Subgroups — C₂×#72240532 #72319462

Order 2048.

At least 9787 conjugacy classes of subgroups; only the 2544 normal subgroups are shown.

The subgroup lattice has 750 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×#146483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#359551	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#146595	C₂	1	4	yes	maximal, complemented
4	C₂×#494587	C₂	1	4	yes	maximal, complemented
5	C₂×#146477	C₂	1	1	yes	maximal, characteristic, complemented
6	#72240532	C₂	1	16	yes	maximal, direct product factor
7	C₂×#359562	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#6437616	C₂	1	1	yes	maximal, characteristic
9	C₂×#493352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10574294	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#62811	C₂²	1	1	yes	characteristic
12	C₂³×#525	C₂²	1	1	yes	characteristic
13	C₂²×#3025	C₂²	1	2	yes	—
14	#10574294	C₂²	1	8	yes	complemented
15	C₂×#60231	C₂²	1	4	yes	—
16	C₂×#60064	C₂²	1	1	yes	characteristic
17	C₂×#60064	C₂²	1	1	yes	characteristic
18	C₂²×#2120	C₂²	1	4	yes	—
19	#6437616	C₄	1	8	yes	complemented
20	#6437616	C₂²	1	8	yes	—
21	C₂×#23902	C₄	1	4	yes	complemented
22	C₂×#23901	C₄	1	2	yes	complemented
23	C₂×#23900	C₄	1	2	yes	complemented
24	C₂×#20959	C₂²	1	2	yes	—
25	C₂×#20620	C₂²	1	2	yes	complemented
26	C₂×#20612	C₂²	1	2	yes	complemented
27	C₂×#20591	C₂²	1	1	yes	characteristic
28	C₂×#20584	C₂²	1	1	yes	characteristic
29	C₂×#20584	C₂²	1	1	yes	characteristic
30	#494587	C₂²	1	32	yes	complemented
31	#493352	C₂²	1	8	yes	complemented
32	C₂×#12589	C₂²	1	4	yes	complemented
33	C₂×#12577	C₂²	1	4	yes	complemented
34	#359562	C₂²	1	8	yes	complemented
35	#359551	C₂²	1	8	yes	complemented
36	C₂×#10756	C₂²	1	2	yes	complemented
37	C₂×#10743	C₂²	1	2	yes	complemented
38	#146595	C₂²	1	32	yes	complemented
39	#146483	C₂²	1	8	yes	complemented
40	#146477	C₂²	1	8	yes	complemented
41	C₂²×#585	C₂³	1	1	yes	characteristic
42	C₂⁴×#41	C₂³	1	1	yes	characteristic
43	C₂⁶×C₄	D₄	1	1	yes	characteristic
44	C₂²×#568	D₄	1	1	yes	characteristic, complemented
45	C₂²×#568	D₄	1	1	yes	characteristic, complemented
46	C₂²×#568	D₄	1	1	yes	characteristic, complemented
47	C₂²×#568	D₄	1	1	yes	characteristic, complemented
48	#62811	C₂×C₄	1	4	yes	—
49	#62811	C₂³	1	4	yes	—
50	C₂×#3485	C₂×C₄	1	2	yes	—
51	C₂×#3484	C₂×C₄	1	2	yes	—
52	C₂²×#525	C₂×C₄	1	2	yes	—
53	C₂²×#525	C₂×C₄	1	4	yes	—
54	C₂²×#525	D₄	1	2	yes	—
55	C₂²×#525	D₄	1	4	yes	—
56	C₂²×#525	D₄	1	2	yes	—
57	C₂²×#525	D₄	1	4	yes	—
58	C₂²×#525	C₂³	1	4	yes	—
59	C₂²×#525	C₂³	1	2	yes	—
60	C₂³×#123	C₂×C₄	1	1	yes	characteristic
61	C₂³×#123	D₄	1	1	yes	characteristic
62	C₂³×#120	C₂×C₄	1	1	yes	characteristic
63	C₂³×#120	D₄	1	1	yes	characteristic
64	C₂×#3428	C₂³	1	1	yes	characteristic
65	C₂³×#117	D₄	1	1	yes	characteristic
66	C₂×#3025	C₂×C₄	1	8	yes	—
67	C₂×#3025	C₂³	1	8	yes	—
68	C₂²×#458	C₂×C₄	1	4	yes	—
69	C₂²×B(4,𝔽₂)	C₂×C₄	1	4	yes	—
70	#60231	D₄	1	16	yes	complemented
71	#60231	C₂³	1	16	yes	—
72	C₂×#2978	D₄	1	8	yes	complemented
73	C₂×#2977	D₄	1	8	yes	complemented
74	C₂²×#413	C₂³	1	2	yes	—
75	C₂²×#410	C₂³	1	2	yes	—
76	C₂²×#410	C₂³	1	2	yes	—
77	#60064	D₄	1	4	yes	complemented
78	#60064	D₄	1	4	yes	complemented
79	#60064	C₂³	1	4	yes	—
80	#60064	C₂³	1	4	yes	—
81	C₂×#2879	C₂³	1	2	yes	—
82	C₂×#2879	C₂³	1	2	yes	—
83	C₂²×#407	D₄	1	2	yes	complemented
84	C₂²×#407	D₄	1	2	yes	complemented
85	C₂×#2120	C₂³	1	16	yes	—
86	#23902	C₂×C₄	1	32	yes	complemented
87	#23901	C₂×C₄	1	16	yes	complemented
88	#23900	C₂×C₄	1	16	yes	complemented
89	#20959	C₂×C₄	1	8	yes	—
90	#20959	C₂³	1	8	yes	—
91	C₂×#1890	C₂×C₄	1	4	yes	—
92	C₂×#1889	C₂×C₄	1	4	yes	—
