Subgroups — #72282443

Order 2048.

At least 10420 conjugacy classes of subgroups; only the 1542 normal subgroups are shown.

The subgroup lattice has 691 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72282405	C₂	1	1	yes	maximal, characteristic, complemented
2	#72282332	C₂	1	1	yes	maximal, characteristic, complemented
3	#72282288	C₂	1	8	yes	maximal, complemented
4	#72282225	C₂	1	8	yes	maximal, complemented
5	#72280868	C₂	1	1	yes	maximal, characteristic, complemented
6	#72280769	C₂	1	2	yes	maximal, complemented
7	#72280748	C₂	1	2	yes	maximal, complemented
8	#72280532	C₂	1	2	yes	maximal, complemented
9	#72280513	C₂	1	2	yes	maximal, complemented
10	C₂×#494587	C₂	1	2	yes	maximal, complemented
11	C₂×#7622868	C₂	1	2	yes	maximal, complemented
12	C₂×#62729	C₂²	1	1	yes	characteristic
13	#10586020	C₂²	1	1	yes	characteristic, complemented
14	C₂×#60398	C₂²	1	2	yes	—
15	C₂²×#3025	C₂²	1	2	yes	—
16	C₂×#60387	C₂²	1	2	yes	—
17	C₂×#60231	C₂²	1	1	yes	characteristic
18	#7625530	C₂²	1	1	yes	characteristic
19	#7622868	C₂²	1	8	yes	complemented
20	#7622868	C₂²	1	8	yes	complemented
21	C₂×#33358	C₂²	1	2	yes	—
22	C₂×#33347	C₂²	1	2	yes	—
23	C₂²×#2120	C₂²	1	2	yes	—
24	#6442724	C₂²	1	4	yes	complemented
25	#6442721	C₂²	1	4	yes	complemented
26	#6393518	C₂²	1	4	yes	complemented
27	#6393517	C₂²	1	4	yes	complemented
28	#6374181	C₂²	1	2	yes	—
29	#6371494	C₂²	1	2	yes	—
30	#6370774	C₂²	1	1	yes	characteristic, complemented
31	C₂×#20620	C₂²	1	2	yes	complemented
32	C₂×#20612	C₂²	1	2	yes	complemented
33	#6370734	C₂²	1	2	yes	complemented
34	#494587	C₂²	1	8	yes	complemented
35	#494587	C₂²	1	8	yes	complemented
36	C₂×#12589	C₂²	1	2	yes	complemented
37	#492906	C₂²	1	1	yes	characteristic, complemented
38	#492899	C₂²	1	1	yes	characteristic, complemented
39	C₂×#12577	C₂²	1	2	yes	complemented
40	#393998	C₂²	1	16	yes	complemented
41	#353324	C₂²	1	2	yes	complemented
42	#148007	C₂²	1	16	yes	complemented
43	#147761	C₂²	1	16	yes	complemented
44	#147757	C₂²	1	16	yes	complemented
45	#146668	C₂²	1	4	yes	complemented
46	#146667	C₂²	1	4	yes	complemented
47	C₂²×#585	C₂³	1	2	yes	—
48	#62812	C₂³	1	4	yes	complemented
49	#62729	D₄	1	2	yes	complemented
50	#62729	D₄	1	2	yes	complemented
51	#62729	C₂³	1	2	yes	—
52	#62729	C₂³	1	2	yes	—
53	C₂×#3540	D₄	1	2	yes	complemented
54	C₂×#3538	D₄	1	1	yes	characteristic, complemented
55	C₂×#3537	D₄	1	1	yes	characteristic, complemented
56	C₂×#3449	C₂³	1	2	yes	—
57	C₂²×#525	C₂³	1	1	yes	characteristic
58	C₂×#3428	C₂³	1	1	yes	characteristic
59	C₂³×#117	D₄	1	1	yes	characteristic, complemented
60	#60398	C₂³	1	8	yes	—
61	C₂×#3025	D₄	1	4	yes	complemented
62	C₂×#3025	D₄	1	4	yes	complemented
63	C₂×#3025	C₂³	1	4	yes	—
64	C₂×#3025	C₂³	1	4	yes	—
65	C₂²×#458	D₄	1	4	yes	complemented
66	C₂²×B(4,𝔽₂)	D₄	1	4	yes	complemented
67	#60387	C₂³	1	8	yes	—
68	#60231	C₂³	1	2	yes	—
69	#60231	C₂³	1	2	yes	—
70	C₂²×#421	D₄	1	2	yes	complemented
71	C₂²×#421	D₄	1	2	yes	complemented
72	C₂²×#413	C₂³	1	2	yes	—
73	C₂²×#410	C₂³	1	2	yes	—
74	C₂²×#410	C₂³	1	2	yes	—
75	C₂×#2879	C₂³	1	2	yes	—
76	#34065	D₄	1	2	yes	complemented
77	#34065	C₂³	1	2	yes	—
78	#34052	D₄	1	1	yes	characteristic, complemented
79	#34044	C₂³	1	1	yes	characteristic
80	C₄×#525	D₄	1	2	yes	complemented
81	C₄×#525	C₂³	1	2	yes	—
