Subgroups — C₂×#72233302 #72316668

Order 2048.

At least 8383 conjugacy classes of subgroups; only the 5168 normal subgroups are shown.

The subgroup lattice has 687 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×#494701	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#494722	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#494583	C₂	1	2	yes	maximal, complemented
4	C₂×#499814	C₂	1	4	yes	maximal, complemented
5	C₂×#498929	C₂	1	2	yes	maximal, complemented
6	C₂×#6628898	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#498885	C₂	1	2	yes	maximal, complemented
8	C₂²×#33553	C₂	1	2	yes	maximal, complemented
9	C₂×#6628872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#493425	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#60399	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#499804	C₂	1	4	yes	maximal, complemented
13	C₂×#499797	C₂	1	4	yes	maximal, complemented
14	#72233302	C₂	1	32	yes	maximal, direct product factor
15	C₂×#499787	C₂	1	4	yes	maximal, complemented
16	C₂×#7837029	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×H(7,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#3537	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#3484	C₂²	1	1	yes	characteristic
20	C₂²×#3027	C₂²	1	2	yes	—
21	C₂²×#3025	C₂²	1	2	yes	complemented
22	C₂²×#3025	C₂²	1	2	yes	complemented
23	C₂×#60399	C₂²	1	16	yes	complemented
24	C₂²×#3026	C₂²	1	4	yes	complemented
25	C₂³×B(4,𝔽₂)	C₂²	1	4	yes	complemented
26	C₂²×#3021	C₂²	1	2	yes	complemented
27	C₂²×#2883	C₂²	1	1	yes	characteristic, complemented
28	#7837029	C₂²	1	16	yes	complemented
29	C₂×#47827	C₂²	1	2	yes	complemented
30	C₂×#47846	C₂²	1	2	yes	complemented
31	C₂×#45438	C₂²	1	2	yes	complemented
32	C₂×#58990	C₂²	1	2	yes	complemented
33	C₂×#37269	C₂²	1	1	yes	characteristic, complemented
34	C₂×#52163	C₂²	1	1	yes	characteristic, complemented
35	C₂×#35527	C₂²	1	1	yes	characteristic
36	C₂×#35512	C₂²	1	1	yes	characteristic
37	C₂×#34415	C₂²	1	1	yes	characteristic, complemented
38	C₂×#33553	C₂²	1	32	yes	complemented
39	C₂²×#2200	C₂²	1	8	yes	complemented
40	C₂²×#2196	C₂²	1	8	yes	complemented
41	C₂²×#2128	C₂²	1	2	yes	complemented
42	C₂²×#2122	C₂²	1	2	yes	complemented
43	C₂²×#2120	C₂²	1	2	yes	complemented
44	C₂²×#2120	C₂²	1	2	yes	complemented
45	#6628898	C₂²	1	16	yes	complemented
46	C₂×#32900	C₂²	1	4	yes	complemented
47	C₂×#32898	C₂²	1	4	yes	complemented
48	#6628872	C₂²	1	16	yes	complemented
49	C₂×#32888	C₂²	1	4	yes	complemented
50	C₂×#32888	C₂²	1	4	yes	complemented
51	C₂×#20615	C₂²	1	2	yes	complemented
52	C₂×#20610	C₂²	1	2	yes	complemented
53	C₂×#20592	C₂²	1	1	yes	characteristic, complemented
54	C₂×#20586	C₂²	1	1	yes	characteristic, complemented
55	#499814	C₂²	1	64	yes	complemented
56	#499804	C₂²	1	64	yes	complemented
57	#499797	C₂²	1	64	yes	complemented
58	#499787	C₂²	1	64	yes	complemented
59	#498929	C₂²	1	32	yes	complemented
60	C₂×#13347	C₂²	1	8	yes	complemented
61	C₂×#13346	C₂²	1	8	yes	complemented
62	#498885	C₂²	1	32	yes	complemented
63	C₂×#13345	C₂²	1	4	yes	complemented
64	C₂×#13344	C₂²	1	4	yes	complemented
65	C₂×#13344	C₂²	1	4	yes	complemented
66	C₂×#13343	C₂²	1	4	yes	complemented
67	#494722	C₂²	1	16	yes	complemented
68	C₂×#13088	C₂²	1	4	yes	complemented
69	C₂×#13088	C₂²	1	4	yes	complemented
70	#494701	C₂²	1	16	yes	complemented
71	C₂×#13086	C₂²	1	4	yes	complemented
72	C₂×#13084	C₂²	1	4	yes	complemented
73	#494583	C₂²	1	32	yes	complemented
74	C₂×#13043	C₂²	1	8	yes	complemented
75	C₂×#13041	C₂²	1	8	yes	complemented
76	#493425	C₂²	1	16	yes	complemented
77	C₂×#12690	C₂²	1	4	yes	complemented
78	C₂×#12687	C₂²	1	4	yes	complemented
79	C₂×#12581	C₂²	1	2	yes	complemented
80	C₂×#12575	C₂²	1	2	yes	complemented
81	C₂×H(7,𝔽₂)	C₂³	1	8	yes	complemented
82	C₂²×#585	C₂³	1	2	yes	—
83	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
84	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
85	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
86	C₂×#3484	D₄	1	8	yes	complemented
87	C₂×#3484	C₂³	1	8	yes	—
88	C₂×#3537	C₂³	1	8	yes	complemented
89	C₂²×D₄²	C₂³	1	2	yes	complemented
90	C₂²×#560	C₂³	1	2	yes	complemented
91	C₂²×#535	D₄	1	1	yes	characteristic, complemented
92	C₂²×#535	D₄	1	1	yes	characteristic, complemented
93	C₂²×#535	C₂³	1	1	yes	characteristic
94	C₂²×#535	C₂³	1	1	yes	characteristic
95	C₂²×#534	D₄	1	2	yes	complemented
96	C₂²×#534	C₂³	1	2	yes	—
97	C₂³×#127	D₄	1	1	yes	characteristic, complemented
