Subgroups — C₂×#72231756 #72278334

Order 2048.

At least 11324 conjugacy classes of subgroups; only the 1704 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×#494571	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#146605	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#7737956	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#147582	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#147820	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#498932	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#498909	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#147787	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#33553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#12755	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#394076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#147577	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#12711	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#23882	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#394022	C₂	1	1	yes	maximal, characteristic, complemented
16	#72231756	C₂	1	16	yes	maximal, direct product factor
17	C₂²×#3585	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#3537	C₂²	1	1	yes	characteristic
19	C₂²×#3484	C₂²	1	1	yes	characteristic
20	C₂²×#3027	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#3025	C₂²	1	1	yes	characteristic
22	C₂²×#3021	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#3021	C₂²	1	1	yes	characteristic, complemented
24	#7737956	C₂²	1	8	yes	complemented
25	C₂×#37297	C₂²	1	1	yes	characteristic
26	C₂×#37297	C₂²	1	1	yes	characteristic
27	C₂×#35527	C₂²	1	1	yes	characteristic
28	C₂×#35527	C₂²	1	1	yes	characteristic
29	C₂×#34152	C₂²	1	1	yes	characteristic
30	C₂×#33553	C₂²	1	8	yes	complemented
31	C₂²×#2134	C₂²	1	1	yes	characteristic, complemented
32	C₂²×#2134	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#2128	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#2128	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#2122	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#2122	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#2120	C₂²	1	1	yes	characteristic
38	C₂²×#2120	C₂²	1	1	yes	characteristic
39	C₂×#23882	C₂²	1	8	yes	complemented
40	C₂²×#1914	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#1910	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#1910	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#1891	C₂²	1	1	yes	characteristic
44	C₂²×#1795	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#1795	C₂²	1	1	yes	characteristic, complemented
46	C₂²×#1795	C₂²	1	1	yes	characteristic, complemented
47	C₂×#20615	C₂²	1	1	yes	characteristic, complemented
48	C₂×#20608	C₂²	1	1	yes	characteristic, complemented
49	#498932	C₂²	1	8	yes	complemented
50	#498909	C₂²	1	8	yes	complemented
51	#494571	C₂²	1	8	yes	complemented
52	C₂×#12755	C₂²	1	8	yes	complemented
53	C₂×#12711	C₂²	1	8	yes	complemented
54	C₂×#12585	C₂²	1	1	yes	characteristic, complemented
55	C₂×#12581	C₂²	1	1	yes	characteristic, complemented
56	C₂×#12573	C₂²	1	1	yes	characteristic, complemented
57	C₂×#12573	C₂²	1	1	yes	characteristic, complemented
58	#394076	C₂²	1	8	yes	complemented
59	#394022	C₂²	1	8	yes	complemented
60	C₂×#10751	C₂²	1	1	yes	characteristic, complemented
61	C₂×#10746	C₂²	1	1	yes	characteristic, complemented
62	#147820	C₂²	1	8	yes	complemented
63	#147787	C₂²	1	8	yes	complemented
64	#147582	C₂²	1	8	yes	complemented
65	#147577	C₂²	1	8	yes	complemented
66	#146605	C₂²	1	8	yes	complemented
67	C₂²×#585	C₂³	1	1	yes	characteristic
68	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
