238	C₂³×D₄	#120	1	2	yes	—
239	C₂³×D₄	#120	1	2	yes	—
240	C₂³×D₄	#120	1	2	yes	—
241	C₂³×D₄	#120	1	1	yes	characteristic
242	C₂³×D₄	#120	1	1	yes	characteristic
243	C₂³×D₄	#120	1	1	yes	characteristic
244	C₂³×D₄	#120	1	2	yes	—
245	C₂³×D₄	#120	1	2	yes	—
246	C₂³×D₄	#120	1	2	yes	—
247	C₂³×D₄	#120	1	2	yes	—
248	C₂³×D₄	#120	1	2	yes	—
249	C₂³×D₄	#120	1	2	yes	—
250	C₂³×D₄	#120	1	2	yes	—
251	C₂³×D₄	#120	1	2	yes	—
252	C₂³×D₄	#121	1	2	yes	—
253	C₂³×D₄	#121	1	2	yes	—
254	C₂³×D₄	#121	1	2	yes	—
255	C₂³×D₄	#121	1	2	yes	—
256	C₂³×D₄	#121	1	1	yes	characteristic
257	C₂³×D₄	#121	1	1	yes	characteristic
258	C₂³×D₄	#121	1	2	yes	—
259	C₂³×D₄	#121	1	1	yes	characteristic
260	C₂³×D₄	#121	1	1	yes	characteristic
261	C₂³×D₄	#121	1	2	yes	—
262	C₂³×D₄	#121	1	1	yes	characteristic
263	C₂³×D₄	#121	1	1	yes	characteristic
264	C₂³×D₄	#121	1	2	yes	—
265	C₂³×D₄	#121	1	1	yes	characteristic
266	C₂³×D₄	#121	1	1	yes	characteristic
267	C₂³×D₄	#121	1	2	yes	—
268	C₂³×D₄	#121	1	2	yes	—
269	C₂³×D₄	#121	1	2	yes	—
270	C₂³×D₄	#121	1	2	yes	—
271	C₂³×D₄	#121	1	2	yes	—
272	C₂³×D₄	#121	1	2	yes	—
273	C₂³×D₄	#121	1	2	yes	—
274	C₂³×D₄	#121	1	2	yes	—
275	C₂³×D₄	#121	1	2	yes	—
276	C₂³×D₄	#121	1	4	yes	complemented
277	C₂³×D₄	#121	1	4	yes	complemented
278	C₂³×D₄	#121	1	4	yes	complemented
279	C₂³×D₄	#127	1	2	yes	—
280	C₂³×D₄	#127	1	2	yes	—
281	C₂³×D₄	#127	1	2	yes	—
282	C₂³×D₄	#127	1	2	yes	—
283	C₂³×D₄	C₂²×D₄	1	2	yes	—
284	C₂³×D₄	C₂²×D₄	1	2	yes	—
285	C₂³×D₄	C₂²×D₄	1	2	yes	—
286	C₂³×D₄	C₂²×D₄	1	2	yes	—
287	C₂³×D₄	C₂²×D₄	1	2	yes	—
288	C₂³×D₄	C₂²×D₄	1	2	yes	—
289	C₂³×D₄	C₂²×D₄	1	4	yes	—
290	C₂³×D₄	C₂²×D₄	1	4	yes	—
291	C₂³×D₄	C₂²×D₄	1	2	yes	—
292	C₂³×D₄	C₂²×D₄	1	2	yes	—
293	C₂³×D₄	C₂²×D₄	1	2	yes	—
294	C₂³×D₄	C₂²×D₄	1	2	yes	—
295	C₂³×D₄	C₂×#41	1	2	yes	—
296	C₂³×D₄	C₂×#41	1	2	yes	—
297	C₂³×D₄	C₂×#41	1	4	yes	—
298	C₂⁴×C₄	#120	1	1	yes	characteristic
299	C₂⁴×C₄	#120	1	1	yes	characteristic
300	C₂⁴×C₄	#120	1	2	yes	—
301	C₂⁴×C₄	#121	1	1	yes	characteristic
302	C₂⁴×C₄	#121	1	1	yes	characteristic
303	C₂⁴×C₄	#121	1	2	yes	—
304	C₂⁴×C₄	#121	1	2	yes	complemented
305	C₂⁴×C₄	#121	1	2	yes	complemented
306	C₂⁴×C₄	#121	1	2	yes	complemented
307	C₂⁴×C₄	#127	1	1	yes	characteristic
308	C₂⁴×C₄	#127	1	1	yes	characteristic
309	C₂⁴×C₄	#127	1	2	yes	—
310	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