93	#20620	C₂³	1	8	yes	complemented
94	#20612	C₂³	1	8	yes	complemented
95	#20591	C₂³	1	4	yes	—
96	#20584	C₂×C₄	1	4	yes	—
97	#20584	C₂³	1	4	yes	—
98	#20584	C₂³	1	4	yes	—
99	C₂×#1782	C₂×C₄	1	2	yes	—
100	C₂×#1781	C₂×C₄	1	2	yes	—
101	#12589	C₂³	1	16	yes	complemented
102	#12577	C₂³	1	16	yes	complemented
103	#10756	C₂³	1	8	yes	complemented
104	#10743	C₂³	1	8	yes	complemented
105	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×#585	C₂²×C₄	1	2	yes	—
107	C₂×#585	C₂⁴	1	2	yes	—
108	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
109	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
110	C₂³×#41	C₂²×C₄	1	2	yes	—
111	C₂³×#41	C₂×D₄	1	1	yes	characteristic
112	C₂³×#41	C₂×D₄	1	2	yes	—
113	C₂³×#41	C₂×D₄	1	1	yes	characteristic
114	C₂³×#41	C₂×D₄	1	2	yes	—
115	C₂³×#41	C₂×D₄	1	1	yes	characteristic
116	C₂³×#41	C₂×D₄	1	2	yes	—
117	C₂³×#41	C₂×D₄	1	1	yes	characteristic
118	C₂³×#41	C₂×D₄	1	2	yes	—
119	C₂³×#41	#41	1	1	yes	characteristic
120	C₂³×#41	#41	1	2	yes	—
121	C₂³×#41	#41	1	1	yes	characteristic
122	C₂³×#41	#41	1	2	yes	—
123	C₂³×#41	C₂⁴	1	2	yes	—
124	C₂³×#41	C₂⁴	1	1	yes	characteristic
125	C₂⁴×Q₈	#41	1	1	yes	characteristic
126	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
127	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
128	C₂⁴×D₄	#41	1	1	yes	characteristic
129	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
130	C₂⁵×C₄	C₂²⋊C₄	1	2	yes	—
131	C₂⁵×C₄	C₂²⋊C₄	1	4	yes	—
132	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
133	C₂⁵×C₄	C₂×D₄	1	4	yes	—
134	C₂⁵×C₄	C₂×D₄	1	2	yes	—
135	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
136	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
137	C₂×#568	C₂×D₄	1	4	yes	complemented
138	C₂×#568	C₂×D₄	1	4	yes	complemented
139	C₂×#568	C₂×D₄	1	4	yes	complemented
140	C₂×#568	C₂×D₄	1	4	yes	complemented
141	C₂³×M₁₆	C₂×D₄	1	2	yes	—
142	C₂³×M₁₆	C₂×D₄	1	2	yes	—
143	C₂³×M₁₆	C₂×D₄	1	2	yes	—
144	C₂³×M₁₆	C₂×D₄	1	2	yes	—
145	#3485	C₂²×C₄	1	8	yes	—
146	#3484	C₂²×C₄	1	8	yes	—
147	C₂×#525	C₂²⋊C₄	1	8	yes	—
148	C₂×#525	C₂²⋊C₄	1	8	yes	—
149	C₂×#525	C₂²⋊C₄	1	8	yes	—
150	C₂×#525	C₂²×C₄	1	8	yes	—
151	C₂×#525	C₂²×C₄	1	4	yes	—
152	C₂×#525	C₂×D₄	1	8	yes	—
153	C₂×#525	C₂×D₄	1	4	yes	—
154	C₂×#525	C₂×D₄	1	4	yes	—
155	C₂×#525	C₂×D₄	1	4	yes	—
156	C₂×#525	C₂×D₄	1	8	yes	—
157	C₂×#525	C₂×D₄	1	8	yes	—
158	C₂×#525	C₂×D₄	1	4	yes	—
159	C₂×#525	#41	1	4	yes	—
160	C₂×#525	#41	1	4	yes	—
161	C₂×#525	#41	1	8	yes	—
162	C₂×#525	C₂⁴	1	4	yes	—
163	C₂²×#123	C₂²⋊C₄	1	4	yes	—
164	C₂²×#123	C₂²⋊C₄	1	4	yes	—
165	C₂²×#123	C₂²⋊C₄	1	2	yes	—
166	C₂²×#123	C₂²⋊C₄	1	2	yes	—
167	C₂²×#123	C₂²×C₄	1	4	yes	—
168	C₂²×#123	C₂²×C₄	1	2	yes	—
169	C₂²×#123	C₂×D₄	1	4	yes	—
170	C₂²×#123	C₂×D₄	1	2	yes	—
171	C₂²×#120	C₂²⋊C₄	1	4	yes	—
172	C₂²×#120	C₂²⋊C₄	1	4	yes	—
173	C₂²×#120	C₂²⋊C₄	1	2	yes	—
174	C₂²×#120	C₂²⋊C₄	1	2	yes	—
175	C₂²×#120	C₂²×C₄	1	4	yes	—
176	C₂²×#120	C₂²×C₄	1	2	yes	—
177	C₂²×#120	C₂×D₄	1	4	yes	—
178	C₂²×#120	C₂×D₄	1	2	yes	—
179	#3428	C₂²×C₄	1	2	yes	—
180	#3428	C₂⁴	1	2	yes	—
181	C₂×#518	C₂²×C₄	1	2	yes	—
182	C₂²×#117	C₂²⋊C₄	1	2	yes	—
183	C₂²×#117	C₂²⋊C₄	1	4	yes	—
184	C₂²×#117	C₂×D₄	1	4	yes	—
185	C₂²×#117	C₂×D₄	1	2	yes	—
186	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
188	C₂×#458	C₂²×C₄	1	16	yes	—
189	C₂×B(4,𝔽₂)	C₂²×C₄	1	16	yes	—
190	#2978	C₂×D₄	1	32	yes	complemented
191	#2977	C₂×D₄	1	32	yes	complemented
192	C₂×#413	C₂⁴	1	4	yes	—
193	C₂×#410	C₂²×C₄	1	4	yes	—
194	C₂×#410	C₂⁴	1	4	yes	—
195	C₂×#410	C₂⁴	1	4	yes	—
196	C₂²×#99	C₂²×C₄	1	4	yes	—
197	#2879	C₂×D₄	1	8	yes	—
198	#2879	C₂×D₄	1	8	yes	—
199	#2879	C₂×D₄	1	4	yes	—
200	#2879	C₂×D₄	1	4	yes	—
201	#2879	C₂⁴	1	4	yes	—