98	C₂²×#525	D₄	1	1	yes	characteristic, complemented
99	C₂²×#525	D₄	1	1	yes	characteristic, complemented
100	C₂²×#525	C₂³	1	1	yes	characteristic
101	C₂²×#525	C₂³	1	1	yes	characteristic
102	C₂³×#121	D₄	1	1	yes	characteristic, complemented
103	C₂³×#120	D₄	1	2	yes	complemented
104	C₂³×#120	C₂³	1	2	yes	—
105	C₂²×#518	D₄	1	1	yes	characteristic, complemented
106	C₂×#3027	D₄	1	32	yes	complemented
107	C₂×#3027	C₂³	1	16	yes	—
108	C₂×#3026	C₂³	1	32	yes	complemented
109	C₂×#3025	C₂³	1	16	yes	complemented
110	C₂×#3025	C₂³	1	16	yes	complemented
111	C₂²×#458	C₂³	1	4	yes	—
112	C₂²×#458	C₂³	1	4	yes	—
113	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
114	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
115	C₂²×B(4,𝔽₂)	C₂³	1	8	yes	—
116	C₂²×B(4,𝔽₂)	C₂³	1	32	yes	complemented
117	C₂×#3021	C₂³	1	16	yes	complemented
118	C₂²×#453	C₂³	1	8	yes	—
119	C₂²×#413	C₂³	1	2	yes	—
120	C₂×#2883	C₂³	1	8	yes	complemented
121	C₂²×#410	C₂³	1	2	yes	—
122	C₂²×#410	C₂³	1	2	yes	—
123	C₂³×#99	C₂³	1	4	yes	—
124	#58990	C₂³	1	16	yes	complemented
125	#52163	C₂³	1	8	yes	complemented
126	C₂×#2724	C₂³	1	1	yes	characteristic, complemented
127	C₂×#2709	C₂³	1	2	yes	complemented
128	C₂×#2697	C₂³	1	1	yes	characteristic, complemented
129	C₂×#2697	C₂³	1	1	yes	characteristic, complemented
130	C₂×#2679	C₂³	1	1	yes	characteristic, complemented
131	C₂×#2669	C₂³	1	2	yes	complemented
132	#47846	C₂³	1	16	yes	complemented
133	#47827	C₂³	1	16	yes	complemented
134	#45438	C₂³	1	16	yes	complemented
135	#37269	C₂³	1	8	yes	complemented
136	#35527	D₄	1	8	yes	complemented
137	#35527	C₂³	1	8	yes	—
138	#35512	D₄	1	8	yes	complemented
139	#35512	C₂³	1	8	yes	—
140	C₂×#2431	D₄	1	2	yes	complemented
141	C₂×#2431	D₄	1	2	yes	complemented
142	C₂×#2433	C₂³	1	2	yes	—
143	C₂×#2433	C₂³	1	2	yes	—
144	C₂×#2405	D₄	1	2	yes	complemented
145	C₂×#2405	C₂³	1	2	yes	—
146	C₂×#2403	D₄	1	2	yes	complemented
147	C₂×#2403	C₂³	1	2	yes	—
148	#34415	C₂³	1	8	yes	complemented
149	C₂×#2375	C₂³	1	2	yes	complemented
150	C₂×#2358	C₂³	1	2	yes	complemented
151	C₂×#2311	D₄	1	1	yes	characteristic, complemented
152	C₂×#2311	C₂³	1	1	yes	characteristic
153	C₂×#2309	D₄	1	1	yes	characteristic, complemented
154	C₂×#2309	D₄	1	1	yes	characteristic, complemented
155	C₂×#2297	D₄	1	1	yes	characteristic, complemented
156	C₂×#2297	C₂³	1	1	yes	characteristic
157	C₂×#2200	C₂³	1	64	yes	complemented
158	C₂×#2196	C₂³	1	64	yes	complemented
159	C₂×#2128	C₂³	1	16	yes	complemented
160	C₂²×#353	C₂³	1	8	yes	complemented
161	C₂×#2122	C₂³	1	16	yes	complemented
162	C₂×#2120	C₂³	1	16	yes	complemented
163	C₂×#2120	C₂³	1	16	yes	complemented
164	C₂²×#352	C₂³	1	4	yes	complemented
165	C₂²×#352	C₂³	1	4	yes	complemented
166	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	8	yes	complemented
167	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
168	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
169	#32900	C₂³	1	32	yes	complemented
170	#32898	C₂³	1	32	yes	complemented
171	#32888	C₂³	1	32	yes	complemented
172	#32888	C₂³	1	32	yes	complemented
173	#20615	C₂³	1	16	yes	complemented
174	C₂×#1792	C₂³	1	4	yes	—
175	C₂×#1792	C₂³	1	4	yes	—
176	#20610	C₂³	1	16	yes	complemented
177	C₂×#1790	C₂³	1	8	yes	—
178	#20592	C₂³	1	8	yes	complemented
179	C₂×#1783	C₂³	1	4	yes	—
180	#20586	C₂³	1	8	yes	complemented
181	C₂×#1781	C₂³	1	4	yes	—
182	#13347	C₂³	1	64	yes	complemented
183	#13346	C₂³	1	64	yes	complemented
184	#13345	C₂³	1	32	yes	complemented
185	#13344	C₂³	1	32	yes	complemented
186	#13344	C₂³	1	32	yes	complemented
187	#13343	C₂³	1	32	yes	complemented
188	#13088	C₂³	1	32	yes	complemented
189	#13088	C₂³	1	32	yes	complemented
190	#13086	C₂³	1	32	yes	complemented
191	#13084	C₂³	1	32	yes	complemented
192	#13043	C₂³	1	64	yes	complemented
193	#13041	C₂³	1	64	yes	complemented
194	#12690	C₂³	1	32	yes	complemented
195	#12687	C₂³	1	32	yes	complemented
196	#12581	C₂³	1	16	yes	complemented
197	C₂×#1393	C₂³	1	4	yes	complemented
198	C₂×#1393	C₂³	1	4	yes	complemented
199	#12575	C₂³	1	16	yes	complemented
200	C₂×#1390	C₂³	1	8	yes	complemented
201	C₂⁷	C₂×D₄	1	2	yes	—
202	C₂×#585	C₂×D₄	1	16	yes	complemented
203	C₂×#585	C₂⁴	1	8	yes	—
204	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
205	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
206	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
207	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