82	C₂×#2280	D₄	1	1	yes	characteristic, complemented
83	#33996	D₄	1	1	yes	characteristic, complemented
84	#33358	C₂³	1	8	yes	—
85	#33347	C₂³	1	8	yes	—
86	C₂×#2120	D₄	1	4	yes	complemented
87	C₂×#2120	D₄	1	4	yes	complemented
88	C₂×#2120	D₄	1	4	yes	complemented
89	C₂×#2120	D₄	1	4	yes	complemented
90	C₂×#2120	C₂³	1	4	yes	—
91	C₂×#2120	C₂³	1	4	yes	—
92	#21775	C₂³	1	8	yes	—
93	#20980	D₄	1	8	yes	complemented
94	#20980	C₂³	1	8	yes	—
95	#20632	C₂³	1	4	yes	complemented
96	#20620	C₂³	1	8	yes	complemented
97	#20612	C₂³	1	8	yes	complemented
98	#20608	C₂³	1	8	yes	complemented
99	C₂×#1733	D₄	1	2	yes	complemented
100	C₂×#1733	D₄	1	2	yes	complemented
101	#12589	C₂³	1	8	yes	complemented
102	#12585	C₂³	1	4	yes	complemented
103	#12581	C₂³	1	4	yes	complemented
104	#12577	C₂³	1	8	yes	complemented
105	#10758	C₂³	1	8	yes	complemented
106	C₂×#585	C₂×D₄	1	4	yes	—
107	C₂×#585	C₂⁴	1	4	yes	—
108	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
109	C₂³×#41	C₂×D₄	1	2	yes	—
110	C₂³×#41	C₂⁴	1	1	yes	characteristic
111	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
112	C₂³×M₁₆	C₂×D₄	1	2	yes	—
113	C₂³×M₁₆	C₂×D₄	1	2	yes	—
114	#3540	C₂×D₄	1	4	yes	complemented
115	#3540	C₂×D₄	1	4	yes	complemented
116	#3538	C₂×D₄	1	2	yes	complemented
117	#3538	C₂×D₄	1	2	yes	complemented
118	#3537	C₂×D₄	1	2	yes	complemented
119	#3537	C₂×D₄	1	2	yes	complemented
120	#3449	C₂×D₄	1	4	yes	—
121	#3449	C₂×D₄	1	4	yes	—
122	#3449	#41	1	4	yes	—
123	#3449	C₂⁴	1	4	yes	—
124	C₂×#536	C₂×D₄	1	2	yes	—
125	C₂×#536	#41	1	2	yes	—
126	C₂×#535	C₂×D₄	1	2	yes	—
127	C₂×#535	#41	1	2	yes	—
128	C₂×#525	C₂×D₄	1	2	yes	—
129	C₂×#525	C₂×D₄	1	2	yes	—
130	C₂×#525	C₂×D₄	1	1	yes	characteristic
131	C₂×#525	C₂×D₄	1	1	yes	characteristic
132	C₂×#525	C₂×D₄	1	1	yes	characteristic
133	C₂×#525	C₂×D₄	1	1	yes	characteristic
134	C₂×#525	C₂×D₄	1	2	yes	—
135	C₂×#525	C₂×D₄	1	2	yes	—
136	C₂×#525	C₂×D₄	1	2	yes	—
137	C₂×#525	C₂×D₄	1	2	yes	—
138	C₂×#525	C₂×D₄	1	1	yes	characteristic
139	C₂×#525	C₂×D₄	1	1	yes	characteristic
140	C₂×#525	#41	1	1	yes	characteristic
141	C₂×#525	#41	1	1	yes	characteristic
142	C₂×#525	#41	1	1	yes	characteristic
143	C₂×#525	#41	1	1	yes	characteristic
144	C₂×#525	C₂⁴	1	1	yes	characteristic
145	C₂×#525	C₂⁴	1	1	yes	characteristic
146	C₂²×#123	C₂×D₄	1	2	yes	—
147	C₂²×#120	C₂×D₄	1	2	yes	—
148	C₂×C₄×#41	C₂×D₄	1	4	yes	—
149	C₂×C₄×#41	C₂×D₄	1	2	yes	—
150	C₂×C₄×#41	C₂⁴	1	2	yes	—
151	C₂²×#117	C₂×D₄	1	1	yes	characteristic
152	C₂²×#117	C₂×D₄	1	2	yes	—
153	C₂²×#117	C₂×D₄	1	2	yes	—
154	C₂²×#117	C₂×D₄	1	2	yes	—
155	C₂²×#117	C₂×D₄	1	1	yes	characteristic
156	C₂²×#117	C₂×D₄	1	1	yes	characteristic
157	C₂²×#117	C₂×D₄	1	1	yes	characteristic
158	C₂²×#117	C₂×D₄	1	1	yes	characteristic
159	C₂²×#117	C₂×D₄	1	2	yes	complemented
160	C₂³×C₄²	C₂×D₄	1	2	yes	complemented
161	C₂×#458	C₂×D₄	1	8	yes	complemented
162	C₂×#458	C₂×D₄	1	8	yes	complemented
163	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	complemented
164	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	complemented
165	C₂×#421	C₂×D₄	1	8	yes	complemented
166	C₂²×#104	C₂×D₄	1	8	yes	complemented
167	C₂×#413	C₂×D₄	1	4	yes	—
168	C₂×#413	C₂×D₄	1	4	yes	—
169	C₂×#413	C₂⁴	1	4	yes	—
170	C₂×#410	C₂×D₄	1	4	yes	—
171	C₂×#410	C₂×D₄	1	4	yes	—
172	C₂×#410	C₂×D₄	1	4	yes	—