202	#2879	C₂⁴	1	4	yes	—
203	C₂×#408	C₂×D₄	1	8	yes	—
204	C₂×#408	C₂×D₄	1	8	yes	—
205	C₂×#407	C₂×D₄	1	8	yes	complemented
206	C₂×#407	C₂×D₄	1	8	yes	complemented
207	#1890	C₂²×C₄	1	16	yes	—
208	#1889	C₂²×C₄	1	16	yes	—
209	#1782	C₂²×C₄	1	8	yes	—
210	#1781	C₂²×C₄	1	8	yes	—
211	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂⁶	C₂×C₂²⋊C₄	1	4	yes	—
213	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂⁶	C₄×D₄	1	1	yes	characteristic
215	C₂⁶	#121	1	1	yes	characteristic
216	C₂×H(5,𝔽₂)	C₂³×C₄	1	4	yes	—
217	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂²×#41	C₄×D₄	1	2	yes	—
221	C₂²×#41	C₄×D₄	1	2	yes	—
222	C₂²×#41	C₄×D₄	1	2	yes	—
223	C₂²×#41	C₄×D₄	1	2	yes	—
224	C₂²×#41	C₄×D₄	1	2	yes	—
225	C₂²×#41	C₄×D₄	1	2	yes	—
226	C₂²×#41	#120	1	2	yes	—
227	C₂²×#41	#120	1	2	yes	—
228	C₂²×#41	#120	1	2	yes	—
229	C₂²×#41	#121	1	2	yes	—
230	C₂²×#41	#121	1	2	yes	—
231	C₂²×#41	#121	1	2	yes	—
232	C₂²×#41	#121	1	2	yes	—
233	C₂²×#41	#121	1	2	yes	—
234	C₂²×#41	#121	1	2	yes	—
235	C₂²×#41	#123	1	2	yes	—
236	C₂²×#41	#123	1	2	yes	—
237	C₂²×#41	#123	1	2	yes	—
238	C₂²×#41	C₂³×C₄	1	2	yes	—
239	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
240	C₂²×#41	C₂²×D₄	1	2	yes	—
241	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
242	C₂²×#41	C₂²×D₄	1	4	yes	—
243	C₂²×#41	C₂²×D₄	1	4	yes	—
244	C₂²×#41	C₂²×D₄	1	2	yes	—
245	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
246	C₂²×#41	C₂²×D₄	1	2	yes	—
247	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
248	C₂²×#41	C₂²×D₄	1	2	yes	—
249	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
250	C₂²×#41	C₂×#41	1	2	yes	—
251	C₂²×#41	C₂×#41	1	1	yes	characteristic
252	C₂²×#41	C₂×#41	1	2	yes	—
253	C₂²×#41	C₂×#41	1	1	yes	characteristic
254	C₂²×#41	C₂×#41	1	4	yes	—
255	C₂²×#41	C₂×#41	1	4	yes	—
256	C₂²×#41	C₂⁵	1	1	yes	characteristic
257	C₂³×Q₈	C₄×D₄	1	1	yes	characteristic
258	C₂³×Q₈	C₄×D₄	1	2	yes	—
259	C₂³×Q₈	#121	1	1	yes	characteristic
260	C₂³×Q₈	#121	1	2	yes	—
261	C₂³×Q₈	#123	1	1	yes	characteristic
262	C₂³×Q₈	#123	1	2	yes	—
263	C₂³×Q₈	C₂×#41	1	2	yes	—
264	C₂³×Q₈	C₂×#41	1	1	yes	characteristic
265	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
269	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
270	C₂³×D₄	C₄×D₄	1	2	yes	—
271	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
272	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
273	C₂³×D₄	C₄×D₄	1	2	yes	—
274	C₂³×D₄	C₄×D₄	1	2	yes	—
275	C₂³×D₄	#121	1	1	yes	characteristic
276	C₂³×D₄	#121	1	2	yes	—
277	C₂³×D₄	#121	1	1	yes	characteristic
278	C₂³×D₄	#121	1	1	yes	characteristic
279	C₂³×D₄	#121	1	2	yes	—
280	C₂³×D₄	#121	1	2	yes	—
281	C₂³×D₄	#123	1	1	yes	characteristic
282	C₂³×D₄	#123	1	2	yes	—
283	C₂³×D₄	C₂³×C₄	1	2	yes	—
284	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
285	C₂³×D₄	C₂²×D₄	1	2	yes	—
286	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
287	C₂³×D₄	C₂×#41	1	2	yes	—
288	C₂³×D₄	C₂×#41	1	1	yes	characteristic
289	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
292	C₂⁴×C₄	C₂×C₂²⋊C₄	1	8	yes	—
293	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
294	C₂⁴×C₄	C₂×C₂²⋊C₄	1	4	yes	—
295	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
296	C₂⁴×C₄	C₄×D₄	1	2	yes	—
297	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
298	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
299	C₂⁴×C₄	C₄×D₄	1	2	yes	—
300	C₂⁴×C₄	#120	1	1	yes	characteristic
301	C₂⁴×C₄	#120	1	1	yes	characteristic
302	C₂⁴×C₄	#120	1	1	yes	characteristic
303	C₂⁴×C₄	#120	1	2	yes	—
304	C₂⁴×C₄	#120	1	1	yes	characteristic
305	C₂⁴×C₄	#120	1	2	yes	—
306	C₂⁴×C₄	#120	1	2	yes	—
307	C₂⁴×C₄	#120	1	4	yes	—