208	C₂²×H(5,𝔽₂)	C₂⁴	1	16	yes	—
209	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
210	C₂³×#41	C₂×D₄	1	2	yes	—
211	C₂³×#41	C₂×D₄	1	1	yes	characteristic
212	C₂³×#41	C₂×D₄	1	1	yes	characteristic
213	C₂³×#41	C₂×D₄	1	1	yes	characteristic
214	C₂³×#41	C₂⁴	1	1	yes	characteristic
215	C₂⁴×D₄	C₂×D₄	1	2	yes	—
216	C₂⁴×D₄	C₂×D₄	1	2	yes	—
217	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
218	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
219	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
220	C₂⁴×D₄	C₂×D₄	1	2	yes	—
221	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
222	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
223	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
224	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
225	C₂⁴×D₄	C₂⁴	1	2	yes	—
226	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
227	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
228	C₂×#560	C₂⁴	1	8	yes	complemented
229	C₂×D₄²	C₂⁴	1	8	yes	complemented
230	C₂×#535	C₂×D₄	1	16	yes	—
231	C₂×#535	C₂×D₄	1	4	yes	—
232	C₂×#535	C₂×D₄	1	8	yes	complemented
233	C₂×#535	C₂×D₄	1	4	yes	complemented
234	C₂×#535	C₂×D₄	1	8	yes	complemented
235	C₂×#535	C₂⁴	1	4	yes	—
236	C₂×#535	C₂⁴	1	4	yes	—
237	C₂×#534	C₂×D₄	1	8	yes	—
238	C₂×#534	C₂×D₄	1	16	yes	complemented
239	C₂×#534	C₂⁴	1	8	yes	—
240	C₂²×#127	C₂×D₄	1	2	yes	complemented
241	C₂²×#127	C₂×D₄	1	2	yes	complemented
242	C₂²×#127	C₂×D₄	1	8	yes	complemented
243	C₂²×#127	C₂⁴	1	2	yes	—
244	C₂²×#124	C₂×D₄	1	2	yes	complemented
245	C₂×#525	C₂×D₄	1	4	yes	—
246	C₂×#525	C₂×D₄	1	8	yes	complemented
247	C₂×#525	C₂×D₄	1	4	yes	complemented
248	C₂×#525	C₂×D₄	1	8	yes	complemented
249	C₂×#525	C₂⁴	1	4	yes	—
250	C₂×#525	C₂⁴	1	4	yes	—
251	C₂²×#123	C₂×D₄	1	1	yes	characteristic
252	C₂²×#123	C₂×D₄	1	2	yes	—
253	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
254	C₂²×#123	C₂×D₄	1	2	yes	complemented
255	C₂²×#123	C₂⁴	1	1	yes	characteristic
256	C₂²×#123	C₂⁴	1	1	yes	characteristic
257	C₂²×#121	C₂×D₄	1	2	yes	complemented
258	C₂²×#121	C₂×D₄	1	2	yes	complemented
259	C₂²×#121	C₂×D₄	1	8	yes	complemented
260	C₂²×#120	C₂×D₄	1	1	yes	characteristic
261	C₂²×#120	C₂×D₄	1	2	yes	—
262	C₂²×#120	C₂×D₄	1	8	yes	—
263	C₂²×#120	C₂×D₄	1	2	yes	—
264	C₂²×#120	C₂×D₄	1	2	yes	—
265	C₂²×#120	C₂×D₄	1	2	yes	—
266	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
267	C₂²×#120	C₂×D₄	1	16	yes	complemented
268	C₂²×#120	C₂×D₄	1	2	yes	complemented
269	C₂²×#120	C₂⁴	1	1	yes	characteristic
270	C₂²×#120	C₂⁴	1	1	yes	characteristic
271	C₂²×#120	C₂⁴	1	8	yes	—
272	C₂²×#120	C₂⁴	1	2	yes	—
273	C₂×#518	C₂×D₄	1	8	yes	complemented
274	C₂²×#117	C₂×D₄	1	1	yes	characteristic
275	C₂²×#117	C₂×D₄	1	1	yes	characteristic
276	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
277	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
278	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
279	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
280	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
281	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
282	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
283	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
284	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
285	#3027	C₂×D₄	1	128	yes	complemented
286	C₂×#458	C₂⁴	1	16	yes	—
287	C₂×#458	C₂⁴	1	16	yes	—
288	C₂×B(4,𝔽₂)	C₂×D₄	1	64	yes	complemented
289	C₂×B(4,𝔽₂)	C₂⁴	1	16	yes	—
290	C₂×B(4,𝔽₂)	C₂⁴	1	16	yes	—
291	C₂×B(4,𝔽₂)	C₂⁴	1	32	yes	—
292	C₂×#453	C₂⁴	1	32	yes	—
293	C₂×#413	C₂⁴	1	8	yes	—
294	C₂²×#100	C₂⁴	1	4	yes	—
295	C₂×#410	C₂×D₄	1	16	yes	complemented
296	C₂×#410	C₂⁴	1	8	yes	—
297	C₂×#410	C₂⁴	1	8	yes	—
298	C₂²×#99	C₂⁴	1	16	yes	—
299	C₂²×#99	C₂⁴	1	4	yes	—
300	C₂²×#99	C₂⁴	1	4	yes	—
301	#2724	C₂⁴	1	4	yes	complemented
302	#2709	C₂⁴	1	8	yes	complemented
303	#2697	C₂⁴	1	4	yes	complemented
304	#2697	C₂⁴	1	4	yes	complemented
305	#2679	C₂⁴	1	4	yes	complemented
306	#2669	C₂⁴	1	8	yes	complemented
307	#2433	C₂×D₄	1	8	yes	complemented
308	#2433	C₂×D₄	1	8	yes	complemented
309	#2433	C₂⁴	1	8	yes	—
310	#2433	C₂⁴	1	8	yes	—
311	#2431	C₂×D₄	1	16	yes	complemented
312	#2431	C₂×D₄	1	16	yes	complemented
313	#2405	C₂×D₄	1	8	yes	complemented
314	#2405	C₂×D₄	1	16	yes	complemented
315	#2405	C₂⁴	1	8	yes	—
316	#2403	C₂×D₄	1	8	yes	complemented
317	#2403	C₂×D₄	1	16	yes	complemented
318	#2403	C₂⁴	1	8	yes	—
319	#2375	C₂⁴	1	8	yes	complemented
320	#2358	C₂⁴	1	8	yes	complemented