311	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
312	C₂²×C₂²⋊C₄	#120	1	2	yes	—
313	C₂²×C₂²⋊C₄	#120	1	2	yes	—
314	C₂²×C₂²⋊C₄	#120	1	8	yes	—
315	C₂²×C₂²⋊C₄	#120	1	2	yes	—
316	C₂²×C₂²⋊C₄	#120	1	2	yes	—
317	C₂²×C₂²⋊C₄	#121	1	4	yes	complemented
318	C₂²×C₂²⋊C₄	#121	1	4	yes	complemented
319	C₂²×C₂²⋊C₄	#121	1	4	yes	complemented
320	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
321	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
322	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
323	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
324	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
325	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
326	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
327	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
328	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
329	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
330	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
331	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
332	C₂²×C₂²⋊C₄	C₂×#41	1	4	yes	—
333	#379	C₂²×D₄	1	8	yes	—
334	C₂⁵	#392	1	1	yes	characteristic
335	C₂⁵	#392	1	1	yes	characteristic
336	C₂⁵	#392	1	1	yes	characteristic
337	C₂⁵	#392	1	2	yes	—
338	C₂⁵	#392	1	1	yes	characteristic
339	C₂⁵	#392	1	2	yes	—
340	C₂⁵	#392	1	2	yes	—
341	C₂⁵	#392	1	2	yes	—
342	C₂⁵	#392	1	2	yes	—
343	C₂⁵	#392	1	2	yes	—
344	C₂⁵	C₂×#120	1	1	yes	characteristic
345	C₂⁵	C₂×#120	1	2	yes	—
346	C₂⁵	C₂×#120	1	1	yes	characteristic
347	C₂⁵	C₂×#120	1	1	yes	characteristic
348	C₂⁵	C₂×#120	1	1	yes	characteristic
349	C₂⁵	C₂×#120	1	1	yes	characteristic
350	C₂⁵	C₂×#120	1	1	yes	characteristic
351	C₂⁵	C₂×#120	1	2	yes	—
352	C₂⁵	C₂×#120	1	1	yes	characteristic
353	C₂⁵	C₂×#120	1	1	yes	characteristic
354	C₂⁵	C₂×#120	1	1	yes	characteristic
355	C₂⁵	C₂×#120	1	2	yes	—
356	C₂⁵	C₂×#120	1	1	yes	characteristic
357	C₂⁵	C₂×#120	1	1	yes	characteristic
358	C₂⁵	C₂×#120	1	1	yes	characteristic
359	C₂⁵	C₂×#120	1	1	yes	characteristic
360	C₂⁵	C₂×#120	1	1	yes	characteristic
361	C₂⁵	C₂×#121	1	1	yes	characteristic
362	C₂⁵	C₂×#121	1	2	yes	—
363	C₂⁵	C₂×#121	1	1	yes	characteristic
364	C₂⁵	C₂×#121	1	1	yes	characteristic
365	C₂⁵	C₂×#121	1	1	yes	characteristic
366	C₂⁵	C₂×#121	1	1	yes	characteristic