69	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
70	C₂×#3585	C₂³	1	4	yes	complemented
71	C₂²×#568	C₂³	1	1	yes	characteristic
72	C₂×#3484	D₄	1	4	yes	complemented
73	C₂×#3484	C₂³	1	4	yes	—
74	C₂×#3537	D₄	1	4	yes	—
75	C₂×#3537	C₂³	1	4	yes	—
76	C₂²×D₄²	D₄	1	2	yes	—
77	C₂²×#560	D₄	1	2	yes	—
78	C₂²×#535	D₄	1	1	yes	characteristic, complemented
79	C₂²×#535	D₄	1	1	yes	characteristic, complemented
80	C₂²×#535	D₄	1	1	yes	characteristic, complemented
81	C₂²×#535	C₂³	1	1	yes	characteristic
82	C₂²×#535	C₂³	1	1	yes	characteristic
83	C₂²×#535	C₂³	1	1	yes	characteristic
84	C₂³×#127	D₄	1	1	yes	characteristic, complemented
85	C₂³×#127	D₄	1	1	yes	characteristic, complemented
86	C₂²×#525	D₄	1	1	yes	characteristic, complemented
87	C₂²×#525	C₂³	1	1	yes	characteristic
88	C₂²×#518	D₄	1	1	yes	characteristic, complemented
89	C₂×#3027	C₂³	1	4	yes	complemented
90	C₂×#3025	D₄	1	8	yes	complemented
91	C₂×#3025	C₂³	1	4	yes	—
92	C₂×#3021	C₂³	1	4	yes	complemented
93	C₂×#3021	C₂³	1	4	yes	complemented
94	C₂²×#413	C₂³	1	1	yes	characteristic
95	C₂²×#413	C₂³	1	1	yes	characteristic
96	C₂²×#413	C₂³	1	1	yes	characteristic
97	C₂²×#410	C₂³	1	1	yes	characteristic
98	C₂²×#410	C₂³	1	1	yes	characteristic
99	C₂²×#410	C₂³	1	1	yes	characteristic
100	C₂×#2733	D₄	1	4	yes	complemented
101	C₂×#2669	D₄	1	4	yes	complemented
102	#37297	D₄	1	4	yes	complemented
103	#37297	D₄	1	4	yes	complemented
104	#37297	C₂³	1	4	yes	—
105	#37297	C₂³	1	4	yes	—
106	#35527	D₄	1	4	yes	complemented
107	#35527	D₄	1	4	yes	complemented
108	#35527	C₂³	1	4	yes	—
109	#35527	C₂³	1	4	yes	—
110	#34152	D₄	1	4	yes	complemented
111	#34152	C₂³	1	4	yes	—
112	C₂×#2374	D₄	1	2	yes	complemented
113	C₂×#2358	D₄	1	2	yes	complemented
114	C₂×#2309	D₄	1	1	yes	characteristic, complemented
115	C₂×#2309	D₄	1	1	yes	characteristic, complemented
116	C₂×#2297	D₄	1	1	yes	characteristic, complemented
117	C₂×#2297	D₄	1	1	yes	characteristic, complemented
118	C₂×#2297	C₂³	1	1	yes	characteristic
119	C₂×#2297	C₂³	1	1	yes	characteristic
120	C₂×#2134	C₂³	1	4	yes	complemented
121	C₂×#2134	C₂³	1	4	yes	complemented
122	C₂×#2128	C₂³	1	4	yes	complemented
123	C₂×#2128	C₂³	1	4	yes	complemented
124	C₂×#2122	C₂³	1	4	yes	complemented
125	C₂×#2122	C₂³	1	4	yes	complemented
126	C₂×#2120	D₄	1	8	yes	complemented
127	C₂×#2120	C₂³	1	4	yes	—
128	C₂×#2120	C₂³	1	4	yes	—
129	C₂×#1914	C₂³	1	4	yes	complemented
130	C₂×#1910	C₂³	1	4	yes	complemented
131	C₂×#1910	C₂³	1	4	yes	complemented
132	C₂×#1891	D₄	1	8	yes	complemented
133	C₂×#1891	C₂³	1	4	yes	—
134	C₂×#1795	C₂³	1	4	yes	complemented
135	C₂×#1795	C₂³	1	4	yes	complemented
136	C₂×#1795	C₂³	1	4	yes	complemented
137	#20615	C₂³	1	4	yes	complemented
138	#20608	C₂³	1	4	yes	complemented
139	#12585	C₂³	1	4	yes	complemented
140	#12581	C₂³	1	4	yes	complemented
141	#12573	C₂³	1	4	yes	complemented
142	#12573	C₂³	1	4	yes	complemented
143	#10751	C₂³	1	4	yes	complemented
144	#10746	C₂³	1	4	yes	complemented
145	C₂×#585	C₂×D₄	1	4	yes	complemented
146	C₂×#585	C₂⁴	1	2	yes	—
147	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
148	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
149	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
150	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
151	C₂³×#41	C₂×D₄	1	1	yes	characteristic
152	C₂³×#41	C₂×D₄	1	1	yes	characteristic
153	C₂³×#41	C₂×D₄	1	1	yes	characteristic
154	C₂³×#41	C₂⁴	1	1	yes	characteristic
155	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
159	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
160	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
161	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
162	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
