Subgroups — C₂×#394133 #72251529

Order 1024.

At least 6491 conjugacy classes of subgroups; only the 1629 normal subgroups are shown.

The subgroup lattice has 748 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#60367	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#60387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#23439	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#23414	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#23412	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#23407	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#20939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#20623	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#20616	C₂	1	1	yes	maximal, characteristic, complemented
11	#394133	C₂	1	16	yes	maximal, direct product factor
12	C₂×#11037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#11034	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11032	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#11012	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10787	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#585	C₂²	1	1	yes	characteristic
18	C₂³×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂×#3585	C₂²	1	8	yes	complemented
20	C₂²×#575	C₂²	1	1	yes	characteristic
21	C₂²×#575	C₂²	1	1	yes	characteristic
22	C₂²×#575	C₂²	1	1	yes	characteristic
23	C₂²×#575	C₂²	1	1	yes	characteristic, complemented
24	C₂³×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂³×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂³×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#568	C₂²	1	1	yes	characteristic
28	C₂×#3449	C₂²	1	1	yes	characteristic, complemented
29	C₂×#3449	C₂²	1	1	yes	characteristic, complemented
30	#60387	C₂²	1	8	yes	complemented
31	#60367	C₂²	1	8	yes	complemented
32	C₂²×#421	C₂²	1	1	yes	characteristic
33	C₂²×#421	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#421	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#421	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#421	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#421	C₂²	1	1	yes	characteristic, complemented
38	C₂×#2896	C₂²	1	1	yes	characteristic
39	C₂×#2896	C₂²	1	1	yes	characteristic
40	C₂×#2896	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#418	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#413	C₂²	1	1	yes	characteristic, complemented
43	C₂²×#413	C₂²	1	1	yes	characteristic, complemented
44	C₂³×#100	C₂²	1	1	yes	characteristic, complemented
45	C₂²×#410	C₂²	1	1	yes	characteristic, complemented
46	C₂×#2879	C₂²	1	1	yes	characteristic, complemented
47	C₂×#2879	C₂²	1	1	yes	characteristic, complemented
48	C₂×#2309	C₂²	1	1	yes	characteristic, complemented
49	#23439	C₂²	1	8	yes	complemented
50	#23414	C₂²	1	8	yes	complemented
51	#23412	C₂²	1	8	yes	complemented
52	#23407	C₂²	1	8	yes	complemented
53	#20939	C₂²	1	8	yes	complemented
54	#20623	C₂²	1	8	yes	complemented
55	#20616	C₂²	1	8	yes	complemented
56	C₂²×#344	C₂²	1	1	yes	characteristic, complemented
57	C₂²×#344	C₂²	1	1	yes	characteristic, complemented
58	C₂×#1742	C₂²	1	1	yes	characteristic, complemented
59	C₂×#1738	C₂²	1	1	yes	characteristic, complemented
60	C₂×#1738	C₂²	1	1	yes	characteristic, complemented
61	C₂²×H(3,ℤ/4)	C₂²	1	1	yes	characteristic, complemented
62	#11037	C₂²	1	8	yes	complemented
63	#11034	C₂²	1	8	yes	complemented
64	#11032	C₂²	1	8	yes	complemented
65	#11012	C₂²	1	8	yes	complemented
66	#10787	C₂²	1	8	yes	complemented
67	C₂×#585	D₄	1	4	yes	complemented
68	C₂×#585	C₂³	1	4	yes	—
69	C₂²×2₋¹⁺⁴	D₄	1	2	yes	complemented
70	C₂²×H(5,𝔽₂)	D₄	1	2	yes	complemented
71	C₂²×H(5,𝔽₂)	D₄	1	4	yes	complemented
72	C₂²×H(5,𝔽₂)	D₄	1	4	yes	complemented
73	C₂²×H(5,𝔽₂)	C₂³	1	4	yes	—
74	C₂³×#41	C₂³	1	1	yes	characteristic
75	C₂³×#41	C₂³	1	1	yes	characteristic
76	C₂³×#41	C₂³	1	1	yes	characteristic
77	C₂³×#41	C₂³	1	1	yes	characteristic
78	C₂³×#41	C₂³	1	1	yes	characteristic
79	C₂⁴×D₄	C₂³	1	1	yes	characteristic
80	C₂×#575	D₄	1	4	yes	—
81	C₂×#575	D₄	1	4	yes	—