367	C₂⁵	C₂×#121	1	2	yes	—
368	C₂⁵	C₂×#121	1	1	yes	characteristic
369	C₂⁵	C₂×#121	1	2	yes	—
370	C₂⁵	C₂×#121	1	2	yes	—
371	C₂⁵	C₂×#121	1	1	yes	characteristic
372	C₂⁵	C₂×#121	1	2	yes	—
373	C₂⁵	C₂×#121	1	2	yes	—
374	C₂⁵	C₂×#121	1	1	yes	characteristic
375	C₂⁵	C₂×#121	1	1	yes	characteristic
376	C₂⁵	C₂×#121	1	1	yes	characteristic
377	C₂⁵	C₂×#121	1	1	yes	characteristic
378	C₂⁵	C₂×#121	1	1	yes	characteristic
379	C₂⁵	C₂×#121	1	4	yes	complemented
380	C₂⁵	#525	1	1	yes	characteristic
381	C₂⁵	#525	1	1	yes	characteristic
382	C₂⁵	#525	1	2	yes	—
383	C₂⁵	#525	1	2	yes	—
384	C₂⁵	#525	1	2	yes	—
385	C₂⁵	#525	1	2	yes	—
386	C₂⁵	#525	1	2	yes	—
387	C₂⁵	C₂×#127	1	1	yes	characteristic
388	C₂⁵	C₂×#127	1	1	yes	characteristic
389	C₂⁵	C₂×#127	1	2	yes	—
390	C₂⁵	C₂×#127	1	1	yes	characteristic
391	C₂⁵	C₂×#127	1	2	yes	—
392	C₂⁵	C₂×#127	1	1	yes	characteristic
393	C₂⁵	#534	1	1	yes	characteristic
394	C₂⁵	#534	1	1	yes	characteristic
395	C₂⁵	#534	1	2	yes	—
396	C₂⁵	#534	1	2	yes	—
397	C₂⁵	#534	1	2	yes	—
398	C₂⁵	#534	1	2	yes	—
399	C₂⁵	#534	1	2	yes	—
400	C₂⁵	#535	1	1	yes	characteristic
401	C₂⁵	#535	1	1	yes	characteristic
402	C₂⁵	#535	1	2	yes	—
403	C₂⁵	#538	1	2	yes	—
404	C₂⁵	#538	1	2	yes	—
405	C₂⁵	#538	1	2	yes	—
406	C₂⁵	#538	1	2	yes	—
407	C₂⁵	D₄²	1	2	yes	—
408	C₂⁵	D₄²	1	2	yes	—
409	C₂⁵	D₄²	1	2	yes	—
410	C₂⁵	D₄²	1	2	yes	—
411	C₂⁵	D₄²	1	2	yes	—
412	C₂⁵	D₄²	1	2	yes	—
413	C₂⁵	D₄²	1	2	yes	—
414	C₂⁵	D₄²	1	2	yes	—
415	C₂⁵	D₄²	1	2	yes	—
416	C₂⁵	D₄²	1	2	yes	—
417	C₂⁵	D₄²	1	2	yes	—
418	C₂⁵	D₄²	1	2	yes	—
419	C₂⁵	D₄²	1	2	yes	—
420	C₂⁵	D₄²	1	2	yes	—
421	C₂⁵	D₄²	1	2	yes	—
422	C₂⁵	D₄²	1	2	yes	—
423	C₂⁵	#546	1	2	yes	—
424	C₂⁵	#546	1	2	yes	—
425	C₂⁵	#546	1	2	yes	—
426	C₂⁵	#546	1	2	yes	—
427	C₂⁵	#546	1	2	yes	—
428	C₂⁵	#546	1	2	yes	—
429	C₂⁵	#546	1	2	yes	—
430	C₂⁵	#546	1	2	yes	—
431	C₂⁵	#546	1	2	yes	—
432	C₂⁵	#546	1	2	yes	—
433	C₂⁵	#546	1	2	yes	—
434	C₂⁵	#546	1	2	yes	—
435	C₂⁵	#546	1	2	yes	—
436	C₂⁵	#546	1	2	yes	—
437	C₂⁵	#546	1	2	yes	—
438	C₂⁵	#546	1	2	yes	—
439	C₂⁵	C₂³×D₄	1	1	yes	characteristic
440	C₂⁵	C₂³×D₄	1	1	yes	characteristic
441	C₂⁵	C₂³×D₄	1	1	yes	characteristic
442	C₂⁵	C₂³×D₄	1	2	yes	—
443	C₂⁵	C₂³×D₄	1	1	yes	characteristic
444	C₂⁵	C₂³×D₄	1	1	yes	characteristic
445	C₂⁵	C₂³×D₄	1	1	yes	characteristic
446	C₂⁵	C₂²×#41	1	2	yes	—