321	#2311	C₂×D₄	1	4	yes	complemented
322	#2311	C₂×D₄	1	8	yes	complemented
323	#2311	C₂⁴	1	4	yes	—
324	#2309	C₂×D₄	1	8	yes	complemented
325	#2309	C₂×D₄	1	8	yes	complemented
326	#2297	C₂×D₄	1	4	yes	complemented
327	#2297	C₂×D₄	1	8	yes	complemented
328	#2297	C₂⁴	1	4	yes	—
329	C₂×#391	C₂×D₄	1	1	yes	characteristic, complemented
330	C₂×#391	C₂×D₄	1	1	yes	characteristic, complemented
331	C₂×#390	C₂×D₄	1	2	yes	complemented
332	C₂×#390	C₂×D₄	1	2	yes	complemented
333	C₂×#390	C₂⁴	1	1	yes	characteristic
334	C₂×#390	C₂⁴	1	1	yes	characteristic
335	C₂×#386	C₂×D₄	1	2	yes	complemented
336	C₂×#386	C₂×D₄	1	2	yes	complemented
337	C₂×#386	C₂×D₄	1	2	yes	complemented
338	C₂×#386	C₂⁴	1	2	yes	—
339	C₂×#379	C₂×D₄	1	2	yes	complemented
340	C₂×#379	C₂×D₄	1	2	yes	complemented
341	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
342	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
343	C₂×#353	C₂⁴	1	32	yes	complemented
344	C₂×#352	C₂⁴	1	16	yes	complemented
345	C₂×#352	C₂⁴	1	16	yes	complemented
346	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	16	yes	complemented
347	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	32	yes	complemented
348	C₂×AΣL(1,𝔽₁₆)	C₂⁴	1	16	yes	complemented
349	#1792	C₂⁴	1	16	yes	—
350	#1792	C₂⁴	1	16	yes	—
351	#1790	C₂⁴	1	32	yes	—
352	#1783	C₂⁴	1	16	yes	—
353	#1781	C₂⁴	1	16	yes	—
354	#1393	C₂⁴	1	16	yes	complemented
355	#1393	C₂⁴	1	16	yes	complemented
356	#1390	C₂⁴	1	32	yes	complemented
357	C₂⁶	#120	1	2	yes	—
358	C₂⁶	C₂²×D₄	1	2	yes	—
359	C₂⁶	C₂²×D₄	1	2	yes	—
360	C₂⁶	C₂²×D₄	1	1	yes	characteristic
361	C₂⁶	C₂²×D₄	1	1	yes	characteristic
362	C₂⁶	C₂²×D₄	1	8	yes	—
363	C₂⁶	C₂²×D₄	1	2	yes	—
364	#585	C₂²×D₄	1	32	yes	complemented
365	C₂×H(5,𝔽₂)	C₂²×D₄	1	16	yes	—
366	C₂×H(5,𝔽₂)	C₂⁵	1	8	yes	—
367	C₂²×#41	#120	1	4	yes	—
368	C₂²×#41	#120	1	4	yes	—
369	C₂²×#41	#120	1	4	yes	—
370	C₂²×#41	#120	1	8	yes	—
371	C₂²×#41	C₂²×D₄	1	8	yes	—
372	C₂²×#41	C₂²×D₄	1	2	yes	—
373	C₂²×#41	C₂²×D₄	1	4	yes	—
374	C₂²×#41	C₂²×D₄	1	4	yes	—
375	C₂²×#41	C₂²×D₄	1	2	yes	—
376	C₂²×#41	C₂²×D₄	1	2	yes	—
377	C₂²×#41	C₂²×D₄	1	8	yes	—
378	C₂²×#41	C₂²×D₄	1	4	yes	—
379	C₂²×#41	H(5,𝔽₂)	1	8	yes	—
380	C₂²×#41	C₂⁵	1	2	yes	—
381	C₂³×Q₈	#120	1	1	yes	characteristic
382	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
383	C₂³×D₄	#120	1	2	yes	—
384	C₂³×D₄	#120	1	4	yes	—
385	C₂³×D₄	#120	1	1	yes	characteristic
386	C₂³×D₄	#120	1	2	yes	—
387	C₂³×D₄	#120	1	2	yes	—
388	C₂³×D₄	#120	1	4	yes	—
389	C₂³×D₄	#120	1	4	yes	—
390	C₂³×D₄	#120	1	1	yes	characteristic
391	C₂³×D₄	#120	1	8	yes	—
392	C₂³×D₄	#120	1	8	yes	—
393	C₂³×D₄	#120	1	1	yes	characteristic
394	C₂³×D₄	#120	1	8	yes	complemented
395	C₂³×D₄	C₂²×D₄	1	2	yes	—
396	C₂³×D₄	C₂²×D₄	1	2	yes	—
397	C₂³×D₄	C₂²×D₄	1	8	yes	—
398	C₂³×D₄	C₂²×D₄	1	8	yes	—
399	C₂³×D₄	C₂²×D₄	1	4	yes	—
400	C₂³×D₄	C₂²×D₄	1	4	yes	—
401	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
402	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
403	C₂³×D₄	C₂²×D₄	1	4	yes	—
404	C₂³×D₄	C₂²×D₄	1	4	yes	—
405	C₂³×D₄	C₂²×D₄	1	2	yes	—
406	C₂³×D₄	C₂²×D₄	1	4	yes	—
407	C₂³×D₄	C₂²×D₄	1	2	yes	—
408	C₂³×D₄	C₂²×D₄	1	8	yes	—
409	C₂³×D₄	C₂²×D₄	1	4	yes	—
410	C₂³×D₄	C₂²×D₄	1	4	yes	—
411	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
412	C₂³×D₄	C₂²×D₄	1	8	yes	complemented
413	C₂³×D₄	C₂⁵	1	4	yes	—
414	C₂³×D₄	C₂⁵	1	1	yes	characteristic
415	C₂⁴×C₄	#120	1	2	yes	—
416	C₂⁴×C₄	#120	1	2	yes	—
417	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
418	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
419	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
420	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
421	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
422	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
423	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
424	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
425	C₂⁴×C₄	C₂²×D₄	1	4	yes	complemented
426	#535	#120	1	32	yes	complemented
427	#535	C₂²×D₄	1	32	yes	—
428	C₂×#127	C₂²×D₄	1	4	yes	—
429	C₂×#127	C₂²×D₄	1	8	yes	complemented
430	C₂×#127	C₂²×D₄	1	8	yes	complemented
431	C₂×#127	C₂⁵	1	4	yes	—
432	C₂×#124	C₂²×D₄	1	8	yes	complemented
433	C₂×#123	C₂²×D₄	1	2	yes	—
434	C₂×#123	C₂²×D₄	1	4	yes	—
435	C₂×#123	C₂²×D₄	1	2	yes	—
436	C₂×#123	C₂²×D₄	1	8	yes	—
437	C₂×#123	C₂²×D₄	1	4	yes	complemented
438	C₂×#123	C₂²×D₄	1	8	yes	complemented
439	C₂×#123	C₂⁵	1	2	yes	—
440	C₂×#123	C₂⁵	1	2	yes	—