173	C₂×#410	C₂⁴	1	4	yes	—
174	C₂×#410	C₂⁴	1	4	yes	—
175	C₂²×#99	C₂×D₄	1	4	yes	—
176	#2879	C₂×D₄	1	4	yes	—
177	#2879	C₂⁴	1	4	yes	—
178	#2297	C₂×D₄	1	2	yes	—
179	#2297	C₂⁴	1	2	yes	—
180	#2296	C₂×D₄	1	2	yes	complemented
181	#2296	C₂×D₄	1	2	yes	complemented
182	#2280	C₂×D₄	1	2	yes	complemented
183	#2280	C₂×D₄	1	2	yes	complemented
184	C₄×#117	C₂×D₄	1	2	yes	complemented
185	C₄×#117	C₂×D₄	1	2	yes	complemented
186	#2120	C₂×D₄	1	8	yes	complemented
187	#2120	C₂×D₄	1	8	yes	complemented
188	#2120	C₂×D₄	1	8	yes	complemented
189	#2120	C₂×D₄	1	8	yes	complemented
190	#1733	C₂×D₄	1	8	yes	complemented
191	C₂×#339	C₂×D₄	1	8	yes	complemented
192	C₂⁶	#120	1	1	yes	characteristic
193	C₂×H(5,𝔽₂)	C₂²×D₄	1	8	yes	—
194	C₂²×#41	#121	1	4	yes	complemented
195	C₂²×#41	C₂²×D₄	1	4	yes	—
196	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
197	C₂²×#41	C₂²×D₄	1	2	yes	—
198	C₂²×#41	C₂²×D₄	1	2	yes	—
199	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
200	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
201	C₂²×#41	C₂²×D₄	1	2	yes	—
202	C₂²×#41	C₂²×D₄	1	2	yes	—
203	C₂²×#41	C₂×#41	1	1	yes	characteristic
204	C₂²×#41	C₂×#41	1	1	yes	characteristic
205	C₂²×#41	C₂×#41	1	2	yes	—
206	C₂²×#41	C₂×#41	1	2	yes	—
207	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂²×#41	C₂⁵	1	1	yes	characteristic
214	C₂³×Q₈	#121	1	2	yes	complemented
215	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂³×D₄	#121	1	2	yes	complemented
217	C₂³×D₄	C₂²×D₄	1	2	yes	—
218	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂⁴×C₄	#120	1	1	yes	characteristic
220	C₂⁴×C₄	#120	1	1	yes	characteristic
221	C₂⁴×C₄	#120	1	1	yes	characteristic
222	C₂⁴×C₄	#121	1	1	yes	characteristic
223	C₂⁴×C₄	#121	1	1	yes	characteristic
224	C₂⁴×C₄	#121	1	1	yes	characteristic
225	C₂⁴×C₄	#121	1	1	yes	characteristic
226	C₂⁴×C₄	#127	1	1	yes	characteristic
227	C₂⁴×C₄	#127	1	1	yes	characteristic
228	C₂⁴×C₄	#127	1	1	yes	characteristic
229	C₂⁴×C₄	#127	1	1	yes	characteristic
230	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
231	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
232	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
234	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
235	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
236	#536	#121	1	4	yes	complemented
237	#536	#121	1	4	yes	complemented
238	#536	C₂²×D₄	1	4	yes	—
239	#536	C₂×#41	1	4	yes	—
240	#535	#121	1	4	yes	complemented
241	#535	#121	1	4	yes	complemented
242	#535	C₂²×D₄	1	4	yes	—
243	#535	C₂×#41	1	4	yes	—
244	#525	#120	1	2	yes	—
245	#525	#120	1	2	yes	—
246	#525	#120	1	2	yes	—
247	#525	#120	1	2	yes	—
248	#525	#120	1	2	yes	—
249	#525	#120	1	2	yes	—
250	#525	#120	1	2	yes	—
251	#525	#120	1	2	yes	—
252	#525	#121	1	1	yes	characteristic
253	#525	#121	1	1	yes	characteristic
254	#525	#121	1	1	yes	characteristic
255	#525	#121	1	1	yes	characteristic
256	#525	#121	1	1	yes	characteristic
257	#525	#121	1	1	yes	characteristic
258	#525	#121	1	1	yes	characteristic
259	#525	#121	1	1	yes	characteristic
260	#525	#121	1	2	yes	—
261	#525	#121	1	2	yes	—
262	#525	#121	1	2	yes	—
263	#525	#121	1	2	yes	—
264	#525	#121	1	2	yes	—
265	#525	#121	1	2	yes	—
266	#525	#121	1	2	yes	—
267	#525	#121	1	2	yes	—
268	#525	#127	1	2	yes	—
269	#525	#127	1	2	yes	—