163	C₂×#568	C₂×D₄	1	4	yes	complemented
164	C₂×#568	C₂⁴	1	2	yes	—
165	C₂×#560	C₂×D₄	1	8	yes	—
166	C₂×D₄²	C₂×D₄	1	8	yes	—
167	C₂×#535	C₂×D₄	1	2	yes	—
168	C₂×#535	C₂×D₄	1	2	yes	—
169	C₂×#535	C₂×D₄	1	2	yes	—
170	C₂×#535	C₂×D₄	1	2	yes	—
171	C₂×#535	C₂×D₄	1	2	yes	—
172	C₂×#535	C₂×D₄	1	2	yes	—
173	C₂×#535	C₂×D₄	1	2	yes	—
174	C₂×#535	C₂×D₄	1	2	yes	—
175	C₂×#535	C₂×D₄	1	2	yes	—
176	C₂×#535	C₂×D₄	1	4	yes	complemented
177	C₂×#535	C₂×D₄	1	4	yes	complemented
178	C₂×#535	C₂×D₄	1	4	yes	complemented
179	C₂×#535	C₂⁴	1	2	yes	—
180	C₂×#535	C₂⁴	1	2	yes	—
181	C₂×#535	C₂⁴	1	2	yes	—
182	C₂²×#127	C₂×D₄	1	2	yes	—
183	C₂²×#127	C₂×D₄	1	2	yes	—
184	C₂²×#127	C₂×D₄	1	4	yes	complemented
185	C₂²×#127	C₂×D₄	1	4	yes	complemented
186	C₂²×#124	C₂×D₄	1	2	yes	—
187	C₂²×#124	C₂×D₄	1	2	yes	—
188	C₂×#525	C₂×D₄	1	4	yes	—
189	C₂×#525	C₂×D₄	1	2	yes	—
190	C₂×#525	C₂×D₄	1	2	yes	—
191	C₂×#525	C₂×D₄	1	4	yes	—
192	C₂×#525	C₂×D₄	1	4	yes	—
193	C₂×#525	C₂×D₄	1	2	yes	—
194	C₂×#525	C₂×D₄	1	4	yes	complemented
195	C₂×#525	#41	1	4	yes	—
196	C₂×#525	C₂⁴	1	2	yes	—
197	C₂²×#123	C₂×D₄	1	1	yes	characteristic
198	C₂²×#123	C₂×D₄	1	1	yes	characteristic
199	C₂²×#120	C₂×D₄	1	2	yes	—
200	C₂²×#120	C₂×D₄	1	2	yes	—
201	C₂²×#120	C₂×D₄	1	1	yes	characteristic
202	C₂²×#120	C₂×D₄	1	1	yes	characteristic
203	C₂×#518	C₂×D₄	1	4	yes	complemented
204	C₂²×#117	C₂×D₄	1	1	yes	characteristic
205	C₂²×#117	C₂×D₄	1	1	yes	characteristic
206	C₂²×#117	C₂×D₄	1	1	yes	characteristic
207	C₂²×#117	C₂×D₄	1	1	yes	characteristic
208	C₂²×#117	C₂×D₄	1	1	yes	characteristic
209	C₂²×#117	C₂×D₄	1	1	yes	characteristic
210	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
211	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
212	#3025	C₂×D₄	1	16	yes	complemented
213	C₂×#413	C₂×D₄	1	4	yes	complemented
214	C₂×#413	C₂×D₄	1	4	yes	complemented
215	C₂×#413	C₂⁴	1	2	yes	—
216	C₂×#413	C₂⁴	1	2	yes	—
217	C₂×#413	C₂⁴	1	2	yes	—
218	C₂×#410	C₂×D₄	1	4	yes	complemented
219	C₂×#410	C₂×D₄	1	4	yes	complemented
220	C₂×#410	C₂⁴	1	2	yes	—
221	C₂×#410	C₂⁴	1	2	yes	—
222	C₂×#410	C₂⁴	1	2	yes	—
223	#2733	C₂×D₄	1	16	yes	complemented
224	#2669	C₂×D₄	1	16	yes	complemented
225	#2374	C₂×D₄	1	8	yes	complemented
226	#2358	C₂×D₄	1	8	yes	complemented
227	#2309	C₂×D₄	1	4	yes	complemented
228	#2309	C₂×D₄	1	4	yes	complemented
229	#2297	C₂×D₄	1	2	yes	—
230	#2297	C₂×D₄	1	2	yes	—
231	#2297	C₂×D₄	1	2	yes	—
232	#2297	C₂×D₄	1	2	yes	—
233	#2297	C₂×D₄	1	2	yes	—
234	#2297	C₂×D₄	1	2	yes	—
235	#2297	C₂×D₄	1	4	yes	complemented
236	#2297	C₂×D₄	1	4	yes	complemented
237	#2297	C₂⁴	1	2	yes	—
238	#2297	C₂⁴	1	2	yes	—
239	C₂×#391	C₂×D₄	1	2	yes	—
240	C₂×#390	C₂×D₄	1	2	yes	—
241	C₂×#386	C₂×D₄	1	2	yes	—
242	C₂×#386	C₂×D₄	1	2	yes	—
243	#2120	C₂×D₄	1	16	yes	complemented
244	#1891	C₂×D₄	1	16	yes	complemented
245	C₂⁶	#120	1	2	yes	—
246	C₂⁶	#120	1	1	yes	characteristic
247	#585	C₂²×D₄	1	4	yes	complemented
248	C₂²×#41	#120	1	2	yes	—
249	C₂²×#41	#120	1	2	yes	—
250	C₂²×#41	#120	1	2	yes	—
251	C₂²×#41	C₂²×D₄	1	2	yes	—
252	C₂²×#41	C₂²×D₄	1	2	yes	—
253	C₂²×#41	C₂²×D₄	1	2	yes	—
254	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
255	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
256	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
257	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
258	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
259	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
260	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
261	C₂²×#41	C₂²×D₄	1	2	yes	—
262	C₂²×#41	C₂²×D₄	1	2	yes	—
263	C₂²×#41	C₂²×D₄	1	2	yes	—
264	C₂²×#41	C₂×#41	1	2	yes	—
265	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