447	C₂⁵	C₂²×#41	1	1	yes	characteristic
448	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
449	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
450	C₂²×D₄	#392	1	2	yes	—
451	C₂²×D₄	#392	1	2	yes	—
452	C₂²×D₄	#392	1	2	yes	—
453	C₂²×D₄	#392	1	2	yes	—
454	C₂²×D₄	#392	1	2	yes	—
455	C₂²×D₄	#392	1	2	yes	—
456	C₂²×D₄	#392	1	2	yes	—
457	C₂²×D₄	#392	1	2	yes	—
458	C₂²×D₄	#392	1	2	yes	—
459	C₂²×D₄	#392	1	2	yes	—
460	C₂²×D₄	#392	1	2	yes	—
461	C₂²×D₄	#392	1	2	yes	—
462	C₂²×D₄	#392	1	2	yes	—
463	C₂²×D₄	#392	1	2	yes	—
464	C₂²×D₄	#392	1	2	yes	—
465	C₂²×D₄	#392	1	2	yes	—
466	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
467	C₂²×D₄	C₂×#120	1	2	yes	—
468	C₂²×D₄	C₂×#120	1	2	yes	—
469	C₂²×D₄	C₂×#120	1	2	yes	—
470	C₂²×D₄	C₂×#120	1	2	yes	—
471	C₂²×D₄	C₂×#120	1	2	yes	—
472	C₂²×D₄	C₂×#120	1	2	yes	—
473	C₂²×D₄	C₂×#120	1	2	yes	—
474	C₂²×D₄	C₂×#120	1	2	yes	—
475	C₂²×D₄	C₂×#121	1	2	yes	—
476	C₂²×D₄	C₂×#121	1	2	yes	—
477	C₂²×D₄	C₂×#121	1	2	yes	—
478	C₂²×D₄	C₂×#121	1	2	yes	—
479	C₂²×D₄	C₂×#121	1	2	yes	—
480	C₂²×D₄	C₂×#121	1	2	yes	—
481	C₂²×D₄	C₂×#121	1	2	yes	—
482	C₂²×D₄	C₂×#121	1	2	yes	—
483	C₂³×C₄	#392	1	1	yes	characteristic
484	C₂³×C₄	#392	1	1	yes	characteristic
485	C₂³×C₄	#392	1	1	yes	characteristic
486	C₂³×C₄	#392	1	2	yes	—
487	C₂³×C₄	#392	1	2	yes	—
488	C₂³×C₄	#392	1	2	yes	—
489	C₂³×C₄	#392	1	1	yes	characteristic
490	C₂³×C₄	#392	1	2	yes	—
491	C₂³×C₄	#392	1	2	yes	—
492	C₂³×C₄	#392	1	2	yes	—
493	C₂³×C₄	C₂×#120	1	2	yes	—
494	C₂³×C₄	C₂×#120	1	2	yes	—
495	C₂³×C₄	C₂×#121	1	2	yes	—
496	C₂³×C₄	C₂×#121	1	2	yes	—
497	C₂³×C₄	C₂×#121	1	4	yes	complemented
498	C₂³×C₄	C₂×#121	1	4	yes	complemented
499	C₂³×C₄	C₂×#121	1	4	yes	complemented
500	C₂³×C₄	C₂×#127	1	2	yes	—
501	C₂³×C₄	C₂×#127	1	2	yes	—
502	C₂×C₂²⋊C₄	B(4,𝔽₂)	1	8	yes	complemented
503	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
505	C₂⁴	#2021	1	4	yes	complemented
506	C₂⁴	C₂×#392	1	1	yes	characteristic
507	C₂⁴	C₂×#392	1	1	yes	characteristic
508	C₂⁴	C₂×#392	1	1	yes	characteristic
509	C₂⁴	C₂×#392	1	1	yes	characteristic
510	C₂⁴	C₂×#392	1	2	yes	—
511	C₂⁴	C₂×#392	1	2	yes	—
512	C₂⁴	C₂×#392	1	2	yes	—
513	C₂⁴	C₂×#392	1	1	yes	characteristic
514	C₂⁴	C₂×#392	1	1	yes	characteristic
515	C₂⁴	C₂×#392	1	1	yes	characteristic
516	C₂⁴	C₂×#392	1	2	yes	—
517	C₂⁴	C₂×#392	1	1	yes	characteristic