308	C₂⁴×C₄	#120	1	2	yes	—
309	C₂⁴×C₄	#120	1	2	yes	—
310	C₂⁴×C₄	#121	1	1	yes	characteristic
311	C₂⁴×C₄	#121	1	2	yes	—
312	C₂⁴×C₄	#121	1	1	yes	characteristic
313	C₂⁴×C₄	#121	1	1	yes	characteristic
314	C₂⁴×C₄	#121	1	2	yes	—
315	C₂⁴×C₄	#123	1	1	yes	characteristic
316	C₂⁴×C₄	#123	1	1	yes	characteristic
317	C₂⁴×C₄	#123	1	2	yes	—
318	C₂⁴×C₄	#123	1	2	yes	—
319	C₂⁴×C₄	#123	1	2	yes	—
320	C₂⁴×C₄	#123	1	4	yes	—
321	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
322	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
324	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
325	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
326	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
327	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
328	C₂²×M₁₆	#120	1	4	yes	complemented
329	C₂²×M₁₆	#120	1	4	yes	complemented
330	C₂²×M₁₆	#120	1	4	yes	complemented
331	C₂²×M₁₆	#120	1	4	yes	complemented
332	C₂²×M₁₆	#120	1	4	yes	complemented
333	C₂²×M₁₆	#120	1	4	yes	complemented
334	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
335	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
336	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
337	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
338	C₂³×C₈	#120	1	4	yes	complemented
339	C₂³×C₈	#120	1	4	yes	complemented
340	#525	C₄×D₄	1	8	yes	—
341	#525	C₄×D₄	1	8	yes	—
342	#525	C₄×D₄	1	8	yes	—
343	#525	C₄×D₄	1	8	yes	—
344	#525	#120	1	8	yes	—
345	#525	#120	1	8	yes	—
346	#525	#121	1	8	yes	—
347	#525	#121	1	8	yes	—
348	#525	#121	1	8	yes	—
349	#525	#121	1	8	yes	—
350	#525	#123	1	8	yes	—
351	#525	#123	1	8	yes	—
352	#525	C₂²×D₄	1	8	yes	—
353	#525	C₂²×D₄	1	8	yes	—
354	#525	C₂×#41	1	8	yes	—
355	#525	C₂×#41	1	8	yes	—
356	C₂×#123	C₂×C₂²⋊C₄	1	8	yes	—
357	C₂×#123	C₂×C₂²⋊C₄	1	8	yes	—
358	C₂×#123	C₂×C₂²⋊C₄	1	4	yes	—
359	C₂×#123	C₂×C₂²⋊C₄	1	4	yes	—
360	C₂×#123	C₄×D₄	1	4	yes	—
361	C₂×#123	C₄×D₄	1	4	yes	—
362	C₂×#123	C₄×D₄	1	8	yes	—
363	C₂×#123	#121	1	4	yes	—
364	C₂×#123	#121	1	4	yes	—
365	C₂×#123	#121	1	8	yes	—
366	C₂×#123	C₂³×C₄	1	4	yes	—
367	C₂×#123	C₂²×D₄	1	4	yes	—
368	C₂×#120	C₂×C₂²⋊C₄	1	8	yes	—
369	C₂×#120	C₂×C₂²⋊C₄	1	8	yes	—
370	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
371	C₂×#120	C₂×C₂²⋊C₄	1	4	yes	—
372	C₂×#120	C₄×D₄	1	4	yes	—
373	C₂×#120	C₄×D₄	1	4	yes	—
374	C₂×#120	C₄×D₄	1	8	yes	—
375	C₂×#120	#121	1	4	yes	—
376	C₂×#120	#121	1	4	yes	—
377	C₂×#120	#121	1	8	yes	—
378	C₂×#120	C₂³×C₄	1	4	yes	—
379	C₂×#120	C₂²×D₄	1	4	yes	—
380	#518	C₂³×C₄	1	4	yes	—
381	C₂×#117	C₂×C₂²⋊C₄	1	8	yes	—
382	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	—
383	C₂×#117	#120	1	4	yes	—
384	C₂×#117	#120	1	4	yes	—
385	C₂×#117	#123	1	4	yes	—
386	C₂×#117	#123	1	4	yes	—
387	C₂×#117	C₂²×D₄	1	4	yes	—
388	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
389	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
390	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
391	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
392	C₂×#99	C₂³×C₄	1	8	yes	—
393	#408	#120	1	16	yes	complemented
394	#408	#120	1	16	yes	complemented
395	#408	C₂²×D₄	1	16	yes	—
396	#408	C₂²×D₄	1	16	yes	—
397	C₂⁵	#386	1	1	yes	characteristic
398	C₂⁵	#386	1	1	yes	characteristic
399	C₂⁵	#386	1	1	yes	characteristic
400	C₂⁵	#386	1	2	yes	—
401	C₂⁵	#386	1	1	yes	characteristic
402	C₂⁵	#386	1	2	yes	—
403	C₂⁵	#386	1	2	yes	—
404	C₂⁵	#386	1	2	yes	—
405	C₂⁵	#386	1	2	yes	—
406	C₂⁵	#386	1	4	yes	—
407	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
408	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
409	C₂⁵	C₂²×C₂²⋊C₄	1	4	yes	—
410	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