266	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
267	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
268	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
269	C₂²×#41	C₂⁵	1	1	yes	characteristic
270	C₂³×Q₈	#120	1	1	yes	characteristic
271	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
272	C₂³×D₄	#120	1	2	yes	—
273	C₂³×D₄	#120	1	2	yes	—
274	C₂³×D₄	#120	1	2	yes	—
275	C₂³×D₄	#120	1	2	yes	—
276	C₂³×D₄	#120	1	2	yes	—
277	C₂³×D₄	#120	1	2	yes	—
278	C₂³×D₄	#120	1	2	yes	—
279	C₂³×D₄	#120	1	2	yes	—
280	C₂³×D₄	#120	1	1	yes	characteristic
281	C₂³×D₄	#120	1	1	yes	characteristic
282	C₂³×D₄	#120	1	1	yes	characteristic
283	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
284	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
285	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
290	C₂³×D₄	C₂²×D₄	1	2	yes	—
291	C₂³×D₄	C₂²×D₄	1	2	yes	—
292	C₂⁴×C₄	#120	1	4	yes	—
293	C₂⁴×C₄	#120	1	1	yes	characteristic
294	C₂⁴×C₄	#120	1	2	yes	—
295	C₂⁴×C₄	#120	1	2	yes	—
296	C₂⁴×C₄	#121	1	4	yes	—
297	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
298	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
299	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
300	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
301	#568	C₂²×D₄	1	4	yes	complemented
302	C₂×#127	#120	1	4	yes	—
303	C₂×#127	#120	1	4	yes	—
304	C₂×#127	C₂²×D₄	1	4	yes	—
305	C₂×#127	C₂²×D₄	1	4	yes	—
306	C₂×#124	#120	1	4	yes	—
307	C₂×#124	#120	1	4	yes	—
308	C₂×#124	C₂²×D₄	1	4	yes	—
309	C₂×#124	C₂²×D₄	1	4	yes	—
310	#525	#120	1	8	yes	—
311	#525	#120	1	8	yes	—
312	#525	#121	1	8	yes	—
313	#525	#121	1	8	yes	—
314	#525	#121	1	8	yes	—
315	#525	#127	1	8	yes	—
316	#525	C₂²×D₄	1	4	yes	—
317	#525	C₂²×D₄	1	4	yes	—
318	#525	C₂²×D₄	1	4	yes	—
319	#525	C₂×#41	1	4	yes	—
320	C₂×#123	#120	1	2	yes	—
321	C₂×#123	#120	1	2	yes	—
322	C₂×#123	#120	1	4	yes	—
323	C₂×#123	#121	1	4	yes	—
324	C₂×#123	#121	1	4	yes	—
325	C₂×#123	#127	1	4	yes	—
326	C₂×#123	C₂²×D₄	1	2	yes	—
327	C₂×#123	C₂²×D₄	1	2	yes	—
328	C₂×#120	#120	1	4	yes	—
329	C₂×#120	#120	1	4	yes	—
330	C₂×#120	#120	1	2	yes	—
331	C₂×#120	#120	1	2	yes	—
332	C₂×#120	#120	1	4	yes	—
333	C₂×#120	#121	1	4	yes	—
334	C₂×#120	#121	1	4	yes	—
335	C₂×#120	#127	1	4	yes	—
336	C₂×#120	C₂²×D₄	1	4	yes	—
337	C₂×#120	C₂²×D₄	1	4	yes	—
338	C₂×#120	C₂²×D₄	1	2	yes	—
339	C₂×#120	C₂²×D₄	1	2	yes	—
340	C₂×#117	#120	1	2	yes	—
341	C₂×#117	#120	1	2	yes	—
342	C₂×#117	#120	1	2	yes	—
343	C₂×#117	#120	1	2	yes	—
344	C₂×#117	#120	1	4	yes	—
345	C₂×#117	#120	1	2	yes	—
346	C₂×#117	#120	1	2	yes	—
347	C₂×#117	#121	1	4	yes	—
348	C₂×#117	C₂²×D₄	1	2	yes	—
349	C₂×#117	C₂²×D₄	1	2	yes	—
350	C₂×#117	C₂²×D₄	1	2	yes	—
351	C₂×#117	C₂²×D₄	1	2	yes	—
352	C₂×#117	C₂²×D₄	1	2	yes	—
353	C₂×#117	C₂²×D₄	1	2	yes	—
354	C₂²×C₄⋊C₄	#120	1	2	yes	—
355	C₂²×C₂²⋊C₄	#120	1	2	yes	—
356	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
358	C₂²×C₂²⋊C₄	#120	1	2	yes	—
359	C₂²×C₄²	#120	1	2	yes	—
360	C₂²×C₄²	#120	1	2	yes	—
361	C₂²×C₄²	#120	1	2	yes	—
362	C₂²×C₄²	#120	1	2	yes	—
363	C₂²×C₄²	#120	1	2	yes	—
364	C₂²×C₄²	C₂²×D₄	1	2	yes	—
365	C₂²×C₄²	C₂²×D₄	1	2	yes	—
366	#413	C₂²×D₄	1	4	yes	complemented
367	#413	C₂²×D₄	1	4	yes	complemented
368	#410	C₂²×D₄	1	4	yes	complemented
369	#410	C₂²×D₄	1	4	yes	complemented
370	#391	#120	1	4	yes	—
371	#391	C₂²×D₄	1	4	yes	—
372	#390	#120	1	4	yes	—
373	#390	C₂²×D₄	1	4	yes	—
374	#386	#120	1	4	yes	—
375	#386	#120	1	4	yes	—
376	#386	C₂²×D₄	1	4	yes	—
377	#386	C₂²×D₄	1	4	yes	—
378	C₂⁵	#392	1	4	yes	—
379	C₂⁵	C₂×#120	1	1	yes	characteristic
380	C₂⁵	C₂×#120	1	1	yes	characteristic
381	C₂⁵	C₂×#120	1	1	yes	characteristic
382	C₂⁵	C₂×#120	1	4	yes	—
383	C₂⁵	C₂×#120	1	2	yes	—
384	C₂×#41	C₂×#120	1	2	yes	—