82	C₂×#575	D₄	1	4	yes	—
83	C₂×#575	D₄	1	4	yes	complemented
84	C₂×#575	C₂³	1	4	yes	—
85	C₂×#575	C₂³	1	4	yes	—
86	C₂×#575	C₂³	1	4	yes	—
87	C₂×#575	C₂³	1	4	yes	complemented
88	C₂²×#137	D₄	1	2	yes	—
89	C₂²×#137	D₄	1	2	yes	complemented
90	C₂²×AGL(1,ℤ/8)	D₄	1	2	yes	—
91	C₂²×AGL(1,ℤ/8)	D₄	1	2	yes	complemented
92	C₂²×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
93	C₂²×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
94	C₂²×AGL(1,ℤ/8)	D₄	1	4	yes	complemented
95	C₂²×AGL(1,ℤ/8)	C₂³	1	4	yes	—
96	C₂²×AGL(1,ℤ/8)	C₂³	1	4	yes	—
97	C₂²×AGL(1,ℤ/8)	C₂³	1	4	yes	complemented
98	C₂³×SD₁₆	D₄	1	2	yes	complemented
99	C₂³×D₈	D₄	1	2	yes	complemented
100	C₂×#568	D₄	1	4	yes	complemented
101	C₂×#568	D₄	1	4	yes	complemented
102	C₂×#568	C₂³	1	4	yes	—
103	C₂³×M₁₆	C₂³	1	1	yes	characteristic
104	C₂³×M₁₆	C₂³	1	1	yes	characteristic
105	C₂³×M₁₆	C₂³	1	1	yes	characteristic
106	C₂³×M₁₆	C₂³	1	1	yes	characteristic
107	C₂³×M₁₆	C₂³	1	1	yes	characteristic
108	C₂³×M₁₆	C₂³	1	1	yes	characteristic
109	#3449	C₂³	1	4	yes	complemented
110	#3449	C₂³	1	4	yes	complemented
111	C₂²×#117	C₂³	1	1	yes	characteristic
112	C₂²×#117	C₂³	1	1	yes	characteristic
113	C₂²×#117	C₂³	1	1	yes	characteristic
114	C₂×#421	D₄	1	4	yes	complemented
115	C₂×#421	C₂³	1	4	yes	—
116	C₂×#421	C₂³	1	4	yes	complemented
117	C₂×#421	C₂³	1	4	yes	complemented
118	C₂×#421	C₂³	1	4	yes	complemented
119	C₂×#421	C₂³	1	4	yes	complemented
120	C₂×#421	C₂³	1	4	yes	complemented
121	C₂²×#104	D₄	1	4	yes	complemented
122	#2896	D₄	1	4	yes	complemented
123	#2896	C₂³	1	4	yes	—
124	#2896	C₂³	1	4	yes	—
125	#2896	C₂³	1	4	yes	complemented
126	C₂×#419	D₄	1	2	yes	complemented
127	C₂×#418	D₄	1	2	yes	complemented
128	C₂×#418	C₂³	1	4	yes	complemented
129	C₂×#413	C₂³	1	4	yes	complemented
130	C₂×#413	C₂³	1	4	yes	complemented
131	C₂²×#100	C₂³	1	4	yes	complemented
132	C₂×#410	C₂³	1	4	yes	complemented
133	#2879	C₂³	1	4	yes	complemented
134	#2879	C₂³	1	4	yes	complemented
135	#2309	C₂³	1	4	yes	complemented
136	C₂×#344	C₂³	1	4	yes	complemented
137	C₂×#344	C₂³	1	4	yes	complemented
138	#1742	C₂³	1	4	yes	complemented
139	#1738	C₂³	1	4	yes	complemented
140	#1738	C₂³	1	4	yes	complemented
141	C₂×H(3,ℤ/4)	C₂³	1	4	yes	complemented
142	C₂×2₋¹⁺⁴	C₂×D₄	1	8	yes	complemented
143	C₂×H(5,𝔽₂)	C₂×D₄	1	16	yes	complemented
144	C₂×H(5,𝔽₂)	C₂×D₄	1	8	yes	complemented
145	C₂²×#41	C₂×D₄	1	2	yes	—
146	C₂²×#41	C₂×D₄	1	2	yes	—
147	C₂²×#41	C₂×D₄	1	2	yes	—
148	C₂²×#41	C₂×D₄	1	2	yes	—
149	C₂²×#41	C₂×D₄	1	2	yes	—
150	C₂²×#41	C₂×D₄	1	2	yes	—
151	C₂²×#41	C₂×D₄	1	2	yes	—
152	C₂²×#41	C₂×D₄	1	2	yes	—
153	C₂²×#41	C₂×D₄	1	2	yes	—
154	C₂²×#41	C₂×D₄	1	2	yes	—
155	C₂²×#41	C₂×D₄	1	2	yes	—
156	C₂²×#41	C₂×D₄	1	2	yes	—
157	C₂²×#41	C₂×D₄	1	2	yes	—
158	C₂²×#41	C₂×D₄	1	2	yes	—
159	C₂²×#41	C₂×D₄	1	2	yes	—
160	C₂²×#41	C₂×D₄	1	2	yes	—
161	C₂²×#41	C₂×D₄	1	2	yes	—
162	C₂²×#41	C₂×D₄	1	2	yes	—
163	C₂²×#41	C₂×D₄	1	2	yes	—
164	C₂²×#41	C₂×D₄	1	2	yes	—
165	C₂²×#41	C₂×D₄	1	2	yes	—
166	C₂²×#41	C₂×D₄	1	2	yes	—
167	C₂²×#41	C₂×D₄	1	2	yes	—
168	C₂²×#41	C₂×D₄	1	2	yes	—
169	C₂²×#41	C₂×D₄	1	2	yes	—
170	C₂²×#41	C₂×D₄	1	2	yes	—
171	C₂²×#41	C₂×D₄	1	2	yes	—
172	C₂²×#41	#41	1	2	yes	—
173	C₂²×#41	#41	1	2	yes	—
174	C₂²×#41	C₂⁴	1	2	yes	—
175	C₂²×#41	C₂⁴	1	2	yes	—
176	C₂²×#41	C₂⁴	1	2	yes	—
177	C₂²×#41	C₂⁴	1	2	yes	—
178	C₂²×#41	C₂⁴	1	2	yes	—
179	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic
180	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic
181	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic
182	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic
183	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic
184	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
185	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂³×D₄	C₂×D₄	1	2	yes	—
187	C₂³×D₄	C₂×D₄	1	2	yes	—
188	C₂³×D₄	C₂×D₄	1	2	yes	—
189	C₂³×D₄	C₂×D₄	1	2	yes	—
190	C₂³×D₄	C₂×D₄	1	2	yes	—
191	C₂³×D₄	C₂×D₄	1	2	yes	—
192	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
193	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