441	C₂×#121	C₂²×D₄	1	8	yes	complemented
442	C₂×#121	C₂²×D₄	1	8	yes	complemented
443	C₂×#120	#120	1	16	yes	complemented
444	C₂×#120	C₂²×D₄	1	16	yes	—
445	C₂×#120	C₂²×D₄	1	2	yes	—
446	C₂×#120	C₂²×D₄	1	2	yes	—
447	C₂×#120	C₂²×D₄	1	4	yes	—
448	C₂×#120	C₂²×D₄	1	8	yes	—
449	C₂×#120	C₂²×D₄	1	8	yes	—
450	C₂×#120	C₂²×D₄	1	8	yes	—
451	C₂×#120	C₂²×D₄	1	4	yes	—
452	C₂×#120	C₂²×D₄	1	8	yes	—
453	C₂×#120	C₂²×D₄	1	4	yes	complemented
454	C₂×#120	C₂²×D₄	1	8	yes	complemented
455	C₂×#120	C₂⁵	1	2	yes	—
456	C₂×#120	C₂⁵	1	2	yes	—
457	C₂×#120	C₂⁵	1	4	yes	—
458	C₂×#117	#120	1	8	yes	complemented
459	C₂×#117	C₂²×D₄	1	4	yes	—
460	C₂×#117	C₂²×D₄	1	4	yes	—
461	C₂×#117	C₂²×D₄	1	4	yes	complemented
462	C₂×#117	C₂²×D₄	1	4	yes	complemented
463	C₂×#117	C₂²×D₄	1	4	yes	complemented
464	C₂×#117	C₂²×D₄	1	4	yes	complemented
465	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
466	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
467	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	complemented
468	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
469	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
470	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
471	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
472	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
473	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
474	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
475	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
476	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
477	C₂²×C₄²	C₂²×D₄	1	2	yes	—
478	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
479	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
480	C₂²×C₄²	C₂²×D₄	1	4	yes	complemented
481	B(4,𝔽₂)	C₂²×D₄	1	128	yes	complemented
482	C₂×#100	C₂⁵	1	8	yes	—
483	#410	C₂²×D₄	1	32	yes	complemented
484	C₂×#99	C₂²×D₄	1	16	yes	—
485	C₂×#99	C₂⁵	1	8	yes	—
486	C₂×#99	C₂⁵	1	8	yes	—
487	#391	C₂²×D₄	1	4	yes	complemented
488	#391	C₂²×D₄	1	4	yes	complemented
489	#390	C₂²×D₄	1	2	yes	—
490	#390	C₂²×D₄	1	2	yes	—
491	#390	C₂²×D₄	1	8	yes	complemented
492	#390	C₂²×D₄	1	8	yes	complemented
493	#390	C₂⁵	1	2	yes	—
494	#390	C₂⁵	1	2	yes	—
495	#386	C₂²×D₄	1	4	yes	—
496	#386	C₂²×D₄	1	8	yes	complemented
497	#386	C₂²×D₄	1	8	yes	complemented
498	#386	C₂²×D₄	1	8	yes	complemented
499	#386	C₂⁵	1	4	yes	—
500	#379	C₂²×D₄	1	8	yes	complemented
501	#379	C₂²×D₄	1	8	yes	complemented
502	C₄×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
503	C₄×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
504	C₂⁵	C₂×#120	1	2	yes	—
505	C₂⁵	C₂×#120	1	4	yes	—
506	C₂⁵	C₂×#120	1	1	yes	characteristic
507	C₂⁵	C₂×#120	1	2	yes	—
508	C₂⁵	C₂×#120	1	2	yes	—
509	C₂⁵	C₂×#120	1	4	yes	—
510	C₂⁵	C₂×#120	1	8	yes	—
511	C₂⁵	C₂×#120	1	8	yes	—
512	C₂⁵	C₂³×D₄	1	4	yes	—
513	C₂⁵	C₂³×D₄	1	1	yes	characteristic
514	C₂⁵	C₂³×D₄	1	1	yes	characteristic
515	C₂⁵	C₂³×D₄	1	4	yes	—
516	C₂⁵	C₂³×D₄	1	2	yes	—
517	C₂⁵	C₂³×D₄	1	2	yes	—
518	C₂⁵	C₂³×D₄	1	4	yes	—
519	H(5,𝔽₂)	C₂³×D₄	1	16	yes	—
520	C₂×#41	C₂×#120	1	8	yes	—
521	C₂×#41	#534	1	8	yes	—
522	C₂×#41	D₄²	1	16	yes	—
523	C₂×#41	D₄²	1	16	yes	—
524	C₂×#41	C₂³×D₄	1	8	yes	—
525	C₂×#41	C₂×H(5,𝔽₂)	1	8	yes	—
526	C₂²×Q₈	C₂×#120	1	4	yes	—
527	C₂²×Q₈	C₂×#120	1	2	yes	—
528	C₂²×Q₈	D₄²	1	8	yes	—
529	C₂²×Q₈	C₂³×D₄	1	2	yes	—
530	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
531	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
532	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
533	C₂²×D₄	C₂×#120	1	4	yes	—
534	C₂²×D₄	C₂×#120	1	8	yes	—
535	C₂²×D₄	C₂×#120	1	4	yes	—
536	C₂²×D₄	C₂×#120	1	8	yes	—
537	C₂²×D₄	C₂×#120	1	4	yes	—
538	C₂²×D₄	C₂×#120	1	8	yes	—
539	C₂²×D₄	C₂×#120	1	4	yes	—
540	C₂²×D₄	C₂×#120	1	4	yes	—
541	C₂²×D₄	C₂×#120	1	4	yes	—
542	C₂²×D₄	C₂×#120	1	4	yes	—
543	C₂²×D₄	C₂×#120	1	2	yes	—
544	C₂²×D₄	C₂×#120	1	2	yes	—
545	C₂²×D₄	C₂×#120	1	16	yes	complemented
546	C₂²×D₄	#534	1	4	yes	—
547	C₂²×D₄	D₄²	1	8	yes	—
548	C₂²×D₄	C₂³×D₄	1	4	yes	—
549	C₂²×D₄	C₂³×D₄	1	4	yes	—
550	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
551	C₂²×D₄	C₂³×D₄	1	4	yes	—
552	C₂²×D₄	C₂³×D₄	1	4	yes	—
553	C₂²×D₄	C₂³×D₄	1	2	yes	—
554	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
555	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
556	C₂²×D₄	C₂³×D₄	1	2	yes	—
557	C₂²×D₄	C₂³×D₄	1	4	yes	—
558	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
559	C₂²×D₄	C₂⁶	1	1	yes	characteristic
560	C₂³×C₄	C₂×#120	1	2	yes	—