411	C₂⁵	C₂×C₄×D₄	1	2	yes	—
412	C₂⁵	C₂×#121	1	1	yes	characteristic
413	C₂⁵	C₂×#121	1	2	yes	—
414	C₂×#41	C₂×C₄×D₄	1	4	yes	—
415	C₂×#41	C₂×C₄×D₄	1	4	yes	—
416	C₂×#41	C₂×#120	1	4	yes	—
417	C₂×#41	C₂×#120	1	4	yes	—
418	C₂×#41	C₂×#120	1	4	yes	—
419	C₂×#41	C₂×#121	1	4	yes	—
420	C₂×#41	C₂×#121	1	4	yes	—
421	C₂×#41	C₂×#123	1	4	yes	—
422	C₂×#41	#525	1	4	yes	—
423	C₂×#41	#525	1	4	yes	—
424	C₂×#41	#525	1	4	yes	—
425	C₂×#41	#525	1	4	yes	—
426	C₂×#41	#525	1	4	yes	—
427	C₂×#41	#525	1	4	yes	—
428	C₂×#41	C₂³×D₄	1	4	yes	—
429	C₂×#41	C₂²×#41	1	4	yes	—
430	C₂²×Q₈	#386	1	2	yes	—
431	C₂²×Q₈	#386	1	2	yes	—
432	C₂²×Q₈	#386	1	2	yes	—
433	C₂²×Q₈	C₂×C₄×D₄	1	2	yes	—
434	C₂²×Q₈	C₂×C₄×D₄	1	1	yes	characteristic
435	C₂²×Q₈	C₂×#121	1	2	yes	—
436	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
437	C₂²×Q₈	C₂×#123	1	2	yes	—
438	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
439	C₂²×Q₈	#525	1	4	yes	—
440	C₂²×Q₈	#525	1	4	yes	—
441	C₂²×Q₈	C₂²×#41	1	1	yes	characteristic
442	C₂²×D₄	#386	1	2	yes	—
443	C₂²×D₄	#386	1	2	yes	—
444	C₂²×D₄	#386	1	2	yes	—
445	C₂²×D₄	#386	1	2	yes	—
446	C₂²×D₄	#386	1	2	yes	—
447	C₂²×D₄	#386	1	2	yes	—
448	C₂²×D₄	#386	1	2	yes	—
449	C₂²×D₄	#386	1	2	yes	—
450	C₂²×D₄	#386	1	2	yes	—
451	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
452	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
453	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
454	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
455	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
456	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
457	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
458	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
459	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
460	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
461	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
462	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
463	C₂²×D₄	C₂×#121	1	4	yes	—
464	C₂²×D₄	C₂×#121	1	4	yes	—
465	C₂²×D₄	C₂×#121	1	2	yes	—
466	C₂²×D₄	C₂×#121	1	1	yes	characteristic
467	C₂²×D₄	C₂×#121	1	2	yes	—
468	C₂²×D₄	C₂×#121	1	2	yes	—
469	C₂²×D₄	C₂×#121	1	1	yes	characteristic
470	C₂²×D₄	C₂×#121	1	1	yes	characteristic
471	C₂²×D₄	C₂×#123	1	2	yes	—
472	C₂²×D₄	C₂×#123	1	1	yes	characteristic
473	C₂²×D₄	#525	1	4	yes	—
474	C₂²×D₄	#525	1	4	yes	—
475	C₂²×D₄	C₂⁴×C₄	1	1	yes	characteristic
476	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
477	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
478	C₂³×C₄	#386	1	1	yes	characteristic
479	C₂³×C₄	#386	1	1	yes	characteristic
480	C₂³×C₄	#386	1	2	yes	—
481	C₂³×C₄	#386	1	2	yes	—
482	C₂³×C₄	#386	1	1	yes	characteristic
483	C₂³×C₄	#386	1	2	yes	—
484	C₂³×C₄	#386	1	2	yes	—
485	C₂³×C₄	#386	1	2	yes	—
486	C₂³×C₄	#386	1	2	yes	—
487	C₂³×C₄	#386	1	1	yes	characteristic
488	C₂³×C₄	#386	1	2	yes	—
489	C₂³×C₄	#386	1	2	yes	—
490	C₂³×C₄	#386	1	2	yes	—
491	C₂³×C₄	#386	1	2	yes	—
492	C₂³×C₄	#386	1	2	yes	—
493	C₂³×C₄	#386	1	2	yes	—
494	C₂³×C₄	#386	1	2	yes	—
495	C₂³×C₄	#386	1	2	yes	—
496	C₂³×C₄	#386	1	2	yes	—
497	C₂³×C₄	#386	1	4	yes	—
498	C₂³×C₄	#386	1	4	yes	—
499	C₂³×C₄	#386	1	4	yes	—
500	C₂³×C₄	#386	1	4	yes	—
501	C₂³×C₄	#386	1	4	yes	—
502	C₂³×C₄	B(4,𝔽₂)	1	2	yes	—
503	C₂³×C₄	B(4,𝔽₂)	1	2	yes	—
504	C₂³×C₄	B(4,𝔽₂)	1	2	yes	—
505	C₂³×C₄	B(4,𝔽₂)	1	2	yes	—
506	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
507	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
508	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
509	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
510	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