194	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
195	C₂³×D₄	C₂⁴	1	2	yes	—
196	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
197	#575	C₂×D₄	1	16	yes	—
198	C₂×#137	C₂×D₄	1	8	yes	—
199	C₂×#137	C₂×D₄	1	8	yes	complemented
200	C₂×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	—
201	C₂×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	complemented
202	C₂×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	complemented
203	C₂²×SD₁₆	C₂×D₄	1	8	yes	complemented
204	C₂²×D₈	C₂×D₄	1	8	yes	complemented
205	#568	C₂×D₄	1	16	yes	complemented
206	C₂²×M₁₆	C₂×D₄	1	2	yes	—
207	C₂²×M₁₆	C₂×D₄	1	2	yes	—
208	C₂²×M₁₆	C₂×D₄	1	2	yes	—
209	C₂²×M₁₆	C₂×D₄	1	2	yes	—
210	C₂²×M₁₆	C₂×D₄	1	2	yes	—
211	C₂²×M₁₆	C₂×D₄	1	2	yes	—
212	C₂²×M₁₆	C₂×D₄	1	2	yes	—
213	C₂²×M₁₆	C₂×D₄	1	2	yes	—
214	C₂²×M₁₆	C₂×D₄	1	2	yes	—
215	C₂²×M₁₆	C₂×D₄	1	2	yes	—
216	C₂²×M₁₆	C₂×D₄	1	2	yes	—
217	C₂²×M₁₆	C₂×D₄	1	2	yes	—
218	C₂²×M₁₆	C₂×D₄	1	2	yes	—
219	C₂²×M₁₆	C₂×D₄	1	2	yes	—
220	C₂²×M₁₆	C₂×D₄	1	2	yes	—
221	C₂²×M₁₆	C₂×D₄	1	2	yes	—
222	C₂²×M₁₆	C₂×D₄	1	2	yes	—
223	C₂²×M₁₆	C₂⁴	1	2	yes	—
224	C₂²×M₁₆	C₂⁴	1	2	yes	—
225	C₂²×M₁₆	C₂⁴	1	2	yes	—
226	C₂²×M₁₆	C₂⁴	1	2	yes	—
227	C₂²×M₁₆	C₂⁴	1	2	yes	—
228	C₂²×M₁₆	C₂⁴	1	2	yes	—
229	C₂³×C₈	C₂×D₄	1	2	yes	—
230	C₂×#117	C₂×D₄	1	2	yes	—
231	C₂×#117	C₂×D₄	1	2	yes	—
232	C₂×#117	C₂×D₄	1	2	yes	—
233	C₂×#117	C₂⁴	1	2	yes	—
234	C₂×#117	C₂⁴	1	2	yes	—
235	C₂×#117	C₂⁴	1	2	yes	—
236	C₂²×C₄²	C₂×D₄	1	2	yes	—
237	C₂×#104	C₂×D₄	1	16	yes	complemented
238	#419	C₂×D₄	1	8	yes	complemented
239	#418	C₂×D₄	1	8	yes	complemented
240	C₂⁵	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×#41	#120	1	4	yes	—
242	C₂×#41	#120	1	4	yes	—
243	C₂×#41	#120	1	4	yes	—
244	C₂×#41	#120	1	4	yes	—
245	C₂×#41	#120	1	4	yes	—
246	C₂×#41	#120	1	4	yes	—
247	C₂×#41	#120	1	4	yes	—
248	C₂×#41	#120	1	4	yes	—
249	C₂×#41	#120	1	4	yes	—
250	C₂×#41	#120	1	4	yes	—
251	C₂×#41	#120	1	4	yes	—
252	C₂×#41	#120	1	4	yes	—
253	C₂×#41	#120	1	4	yes	—
254	C₂×#41	#120	1	4	yes	—
255	C₂×#41	#120	1	4	yes	—
256	C₂×#41	#120	1	4	yes	—
257	C₂×#41	#121	1	4	yes	—
258	C₂×#41	#121	1	4	yes	—
259	C₂×#41	#121	1	4	yes	—
260	C₂×#41	#121	1	4	yes	—
261	C₂×#41	#121	1	4	yes	—
262	C₂×#41	#121	1	4	yes	—
263	C₂×#41	#121	1	4	yes	—
264	C₂×#41	#121	1	4	yes	—
265	C₂×#41	#121	1	4	yes	—
266	C₂×#41	#121	1	4	yes	—
267	C₂×#41	#127	1	4	yes	—
268	C₂×#41	#127	1	4	yes	—
269	C₂×#41	C₂²×D₄	1	4	yes	—
270	C₂×#41	C₂²×D₄	1	4	yes	—
271	C₂×#41	C₂²×D₄	1	4	yes	—
272	C₂×#41	C₂²×D₄	1	4	yes	—
273	C₂×#41	C₂²×D₄	1	4	yes	—
274	C₂×#41	C₂²×D₄	1	4	yes	—
275	C₂×#41	C₂²×D₄	1	4	yes	—
276	C₂×#41	C₂²×D₄	1	4	yes	—
277	C₂×#41	C₂²×D₄	1	4	yes	—
278	C₂×#41	C₂²×D₄	1	4	yes	—
279	C₂×#41	C₂²×D₄	1	4	yes	—
280	C₂×#41	C₂×#41	1	4	yes	—
281	C₂²×Q₈	#120	1	2	yes	—
282	C₂²×Q₈	#120	1	2	yes	—
283	C₂²×Q₈	#120	1	2	yes	—
284	C₂²×Q₈	#120	1	2	yes	—
285	C₂²×Q₈	#120	1	2	yes	—
286	C₂²×Q₈	#120	1	2	yes	—
287	C₂²×Q₈	#120	1	2	yes	—
288	C₂²×Q₈	#120	1	2	yes	—
289	C₂²×Q₈	#121	1	2	yes	—
290	C₂²×Q₈	#121	1	2	yes	—
291	C₂²×Q₈	#127	1	2	yes	—
292	C₂²×Q₈	#127	1	2	yes	—
293	C₂²×Q₈	C₂²×D₄	1	2	yes	—
294	C₂²×Q₈	C₂²×D₄	1	2	yes	—
295	C₂²×Q₈	C₂²×D₄	1	2	yes	—
296	C₂²×Q₈	C₂²×D₄	1	2	yes	—
297	C₂²×Q₈	C₂²×D₄	1	2	yes	—
298	C₂²×D₄	#120	1	2	yes	—
299	C₂²×D₄	#120	1	2	yes	—
300	C₂²×D₄	#120	1	2	yes	—
301	C₂²×D₄	#120	1	2	yes	—
302	C₂²×D₄	#120	1	2	yes	—
303	C₂²×D₄	#120	1	2	yes	—
304	C₂²×D₄	#120	1	4	yes	—
305	C₂²×D₄	#120	1	4	yes	—
306	C₂²×D₄	#120	1	4	yes	—
307	C₂²×D₄	#120	1	4	yes	—
308	C₂²×D₄	#120	1	2	yes	—
309	C₂²×D₄	#120	1	2	yes	—
310	C₂²×D₄	#121	1	2	yes	—
311	C₂²×D₄	#121	1	2	yes	—
312	C₂²×D₄	#127	1	2	yes	—
313	C₂²×D₄	#127	1	2	yes	—
314	C₂²×D₄	C₂²×D₄	1	2	yes	—
315	C₂²×D₄	C₂²×D₄	1	2	yes	—
316	C₂²×D₄	C₂²×D₄	1	2	yes	—
317	C₂²×D₄	C₂²×D₄	1	2	yes	—
318	C₂²×D₄	C₂²×D₄	1	4	yes	—
319	C₂²×D₄	C₂²×D₄	1	4	yes	—
320	C₂²×D₄	C₂²×D₄	1	4	yes	—
321	C₂²×D₄	C₂²×D₄	1	2	yes	—
322	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
324	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
325	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
329	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