270	#525	#127	1	2	yes	—
271	#525	#127	1	2	yes	—
272	#525	C₂²×D₄	1	1	yes	characteristic
273	#525	C₂²×D₄	1	1	yes	characteristic
274	#525	C₂²×D₄	1	1	yes	characteristic
275	#525	C₂²×D₄	1	1	yes	characteristic
276	#525	C₂²×D₄	1	2	yes	—
277	#525	C₂²×D₄	1	2	yes	—
278	#525	C₂²×D₄	1	2	yes	—
279	#525	C₂²×D₄	1	2	yes	—
280	#525	C₂×#41	1	1	yes	characteristic
281	#525	C₂×#41	1	1	yes	characteristic
282	#525	C₂×#41	1	1	yes	characteristic
283	#525	C₂×#41	1	1	yes	characteristic
284	C₂×#123	#120	1	2	yes	—
285	C₂×#123	#120	1	2	yes	—
286	C₂×#123	#120	1	2	yes	—
287	C₂×#123	#120	1	2	yes	—
288	C₂×#123	#120	1	2	yes	—
289	C₂×#123	#120	1	2	yes	—
290	C₂×#123	#121	1	2	yes	—
291	C₂×#123	#121	1	2	yes	—
292	C₂×#123	#121	1	2	yes	—
293	C₂×#123	#121	1	2	yes	—
294	C₂×#123	C₂²×D₄	1	2	yes	—
295	C₂×#123	C₂²×D₄	1	2	yes	—
296	C₂×#120	#120	1	2	yes	—
297	C₂×#120	#120	1	2	yes	—
298	C₂×#120	#120	1	2	yes	—
299	C₂×#120	#120	1	2	yes	—
300	C₂×#120	#120	1	2	yes	—
301	C₂×#120	#120	1	2	yes	—
302	C₂×#120	#121	1	2	yes	—
303	C₂×#120	#121	1	2	yes	—
304	C₂×#120	#121	1	2	yes	—
305	C₂×#120	#121	1	2	yes	—
306	C₂×#120	C₂²×D₄	1	2	yes	—
307	C₂×#120	C₂²×D₄	1	2	yes	—
308	C₂×#117	#120	1	2	yes	—
309	C₂×#117	#120	1	2	yes	—
310	C₂×#117	#120	1	2	yes	—
311	C₂×#117	#120	1	4	yes	—
312	C₂×#117	#120	1	1	yes	characteristic
313	C₂×#117	#120	1	1	yes	characteristic
314	C₂×#117	#121	1	1	yes	characteristic
315	C₂×#117	#121	1	1	yes	characteristic
316	C₂×#117	#121	1	1	yes	characteristic
317	C₂×#117	#121	1	1	yes	characteristic
318	C₂×#117	#121	1	2	yes	complemented
319	C₂×#117	#121	1	2	yes	complemented
320	C₂×#117	#121	1	4	yes	complemented
321	C₂×#117	#127	1	2	yes	—
322	C₂×#117	#127	1	2	yes	—
323	C₂×#117	C₂²×D₄	1	4	yes	—
324	C₂×#117	C₂²×D₄	1	2	yes	—
325	C₂×#117	C₂²×D₄	1	1	yes	characteristic
326	C₂×#117	C₂²×D₄	1	1	yes	characteristic
327	C₂×#117	C₂²×D₄	1	4	yes	—
328	C₂×#117	C₂²×D₄	1	2	yes	—
329	C₂²×C₂²⋊C₄	#120	1	2	yes	—
330	C₂²×C₄²	#120	1	4	yes	—
331	C₂²×C₄²	#120	1	2	yes	—
332	C₂²×C₄²	C₂²×D₄	1	2	yes	—
333	C₂²×C₄²	C₂²×D₄	1	4	yes	—
334	C₂²×C₄²	C₂²×D₄	1	2	yes	—
335	#413	C₂²×D₄	1	8	yes	—
336	#410	C₂²×D₄	1	8	yes	—
337	C₂×#99	C₂²×D₄	1	8	yes	—
338	C₂⁵	#392	1	1	yes	characteristic
339	C₂⁵	#392	1	1	yes	characteristic
340	C₂⁵	#392	1	1	yes	characteristic
341	C₂⁵	#392	1	1	yes	characteristic
342	C₂⁵	C₂×#120	1	1	yes	characteristic
343	C₂⁵	C₂×#120	1	1	yes	characteristic
344	C₂⁵	C₂×#120	1	1	yes	characteristic
345	C₂⁵	D₄²	1	2	yes	—
346	C₂×#41	C₂×#120	1	2	yes	—
347	C₂×#41	C₂×#120	1	2	yes	—
348	C₂×#41	C₂×#121	1	1	yes	characteristic
349	C₂×#41	C₂×#121	1	1	yes	characteristic
350	C₂×#41	C₂×#121	1	2	yes	—
351	C₂×#41	C₂×#121	1	2	yes	—
352	C₂×#41	C₂×#121	1	2	yes	—
353	C₂×#41	C₂×#121	1	2	yes	—
354	C₂×#41	#525	1	2	yes	—
355	C₂×#41	#525	1	2	yes	—
356	C₂×#41	#525	1	2	yes	—
357	C₂×#41	C₂×#127	1	2	yes	—
358	C₂×#41	#534	1	1	yes	characteristic
359	C₂×#41	#534	1	1	yes	characteristic
360	C₂×#41	#534	1	1	yes	characteristic
361	C₂×#41	#534	1	1	yes	characteristic
362	C₂×#41	#535	1	1	yes	characteristic
363	C₂×#41	#535	1	1	yes	characteristic
364	C₂×#41	#538	1	1	yes	characteristic
365	C₂×#41	#538	1	1	yes	characteristic
366	C₂×#41	#538	1	1	yes	characteristic
367	C₂×#41	#538	1	1	yes	characteristic
368	C₂×#41	D₄²	1	2	yes	—
369	C₂×#41	D₄²	1	2	yes	—