385	C₂×#41	C₂×#120	1	2	yes	—
386	C₂×#41	C₂×#121	1	2	yes	—
387	C₂×#41	C₂×#121	1	2	yes	—
388	C₂×#41	C₂×#121	1	2	yes	—
389	C₂×#41	C₂×#127	1	2	yes	—
390	C₂×#41	#534	1	2	yes	—
391	C₂×#41	#534	1	2	yes	—
392	C₂×#41	#534	1	2	yes	—
393	C₂×#41	#534	1	2	yes	—
394	C₂×#41	#535	1	2	yes	—
395	C₂×#41	#535	1	2	yes	—
396	C₂×#41	D₄²	1	2	yes	—
397	C₂×#41	D₄²	1	2	yes	—
398	C₂×#41	D₄²	1	2	yes	—
399	C₂×#41	D₄²	1	2	yes	—
400	C₂×#41	D₄²	1	2	yes	—
401	C₂×#41	D₄²	1	2	yes	—
402	C₂×#41	D₄²	1	2	yes	—
403	C₂×#41	D₄²	1	2	yes	—
404	C₂×#41	D₄²	1	2	yes	—
405	C₂×#41	D₄²	1	2	yes	—
406	C₂×#41	D₄²	1	2	yes	—
407	C₂×#41	D₄²	1	2	yes	—
408	C₂×#41	#546	1	2	yes	—
409	C₂×#41	#546	1	2	yes	—
410	C₂×#41	#546	1	2	yes	—
411	C₂×#41	#546	1	2	yes	—
412	C₂×#41	C₂³×D₄	1	1	yes	characteristic
413	C₂×#41	C₂³×D₄	1	1	yes	characteristic
414	C₂×#41	C₂³×D₄	1	1	yes	characteristic
415	C₂×#41	C₂²×#41	1	1	yes	characteristic
416	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²×Q₈	C₂×#120	1	2	yes	—
421	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
422	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
423	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
424	C₂²×Q₈	D₄²	1	2	yes	—
425	C₂²×Q₈	D₄²	1	2	yes	—
426	C₂²×Q₈	D₄²	1	2	yes	—
427	C₂²×Q₈	#546	1	2	yes	—
428	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
429	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
430	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
431	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
432	C₂²×D₄	C₂×#120	1	1	yes	characteristic
433	C₂²×D₄	C₂×#120	1	1	yes	characteristic
434	C₂²×D₄	C₂×#120	1	1	yes	characteristic
435	C₂²×D₄	C₂×#120	1	1	yes	characteristic
436	C₂²×D₄	C₂×#120	1	1	yes	characteristic
437	C₂²×D₄	C₂×#120	1	1	yes	characteristic
438	C₂²×D₄	C₂×#120	1	2	yes	—
439	C₂²×D₄	C₂×#120	1	2	yes	—
440	C₂²×D₄	C₂×#120	1	2	yes	—
441	C₂²×D₄	C₂×#120	1	2	yes	—
442	C₂²×D₄	C₂×#120	1	4	yes	—
443	C₂²×D₄	C₂×#120	1	4	yes	—
444	C₂²×D₄	C₂×#120	1	1	yes	characteristic
445	C₂²×D₄	C₂×#120	1	1	yes	characteristic
446	C₂²×D₄	C₂×#120	1	1	yes	characteristic
447	C₂²×D₄	C₂×#121	1	2	yes	—
448	C₂²×D₄	C₂×#121	1	2	yes	—
449	C₂²×D₄	C₂×#127	1	2	yes	—
450	C₂²×D₄	#534	1	2	yes	—
451	C₂²×D₄	#534	1	2	yes	—
452	C₂²×D₄	#535	1	2	yes	—
453	C₂²×D₄	#535	1	2	yes	—
454	C₂²×D₄	D₄²	1	2	yes	—
455	C₂²×D₄	D₄²	1	2	yes	—
456	C₂²×D₄	D₄²	1	2	yes	—
457	C₂²×D₄	#546	1	2	yes	—
458	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
459	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
460	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
461	C₂³×C₄	#392	1	4	yes	—
462	C₂³×C₄	#392	1	8	yes	—
463	C₂³×C₄	C₂×#120	1	1	yes	characteristic
464	C₂³×C₄	C₂×#120	1	1	yes	characteristic
465	C₂³×C₄	C₂×#120	1	1	yes	characteristic
466	C₂³×C₄	C₂×#120	1	1	yes	characteristic
467	C₂³×C₄	C₂×#120	1	1	yes	characteristic
468	C₂³×C₄	C₂×#120	1	1	yes	characteristic
469	C₂³×C₄	C₂×#120	1	1	yes	characteristic
470	C₂³×C₄	C₂×#120	1	1	yes	characteristic
471	C₂³×C₄	C₂×#120	1	1	yes	characteristic
472	C₂³×C₄	C₂×#120	1	1	yes	characteristic
473	C₂³×C₄	C₂×#120	1	1	yes	characteristic
474	C₂³×C₄	C₂×#120	1	1	yes	characteristic
475	C₂³×C₄	C₂×#120	1	2	yes	—
476	C₂³×C₄	C₂×#120	1	2	yes	—
477	C₂³×C₄	C₂×#120	1	4	yes	—
478	C₂³×C₄	C₂×#120	1	4	yes	—
479	C₂³×C₄	C₂×#120	1	1	yes	characteristic
480	C₂³×C₄	C₂×#121	1	2	yes	—
481	C₂³×C₄	C₂×#121	1	4	yes	—
482	C₂³×C₄	#534	1	2	yes	—
483	C₂³×C₄	#534	1	2	yes	—
484	C₂³×C₄	D₄²	1	2	yes	—
485	C₂³×C₄	D₄²	1	2	yes	—
486	C₂³×C₄	D₄²	1	2	yes	—
487	C₂³×C₄	D₄²	1	2	yes	—
488	C₂³×C₄	D₄²	1	2	yes	—
489	C₂³×C₄	D₄²	1	2	yes	—
490	C₂³×C₄	#546	1	2	yes	—
491	C₂³×C₄	#546	1	2	yes	—
492	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