330	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
336	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
337	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
339	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
340	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
341	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
342	C₂³×C₄	C₂×#41	1	1	yes	characteristic
343	C₂³×C₄	C₂×#41	1	1	yes	characteristic
344	C₂³×C₄	H(5,𝔽₂)	1	1	yes	characteristic
345	C₂³×C₄	H(5,𝔽₂)	1	1	yes	characteristic
346	C₂³×C₄	H(5,𝔽₂)	1	1	yes	characteristic
347	C₂³×C₄	H(5,𝔽₂)	1	1	yes	characteristic
348	C₂³×C₄	H(5,𝔽₂)	1	1	yes	characteristic
349	C₂³×C₄	H(5,𝔽₂)	1	1	yes	characteristic
350	C₂³×C₄	H(5,𝔽₂)	1	1	yes	characteristic
351	C₂³×C₄	C₂⁵	1	1	yes	characteristic
352	C₂×M₁₆	#120	1	4	yes	—
353	C₂×M₁₆	#120	1	4	yes	—
354	C₂×M₁₆	#120	1	4	yes	—
355	C₂×M₁₆	#120	1	4	yes	—
356	C₂×M₁₆	#120	1	4	yes	—
357	C₂×M₁₆	#120	1	4	yes	—
358	C₂×M₁₆	C₂²×D₄	1	4	yes	—
359	C₂×M₁₆	C₂²×D₄	1	4	yes	—
360	C₂×M₁₆	C₂²×D₄	1	4	yes	—
361	C₂×M₁₆	C₂²×D₄	1	4	yes	—
362	C₂×M₁₆	C₂²×D₄	1	4	yes	—
363	C₂×M₁₆	C₂²×D₄	1	4	yes	—
364	C₂×M₁₆	C₂²×D₄	1	4	yes	—
365	C₂×M₁₆	C₂²×D₄	1	4	yes	—
366	C₂²×C₈	#120	1	4	yes	—
367	C₂²×C₈	#120	1	4	yes	—
368	C₂²×C₈	C₂²×D₄	1	4	yes	—
369	#117	C₂²×D₄	1	4	yes	—
370	C₂×C₄²	C₂²×D₄	1	4	yes	—
371	C₂⁴	#534	1	1	yes	characteristic
372	C₂⁴	#534	1	1	yes	characteristic
373	C₂⁴	#534	1	1	yes	characteristic
374	C₂⁴	#534	1	1	yes	characteristic
375	C₂⁴	#535	1	1	yes	characteristic
376	C₂⁴	#535	1	1	yes	characteristic
377	C₂⁴	D₄²	1	1	yes	characteristic
378	C₂⁴	D₄²	1	1	yes	characteristic
379	C₂⁴	D₄²	1	1	yes	characteristic
380	C₂⁴	D₄²	1	1	yes	characteristic
381	C₂⁴	D₄²	1	1	yes	characteristic
382	C₂⁴	D₄²	1	1	yes	characteristic
383	C₂⁴	#546	1	1	yes	characteristic
384	C₂⁴	#546	1	1	yes	characteristic
385	C₂⁴	C₂×H(5,𝔽₂)	1	1	yes	characteristic
386	#41	#392	1	8	yes	—
387	#41	#392	1	8	yes	—
388	#41	#392	1	8	yes	—
389	#41	#392	1	8	yes	—
390	#41	C₂×#120	1	8	yes	—
391	#41	C₂×#120	1	8	yes	—
392	#41	C₂×#121	1	8	yes	—
393	#41	C₂×#121	1	8	yes	—
394	C₂×Q₈	#392	1	4	yes	—
395	C₂×Q₈	#392	1	4	yes	—
396	C₂×Q₈	#392	1	4	yes	—
397	C₂×Q₈	#392	1	4	yes	—
398	C₂×Q₈	C₂×#120	1	4	yes	—
399	C₂×Q₈	C₂×#120	1	4	yes	—
400	C₂×Q₈	C₂×#120	1	4	yes	—
401	C₂×Q₈	C₂×#120	1	4	yes	—
402	C₂×Q₈	C₂×#121	1	4	yes	—
403	C₂×Q₈	C₂×#127	1	4	yes	—
404	C₂×D₄	#392	1	4	yes	—
405	C₂×D₄	#392	1	4	yes	—
406	C₂×D₄	#392	1	4	yes	—
407	C₂×D₄	#392	1	4	yes	—
408	C₂×D₄	C₂×#120	1	4	yes	—
409	C₂×D₄	C₂×#120	1	4	yes	—
410	C₂×D₄	C₂×#120	1	4	yes	—
411	C₂×D₄	C₂×#120	1	8	yes	—
412	C₂×D₄	C₂×#120	1	4	yes	—
413	C₂×D₄	C₂×#121	1	4	yes	—
414	C₂×D₄	C₂×#127	1	4	yes	—
415	C₂²×C₄	C₂×#120	1	1	yes	characteristic
416	C₂²×C₄	C₂×#120	1	1	yes	characteristic
417	C₂²×C₄	C₂×#120	1	1	yes	characteristic
418	C₂²×C₄	C₂×#120	1	1	yes	characteristic
419	C₂²×C₄	C₂×#120	1	1	yes	characteristic
420	C₂²×C₄	C₂×#120	1	1	yes	characteristic
421	C₂²×C₄	C₂×#120	1	1	yes	characteristic
422	C₂²×C₄	C₂×#120	1	1	yes	characteristic
423	C₂²×C₄	C₂×#120	1	1	yes	characteristic
424	C₂²×C₄	C₂×#120	1	1	yes	characteristic
425	C₂²×C₄	C₂×#120	1	1	yes	characteristic
426	C₂²×C₄	C₂×#120	1	1	yes	characteristic
427	C₂²×C₄	C₂×#120	1	1	yes	characteristic
428	C₂²×C₄	C₂×#120	1	1	yes	characteristic
429	C₂²×C₄	C₂×#120	1	1	yes	characteristic
430	C₂²×C₄	C₂×#120	1	1	yes	characteristic
431	C₂²×C₄	C₂×#120	1	1	yes	characteristic
432	C₂²×C₄	C₂×#120	1	1	yes	characteristic
433	C₂²×C₄	C₂×#120	1	1	yes	characteristic
434	C₂²×C₄	C₂×#120	1	1	yes	characteristic
435	C₂²×C₄	C₂×#120	1	1	yes	characteristic
436	C₂²×C₄	C₂×#120	1	1	yes	characteristic
437	C₂²×C₄	C₂×#120	1	1	yes	characteristic
438	C₂²×C₄	C₂×#120	1	1	yes	characteristic
439	C₂²×C₄	C₂×#120	1	1	yes	characteristic
440	C₂²×C₄	C₂×#120	1	1	yes	characteristic
441	C₂²×C₄	C₂×#120	1	1	yes	characteristic
442	C₂²×C₄	C₂×#120	1	1	yes	characteristic
443	C₂²×C₄	C₂×#120	1	1	yes	characteristic
444	C₂²×C₄	C₂×#120	1	1	yes	characteristic
445	C₂²×C₄	C₂×#120	1	1	yes	characteristic
446	C₂²×C₄	C₂×#120	1	1	yes	characteristic