561	C₂³×C₄	C₂×#120	1	8	yes	—
562	C₂³×C₄	C₂×#120	1	4	yes	—
563	C₂³×C₄	C₂×#120	1	1	yes	characteristic
564	C₂³×C₄	C₂×#120	1	1	yes	characteristic
565	C₂³×C₄	C₂×#120	1	2	yes	—
566	C₂³×C₄	C₂×#120	1	4	yes	—
567	C₂³×C₄	C₂×#120	1	2	yes	—
568	C₂³×C₄	C₂×#120	1	2	yes	—
569	C₂³×C₄	C₂×#120	1	8	yes	—
570	C₂³×C₄	C₂×#120	1	1	yes	characteristic
571	C₂³×C₄	#534	1	4	yes	—
572	C₂³×C₄	D₄²	1	8	yes	—
573	C₂³×C₄	D₄²	1	8	yes	—
574	C₂³×C₄	C₂³×D₄	1	4	yes	—
575	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
576	C₂³×C₄	C₂³×D₄	1	2	yes	—
577	C₂³×C₄	C₂³×D₄	1	2	yes	—
578	C₂³×C₄	C₂³×D₄	1	2	yes	—
579	C₂³×C₄	C₂³×D₄	1	2	yes	—
580	C₂³×C₄	C₂³×D₄	1	2	yes	—
581	C₂³×C₄	C₂³×D₄	1	4	yes	—
582	#120	C₂×#120	1	16	yes	—
583	#120	C₂×#120	1	32	yes	complemented
584	#120	C₂³×D₄	1	16	yes	—
585	#117	C₂×#120	1	16	yes	complemented
586	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
589	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×D₄	1	4	yes	—
595	C₂×C₄²	C₂³×D₄	1	4	yes	—
596	C₂×C₄²	C₂³×D₄	1	2	yes	—
597	C₂×C₄²	C₂³×D₄	1	2	yes	—
598	#99	C₂³×D₄	1	16	yes	—
599	C₂⁴	#2403	1	4	yes	—
600	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
601	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
602	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
603	C₂⁴	C₂²×#120	1	1	yes	characteristic
604	C₂⁴	C₂²×#120	1	4	yes	—
605	C₂⁴	C₂²×#120	1	1	yes	characteristic
606	C₂⁴	C₂²×#120	1	2	yes	—
607	C₂⁴	C₂²×#120	1	2	yes	—
608	C₂⁴	C₂²×#120	1	1	yes	characteristic
609	C₂⁴	C₂²×#120	1	4	yes	—
610	C₂⁴	C₂²×#120	1	4	yes	—
611	C₂⁴	C₂²×#120	1	8	yes	—
612	C₂⁴	C₂×#534	1	2	yes	—
613	C₂⁴	C₂×D₄²	1	4	yes	—
614	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
615	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
616	C₂×Q₈	#2403	1	8	yes	—
617	C₂×Q₈	C₂×D₄²	1	8	yes	—
618	C₂×D₄	#2403	1	8	yes	—
619	C₂×D₄	#2403	1	8	yes	—
620	C₂×D₄	C₂×B(4,𝔽₂)	1	16	yes	—
621	C₂×D₄	C₂×B(4,𝔽₂)	1	16	yes	—
622	C₂×D₄	C₂²×#120	1	4	yes	—
623	C₂×D₄	C₂²×#120	1	2	yes	—
624	C₂×D₄	C₂×#534	1	4	yes	—
625	C₂×D₄	C₂×#534	1	2	yes	—
626	C₂×D₄	C₂×D₄²	1	4	yes	—
627	C₂×D₄	C₂×D₄²	1	8	yes	—
628	C₂×D₄	C₂×D₄²	1	4	yes	—
629	C₂×D₄	C₂⁴×D₄	1	2	yes	—
630	C₂×D₄	C₂²×H(5,𝔽₂)	1	2	yes	—
631	C₂²×C₄	#2403	1	4	yes	—
632	C₂²×C₄	#2403	1	4	yes	—
633	C₂²×C₄	#2403	1	8	yes	—
634	C₂²×C₄	#2403	1	8	yes	—
635	C₂²×C₄	#2403	1	8	yes	—
636	C₂²×C₄	#2403	1	4	yes	—
637	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
638	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
639	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
640	C₂²×C₄	C₂²×#120	1	4	yes	—
641	C₂²×C₄	C₂²×#120	1	2	yes	—
642	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
643	C₂²×C₄	C₂²×#120	1	2	yes	—
644	C₂²×C₄	C₂²×#120	1	4	yes	—
645	C₂²×C₄	C₂²×#120	1	2	yes	—
646	C₂²×C₄	C₂×#534	1	4	yes	—
647	C₂²×C₄	C₂×D₄²	1	8	yes	—
648	C₂²×C₄	C₂×D₄²	1	4	yes	—
649	C₂²×C₄	C₂×D₄²	1	8	yes	—
650	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
651	C₂²⋊C₄	C₂²×#120	1	8	yes	—
652	C₂³	C₂×#2403	1	2	yes	—
653	C₂³	C₂×#2403	1	2	yes	—
654	C₂³	C₂×#2403	1	4	yes	—
655	C₂³	C₂×#2403	1	2	yes	—
656	C₂³	C₂²×B(4,𝔽₂)	1	8	yes	—
657	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
658	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
659	C₂³	C₂²×B(4,𝔽₂)	1	8	yes	—
660	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
661	C₂³	C₂³×#120	1	1	yes	characteristic
662	C₂³	C₂³×#120	1	1	yes	characteristic
663	C₂³	C₂²×#534	1	1	yes	characteristic
664	C₂³	C₂²×D₄²	1	2	yes	—
665	C₂×C₄	#23900	1	8	yes	—
666	C₂×C₄	#23900	1	8	yes	—
667	C₂×C₄	C₂×#2403	1	4	yes	—
668	C₂×C₄	C₂×#2403	1	2	yes	—
669	C₂×C₄	C₂×#2403	1	4	yes	—
670	C₂×C₄	C₂×#2403	1	4	yes	—
671	C₂×C₄	C₂²×B(4,𝔽₂)	1	4	yes	—
672	C₂×C₄	C₂²×B(4,𝔽₂)	1	4	yes	—
673	C₂×C₄	C₂²×D₄²	1	2	yes	—
674	C₂²	C₂×#23900	1	2	yes	—
675	C₂²	C₂×#23900	1	2	yes	—
676	C₂²	#7622880	1	2	yes	—
677	C₂²	#7622887	1	2	yes	—
678	C₂²	C₂²×#2403	1	1	yes	characteristic
679	C₂²	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
680	C₂²	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
681	C₄	C₂×#23900	1	8	yes	—
682	C₂	C₂²×#23900	1	1	yes	characteristic
683	C₂	#72233302	1	4	yes	direct product factor
684	C₂	C₂×#7622880	1	1	yes	characteristic
685	C₂	C₂×#7622887	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂²×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂⁶
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#494701	C₂	semidirect
2. C₂×#494722	C₂	semidirect
3. C₂×#494583	C₂	semidirect
4. C₂×#499814	C₂	semidirect