518	C₂⁴	#2403	1	1	yes	characteristic
519	C₂⁴	#2403	1	2	yes	—
520	C₂⁴	#2403	1	1	yes	characteristic
521	C₂⁴	#2403	1	2	yes	—
522	C₂⁴	#2403	1	1	yes	characteristic
523	C₂⁴	#2403	1	1	yes	characteristic
524	C₂⁴	#2404	1	1	yes	characteristic
525	C₂⁴	#2404	1	1	yes	characteristic
526	C₂⁴	#2404	1	2	yes	—
527	C₂⁴	#2404	1	1	yes	characteristic
528	C₂⁴	#2404	1	1	yes	characteristic
529	C₂⁴	#2404	1	2	yes	—
530	C₂⁴	#2410	1	2	yes	—
531	C₂⁴	#2410	1	2	yes	—
532	C₂⁴	#2410	1	2	yes	—
533	C₂⁴	#2410	1	2	yes	—
534	C₂⁴	#2410	1	2	yes	—
535	C₂⁴	#2410	1	2	yes	—
536	C₂⁴	#2410	1	2	yes	—
537	C₂⁴	#2410	1	2	yes	—
538	C₂⁴	#2410	1	2	yes	—
539	C₂⁴	#2410	1	2	yes	—
540	C₂⁴	#2410	1	2	yes	—
541	C₂⁴	#2410	1	2	yes	—
542	C₂⁴	#2410	1	2	yes	—
543	C₂⁴	#2410	1	2	yes	—
544	C₂⁴	#2410	1	2	yes	—
545	C₂⁴	#2410	1	2	yes	—
546	C₂⁴	#2424	1	2	yes	—
547	C₂⁴	#2424	1	2	yes	—
548	C₂⁴	#2424	1	2	yes	—
549	C₂⁴	#2424	1	2	yes	—
550	C₂⁴	#2424	1	2	yes	—
551	C₂⁴	#2424	1	2	yes	—
552	C₂⁴	#2424	1	2	yes	—
553	C₂⁴	#2424	1	2	yes	—
554	C₂⁴	#2424	1	2	yes	—
555	C₂⁴	#2424	1	2	yes	—
556	C₂⁴	#2424	1	2	yes	—
557	C₂⁴	#2424	1	2	yes	—
558	C₂⁴	#2424	1	2	yes	—
559	C₂⁴	#2424	1	2	yes	—
560	C₂⁴	#2424	1	2	yes	—
561	C₂⁴	#2424	1	2	yes	—
562	C₂⁴	#2433	1	1	yes	characteristic
563	C₂⁴	#2433	1	1	yes	characteristic
564	C₂⁴	#2433	1	2	yes	—
565	C₂⁴	#2433	1	1	yes	characteristic
566	C₂⁴	#2433	1	2	yes	—
567	C₂⁴	#2433	1	1	yes	characteristic
568	C₂⁴	#2539	1	1	yes	characteristic
569	C₂⁴	#2539	1	1	yes	characteristic
570	C₂⁴	#2539	1	1	yes	characteristic
571	C₂⁴	#2539	1	2	yes	—
572	C₂⁴	#2539	1	1	yes	characteristic
573	C₂⁴	#2539	1	2	yes	—
574	C₂⁴	#2617	1	1	yes	characteristic
575	C₂⁴	#2617	1	1	yes	characteristic
576	C₂⁴	#2617	1	1	yes	characteristic
577	C₂⁴	#2617	1	2	yes	—
578	C₂⁴	#2617	1	1	yes	characteristic
579	C₂⁴	#2617	1	2	yes	—
580	C₂⁴	#2847	1	1	yes	characteristic
581	C₂⁴	#2847	1	1	yes	characteristic
582	C₂⁴	#2847	1	2	yes	—
583	C₂⁴	#2847	1	1	yes	characteristic
584	C₂⁴	#2847	1	2	yes	—
585	C₂⁴	#2847	1	1	yes	characteristic
586	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
587	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
588	C₂⁴	#3026	1	4	yes	—
589	C₂⁴	#3027	1	4	yes	—
590	C₂⁴	C₂²×#120	1	1	yes	characteristic
591	C₂⁴	C₂²×#120	1	1	yes	characteristic
592	C₂⁴	C₂²×#120	1	1	yes	characteristic