511	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
512	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
513	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
514	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
515	C₂³×C₄	C₂×#120	1	2	yes	—
516	C₂³×C₄	C₂×#120	1	2	yes	—
517	C₂³×C₄	C₂×#120	1	2	yes	—
518	C₂³×C₄	C₂×#120	1	2	yes	—
519	C₂³×C₄	C₂×#120	1	2	yes	—
520	C₂³×C₄	C₂×#120	1	2	yes	—
521	C₂³×C₄	C₂×#120	1	2	yes	—
522	C₂³×C₄	C₂×#120	1	1	yes	characteristic
523	C₂³×C₄	C₂×#120	1	2	yes	—
524	C₂³×C₄	C₂×#120	1	2	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	2	yes	—
528	C₂³×C₄	C₂×#120	1	4	yes	—
529	C₂³×C₄	C₂×#120	1	4	yes	—
530	C₂³×C₄	C₂×#120	1	1	yes	characteristic
531	C₂³×C₄	C₂×#121	1	1	yes	characteristic
532	C₂³×C₄	C₂×#121	1	1	yes	characteristic
533	C₂³×C₄	C₂×#121	1	1	yes	characteristic
534	C₂³×C₄	C₂×#121	1	2	yes	—
535	C₂³×C₄	C₂×#121	1	2	yes	—
536	C₂³×C₄	C₂×#121	1	2	yes	—
537	C₂³×C₄	C₂×#123	1	2	yes	—
538	C₂³×C₄	C₂×#123	1	2	yes	—
539	C₂³×C₄	C₂×#123	1	1	yes	characteristic
540	C₂³×C₄	C₂×#123	1	1	yes	characteristic
541	C₂³×C₄	C₂×#123	1	2	yes	—
542	C₂³×C₄	C₂×#123	1	2	yes	—
543	C₂³×C₄	C₂×#123	1	4	yes	—
544	C₂³×C₄	C₂×#123	1	4	yes	—
545	C₂³×C₄	#525	1	2	yes	—
546	C₂³×C₄	#525	1	2	yes	—
547	C₂³×C₄	#525	1	2	yes	—
548	C₂³×C₄	#525	1	2	yes	—
549	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
550	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
551	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
552	C₂×M₁₆	C₂×#120	1	8	yes	complemented
553	C₂×M₁₆	C₂×#120	1	8	yes	complemented
554	C₂²×C₈	C₂×#120	1	8	yes	complemented
555	C₂²×C₈	C₂×#120	1	8	yes	complemented
556	#123	#386	1	8	yes	—
557	#123	#386	1	8	yes	—
558	#123	#386	1	8	yes	—
559	#123	#386	1	8	yes	—
560	#123	C₂×C₄×D₄	1	8	yes	—
561	#123	C₂×C₄×D₄	1	8	yes	—
562	#123	C₂×#121	1	8	yes	—
563	#123	C₂×#121	1	8	yes	—
564	#120	#386	1	8	yes	—
565	#120	#386	1	8	yes	—
566	#120	#386	1	8	yes	—
567	#120	#386	1	8	yes	—
568	#120	C₂×C₄×D₄	1	8	yes	—
569	#120	C₂×C₄×D₄	1	8	yes	—
570	#120	C₂×#121	1	8	yes	—
571	#120	C₂×#121	1	8	yes	—
572	#117	#386	1	8	yes	—
573	#117	#386	1	8	yes	—
574	#117	C₂×#120	1	8	yes	—
575	#117	C₂×#123	1	8	yes	—
576	C₂×C₂²⋊C₄	#386	1	4	yes	—
577	C₂×C₂²⋊C₄	#386	1	4	yes	—
578	C₂×C₂²⋊C₄	#386	1	4	yes	—
579	C₂×C₂²⋊C₄	#386	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
582	C₂⁴	#1889	1	2	yes	—
583	C₂⁴	#1889	1	2	yes	—
584	C₂⁴	C₂×#386	1	2	yes	—
585	C₂⁴	C₂×#386	1	2	yes	—
586	C₂⁴	C₂×#386	1	2	yes	—
587	C₂⁴	C₂×#386	1	2	yes	—
588	C₂⁴	C₂×#386	1	1	yes	characteristic
589	C₂⁴	C₂×#386	1	1	yes	characteristic
590	C₂⁴	C₂×#386	1	1	yes	characteristic
591	C₂⁴	C₂×#386	1	2	yes	—
592	C₂⁴	C₂×#386	1	2	yes	—
593	C₂⁴	C₂×#386	1	4	yes	—
594	C₂⁴	C₂×#386	1	4	yes	—
595	C₂⁴	C₂×#386	1	1	yes	characteristic
596	C₂⁴	C₄×#120	1	2	yes	—
597	C₂⁴	C₄×#120	1	2	yes	—
598	C₂⁴	#2847	1	2	yes	—
599	C₂⁴	#2847	1	2	yes	—
600	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
601	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
602	C₂⁴	C₂²×#121	1	1	yes	characteristic
603	C₂×Q₈	C₄×#120	1	4	yes	—
604	C₂×Q₈	#2847	1	4	yes	—
605	C₂×Q₈	#2849	1	4	yes	—
606	C₂×Q₈	C₂×#525	1	4	yes	—
607	C₂×D₄	C₂×#386	1	4	yes	—
608	C₂×D₄	C₂×#386	1	4	yes	—
609	C₂×D₄	C₄×#120	1	4	yes	—
610	C₂×D₄	C₄×#120	1	4	yes	—
611	C₂×D₄	C₄×#120	1	4	yes	—
612	C₂×D₄	#2847	1	4	yes	—
613	C₂×D₄	#2847	1	4	yes	—
614	C₂×D₄	#2847	1	4	yes	—
615	C₂×D₄	#2849	1	4	yes	—
616	C₂×D₄	C₂²×C₄×D₄	1	4	yes	—
617	C₂×D₄	C₂²×#121	1	4	yes	—
618	C₂×D₄	C₂×#525	1	4	yes	—
619	C₂²×C₄	#1889	1	2	yes	—
620	C₂²×C₄	#1889	1	4	yes	—
621	C₂²×C₄	#1889	1	4	yes	—
622	C₂²×C₄	#1889	1	2	yes	—
623	C₂²×C₄	C₂×#386	1	2	yes	—
624	C₂²×C₄	C₂×#386	1	2	yes	—