370	C₂×#41	D₄²	1	2	yes	—
371	C₂×#41	D₄²	1	2	yes	—
372	C₂×#41	#546	1	2	yes	—
373	C₂×#41	#546	1	2	yes	—
374	C₂×#41	#546	1	2	yes	—
375	C₂×#41	#546	1	2	yes	—
376	C₂×#41	#546	1	2	yes	—
377	C₂×#41	#546	1	2	yes	—
378	C₂×#41	#546	1	2	yes	—
379	C₂×#41	#546	1	2	yes	—
380	C₂×#41	C₂³×D₄	1	1	yes	characteristic
381	C₂×#41	C₂³×D₄	1	2	yes	—
382	C₂×#41	C₂²×#41	1	1	yes	characteristic
383	C₂×#41	C₂²×#41	1	2	yes	—
384	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
385	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
386	C₂²×Q₈	C₂×#121	1	4	yes	—
387	C₂²×Q₈	#534	1	1	yes	characteristic
388	C₂²×Q₈	#534	1	1	yes	characteristic
389	C₂²×Q₈	#534	1	1	yes	characteristic
390	C₂²×Q₈	#538	1	1	yes	characteristic
391	C₂²×Q₈	#538	1	1	yes	characteristic
392	C₂²×Q₈	D₄²	1	2	yes	—
393	C₂²×Q₈	#546	1	2	yes	—
394	C₂²×Q₈	#546	1	2	yes	—
395	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂²×D₄	C₂×#120	1	2	yes	—
397	C₂²×D₄	C₂×#120	1	2	yes	—
398	C₂²×D₄	C₂×#120	1	2	yes	—
399	C₂²×D₄	C₂×#121	1	4	yes	—
400	C₂²×D₄	C₂×#121	1	2	yes	—
401	C₂²×D₄	C₂×#121	1	2	yes	—
402	C₂²×D₄	#534	1	1	yes	characteristic
403	C₂²×D₄	#534	1	1	yes	characteristic
404	C₂²×D₄	#534	1	1	yes	characteristic
405	C₂²×D₄	#538	1	1	yes	characteristic
406	C₂²×D₄	#538	1	1	yes	characteristic
407	C₂²×D₄	D₄²	1	2	yes	—
408	C₂²×D₄	D₄²	1	2	yes	—
409	C₂²×D₄	D₄²	1	2	yes	—
410	C₂²×D₄	#546	1	2	yes	—
411	C₂²×D₄	#546	1	2	yes	—
412	C₂²×D₄	#546	1	2	yes	—
413	C₂²×D₄	#546	1	2	yes	—
414	C₂²×D₄	#546	1	2	yes	—
415	C₂²×D₄	#546	1	2	yes	—
416	C₂²×D₄	C₂³×D₄	1	2	yes	—
417	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂³×C₄	#392	1	1	yes	characteristic
419	C₂³×C₄	#392	1	1	yes	characteristic
420	C₂³×C₄	#392	1	1	yes	characteristic
421	C₂³×C₄	#392	1	1	yes	characteristic
422	C₂³×C₄	#392	1	1	yes	characteristic
423	C₂³×C₄	#392	1	1	yes	characteristic
424	C₂³×C₄	#392	1	1	yes	characteristic
425	C₂³×C₄	#392	1	1	yes	characteristic
426	C₂³×C₄	#392	1	1	yes	characteristic
427	C₂³×C₄	#392	1	1	yes	characteristic
428	C₂³×C₄	#392	1	1	yes	characteristic
429	C₂³×C₄	#392	1	1	yes	characteristic
430	C₂³×C₄	C₂×#120	1	1	yes	characteristic
431	C₂³×C₄	C₂×#120	1	2	yes	—
432	C₂³×C₄	C₂×#120	1	1	yes	characteristic
433	C₂³×C₄	C₂×#120	1	1	yes	characteristic
434	C₂³×C₄	C₂×#120	1	1	yes	characteristic
435	C₂³×C₄	C₂×#120	1	1	yes	characteristic
436	C₂³×C₄	C₂×#121	1	1	yes	characteristic
437	C₂³×C₄	C₂×#121	1	1	yes	characteristic
438	C₂³×C₄	C₂×#121	1	2	yes	—
439	C₂³×C₄	C₂×#121	1	2	yes	—
440	C₂³×C₄	C₂×#121	1	1	yes	characteristic
441	C₂³×C₄	C₂×#121	1	1	yes	characteristic
442	C₂³×C₄	C₂×#121	1	1	yes	characteristic
443	C₂³×C₄	C₂×#121	1	1	yes	characteristic
444	C₂³×C₄	#525	1	1	yes	characteristic
445	C₂³×C₄	#525	1	1	yes	characteristic
446	C₂³×C₄	#525	1	2	yes	—
447	C₂³×C₄	#525	1	2	yes	—
448	C₂³×C₄	C₂×#127	1	1	yes	characteristic
449	C₂³×C₄	C₂×#127	1	1	yes	characteristic
450	C₂³×C₄	C₂×#127	1	1	yes	characteristic
451	C₂³×C₄	C₂×#127	1	1	yes	characteristic
452	C₂³×C₄	C₂×#127	1	1	yes	characteristic
453	C₂³×C₄	C₂×#127	1	1	yes	characteristic
454	C₂³×C₄	#534	1	1	yes	characteristic
455	C₂³×C₄	#534	1	1	yes	characteristic
456	C₂³×C₄	#535	1	1	yes	characteristic
457	C₂³×C₄	#535	1	1	yes	characteristic
458	C₂³×C₄	D₄²	1	2	yes	—
459	C₂³×C₄	D₄²	1	2	yes	—
460	C₂³×C₄	D₄²	1	2	yes	—