493	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
494	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
495	#123	#392	1	8	yes	—
496	#123	#392	1	8	yes	—
497	#123	C₂×#120	1	4	yes	—
498	#123	C₂×#121	1	4	yes	—
499	#123	C₂×#121	1	4	yes	—
500	#123	C₂×#127	1	4	yes	—
501	#120	#392	1	8	yes	—
502	#120	#392	1	8	yes	—
503	#120	C₂×#120	1	4	yes	—
504	#120	C₂×#121	1	4	yes	—
505	#120	C₂×#121	1	4	yes	—
506	#120	C₂×#127	1	4	yes	—
507	#117	#392	1	8	yes	—
508	#117	C₂×#120	1	4	yes	—
509	#117	C₂×#121	1	4	yes	—
510	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
511	C₂×C₂²⋊C₄	#392	1	4	yes	—
512	C₂×C₂²⋊C₄	#392	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
517	C₂×C₄²	C₂×#120	1	4	yes	—
518	C₂×C₄²	C₂×#120	1	4	yes	—
519	C₂×C₄²	C₂×#120	1	4	yes	—
520	C₂⁴	C₂×#392	1	2	yes	—
521	C₂⁴	C₂×#392	1	4	yes	—
522	C₂⁴	#2403	1	2	yes	—
523	C₂⁴	#2408	1	2	yes	—
524	C₂⁴	#2410	1	2	yes	—
525	C₂⁴	#2433	1	2	yes	—
526	C₂⁴	#2613	1	2	yes	—
527	C₂⁴	#2846	1	1	yes	characteristic
528	C₂⁴	#2846	1	1	yes	characteristic
529	C₂⁴	#2846	1	1	yes	characteristic
530	C₂⁴	#2846	1	1	yes	characteristic
531	C₂⁴	C₂²×#120	1	1	yes	characteristic
532	C₂⁴	C₂²×#120	1	1	yes	characteristic
533	C₂⁴	C₂²×#120	1	1	yes	characteristic
534	C₂×Q₈	#2403	1	2	yes	—
535	C₂×Q₈	#2403	1	2	yes	—
536	C₂×Q₈	#2408	1	2	yes	—
537	C₂×Q₈	#2410	1	2	yes	—
538	C₂×Q₈	#2410	1	2	yes	—
539	C₂×Q₈	#2433	1	2	yes	—
540	C₂×Q₈	C₂×D₄²	1	1	yes	characteristic
541	C₂×Q₈	C₂×D₄²	1	1	yes	characteristic
542	C₂×Q₈	C₂×D₄²	1	1	yes	characteristic
543	C₂×Q₈	C₂×#546	1	1	yes	characteristic
544	C₂×D₄	C₂×#392	1	2	yes	—
545	C₂×D₄	C₂×#392	1	2	yes	—
546	C₂×D₄	#2403	1	2	yes	—
547	C₂×D₄	#2403	1	2	yes	—
548	C₂×D₄	#2403	1	2	yes	—
549	C₂×D₄	#2403	1	2	yes	—
550	C₂×D₄	#2408	1	2	yes	—
551	C₂×D₄	#2408	1	2	yes	—
552	C₂×D₄	#2408	1	2	yes	—
553	C₂×D₄	#2410	1	2	yes	—
554	C₂×D₄	#2410	1	2	yes	—
555	C₂×D₄	#2410	1	2	yes	—
556	C₂×D₄	#2410	1	2	yes	—
557	C₂×D₄	#2433	1	2	yes	—
558	C₂×D₄	#2433	1	2	yes	—
559	C₂×D₄	#2433	1	2	yes	—
560	C₂×D₄	#2613	1	2	yes	—
561	C₂×D₄	#2613	1	2	yes	—
562	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
563	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
564	C₂×D₄	C₂²×#120	1	1	yes	characteristic
565	C₂×D₄	C₂²×#121	1	1	yes	characteristic
566	C₂×D₄	C₂²×#121	1	1	yes	characteristic
567	C₂×D₄	C₂²×#127	1	1	yes	characteristic
568	C₂×D₄	C₂×#534	1	1	yes	characteristic
569	C₂×D₄	C₂×#534	1	1	yes	characteristic
570	C₂×D₄	C₂×#535	1	1	yes	characteristic
571	C₂×D₄	C₂×#535	1	1	yes	characteristic
572	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
573	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
574	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
575	C₂×D₄	C₂×#546	1	1	yes	characteristic
576	C₂²×C₄	C₂×#392	1	2	yes	—
577	C₂²×C₄	C₂×#392	1	4	yes	—
578	C₂²×C₄	#2403	1	2	yes	—
579	C₂²×C₄	#2403	1	2	yes	—
580	C₂²×C₄	#2403	1	2	yes	—
581	C₂²×C₄	#2403	1	2	yes	—
582	C₂²×C₄	#2403	1	2	yes	—
583	C₂²×C₄	#2403	1	2	yes	—
584	C₂²×C₄	#2403	1	2	yes	—
585	C₂²×C₄	#2403	1	2	yes	—
586	C₂²×C₄	#2403	1	2	yes	—
587	C₂²×C₄	#2408	1	2	yes	—
588	C₂²×C₄	#2408	1	2	yes	—
589	C₂²×C₄	#2408	1	2	yes	—
590	C₂²×C₄	#2410	1	2	yes	—
591	C₂²×C₄	#2410	1	2	yes	—
592	C₂²×C₄	#2410	1	2	yes	—
593	C₂²×C₄	#2410	1	2	yes	—
594	C₂²×C₄	#2410	1	2	yes	—
595	C₂²×C₄	#2410	1	2	yes	—
596	C₂²×C₄	#2410	1	2	yes	—
597	C₂²×C₄	#2410	1	2	yes	—
598	C₂²×C₄	#2410	1	2	yes	—
599	C₂²×C₄	#2433	1	2	yes	—
600	C₂²×C₄	#2433	1	2	yes	—
601	C₂²×C₄	#2433	1	2	yes	—
602	C₂²×C₄	#2613	1	2	yes	—
603	C₂²×C₄	#2846	1	1	yes	characteristic
604	C₂²×C₄	#2846	1	1	yes	characteristic
605	C₂²×C₄	#2846	1	1	yes	characteristic
606	C₂²×C₄	#2846	1	1	yes	characteristic
607	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