447	C₂²×C₄	C₂×#120	1	1	yes	characteristic
448	C₂²×C₄	C₂×#120	1	1	yes	characteristic
449	C₂²×C₄	C₂×#120	1	1	yes	characteristic
450	C₂²×C₄	C₂×#120	1	1	yes	characteristic
451	C₂²×C₄	C₂×#121	1	1	yes	characteristic
452	C₂²×C₄	C₂×#121	1	1	yes	characteristic
453	C₂²×C₄	C₂×#121	1	1	yes	characteristic
454	C₂²×C₄	C₂×#121	1	1	yes	characteristic
455	C₂²×C₄	C₂×#121	1	1	yes	characteristic
456	C₂²×C₄	C₂×#121	1	1	yes	characteristic
457	C₂²×C₄	C₂×#121	1	1	yes	characteristic
458	C₂²×C₄	C₂×#121	1	1	yes	characteristic
459	C₂²×C₄	C₂×#121	1	1	yes	characteristic
460	C₂²×C₄	C₂×#121	1	1	yes	characteristic
461	C₂²×C₄	C₂×#121	1	1	yes	characteristic
462	C₂²×C₄	C₂×#121	1	1	yes	characteristic
463	C₂²×C₄	C₂×#127	1	1	yes	characteristic
464	C₂²×C₄	C₂×#127	1	1	yes	characteristic
465	C₂²×C₄	C₂×#127	1	1	yes	characteristic
466	C₂²×C₄	C₂×#127	1	1	yes	characteristic
467	C₂²×C₄	#534	1	1	yes	characteristic
468	C₂²×C₄	#534	1	1	yes	characteristic
469	C₂²×C₄	#534	1	1	yes	characteristic
470	C₂²×C₄	#534	1	1	yes	characteristic
471	C₂²×C₄	#534	1	1	yes	characteristic
472	C₂²×C₄	#534	1	1	yes	characteristic
473	C₂²×C₄	#534	1	1	yes	characteristic
474	C₂²×C₄	#534	1	1	yes	characteristic
475	C₂²×C₄	#534	1	1	yes	characteristic
476	C₂²×C₄	#534	1	1	yes	characteristic
477	C₂²×C₄	#534	1	1	yes	characteristic
478	C₂²×C₄	#534	1	1	yes	characteristic
479	C₂²×C₄	#535	1	1	yes	characteristic
480	C₂²×C₄	#535	1	1	yes	characteristic
481	C₂²×C₄	#535	1	1	yes	characteristic
482	C₂²×C₄	#535	1	1	yes	characteristic
483	C₂²×C₄	#535	1	1	yes	characteristic
484	C₂²×C₄	#535	1	1	yes	characteristic
485	C₂²×C₄	D₄²	1	1	yes	characteristic
486	C₂²×C₄	D₄²	1	1	yes	characteristic
487	C₂²×C₄	D₄²	1	1	yes	characteristic
488	C₂²×C₄	D₄²	1	1	yes	characteristic
489	C₂²×C₄	D₄²	1	1	yes	characteristic
490	C₂²×C₄	D₄²	1	1	yes	characteristic
491	C₂²×C₄	D₄²	1	1	yes	characteristic
492	C₂²×C₄	D₄²	1	1	yes	characteristic
493	C₂²×C₄	D₄²	1	1	yes	characteristic
494	C₂²×C₄	D₄²	1	1	yes	characteristic
495	C₂²×C₄	D₄²	1	1	yes	characteristic
496	C₂²×C₄	D₄²	1	1	yes	characteristic
497	C₂²×C₄	D₄²	1	1	yes	characteristic
498	C₂²×C₄	D₄²	1	1	yes	characteristic
499	C₂²×C₄	D₄²	1	1	yes	characteristic
500	C₂²×C₄	D₄²	1	1	yes	characteristic
501	C₂²×C₄	D₄²	1	1	yes	characteristic
502	C₂²×C₄	D₄²	1	1	yes	characteristic
503	C₂²×C₄	D₄²	1	1	yes	characteristic
504	C₂²×C₄	D₄²	1	1	yes	characteristic
505	C₂²×C₄	D₄²	1	1	yes	characteristic
506	C₂²×C₄	D₄²	1	1	yes	characteristic
507	C₂²×C₄	D₄²	1	1	yes	characteristic
508	C₂²×C₄	D₄²	1	1	yes	characteristic
509	C₂²×C₄	D₄²	1	1	yes	characteristic
510	C₂²×C₄	D₄²	1	1	yes	characteristic
511	C₂²×C₄	D₄²	1	1	yes	characteristic
512	C₂²×C₄	D₄²	1	1	yes	characteristic
513	C₂²×C₄	D₄²	1	1	yes	characteristic
514	C₂²×C₄	D₄²	1	1	yes	characteristic
515	C₂²×C₄	D₄²	1	1	yes	characteristic
516	C₂²×C₄	D₄²	1	1	yes	characteristic
517	C₂²×C₄	D₄²	1	1	yes	characteristic
518	C₂²×C₄	D₄²	1	1	yes	characteristic
519	C₂²×C₄	D₄²	1	1	yes	characteristic
520	C₂²×C₄	D₄²	1	1	yes	characteristic
521	C₂²×C₄	D₄²	1	1	yes	characteristic
522	C₂²×C₄	D₄²	1	1	yes	characteristic
523	C₂²×C₄	D₄²	1	1	yes	characteristic
524	C₂²×C₄	D₄²	1	1	yes	characteristic
525	C₂²×C₄	D₄²	1	1	yes	characteristic
526	C₂²×C₄	D₄²	1	1	yes	characteristic
527	C₂²×C₄	#546	1	1	yes	characteristic
528	C₂²×C₄	#546	1	1	yes	characteristic
529	C₂²×C₄	#546	1	1	yes	characteristic
530	C₂²×C₄	#546	1	1	yes	characteristic
531	C₂²×C₄	#546	1	1	yes	characteristic
532	C₂²×C₄	#546	1	1	yes	characteristic
533	C₂²×C₄	#546	1	1	yes	characteristic
534	C₂²×C₄	#546	1	1	yes	characteristic
535	C₂²×C₄	#546	1	1	yes	characteristic
536	C₂²×C₄	#546	1	1	yes	characteristic
537	C₂²×C₄	#546	1	1	yes	characteristic
538	C₂²×C₄	#546	1	1	yes	characteristic
539	C₂²×C₄	#546	1	1	yes	characteristic
540	C₂²×C₄	#546	1	1	yes	characteristic
541	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
542	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
543	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
544	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