593	C₂⁴	C₂²×#120	1	1	yes	characteristic
594	C₂⁴	C₂²×#121	1	2	yes	—
595	C₂⁴	C₂²×#121	1	1	yes	characteristic
596	C₂⁴	C₂²×#121	1	1	yes	characteristic
597	C₂⁴	C₂²×#121	1	1	yes	characteristic
598	C₂⁴	C₂×#525	1	1	yes	characteristic
599	C₂⁴	C₂×#525	1	2	yes	—
600	C₂⁴	C₂²×#127	1	1	yes	characteristic
601	C₂⁴	C₂×#534	1	1	yes	characteristic
602	C₂⁴	C₂×#534	1	2	yes	—
603	C₂⁴	C₂×#535	1	1	yes	characteristic
604	C₂⁴	C₂×#538	1	2	yes	—
605	C₂⁴	C₂×D₄²	1	2	yes	—
606	C₂⁴	C₂×D₄²	1	2	yes	—
607	C₂⁴	C₂×D₄²	1	2	yes	—
608	C₂⁴	C₂×D₄²	1	2	yes	—
609	C₂⁴	C₂×#546	1	2	yes	—
610	C₂⁴	C₂×#546	1	2	yes	—
611	C₂⁴	C₂×#546	1	2	yes	—
612	C₂⁴	C₂×#546	1	2	yes	—
613	C₂×D₄	#2021	1	8	yes	complemented
614	C₂×D₄	C₂×B(4,𝔽₂)	1	8	yes	—
615	C₂²×C₄	#2021	1	4	yes	complemented
616	C₂²×C₄	C₂×#392	1	2	yes	—
617	C₂²×C₄	C₂×#392	1	2	yes	—
618	C₂²×C₄	C₂×#392	1	2	yes	—
619	C₂²×C₄	C₂×#392	1	2	yes	—
620	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	8	yes	complemented
621	C₂³	#14716	1	1	yes	characteristic
622	C₂³	#14716	1	1	yes	characteristic
623	C₂³	#14716	1	2	yes	—
624	C₂³	#14716	1	2	yes	—
625	C₂³	#14716	1	2	yes	—
626	C₂³	#14716	1	1	yes	characteristic
627	C₂³	#14716	1	2	yes	—
628	C₂³	#14716	1	1	yes	characteristic
629	C₂³	#14716	1	1	yes	characteristic
630	C₂³	#14716	1	1	yes	characteristic
631	C₂³	#14716	1	1	yes	characteristic
632	C₂³	#14716	1	1	yes	characteristic
633	C₂³	C₂×#2021	1	2	yes	—
634	C₂³	C₂×#2021	1	2	yes	—
635	C₂³	C₂×#2021	1	4	yes	complemented
636	C₂³	#23444	1	2	yes	—
637	C₂³	#23444	1	2	yes	—
638	C₂³	#23900	1	2	yes	—
639	C₂³	#23900	1	2	yes	—
640	C₂³	#23904	1	2	yes	—
641	C₂³	#23904	1	2	yes	—
642	C₂³	#23996	1	4	yes	—
643	C₂³	#24404	1	8	yes	—
644	C₂³	#24404	1	8	yes	—
645	C₂³	#25771	1	4	yes	—
646	C₂³	#25771	1	4	yes	—
647	C₂³	#32926	1	4	yes	—
648	C₂³	#32926	1	4	yes	—
649	C₂³	C₂²×#392	1	1	yes	characteristic
650	C₂³	C₂×#2617	1	1	yes	characteristic
651	C₂³	C₂×#2403	1	1	yes	characteristic
652	C₂³	C₂×#2410	1	2	yes	—
653	C₂³	C₂×#2410	1	2	yes	—
654	C₂³	C₂×#2424	1	2	yes	—
655	C₂³	C₂×#2424	1	2	yes	—
656	C₂³	C₂×#2433	1	1	yes	characteristic
657	C₂³	C₂×#2404	1	1	yes	characteristic
658	C₂³	C₂×#2539	1	1	yes	characteristic
659	C₂³	C₂×#2847	1	1	yes	characteristic
660	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