5. C₂×#498929	C₂	semidirect
6. C₂×#6628898	C₂	semidirect
7. C₂×#498885	C₂	semidirect
8. C₂²×#33553	C₂	semidirect
9. C₂×#6628872	C₂	semidirect
10. C₂×#493425	C₂	semidirect
11. C₂²×#60399	C₂	semidirect
12. C₂×#499804	C₂	semidirect
13. C₂×#499797	C₂	semidirect
14. #72233302	C₂	direct (N × H)
15. C₂×#499787	C₂	semidirect
16. C₂×#7837029	C₂	semidirect
17. C₂²×H(7,𝔽₂)	C₂²	semidirect
18. C₂²×#3537	C₂²	semidirect
21. C₂²×#3025	C₂²	semidirect
22. C₂²×#3025	C₂²	semidirect
23. C₂×#60399	C₂²	semidirect
24. C₂²×#3026	C₂²	semidirect
25. C₂³×B(4,𝔽₂)	C₂²	semidirect
26. C₂²×#3021	C₂²	semidirect
27. C₂²×#2883	C₂²	semidirect
28. #7837029	C₂²	semidirect
29. C₂×#47827	C₂²	semidirect
30. C₂×#47846	C₂²	semidirect
31. C₂×#45438	C₂²	semidirect
32. C₂×#58990	C₂²	semidirect
33. C₂×#37269	C₂²	semidirect
34. C₂×#52163	C₂²	semidirect
37. C₂×#34415	C₂²	semidirect
38. C₂×#33553	C₂²	semidirect
39. C₂²×#2200	C₂²	semidirect
40. C₂²×#2196	C₂²	semidirect
41. C₂²×#2128	C₂²	semidirect
42. C₂²×#2122	C₂²	semidirect
43. C₂²×#2120	C₂²	semidirect
44. C₂²×#2120	C₂²	semidirect
45. #6628898	C₂²	semidirect
46. C₂×#32900	C₂²	semidirect
47. C₂×#32898	C₂²	semidirect
48. #6628872	C₂²	semidirect
49. C₂×#32888	C₂²	semidirect
50. C₂×#32888	C₂²	semidirect
51. C₂×#20615	C₂²	semidirect
52. C₂×#20610	C₂²	semidirect
53. C₂×#20592	C₂²	semidirect
54. C₂×#20586	C₂²	semidirect
55. #499814	C₂²	semidirect
56. #499804	C₂²	semidirect
57. #499797	C₂²	semidirect
58. #499787	C₂²	semidirect
59. #498929	C₂²	semidirect
60. C₂×#13347	C₂²	semidirect
61. C₂×#13346	C₂²	semidirect
62. #498885	C₂²	semidirect
63. C₂×#13345	C₂²	semidirect
64. C₂×#13344	C₂²	semidirect
65. C₂×#13344	C₂²	semidirect
66. C₂×#13343	C₂²	semidirect
67. #494722	C₂²	semidirect
68. C₂×#13088	C₂²	semidirect
69. C₂×#13088	C₂²	semidirect
70. #494701	C₂²	semidirect
71. C₂×#13086	C₂²	semidirect
72. C₂×#13084	C₂²	semidirect
73. #494583	C₂²	semidirect
74. C₂×#13043	C₂²	semidirect
75. C₂×#13041	C₂²	semidirect
76. #493425	C₂²	semidirect
77. C₂×#12690	C₂²	semidirect
78. C₂×#12687	C₂²	semidirect
79. C₂×#12581	C₂²	semidirect
80. C₂×#12575	C₂²	semidirect
81. C₂×H(7,𝔽₂)	C₂³	semidirect
85. C₂⁵×D₄	D₄	semidirect
86. C₂×#3484	D₄	semidirect
88. C₂×#3537	C₂³	semidirect
89. C₂²×D₄²	C₂³	semidirect
90. C₂²×#560	C₂³	semidirect
91. C₂²×#535	D₄	semidirect
92. C₂²×#535	D₄	semidirect
95. C₂²×#534	D₄	semidirect
97. C₂³×#127	D₄	semidirect
98. C₂²×#525	D₄	semidirect
99. C₂²×#525	D₄	semidirect
102. C₂³×#121	D₄	semidirect
103. C₂³×#120	D₄	semidirect
105. C₂²×#518	D₄	semidirect
106. C₂×#3027	D₄	semidirect
108. C₂×#3026	C₂³	semidirect
109. C₂×#3025	C₂³	semidirect
110. C₂×#3025	C₂³	semidirect
116. C₂²×B(4,𝔽₂)	C₂³	semidirect
117. C₂×#3021	C₂³	semidirect
120. C₂×#2883	C₂³	semidirect
124. #58990	C₂³	semidirect
125. #52163	C₂³	semidirect
126. C₂×#2724	C₂³	semidirect
127. C₂×#2709	C₂³	semidirect
128. C₂×#2697	C₂³	semidirect
129. C₂×#2697	C₂³	semidirect
130. C₂×#2679	C₂³	semidirect
131. C₂×#2669	C₂³	semidirect
132. #47846	C₂³	semidirect
133. #47827	C₂³	semidirect
134. #45438	C₂³	semidirect
135. #37269	C₂³	semidirect
136. #35527	D₄	semidirect
138. #35512	D₄	semidirect
140. C₂×#2431	D₄	semidirect
141. C₂×#2431	D₄	semidirect
144. C₂×#2405	D₄	semidirect
146. C₂×#2403	D₄	semidirect
148. #34415	C₂³	semidirect
149. C₂×#2375	C₂³	semidirect
150. C₂×#2358	C₂³	semidirect
151. C₂×#2311	D₄	semidirect
153. C₂×#2309	D₄	semidirect
154. C₂×#2309	D₄	semidirect
155. C₂×#2297	D₄	semidirect
157. C₂×#2200	C₂³	semidirect
158. C₂×#2196	C₂³	semidirect
159. C₂×#2128	C₂³	semidirect
160. C₂²×#353	C₂³	semidirect
161. C₂×#2122	C₂³	semidirect
162. C₂×#2120	C₂³	semidirect
163. C₂×#2120	C₂³	semidirect
164. C₂²×#352	C₂³	semidirect
165. C₂²×#352	C₂³	semidirect
166. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
167. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
168. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
169. #32900	C₂³	semidirect
170. #32898	C₂³	semidirect
171. #32888	C₂³	semidirect
172. #32888	C₂³	semidirect
173. #20615	C₂³	semidirect
176. #20610	C₂³	semidirect
178. #20592	C₂³	semidirect
180. #20586	C₂³	semidirect
182. #13347	C₂³	semidirect
183. #13346	C₂³	semidirect
184. #13345	C₂³	semidirect
185. #13344	C₂³	semidirect
186. #13344	C₂³	semidirect
187. #13343	C₂³	semidirect
188. #13088	C₂³	semidirect
189. #13088	C₂³	semidirect
190. #13086	C₂³	semidirect
191. #13084	C₂³	semidirect