545	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
546	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
547	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
548	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
549	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
550	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
551	C₂²×C₄	C₂²×#41	1	1	yes	characteristic
552	C₂²×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂²×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
554	C₂²×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
555	M₁₆	C₂×#120	1	8	yes	—
556	C₂×C₈	C₂×#120	1	8	yes	—
557	C₂³	#2403	1	1	yes	characteristic
558	C₂³	#2403	1	1	yes	characteristic
559	C₂³	#2403	1	1	yes	characteristic
560	C₂³	#2403	1	1	yes	characteristic
561	C₂³	#2403	1	1	yes	characteristic
562	C₂³	#2403	1	1	yes	characteristic
563	C₂³	#2403	1	1	yes	characteristic
564	C₂³	#2403	1	1	yes	characteristic
565	C₂³	#2408	1	1	yes	characteristic
566	C₂³	#2408	1	1	yes	characteristic
567	C₂³	#2408	1	1	yes	characteristic
568	C₂³	#2408	1	1	yes	characteristic
569	C₂³	#2410	1	1	yes	characteristic
570	C₂³	#2410	1	1	yes	characteristic
571	C₂³	#2410	1	1	yes	characteristic
572	C₂³	#2410	1	1	yes	characteristic
573	C₂³	#2410	1	1	yes	characteristic
574	C₂³	#2410	1	1	yes	characteristic
575	C₂³	#2410	1	1	yes	characteristic
576	C₂³	#2410	1	1	yes	characteristic
577	C₂³	#2433	1	1	yes	characteristic
578	C₂³	#2433	1	1	yes	characteristic
579	C₂³	#2433	1	1	yes	characteristic
580	C₂³	#2433	1	1	yes	characteristic
581	C₂³	#2613	1	1	yes	characteristic
582	C₂³	#2613	1	1	yes	characteristic
583	C₂³	#2613	1	1	yes	characteristic
584	C₂³	#2613	1	1	yes	characteristic
585	C₂³	C₂×#534	1	1	yes	characteristic
586	C₂³	C₂×#534	1	1	yes	characteristic
587	C₂³	C₂×#535	1	1	yes	characteristic
588	C₂³	C₂×D₄²	1	1	yes	characteristic
589	C₂³	C₂×D₄²	1	1	yes	characteristic
590	C₂³	C₂×D₄²	1	1	yes	characteristic
591	C₂³	C₂×#546	1	1	yes	characteristic
592	Q₈	C₂×#392	1	8	yes	—
593	D₄	C₂×#392	1	8	yes	—
594	C₂×C₄	C₂×#392	1	1	yes	characteristic
595	C₂×C₄	C₂×#392	1	1	yes	characteristic
596	C₂×C₄	C₂×#392	1	1	yes	characteristic
597	C₂×C₄	C₂×#392	1	1	yes	characteristic
598	C₂×C₄	C₂×#392	1	1	yes	characteristic
599	C₂×C₄	C₂×#392	1	1	yes	characteristic
600	C₂×C₄	C₂×#392	1	1	yes	characteristic
601	C₂×C₄	C₂×#392	1	1	yes	characteristic
602	C₂×C₄	#2403	1	1	yes	characteristic
603	C₂×C₄	#2403	1	1	yes	characteristic
604	C₂×C₄	#2403	1	1	yes	characteristic
605	C₂×C₄	#2403	1	1	yes	characteristic
606	C₂×C₄	#2403	1	1	yes	characteristic
607	C₂×C₄	#2403	1	1	yes	characteristic
608	C₂×C₄	#2403	1	1	yes	characteristic
609	C₂×C₄	#2403	1	1	yes	characteristic
610	C₂×C₄	#2403	1	1	yes	characteristic
611	C₂×C₄	#2403	1	1	yes	characteristic
612	C₂×C₄	#2403	1	1	yes	characteristic
613	C₂×C₄	#2403	1	1	yes	characteristic
614	C₂×C₄	#2403	1	1	yes	characteristic
615	C₂×C₄	#2403	1	1	yes	characteristic
616	C₂×C₄	#2403	1	1	yes	characteristic
617	C₂×C₄	#2403	1	1	yes	characteristic
618	C₂×C₄	#2403	1	1	yes	characteristic
619	C₂×C₄	#2403	1	1	yes	characteristic
620	C₂×C₄	#2403	1	1	yes	characteristic
621	C₂×C₄	#2403	1	1	yes	characteristic
622	C₂×C₄	#2403	1	1	yes	characteristic
623	C₂×C₄	#2403	1	1	yes	characteristic
624	C₂×C₄	#2403	1	1	yes	characteristic
625	C₂×C₄	#2403	1	1	yes	characteristic
626	C₂×C₄	#2408	1	1	yes	characteristic
627	C₂×C₄	#2408	1	1	yes	characteristic
628	C₂×C₄	#2408	1	1	yes	characteristic
629	C₂×C₄	#2408	1	1	yes	characteristic
630	C₂×C₄	#2408	1	1	yes	characteristic
631	C₂×C₄	#2408	1	1	yes	characteristic
632	C₂×C₄	#2408	1	1	yes	characteristic
633	C₂×C₄	#2408	1	1	yes	characteristic
634	C₂×C₄	#2408	1	1	yes	characteristic
635	C₂×C₄	#2408	1	1	yes	characteristic
636	C₂×C₄	#2408	1	1	yes	characteristic
637	C₂×C₄	#2408	1	1	yes	characteristic
638	C₂×C₄	#2410	1	1	yes	characteristic
639	C₂×C₄	#2410	1	1	yes	characteristic
640	C₂×C₄	#2410	1	1	yes	characteristic
641	C₂×C₄	#2410	1	1	yes	characteristic
642	C₂×C₄	#2410	1	1	yes	characteristic
643	C₂×C₄	#2410	1	1	yes	characteristic