461	C₂³×C₄	D₄²	1	2	yes	—
462	C₂³×C₄	D₄²	1	2	yes	—
463	C₂³×C₄	D₄²	1	2	yes	—
464	C₂³×C₄	D₄²	1	2	yes	—
465	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
466	C₂³×C₄	C₂³×D₄	1	2	yes	—
467	#123	#392	1	2	yes	—
468	#123	#392	1	2	yes	—
469	#123	#392	1	2	yes	—
470	#123	#392	1	2	yes	—
471	#123	#392	1	2	yes	—
472	#123	#392	1	2	yes	—
473	#123	#392	1	2	yes	—
474	#123	#392	1	2	yes	—
475	#123	C₂×#120	1	2	yes	—
476	#123	C₂×#120	1	2	yes	—
477	#123	C₂×#120	1	2	yes	—
478	#123	C₂×#120	1	2	yes	—
479	#123	C₂×#121	1	2	yes	—
480	#123	C₂×#121	1	2	yes	—
481	#123	C₂×#121	1	2	yes	—
482	#123	C₂×#121	1	2	yes	—
483	#120	#392	1	2	yes	—
484	#120	#392	1	2	yes	—
485	#120	#392	1	2	yes	—
486	#120	#392	1	2	yes	—
487	#120	#392	1	2	yes	—
488	#120	#392	1	2	yes	—
489	#120	#392	1	2	yes	—
490	#120	#392	1	2	yes	—
491	#120	C₂×#120	1	2	yes	—
492	#120	C₂×#120	1	2	yes	—
493	#120	C₂×#120	1	2	yes	—
494	#120	C₂×#120	1	2	yes	—
495	#120	C₂×#121	1	2	yes	—
496	#120	C₂×#121	1	2	yes	—
497	#120	C₂×#121	1	2	yes	—
498	#120	C₂×#121	1	2	yes	—
499	#117	#392	1	2	yes	—
500	#117	#392	1	2	yes	—
501	#117	#392	1	2	yes	—
502	#117	#392	1	2	yes	—
503	#117	B(4,𝔽₂)	1	4	yes	—
504	#117	B(4,𝔽₂)	1	4	yes	—
505	#117	C₂×#121	1	4	yes	—
506	#117	C₂×#121	1	4	yes	—
507	#117	C₂×#121	1	1	yes	characteristic
508	#117	C₂×#121	1	1	yes	characteristic
509	#117	C₂×#121	1	1	yes	characteristic
510	#117	C₂×#121	1	1	yes	characteristic
511	#117	C₂×#127	1	2	yes	—
512	#117	C₂×#127	1	2	yes	—
513	C₂×C₂²⋊C₄	#392	1	2	yes	—
514	C₂×C₂²⋊C₄	#392	1	2	yes	—
515	C₂×C₂²⋊C₄	#392	1	2	yes	—
516	C₂×C₂²⋊C₄	#392	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
519	C₂×C₄²	C₂×#120	1	4	yes	—
520	C₂×C₄²	C₂×#120	1	2	yes	—
521	C₂×C₄²	C₂×#120	1	2	yes	—
522	C₂⁴	C₂×#392	1	1	yes	characteristic
523	C₂⁴	C₂×#392	1	1	yes	characteristic
524	C₂⁴	C₂×#392	1	1	yes	characteristic
525	C₂⁴	C₂×#392	1	1	yes	characteristic
526	C₂⁴	C₂×#392	1	1	yes	characteristic
527	C₂⁴	C₂×#392	1	1	yes	characteristic
528	C₂⁴	#2403	1	2	yes	—
529	C₂⁴	#2403	1	1	yes	characteristic
530	C₂⁴	#2403	1	1	yes	characteristic
531	C₂⁴	#2404	1	1	yes	characteristic
532	C₂⁴	#2404	1	1	yes	characteristic
533	C₂⁴	#2410	1	2	yes	—
534	C₂⁴	#2410	1	2	yes	—
535	C₂⁴	#2424	1	2	yes	—
536	C₂⁴	#2424	1	2	yes	—
537	C₂⁴	C₂²×#120	1	1	yes	characteristic
538	C₂⁴	C₂×D₄²	1	2	yes	—
539	C₂×Q₈	#2410	1	2	yes	—
540	C₂×Q₈	#2410	1	2	yes	—
541	C₂×Q₈	#2424	1	2	yes	—
542	C₂×Q₈	#2424	1	2	yes	—
543	C₂×Q₈	#2539	1	2	yes	—
544	C₂×Q₈	#2617	1	1	yes	characteristic
545	C₂×Q₈	#2617	1	1	yes	characteristic
546	C₂×Q₈	C₂×#534	1	1	yes	characteristic
547	C₂×Q₈	C₂×#538	1	1	yes	characteristic
548	C₂×Q₈	C₂×#546	1	2	yes	—
549	C₂×D₄	C₂×#392	1	2	yes	—
550	C₂×D₄	C₂×#392	1	2	yes	—
551	C₂×D₄	#2404	1	2	yes	—
552	C₂×D₄	#2404	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	#2410	1	2	yes	—
558	C₂×D₄	#2410	1	2	yes	—
559	C₂×D₄	#2424	1	2	yes	—
560	C₂×D₄	#2424	1	2	yes	—
561	C₂×D₄	#2424	1	2	yes	—
562	C₂×D₄	#2424	1	2	yes	—
563	C₂×D₄	#2424	1	2	yes	—
564	C₂×D₄	#2424	1	2	yes	—
565	C₂×D₄	#2539	1	2	yes	—
566	C₂×D₄	#2617	1	1	yes	characteristic
567	C₂×D₄	#2617	1	1	yes	characteristic
568	C₂×D₄	C₂²×#120	1	2	yes	—
569	C₂×D₄	C₂²×#121	1	2	yes	—
570	C₂×D₄	C₂×#534	1	1	yes	characteristic
571	C₂×D₄	C₂×#538	1	1	yes	characteristic
572	C₂×D₄	C₂×#546	1	2	yes	—
573	C₂×D₄	C₂×#546	1	2	yes	—