608	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
609	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
610	C₂²×C₄	#3026	1	2	yes	—
611	C₂²×C₄	#3026	1	1	yes	characteristic
612	C₂²×C₄	#3026	1	1	yes	characteristic
613	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
614	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
615	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
616	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
617	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
618	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
619	C₂²×C₄	C₂×#534	1	1	yes	characteristic
620	C₂²×C₄	C₂×#534	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
627	C₂²×C₄	C₂×#546	1	1	yes	characteristic
628	C₂²×C₄	C₂×#546	1	1	yes	characteristic
629	C₂²⋊C₄	C₂×#392	1	4	yes	—
630	C₂²⋊C₄	C₂×#392	1	4	yes	—
631	C₂³	#14715	1	2	yes	—
632	C₂³	#14715	1	2	yes	—
633	C₂³	#14715	1	2	yes	—
634	C₂³	#14715	1	2	yes	—
635	C₂³	#32898	1	2	yes	—
636	C₂³	#32898	1	1	yes	characteristic
637	C₂³	#32898	1	1	yes	characteristic
638	C₂³	C₂²×#392	1	1	yes	characteristic
639	C₂³	C₂×#2613	1	1	yes	characteristic
640	C₂³	C₂×#2403	1	1	yes	characteristic
641	C₂³	C₂×#2410	1	1	yes	characteristic
642	C₂³	C₂×#2408	1	1	yes	characteristic
643	C₂³	C₂×#2433	1	1	yes	characteristic
644	C₂³	C₂×#2846	1	1	yes	characteristic
645	C₂×C₄	#14715	1	2	yes	—
646	C₂×C₄	#14715	1	2	yes	—
647	C₂×C₄	#14715	1	2	yes	—
648	C₂×C₄	#14715	1	2	yes	—
649	C₂×C₄	#23900	1	2	yes	—
650	C₂×C₄	#23900	1	2	yes	—
651	C₂×C₄	#23903	1	2	yes	—
652	C₂×C₄	#23903	1	2	yes	—
653	C₂×C₄	#24404	1	2	yes	—
654	C₂×C₄	#24404	1	2	yes	—
655	C₂×C₄	#24404	1	2	yes	—
656	C₂×C₄	#24404	1	2	yes	—
657	C₂×C₄	#32898	1	1	yes	characteristic
658	C₂×C₄	#32898	1	1	yes	characteristic
659	C₂×C₄	#32898	1	2	yes	—
660	C₂×C₄	C₂×#2403	1	1	yes	characteristic
661	C₂×C₄	C₂×#2403	1	1	yes	characteristic
662	C₂×C₄	C₂×#2403	1	1	yes	characteristic
663	C₂×C₄	C₂×#2410	1	1	yes	characteristic
664	C₂×C₄	C₂×#2410	1	1	yes	characteristic
665	C₂×C₄	C₂×#2410	1	1	yes	characteristic
666	C₂×C₄	C₂×#2408	1	1	yes	characteristic
667	C₂×C₄	C₂×#2433	1	1	yes	characteristic
668	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
669	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
670	C₂×C₄	C₂×#3026	1	1	yes	characteristic
671	C₂×C₄	C₂×#3026	1	1	yes	characteristic
672	C₂²	#394066	1	2	yes	—
673	C₂²	#394066	1	2	yes	—
674	C₂²	#511819	1	4	yes	—
675	C₂²	C₂×#14715	1	1	yes	characteristic
676	C₂²	C₂×#32898	1	1	yes	characteristic
677	C₂²	C₂×#32898	1	1	yes	characteristic
678	C₄	#394066	1	2	yes	—
679	C₄	#394066	1	2	yes	—
680	C₄	C₂×#23900	1	1	yes	characteristic
681	C₄	C₂×#23903	1	1	yes	characteristic
682	C₄	C₂×#24404	1	1	yes	characteristic
683	C₄	C₂×#24404	1	1	yes	characteristic
684	C₂	C₂×#511819	1	2	yes	—
685	C₂	#72231756	1	4	yes	direct product factor
686	C₂	C₂×#394066	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	#32898
commutator, Frattini, cosocle	C₂²×#41	C₂⁵
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#494571	C₂	semidirect
2. C₂×#146605	C₂	semidirect
3. C₂×#7737956	C₂	semidirect
4. C₂×#147582	C₂	semidirect
5. C₂×#147820	C₂	semidirect
6. C₂×#498932	C₂	semidirect
7. C₂×#498909	C₂	semidirect
8. C₂×#147787	C₂	semidirect
9. C₂²×#33553	C₂	semidirect
10. C₂²×#12755	C₂	semidirect
11. C₂×#394076	C₂	semidirect
12. C₂×#147577	C₂	semidirect
13. C₂²×#12711	C₂	semidirect
14. C₂²×#23882	C₂	semidirect
15. C₂×#394022	C₂	semidirect
16. #72231756	C₂	direct (N × H)
17. C₂²×#3585	C₂²	semidirect
20. C₂²×#3027	C₂²	semidirect
22. C₂²×#3021	C₂²	semidirect
23. C₂²×#3021	C₂²	semidirect
24. #7737956	C₂²	semidirect
30. C₂×#33553	C₂²	semidirect