644	C₂×C₄	#2410	1	1	yes	characteristic
645	C₂×C₄	#2410	1	1	yes	characteristic
646	C₂×C₄	#2410	1	1	yes	characteristic
647	C₂×C₄	#2410	1	1	yes	characteristic
648	C₂×C₄	#2410	1	1	yes	characteristic
649	C₂×C₄	#2410	1	1	yes	characteristic
650	C₂×C₄	#2410	1	1	yes	characteristic
651	C₂×C₄	#2410	1	1	yes	characteristic
652	C₂×C₄	#2410	1	1	yes	characteristic
653	C₂×C₄	#2410	1	1	yes	characteristic
654	C₂×C₄	#2410	1	1	yes	characteristic
655	C₂×C₄	#2410	1	1	yes	characteristic
656	C₂×C₄	#2410	1	1	yes	characteristic
657	C₂×C₄	#2410	1	1	yes	characteristic
658	C₂×C₄	#2410	1	1	yes	characteristic
659	C₂×C₄	#2410	1	1	yes	characteristic
660	C₂×C₄	#2410	1	1	yes	characteristic
661	C₂×C₄	#2410	1	1	yes	characteristic
662	C₂×C₄	#2433	1	1	yes	characteristic
663	C₂×C₄	#2433	1	1	yes	characteristic
664	C₂×C₄	#2433	1	1	yes	characteristic
665	C₂×C₄	#2433	1	1	yes	characteristic
666	C₂×C₄	#2433	1	1	yes	characteristic
667	C₂×C₄	#2433	1	1	yes	characteristic
668	C₂×C₄	#2433	1	1	yes	characteristic
669	C₂×C₄	#2433	1	1	yes	characteristic
670	C₂×C₄	#2433	1	1	yes	characteristic
671	C₂×C₄	#2433	1	1	yes	characteristic
672	C₂×C₄	#2433	1	1	yes	characteristic
673	C₂×C₄	#2433	1	1	yes	characteristic
674	C₂×C₄	#2613	1	1	yes	characteristic
675	C₂×C₄	#2613	1	1	yes	characteristic
676	C₂×C₄	#2613	1	1	yes	characteristic
677	C₂×C₄	#2613	1	1	yes	characteristic
678	C₂×C₄	#2846	1	1	yes	characteristic
679	C₂×C₄	#2846	1	1	yes	characteristic
680	C₂×C₄	#2846	1	1	yes	characteristic
681	C₂×C₄	#2846	1	1	yes	characteristic
682	C₂×C₄	#2846	1	1	yes	characteristic
683	C₂×C₄	#2846	1	1	yes	characteristic
684	C₂×C₄	#2846	1	1	yes	characteristic
685	C₂×C₄	#2846	1	1	yes	characteristic
686	C₂×C₄	C₂²×#120	1	1	yes	characteristic
687	C₂×C₄	C₂²×#120	1	1	yes	characteristic
688	C₂×C₄	C₂²×#120	1	1	yes	characteristic
689	C₂×C₄	C₂²×#120	1	1	yes	characteristic
690	C₂×C₄	C₂²×#120	1	1	yes	characteristic
691	C₂×C₄	C₂²×#120	1	1	yes	characteristic
692	C₂×C₄	C₂²×#120	1	1	yes	characteristic
693	C₂×C₄	C₂²×#120	1	1	yes	characteristic
694	C₂×C₄	C₂²×#120	1	1	yes	characteristic
695	C₂×C₄	C₂²×#121	1	1	yes	characteristic
696	C₂×C₄	C₂²×#121	1	1	yes	characteristic
697	C₂×C₄	C₂²×#121	1	1	yes	characteristic
698	C₂×C₄	C₂²×#127	1	1	yes	characteristic
699	C₂×C₄	C₂×#534	1	1	yes	characteristic
700	C₂×C₄	C₂×#534	1	1	yes	characteristic
701	C₂×C₄	C₂×#535	1	1	yes	characteristic
702	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
703	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
704	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
705	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
706	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
707	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
708	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
709	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
710	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
711	C₂×C₄	C₂×#546	1	1	yes	characteristic
712	C₂×C₄	C₂×#546	1	1	yes	characteristic
713	C₂×C₄	C₂×#546	1	1	yes	characteristic
714	C₂²	#14715	1	1	yes	characteristic
715	C₂²	#14715	1	1	yes	characteristic
716	C₂²	#14715	1	1	yes	characteristic
717	C₂²	#14715	1	1	yes	characteristic
718	C₂²	#14715	1	1	yes	characteristic
719	C₂²	#14715	1	1	yes	characteristic
720	C₂²	#14715	1	1	yes	characteristic
721	C₂²	#14715	1	1	yes	characteristic
722	C₂²	C₂×#2613	1	1	yes	characteristic
723	C₂²	C₂×#2403	1	1	yes	characteristic
724	C₂²	C₂×#2403	1	1	yes	characteristic
725	C₂²	C₂×#2410	1	1	yes	characteristic
726	C₂²	C₂×#2410	1	1	yes	characteristic
727	C₂²	C₂×#2408	1	1	yes	characteristic
728	C₂²	C₂×#2433	1	1	yes	characteristic
729	C₄	#14715	1	1	yes	characteristic
730	C₄	#14715	1	1	yes	characteristic
731	C₄	#14715	1	1	yes	characteristic
732	C₄	#14715	1	1	yes	characteristic
733	C₄	#14715	1	1	yes	characteristic
734	C₄	#14715	1	1	yes	characteristic
735	C₄	#14715	1	1	yes	characteristic
736	C₄	#14715	1	1	yes	characteristic
737	C₄	C₂²×#392	1	1	yes	characteristic
738	C₄	C₂×#2403	1	1	yes	characteristic