574	C₂×D₄	C₂×#546	1	2	yes	—
575	C₂²×C₄	C₂×#392	1	1	yes	characteristic
576	C₂²×C₄	C₂×#392	1	1	yes	characteristic
577	C₂²×C₄	C₂×#392	1	1	yes	characteristic
578	C₂²×C₄	C₂×#392	1	1	yes	characteristic
579	C₂²×C₄	C₂×#392	1	1	yes	characteristic
580	C₂²×C₄	C₂×#392	1	1	yes	characteristic
581	C₂²×C₄	#2403	1	2	yes	—
582	C₂²×C₄	#2403	1	1	yes	characteristic
583	C₂²×C₄	#2403	1	1	yes	characteristic
584	C₂²×C₄	#2404	1	1	yes	characteristic
585	C₂²×C₄	#2404	1	1	yes	characteristic
586	C₂²×C₄	#2410	1	2	yes	—
587	C₂²×C₄	#2410	1	2	yes	—
588	C₂²×C₄	#2410	1	2	yes	—
589	C₂²×C₄	#2410	1	2	yes	—
590	C₂²×C₄	#2410	1	2	yes	—
591	C₂²×C₄	#2410	1	2	yes	—
592	C₂²×C₄	#2424	1	2	yes	—
593	C₂²×C₄	#2424	1	2	yes	—
594	C₂²×C₄	#2424	1	2	yes	—
595	C₂²×C₄	#2424	1	2	yes	—
596	C₂²×C₄	#2424	1	2	yes	—
597	C₂²×C₄	#2424	1	2	yes	—
598	C₂²×C₄	#2433	1	1	yes	characteristic
599	C₂²×C₄	#2433	1	1	yes	characteristic
600	C₂²×C₄	#2433	1	2	yes	—
601	C₂²×C₄	#2433	1	2	yes	—
602	C₂²×C₄	#2433	1	1	yes	characteristic
603	C₂²×C₄	#2433	1	1	yes	characteristic
604	C₂²×C₄	#2539	1	1	yes	characteristic
605	C₂²×C₄	#2539	1	1	yes	characteristic
606	C₂²×C₄	#2539	1	1	yes	characteristic
607	C₂²×C₄	#2539	1	1	yes	characteristic
608	C₂²×C₄	#2617	1	1	yes	characteristic
609	C₂²×C₄	#2617	1	1	yes	characteristic
610	C₂²×C₄	#2617	1	1	yes	characteristic
611	C₂²×C₄	#2617	1	1	yes	characteristic
612	C₂²×C₄	#2847	1	2	yes	—
613	C₂²×C₄	#2847	1	2	yes	—
614	C₂²×C₄	#2847	1	1	yes	characteristic
615	C₂²×C₄	#2847	1	1	yes	characteristic
616	C₂²×C₄	#2847	1	1	yes	characteristic
617	C₂²×C₄	#2847	1	1	yes	characteristic
618	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
619	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
620	C₂²×C₄	#3027	1	2	yes	—
621	C₂²×C₄	#3027	1	2	yes	—
622	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
623	C₂²×C₄	C₂²×#121	1	2	yes	—
624	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
625	C₂²×C₄	C₂×#525	1	1	yes	characteristic
626	C₂²×C₄	C₂×#525	1	2	yes	—
627	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
628	C₂²×C₄	C₂×#534	1	1	yes	characteristic
629	C₂²×C₄	C₂×#535	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄²	1	2	yes	—
631	C₂²×C₄	C₂×D₄²	1	2	yes	—
632	C₂²×C₄	C₂×D₄²	1	2	yes	—
633	C₂²⋊C₄	C₂×#392	1	2	yes	—
634	C₂²⋊C₄	C₂×#392	1	2	yes	—
635	C₂²⋊C₄	C₂×#392	1	2	yes	—
636	C₂²⋊C₄	C₂×#392	1	2	yes	—
637	C₄²	C₂×B(4,𝔽₂)	1	4	yes	—
638	C₄²	C₂×B(4,𝔽₂)	1	4	yes	—
639	C₂³	#14716	1	1	yes	characteristic
640	C₂³	#14716	1	1	yes	characteristic
641	C₂³	#14716	1	2	yes	—
642	C₂³	#14716	1	2	yes	—
643	C₂³	#14716	1	1	yes	characteristic
644	C₂³	#14716	1	1	yes	characteristic
645	C₂³	#23900	1	2	yes	—
646	C₂³	#23904	1	2	yes	—
647	C₂³	C₂²×#392	1	1	yes	characteristic
648	C₂³	C₂×#2403	1	1	yes	characteristic
649	C₂³	C₂×#2410	1	2	yes	—
650	C₂³	C₂×#2424	1	2	yes	—
651	C₂³	C₂×#2404	1	1	yes	characteristic
652	C₂×C₄	#14716	1	2	yes	—
653	C₂×C₄	#14716	1	2	yes	—
654	C₂×C₄	#14716	1	1	yes	characteristic
655	C₂×C₄	#14716	1	1	yes	characteristic
656	C₂×C₄	#14716	1	1	yes	characteristic
657	C₂×C₄	#14716	1	1	yes	characteristic
658	C₂×C₄	#23900	1	2	yes	—
659	C₂×C₄	#23904	1	2	yes	—
660	C₂×C₄	#25771	1	2	yes	—
661	C₂×C₄	#25771	1	2	yes	—
662	C₂×C₄	#25771	1	2	yes	—
663	C₂×C₄	#25771	1	2	yes	—
664	C₂×C₄	#32926	1	2	yes	—