192. #13043	C₂³	semidirect
193. #13041	C₂³	semidirect
194. #12690	C₂³	semidirect
195. #12687	C₂³	semidirect
196. #12581	C₂³	semidirect
197. C₂×#1393	C₂³	semidirect
198. C₂×#1393	C₂³	semidirect
199. #12575	C₂³	semidirect
200. C₂×#1390	C₂³	semidirect
202. C₂×#585	C₂×D₄	semidirect
222. C₂⁴×D₄	C₂×D₄	semidirect
223. C₂⁴×D₄	C₂×D₄	semidirect
224. C₂⁴×D₄	C₂×D₄	semidirect
227. C₂⁵×C₄	C₂×D₄	semidirect
228. C₂×#560	C₂⁴	semidirect
229. C₂×D₄²	C₂⁴	semidirect
232. C₂×#535	C₂×D₄	semidirect
233. C₂×#535	C₂×D₄	semidirect
234. C₂×#535	C₂×D₄	semidirect
238. C₂×#534	C₂×D₄	semidirect
240. C₂²×#127	C₂×D₄	semidirect
241. C₂²×#127	C₂×D₄	semidirect
242. C₂²×#127	C₂×D₄	semidirect
244. C₂²×#124	C₂×D₄	semidirect
246. C₂×#525	C₂×D₄	semidirect
247. C₂×#525	C₂×D₄	semidirect
248. C₂×#525	C₂×D₄	semidirect
253. C₂²×#123	C₂×D₄	semidirect
254. C₂²×#123	C₂×D₄	semidirect
257. C₂²×#121	C₂×D₄	semidirect
258. C₂²×#121	C₂×D₄	semidirect
259. C₂²×#121	C₂×D₄	semidirect
266. C₂²×#120	C₂×D₄	semidirect
267. C₂²×#120	C₂×D₄	semidirect
268. C₂²×#120	C₂×D₄	semidirect
273. C₂×#518	C₂×D₄	semidirect
276. C₂²×#117	C₂×D₄	semidirect
277. C₂²×#117	C₂×D₄	semidirect
278. C₂²×#117	C₂×D₄	semidirect
279. C₂²×#117	C₂×D₄	semidirect
280. C₂³×C₄⋊C₄	C₂×D₄	semidirect
283. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
284. C₂³×C₄²	C₂×D₄	semidirect
285. #3027	C₂×D₄	semidirect
288. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
295. C₂×#410	C₂×D₄	semidirect
301. #2724	C₂⁴	semidirect
302. #2709	C₂⁴	semidirect
303. #2697	C₂⁴	semidirect
304. #2697	C₂⁴	semidirect
305. #2679	C₂⁴	semidirect
306. #2669	C₂⁴	semidirect
307. #2433	C₂×D₄	semidirect
308. #2433	C₂×D₄	semidirect
311. #2431	C₂×D₄	semidirect
312. #2431	C₂×D₄	semidirect
313. #2405	C₂×D₄	semidirect
314. #2405	C₂×D₄	semidirect
316. #2403	C₂×D₄	semidirect
317. #2403	C₂×D₄	semidirect
319. #2375	C₂⁴	semidirect
320. #2358	C₂⁴	semidirect
321. #2311	C₂×D₄	semidirect
322. #2311	C₂×D₄	semidirect
324. #2309	C₂×D₄	semidirect
325. #2309	C₂×D₄	semidirect
326. #2297	C₂×D₄	semidirect
327. #2297	C₂×D₄	semidirect
329. C₂×#391	C₂×D₄	semidirect
330. C₂×#391	C₂×D₄	semidirect
331. C₂×#390	C₂×D₄	semidirect
332. C₂×#390	C₂×D₄	semidirect
335. C₂×#386	C₂×D₄	semidirect
336. C₂×#386	C₂×D₄	semidirect
337. C₂×#386	C₂×D₄	semidirect
339. C₂×#379	C₂×D₄	semidirect
340. C₂×#379	C₂×D₄	semidirect
341. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
342. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
343. C₂×#353	C₂⁴	semidirect
344. C₂×#352	C₂⁴	semidirect
345. C₂×#352	C₂⁴	semidirect
346. C₂×AΣL(1,𝔽₁₆)	C₂⁴	semidirect
347. C₂×AΣL(1,𝔽₁₆)	C₂⁴	semidirect
348. C₂×AΣL(1,𝔽₁₆)	C₂⁴	semidirect
354. #1393	C₂⁴	semidirect
355. #1393	C₂⁴	semidirect
356. #1390	C₂⁴	semidirect
364. #585	C₂²×D₄	semidirect
394. C₂³×D₄	#120	semidirect
411. C₂³×D₄	C₂²×D₄	semidirect
412. C₂³×D₄	C₂²×D₄	semidirect
425. C₂⁴×C₄	C₂²×D₄	semidirect
426. #535	#120	semidirect
429. C₂×#127	C₂²×D₄	semidirect
430. C₂×#127	C₂²×D₄	semidirect
432. C₂×#124	C₂²×D₄	semidirect
437. C₂×#123	C₂²×D₄	semidirect
438. C₂×#123	C₂²×D₄	semidirect
441. C₂×#121	C₂²×D₄	semidirect
442. C₂×#121	C₂²×D₄	semidirect
443. C₂×#120	#120	semidirect
453. C₂×#120	C₂²×D₄	semidirect
454. C₂×#120	C₂²×D₄	semidirect
458. C₂×#117	#120	semidirect
461. C₂×#117	C₂²×D₄	semidirect
462. C₂×#117	C₂²×D₄	semidirect
463. C₂×#117	C₂²×D₄	semidirect
464. C₂×#117	C₂²×D₄	semidirect
467. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
476. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
480. C₂²×C₄²	C₂²×D₄	semidirect
481. B(4,𝔽₂)	C₂²×D₄	semidirect
483. #410	C₂²×D₄	semidirect
487. #391	C₂²×D₄	semidirect
488. #391	C₂²×D₄	semidirect
491. #390	C₂²×D₄	semidirect
492. #390	C₂²×D₄	semidirect
496. #386	C₂²×D₄	semidirect
497. #386	C₂²×D₄	semidirect
498. #386	C₂²×D₄	semidirect
500. #379	C₂²×D₄	semidirect
501. #379	C₂²×D₄	semidirect
502. C₄×C₂²⋊C₄	C₂²×D₄	semidirect
503. C₄×C₂²⋊C₄	C₂²×D₄	semidirect
545. C₂²×D₄	C₂×#120	semidirect
583. #120	C₂×#120	semidirect
585. #117	C₂×#120	semidirect
683. C₂	#72233302	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×#494701	2
C₂×#494722	2
C₂×#494583	2
C₂×#499814	2
C₂×#498929	2
C₂×#6628898	2
C₂×#498885	2
C₂²×#33553	2
C₂×#6628872	2
C₂×#493425	2
C₂²×#60399	2
C₂×#499804	2
C₂×#499797	2
#72233302	2
C₂×#499787	2
C₂×#7837029	2

Subgroups — C2×#72233302 #72316668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72233302 #72316668