739	C₄	C₂×#2403	1	1	yes	characteristic
740	C₄	C₂×#2410	1	1	yes	characteristic
741	C₄	C₂×#2410	1	1	yes	characteristic
742	C₄	C₂×#2408	1	1	yes	characteristic
743	C₄	C₂×#2433	1	1	yes	characteristic
744	C₄	C₂×#2846	1	1	yes	characteristic
745	C₂	#394133	1	2	yes	direct product factor
746	C₂	C₂×#14715	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#14715
commutator, Frattini, cosocle	C₂³×C₄	C₂⁵
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×#3585	C₂	semidirect
2. C₂×#60367	C₂	semidirect
3. C₂×#60387	C₂	semidirect
4. C₂×#23439	C₂	semidirect
5. C₂×#23414	C₂	semidirect
6. C₂×#23412	C₂	semidirect
7. C₂×#23407	C₂	semidirect
8. C₂×#20939	C₂	semidirect
9. C₂×#20623	C₂	semidirect
10. C₂×#20616	C₂	semidirect
11. #394133	C₂	direct (N × H)
12. C₂×#11037	C₂	semidirect
13. C₂×#11034	C₂	semidirect
14. C₂×#11032	C₂	semidirect
15. C₂×#11012	C₂	semidirect
16. C₂×#10787	C₂	semidirect
19. C₂×#3585	C₂²	semidirect
23. C₂²×#575	C₂²	semidirect
26. C₂³×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×#3449	C₂²	semidirect
29. C₂×#3449	C₂²	semidirect
30. #60387	C₂²	semidirect
31. #60367	C₂²	semidirect
33. C₂²×#421	C₂²	semidirect
34. C₂²×#421	C₂²	semidirect
35. C₂²×#421	C₂²	semidirect
36. C₂²×#421	C₂²	semidirect
37. C₂²×#421	C₂²	semidirect
40. C₂×#2896	C₂²	semidirect
41. C₂²×#418	C₂²	semidirect
42. C₂²×#413	C₂²	semidirect
43. C₂²×#413	C₂²	semidirect
44. C₂³×#100	C₂²	semidirect
45. C₂²×#410	C₂²	semidirect
46. C₂×#2879	C₂²	semidirect
47. C₂×#2879	C₂²	semidirect
48. C₂×#2309	C₂²	semidirect
49. #23439	C₂²	semidirect
50. #23414	C₂²	semidirect
51. #23412	C₂²	semidirect
52. #23407	C₂²	semidirect
53. #20939	C₂²	semidirect
54. #20623	C₂²	semidirect
55. #20616	C₂²	semidirect
56. C₂²×#344	C₂²	semidirect
57. C₂²×#344	C₂²	semidirect
58. C₂×#1742	C₂²	semidirect
59. C₂×#1738	C₂²	semidirect
60. C₂×#1738	C₂²	semidirect
61. C₂²×H(3,ℤ/4)	C₂²	semidirect
62. #11037	C₂²	semidirect
63. #11034	C₂²	semidirect
64. #11032	C₂²	semidirect
65. #11012	C₂²	semidirect
66. #10787	C₂²	semidirect
67. C₂×#585	D₄	semidirect
69. C₂²×2₋¹⁺⁴	D₄	semidirect
70. C₂²×H(5,𝔽₂)	D₄	semidirect
71. C₂²×H(5,𝔽₂)	D₄	semidirect
72. C₂²×H(5,𝔽₂)	D₄	semidirect
83. C₂×#575	D₄	semidirect
87. C₂×#575	C₂³	semidirect
89. C₂²×#137	D₄	semidirect
91. C₂²×AGL(1,ℤ/8)	D₄	semidirect
92. C₂²×AGL(1,ℤ/8)	D₄	semidirect
93. C₂²×AGL(1,ℤ/8)	D₄	semidirect
94. C₂²×AGL(1,ℤ/8)	D₄	semidirect
97. C₂²×AGL(1,ℤ/8)	C₂³	semidirect
98. C₂³×SD₁₆	D₄	semidirect
99. C₂³×D₈	D₄	semidirect
100. C₂×#568	D₄	semidirect
101. C₂×#568	D₄	semidirect
109. #3449	C₂³	semidirect
110. #3449	C₂³	semidirect
114. C₂×#421	D₄	semidirect
116. C₂×#421	C₂³	semidirect
117. C₂×#421	C₂³	semidirect
118. C₂×#421	C₂³	semidirect
119. C₂×#421	C₂³	semidirect
120. C₂×#421	C₂³	semidirect
121. C₂²×#104	D₄	semidirect
122. #2896	D₄	semidirect
125. #2896	C₂³	semidirect
126. C₂×#419	D₄	semidirect
127. C₂×#418	D₄	semidirect
128. C₂×#418	C₂³	semidirect
129. C₂×#413	C₂³	semidirect
130. C₂×#413	C₂³	semidirect
131. C₂²×#100	C₂³	semidirect
132. C₂×#410	C₂³	semidirect
133. #2879	C₂³	semidirect
134. #2879	C₂³	semidirect
135. #2309	C₂³	semidirect
136. C₂×#344	C₂³	semidirect
137. C₂×#344	C₂³	semidirect
138. #1742	C₂³	semidirect
139. #1738	C₂³	semidirect
140. #1738	C₂³	semidirect
141. C₂×H(3,ℤ/4)	C₂³	semidirect
142. C₂×2₋¹⁺⁴	C₂×D₄	semidirect
143. C₂×H(5,𝔽₂)	C₂×D₄	semidirect
144. C₂×H(5,𝔽₂)	C₂×D₄	semidirect
199. C₂×#137	C₂×D₄	semidirect
201. C₂×AGL(1,ℤ/8)	C₂×D₄	semidirect
202. C₂×AGL(1,ℤ/8)	C₂×D₄	semidirect
203. C₂²×SD₁₆	C₂×D₄	semidirect
204. C₂²×D₈	C₂×D₄	semidirect
205. #568	C₂×D₄	semidirect
237. C₂×#104	C₂×D₄	semidirect
238. #419	C₂×D₄	semidirect
239. #418	C₂×D₄	semidirect
745. C₂	#394133	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#3585	2
C₂×#60367	2
C₂×#60387	2
C₂×#23439	2
C₂×#23414	2
C₂×#23412	2
C₂×#23407	2
C₂×#20939	2
C₂×#20623	2
C₂×#20616	2
#394133	2
C₂×#11037	2
C₂×#11034	2
C₂×#11032	2
C₂×#11012	2
C₂×#10787	2

Subgroups — C2×#394133 #72251529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#394133 #72251529