625	C₂²×C₄	C₂×#386	1	2	yes	—
626	C₂²×C₄	C₂×#386	1	1	yes	characteristic
627	C₂²×C₄	C₂×#386	1	1	yes	characteristic
628	C₂²×C₄	C₂×#386	1	1	yes	characteristic
629	C₂²×C₄	C₂×#386	1	2	yes	—
630	C₂²×C₄	C₂×#386	1	2	yes	—
631	C₂²×C₄	C₂×#386	1	2	yes	—
632	C₂²×C₄	C₂×#386	1	4	yes	—
633	C₂²×C₄	C₂×#386	1	4	yes	—
634	C₂²×C₄	C₂×#386	1	1	yes	characteristic
635	C₂²×C₄	C₄×#120	1	2	yes	—
636	C₂²×C₄	C₄×#120	1	2	yes	—
637	C₂²×C₄	C₄×#120	1	2	yes	—
638	C₂²×C₄	C₄×#120	1	2	yes	—
639	C₂²×C₄	C₄×#120	1	2	yes	—
640	C₂²×C₄	C₄×#120	1	2	yes	—
641	C₂²×C₄	#2846	1	2	yes	—
642	C₂²×C₄	#2846	1	2	yes	—
643	C₂²×C₄	#2846	1	2	yes	—
644	C₂²×C₄	#2846	1	1	yes	characteristic
645	C₂²×C₄	#2846	1	1	yes	characteristic
646	C₂²×C₄	#2847	1	2	yes	—
647	C₂²×C₄	#2847	1	2	yes	—
648	C₂²×C₄	#2847	1	2	yes	—
649	C₂²×C₄	#2847	1	2	yes	—
650	C₂²×C₄	#2847	1	2	yes	—
651	C₂²×C₄	#2847	1	2	yes	—
652	C₂²×C₄	#2849	1	2	yes	—
653	C₂²×C₄	#2849	1	2	yes	—
654	C₂²×C₄	#2849	1	2	yes	—
655	C₂²×C₄	#2849	1	2	yes	—
656	C₂²×C₄	#2849	1	2	yes	—
657	C₂²×C₄	#2849	1	2	yes	—
658	C₂²×C₄	#2849	1	2	yes	—
659	C₂²×C₄	#2849	1	1	yes	characteristic
660	C₂²×C₄	#2849	1	1	yes	characteristic
661	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
662	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
663	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
664	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
665	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
666	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
667	C₂²×C₄	#3026	1	1	yes	characteristic
668	C₂²×C₄	#3026	1	1	yes	characteristic
669	C₂²×C₄	#3026	1	1	yes	characteristic
670	C₂²×C₄	#3026	1	1	yes	characteristic
671	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
672	C₂²×C₄	C₂²×#120	1	2	yes	—
673	C₂²×C₄	C₂²×#120	1	2	yes	—
674	C₂²×C₄	C₂²×#120	1	2	yes	—
675	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
676	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
677	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
678	C₂²×C₄	C₂²×#123	1	2	yes	—
679	C₂²×C₄	C₂×#525	1	2	yes	—
680	C₂²×C₄	C₂×#525	1	2	yes	—
681	C₂²⋊C₄	C₂×#386	1	8	yes	—
682	C₂²⋊C₄	C₂×#386	1	8	yes	—
683	C₂³	#14694	1	1	yes	characteristic
684	C₂³	#14694	1	2	yes	—
685	C₂³	#14694	1	2	yes	—
686	C₂³	#14694	1	2	yes	—
687	C₂³	#14694	1	1	yes	characteristic
688	C₂³	C₂×#1889	1	1	yes	characteristic
689	C₂³	C₂×#1889	1	4	yes	—
690	C₂³	C₂×#1889	1	1	yes	characteristic
691	C₂³	#20960	1	1	yes	characteristic
692	C₂³	#20960	1	1	yes	characteristic
693	C₂³	C₂²×#386	1	2	yes	—
694	C₂³	C₂²×#386	1	1	yes	characteristic
695	C₂³	C₂×C₄×#120	1	2	yes	—
696	C₂³	C₂×#2847	1	2	yes	—
697	C₂×C₄	#14694	1	2	yes	—
698	C₂×C₄	#14694	1	2	yes	—
699	C₂×C₄	#14694	1	2	yes	—
700	C₂×C₄	#14694	1	1	yes	characteristic
701	C₂×C₄	#14694	1	1	yes	characteristic
702	C₂×C₄	C₂×#1889	1	4	yes	—
703	C₂×C₄	C₂×#1889	1	1	yes	characteristic
704	C₂×C₄	C₂×#1889	1	1	yes	characteristic
705	C₂×C₄	#20960	1	1	yes	characteristic
706	C₂×C₄	#20960	1	1	yes	characteristic
707	C₂×C₄	#32898	1	1	yes	characteristic
708	C₂×C₄	#32898	1	1	yes	characteristic
709	C₂×C₄	#32898	1	1	yes	characteristic
710	C₂×C₄	#32898	1	1	yes	characteristic
711	C₂×C₄	#32898	1	1	yes	characteristic
712	C₂×C₄	#32898	1	1	yes	characteristic
713	C₂×C₄	#32898	1	1	yes	characteristic
714	C₂×C₄	#32898	1	1	yes	characteristic
715	C₂×C₄	#33020	1	1	yes	characteristic
716	C₂×C₄	#33020	1	1	yes	characteristic
717	C₂×C₄	#33020	1	1	yes	characteristic
718	C₂×C₄	#33020	1	1	yes	characteristic
719	C₂×C₄	#33020	1	1	yes	characteristic
720	C₂×C₄	#33020	1	1	yes	characteristic
721	C₂×C₄	#33020	1	1	yes	characteristic
722	C₂×C₄	#33020	1	1	yes	characteristic