661	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
662	C₂³	C₂×#3026	1	2	yes	—
663	C₂³	C₂×#3027	1	2	yes	—
664	C₂×C₄	C₂×#2021	1	4	yes	complemented
665	C₂²	#394174	1	2	yes	—
666	C₂²	#394174	1	2	yes	—
667	C₂²	#394174	1	2	yes	—
668	C₂²	#394174	1	2	yes	—
669	C₂²	#394267	1	2	yes	—
670	C₂²	#394267	1	4	yes	—
671	C₂²	#394267	1	2	yes	—
672	C₂²	#394273	1	2	yes	—
673	C₂²	#394273	1	2	yes	—
674	C₂²	C₂×#14716	1	1	yes	characteristic
675	C₂²	C₂²×#2021	1	1	yes	characteristic
676	C₂²	C₂×#23444	1	1	yes	characteristic
677	C₂²	C₂×#23900	1	1	yes	characteristic
678	C₂²	C₂×#23904	1	1	yes	characteristic
679	C₂²	C₂×#24404	1	4	yes	—
680	C₂²	C₂×#25771	1	2	yes	—
681	C₂²	C₂×#23996	1	2	yes	—
682	C₂²	C₂×#32926	1	2	yes	—
683	C₂	#72216587	1	4	yes	direct product factor
684	C₂	C₂×#394273	1	1	yes	characteristic
685	C₂	C₂×#394267	1	1	yes	characteristic
686	C₂	C₂×#394174	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	#14716
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#115995	C₂	semidirect
2. C₂×#647670	C₂	semidirect
3. C₂×#359501	C₂	semidirect
4. C₂×#6470225	C₂	semidirect
5. C₂×#115204	C₂	semidirect
6. C₂×#201664	C₂	semidirect
7. C₂×#6393523	C₂	semidirect
8. C₂×#106654	C₂	semidirect
9. C₂×#394058	C₂	semidirect
10. C₂²×#23900	C₂	semidirect
11. C₂×#115690	C₂	semidirect
12. #72216587	C₂	direct (N × H)
15. C₂⁴×#120	C₂²	semidirect
21. #6470225	C₂²	semidirect
22. C₂×#23900	C₂²	semidirect
23. #6393523	C₂²	semidirect
30. C₂²×#1781	C₂²	semidirect
31. #647670	C₂²	semidirect
32. C₂×#14679	C₂²	semidirect
33. C₂×#14679	C₂²	semidirect
34. C₂×#13877	C₂²	semidirect
35. C₂×#13867	C₂²	semidirect
36. #394058	C₂²	semidirect
37. #359501	C₂²	semidirect
38. C₂×#10735	C₂²	semidirect
39. C₂×#10735	C₂²	semidirect
40. #201664	C₂²	semidirect
41. C₂×#8101	C₂²	semidirect
42. C₂×#8101	C₂²	semidirect
43. #115995	C₂²	semidirect
44. #115690	C₂²	semidirect
45. #115204	C₂²	semidirect
46. #106654	C₂²	semidirect
48. C₂³×H(5,𝔽₂)	D₄	semidirect
51. C₂×#3484	D₄	semidirect
53. C₂²×#534	D₄	semidirect
54. C₂³×#120	D₄	semidirect
55. C₂³×#120	D₄	semidirect
56. C₂³×#120	D₄	semidirect
57. C₂³×#120	D₄	semidirect
58. C₂³×#120	D₄	semidirect
61. C₂³×#120	C₂³	semidirect
62. C₂²×#518	D₄	semidirect
63. C₂⁴×C₂²⋊C₄	D₄	semidirect
66. C₂³×#99	D₄	semidirect
67. C₂³×#99	D₄	semidirect