31. C₂²×#2134	C₂²	semidirect
32. C₂²×#2134	C₂²	semidirect
33. C₂²×#2128	C₂²	semidirect
34. C₂²×#2128	C₂²	semidirect
35. C₂²×#2122	C₂²	semidirect
36. C₂²×#2122	C₂²	semidirect
39. C₂×#23882	C₂²	semidirect
40. C₂²×#1914	C₂²	semidirect
41. C₂²×#1910	C₂²	semidirect
42. C₂²×#1910	C₂²	semidirect
44. C₂²×#1795	C₂²	semidirect
45. C₂²×#1795	C₂²	semidirect
46. C₂²×#1795	C₂²	semidirect
47. C₂×#20615	C₂²	semidirect
48. C₂×#20608	C₂²	semidirect
49. #498932	C₂²	semidirect
50. #498909	C₂²	semidirect
51. #494571	C₂²	semidirect
52. C₂×#12755	C₂²	semidirect
53. C₂×#12711	C₂²	semidirect
54. C₂×#12585	C₂²	semidirect
55. C₂×#12581	C₂²	semidirect
56. C₂×#12573	C₂²	semidirect
57. C₂×#12573	C₂²	semidirect
58. #394076	C₂²	semidirect
59. #394022	C₂²	semidirect
60. C₂×#10751	C₂²	semidirect
61. C₂×#10746	C₂²	semidirect
62. #147820	C₂²	semidirect
63. #147787	C₂²	semidirect
64. #147582	C₂²	semidirect
65. #147577	C₂²	semidirect
66. #146605	C₂²	semidirect
69. C₂⁵×D₄	D₄	semidirect
70. C₂×#3585	C₂³	semidirect
72. C₂×#3484	D₄	semidirect
78. C₂²×#535	D₄	semidirect
79. C₂²×#535	D₄	semidirect
80. C₂²×#535	D₄	semidirect
84. C₂³×#127	D₄	semidirect
85. C₂³×#127	D₄	semidirect
86. C₂²×#525	D₄	semidirect
88. C₂²×#518	D₄	semidirect
89. C₂×#3027	C₂³	semidirect
90. C₂×#3025	D₄	semidirect
92. C₂×#3021	C₂³	semidirect
93. C₂×#3021	C₂³	semidirect
100. C₂×#2733	D₄	semidirect
101. C₂×#2669	D₄	semidirect
102. #37297	D₄	semidirect
103. #37297	D₄	semidirect
106. #35527	D₄	semidirect
107. #35527	D₄	semidirect
110. #34152	D₄	semidirect
112. C₂×#2374	D₄	semidirect
113. C₂×#2358	D₄	semidirect
114. C₂×#2309	D₄	semidirect
115. C₂×#2309	D₄	semidirect
116. C₂×#2297	D₄	semidirect
117. C₂×#2297	D₄	semidirect
120. C₂×#2134	C₂³	semidirect
121. C₂×#2134	C₂³	semidirect
122. C₂×#2128	C₂³	semidirect
123. C₂×#2128	C₂³	semidirect
124. C₂×#2122	C₂³	semidirect
125. C₂×#2122	C₂³	semidirect
126. C₂×#2120	D₄	semidirect
129. C₂×#1914	C₂³	semidirect
130. C₂×#1910	C₂³	semidirect
131. C₂×#1910	C₂³	semidirect
132. C₂×#1891	D₄	semidirect
134. C₂×#1795	C₂³	semidirect
135. C₂×#1795	C₂³	semidirect
136. C₂×#1795	C₂³	semidirect
137. #20615	C₂³	semidirect
138. #20608	C₂³	semidirect
139. #12585	C₂³	semidirect
140. #12581	C₂³	semidirect
141. #12573	C₂³	semidirect
142. #12573	C₂³	semidirect
143. #10751	C₂³	semidirect
144. #10746	C₂³	semidirect
145. C₂×#585	C₂×D₄	semidirect
161. C₂⁴×D₄	C₂×D₄	semidirect
163. C₂×#568	C₂×D₄	semidirect
176. C₂×#535	C₂×D₄	semidirect
177. C₂×#535	C₂×D₄	semidirect
178. C₂×#535	C₂×D₄	semidirect
184. C₂²×#127	C₂×D₄	semidirect
185. C₂²×#127	C₂×D₄	semidirect
194. C₂×#525	C₂×D₄	semidirect
203. C₂×#518	C₂×D₄	semidirect
212. #3025	C₂×D₄	semidirect
213. C₂×#413	C₂×D₄	semidirect
214. C₂×#413	C₂×D₄	semidirect
218. C₂×#410	C₂×D₄	semidirect
219. C₂×#410	C₂×D₄	semidirect
223. #2733	C₂×D₄	semidirect
224. #2669	C₂×D₄	semidirect
225. #2374	C₂×D₄	semidirect
226. #2358	C₂×D₄	semidirect
227. #2309	C₂×D₄	semidirect
228. #2309	C₂×D₄	semidirect
235. #2297	C₂×D₄	semidirect
236. #2297	C₂×D₄	semidirect
243. #2120	C₂×D₄	semidirect
244. #1891	C₂×D₄	semidirect
247. #585	C₂²×D₄	semidirect
301. #568	C₂²×D₄	semidirect
366. #413	C₂²×D₄	semidirect
367. #413	C₂²×D₄	semidirect
368. #410	C₂²×D₄	semidirect
369. #410	C₂²×D₄	semidirect
685. C₂	#72231756	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×#494571	2
C₂×#146605	2
C₂×#7737956	2
C₂×#147582	2
C₂×#147820	2
C₂×#498932	2
C₂×#498909	2
C₂×#147787	2
C₂²×#33553	2
C₂²×#12755	2
C₂×#394076	2
C₂×#147577	2
C₂²×#12711	2
C₂²×#23882	2
C₂×#394022	2
#72231756	2

Subgroups — C2×#72231756 #72278334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72231756 #72278334