723	C₂×C₄	C₂×C₄×#120	1	2	yes	—
724	C₂×C₄	C₂×#2846	1	1	yes	characteristic
725	C₂×C₄	C₂×#2847	1	2	yes	—
726	C₂×C₄	C₂×#2849	1	2	yes	—
727	C₂×C₄	C₂×#2849	1	1	yes	characteristic
728	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
729	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
730	C₂×C₄	C₂×#3026	1	1	yes	characteristic
731	C₂×C₄	C₂×#3026	1	1	yes	characteristic
732	C₂²	#392658	1	1	yes	characteristic
733	C₂²	#392658	1	1	yes	characteristic
734	C₂²	#392658	1	1	yes	characteristic
735	C₂²	#392658	1	1	yes	characteristic
736	C₂²	C₂×#14694	1	1	yes	characteristic
737	C₂²	C₂²×#1889	1	1	yes	characteristic
738	C₂²	C₂×#20960	1	1	yes	characteristic
739	C₄	#392658	1	1	yes	characteristic
740	C₄	#392658	1	1	yes	characteristic
741	C₄	#392658	1	1	yes	characteristic
742	C₄	#392658	1	1	yes	characteristic
743	C₄	C₂×#32898	1	1	yes	characteristic
744	C₄	C₂×#32898	1	1	yes	characteristic
745	C₄	C₂×#33020	1	1	yes	characteristic
746	C₄	C₂×#33020	1	1	yes	characteristic
747	C₂	C₂×#392658	1	1	yes	characteristic
748	C₂	#72240532	1	2	yes	direct product factor

	subgroup	G/H
center	C₂×C₄	#32898
commutator	C₂²×D₄	C₂⁴×C₄
Frattini, cosocle	C₂²×#41	C₂⁵
socle	C₂²	#392658
prime radical	C₂×#6437616	C₂
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂⁴×#41 ◁ 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×#146483	C₂	semidirect
2. C₂×#359551	C₂	semidirect
3. C₂×#146595	C₂	semidirect
4. C₂×#494587	C₂	semidirect
5. C₂×#146477	C₂	semidirect
6. #72240532	C₂	direct (N × H)
7. C₂×#359562	C₂	semidirect
9. C₂×#493352	C₂	semidirect
10. C₂×#10574294	C₂	semidirect
14. #10574294	C₂²	semidirect
19. #6437616	C₄	semidirect
21. C₂×#23902	C₄	semidirect
22. C₂×#23901	C₄	semidirect
23. C₂×#23900	C₄	semidirect
25. C₂×#20620	C₂²	semidirect
26. C₂×#20612	C₂²	semidirect
30. #494587	C₂²	semidirect
31. #493352	C₂²	semidirect
32. C₂×#12589	C₂²	semidirect
33. C₂×#12577	C₂²	semidirect
34. #359562	C₂²	semidirect
35. #359551	C₂²	semidirect
36. C₂×#10756	C₂²	semidirect
37. C₂×#10743	C₂²	semidirect
38. #146595	C₂²	semidirect
39. #146483	C₂²	semidirect
40. #146477	C₂²	semidirect
44. C₂²×#568	D₄	semidirect
45. C₂²×#568	D₄	semidirect
46. C₂²×#568	D₄	semidirect
47. C₂²×#568	D₄	semidirect
70. #60231	D₄	semidirect
72. C₂×#2978	D₄	semidirect
73. C₂×#2977	D₄	semidirect
77. #60064	D₄	semidirect
78. #60064	D₄	semidirect
83. C₂²×#407	D₄	semidirect
84. C₂²×#407	D₄	semidirect
86. #23902	C₂×C₄	semidirect
87. #23901	C₂×C₄	semidirect
88. #23900	C₂×C₄	semidirect
93. #20620	C₂³	semidirect
94. #20612	C₂³	semidirect
101. #12589	C₂³	semidirect
102. #12577	C₂³	semidirect
103. #10756	C₂³	semidirect
104. #10743	C₂³	semidirect
137. C₂×#568	C₂×D₄	semidirect
138. C₂×#568	C₂×D₄	semidirect
139. C₂×#568	C₂×D₄	semidirect
140. C₂×#568	C₂×D₄	semidirect
190. #2978	C₂×D₄	semidirect
191. #2977	C₂×D₄	semidirect
205. C₂×#407	C₂×D₄	semidirect
206. C₂×#407	C₂×D₄	semidirect
328. C₂²×M₁₆	#120	semidirect
329. C₂²×M₁₆	#120	semidirect
330. C₂²×M₁₆	#120	semidirect
331. C₂²×M₁₆	#120	semidirect
332. C₂²×M₁₆	#120	semidirect
333. C₂²×M₁₆	#120	semidirect
338. C₂³×C₈	#120	semidirect
339. C₂³×C₈	#120	semidirect
393. #408	#120	semidirect
394. #408	#120	semidirect
552. C₂×M₁₆	C₂×#120	semidirect
553. C₂×M₁₆	C₂×#120	semidirect
554. C₂²×C₈	C₂×#120	semidirect
555. C₂²×C₈	C₂×#120	semidirect
748. C₂	#72240532	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×#146483	2
C₂×#359551	2
C₂×#146595	2
C₂×#494587	2
C₂×#146477	2
#72240532	2
C₂×#359562	2
C₂×#6437616	2
C₂×#493352	2
C₂×#10574294	2

Subgroups — C2×#72240532 #72319462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72240532 #72319462