68. C₂³×#99	D₄	semidirect
71. C₂×#2403	D₄	semidirect
74. C₂×D₄×C₂²⋊C₄	D₄	semidirect
76. C₂²×#386	D₄	semidirect
77. C₂²×#386	D₄	semidirect
78. C₂²×#380	D₄	semidirect
79. C₂²×#379	D₄	semidirect
85. C₂²×C₄×C₂²⋊C₄	D₄	semidirect
88. C₂×#1898	D₄	semidirect
91. C₂×#1781	D₄	semidirect
92. C₂×#1781	D₄	semidirect
93. C₂×#1781	D₄	semidirect
94. C₂×#1781	D₄	semidirect
97. C₂×#1781	C₂³	semidirect
98. C₂²×#342	D₄	semidirect
99. #14679	C₂³	semidirect
100. #14679	C₂³	semidirect
101. #13877	C₂³	semidirect
102. #13867	C₂³	semidirect
103. #10735	C₂³	semidirect
104. #10735	C₂³	semidirect
105. #8101	C₂³	semidirect
106. #8101	C₂³	semidirect
113. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
141. C₂×#534	C₂×D₄	semidirect
144. C₂²×#120	C₂×D₄	semidirect
145. C₂²×#120	C₂×D₄	semidirect
146. C₂²×#120	C₂×D₄	semidirect
147. C₂²×#120	C₂×D₄	semidirect
150. C₂×#518	C₂×D₄	semidirect
166. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
170. C₂²×#99	C₂×D₄	semidirect
171. C₂²×#99	C₂×D₄	semidirect
172. C₂²×#99	C₂×D₄	semidirect
173. C₂×#386	C₂×D₄	semidirect
174. C₂×#386	C₂×D₄	semidirect
175. C₂×#380	C₂×D₄	semidirect
182. C₂×#379	C₂×D₄	semidirect
188. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
189. #1781	C₂×D₄	semidirect
190. #1781	C₂×D₄	semidirect
191. C₂×#342	C₂×D₄	semidirect
198. C₂⁶	#121	semidirect
276. C₂³×D₄	#121	semidirect
277. C₂³×D₄	#121	semidirect
278. C₂³×D₄	#121	semidirect
304. C₂⁴×C₄	#121	semidirect
305. C₂⁴×C₄	#121	semidirect
306. C₂⁴×C₄	#121	semidirect
317. C₂²×C₂²⋊C₄	#121	semidirect
318. C₂²×C₂²⋊C₄	#121	semidirect
319. C₂²×C₂²⋊C₄	#121	semidirect
379. C₂⁵	C₂×#121	semidirect
497. C₂³×C₄	C₂×#121	semidirect
498. C₂³×C₄	C₂×#121	semidirect
499. C₂³×C₄	C₂×#121	semidirect
502. C₂×C₂²⋊C₄	B(4,𝔽₂)	semidirect
505. C₂⁴	#2021	semidirect
613. C₂×D₄	#2021	semidirect
615. C₂²×C₄	#2021	semidirect
620. C₂²⋊C₄	C₂×B(4,𝔽₂)	semidirect
635. C₂³	C₂×#2021	semidirect
664. C₂×C₄	C₂×#2021	semidirect
683. C₂	#72216587	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×#115995	2
C₂×#647670	2
C₂×#359501	2
C₂×#6470225	2
C₂×#115204	2
C₂×#201664	2
C₂×#6393523	2
C₂×#106654	2
C₂×#394058	2
C₂²×#23900	2
C₂×#115690	2
#72216587	2

Subgroups — C2×#72216587 #72275378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72216587 #72275378