665	C₂×C₄	#32926	1	2	yes	—
666	C₂×C₄	#32926	1	2	yes	—
667	C₂×C₄	#32926	1	2	yes	—
668	C₂×C₄	C₂×#2617	1	1	yes	characteristic
669	C₂×C₄	C₂×#2410	1	2	yes	—
670	C₂×C₄	C₂×#2424	1	2	yes	—
671	C₂×C₄	C₂×#2433	1	1	yes	characteristic
672	C₂×C₄	C₂×#2539	1	1	yes	characteristic
673	C₂×C₄	C₂×#2847	1	1	yes	characteristic
674	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
675	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
676	C₂×C₄	C₂×#3027	1	1	yes	characteristic
677	C₂×C₄	C₂×#3027	1	1	yes	characteristic
678	C₂²	#394174	1	2	yes	—
679	C₂²	#394174	1	2	yes	—
680	C₂²	C₂×#14716	1	1	yes	characteristic
681	C₂²	C₂×#23900	1	1	yes	characteristic
682	C₂²	C₂×#23904	1	1	yes	characteristic
683	C₄	#394174	1	2	yes	—
684	C₄	#394174	1	2	yes	—
685	C₄	C₂×#25771	1	1	yes	characteristic
686	C₄	C₂×#25771	1	1	yes	characteristic
687	C₄	C₂×#32926	1	1	yes	characteristic
688	C₄	C₂×#32926	1	1	yes	characteristic
689	C₂	C₂×#394174	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#25771
commutator, Frattini, cosocle	C₂²×#41	C₂⁵
socle	C₂	C₂×#394174
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#3428 ◁ 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. #72282405	C₂	semidirect
2. #72282332	C₂	semidirect
3. #72282288	C₂	semidirect
4. #72282225	C₂	semidirect
5. #72280868	C₂	semidirect
6. #72280769	C₂	semidirect
7. #72280748	C₂	semidirect
8. #72280532	C₂	semidirect
9. #72280513	C₂	semidirect
10. C₂×#494587	C₂	semidirect
11. C₂×#7622868	C₂	semidirect
13. #10586020	C₂²	semidirect
19. #7622868	C₂²	semidirect
20. #7622868	C₂²	semidirect
24. #6442724	C₂²	semidirect
25. #6442721	C₂²	semidirect
26. #6393518	C₂²	semidirect
27. #6393517	C₂²	semidirect
30. #6370774	C₂²	semidirect
31. C₂×#20620	C₂²	semidirect
32. C₂×#20612	C₂²	semidirect
33. #6370734	C₂²	semidirect
34. #494587	C₂²	semidirect
35. #494587	C₂²	semidirect
36. C₂×#12589	C₂²	semidirect
37. #492906	C₂²	semidirect
38. #492899	C₂²	semidirect
39. C₂×#12577	C₂²	semidirect
40. #393998	C₂²	semidirect
41. #353324	C₂²	semidirect
42. #148007	C₂²	semidirect
43. #147761	C₂²	semidirect
44. #147757	C₂²	semidirect
45. #146668	C₂²	semidirect
46. #146667	C₂²	semidirect
48. #62812	C₂³	semidirect
49. #62729	D₄	semidirect
50. #62729	D₄	semidirect
53. C₂×#3540	D₄	semidirect
54. C₂×#3538	D₄	semidirect
55. C₂×#3537	D₄	semidirect
59. C₂³×#117	D₄	semidirect
61. C₂×#3025	D₄	semidirect
62. C₂×#3025	D₄	semidirect
65. C₂²×#458	D₄	semidirect
66. C₂²×B(4,𝔽₂)	D₄	semidirect
70. C₂²×#421	D₄	semidirect
71. C₂²×#421	D₄	semidirect
76. #34065	D₄	semidirect
78. #34052	D₄	semidirect
80. C₄×#525	D₄	semidirect
82. C₂×#2280	D₄	semidirect
83. #33996	D₄	semidirect
86. C₂×#2120	D₄	semidirect
87. C₂×#2120	D₄	semidirect
88. C₂×#2120	D₄	semidirect
89. C₂×#2120	D₄	semidirect
93. #20980	D₄	semidirect
95. #20632	C₂³	semidirect
96. #20620	C₂³	semidirect
97. #20612	C₂³	semidirect
98. #20608	C₂³	semidirect
99. C₂×#1733	D₄	semidirect
100. C₂×#1733	D₄	semidirect
101. #12589	C₂³	semidirect
102. #12585	C₂³	semidirect
103. #12581	C₂³	semidirect
104. #12577	C₂³	semidirect
105. #10758	C₂³	semidirect
114. #3540	C₂×D₄	semidirect
115. #3540	C₂×D₄	semidirect
116. #3538	C₂×D₄	semidirect
117. #3538	C₂×D₄	semidirect
118. #3537	C₂×D₄	semidirect
119. #3537	C₂×D₄	semidirect
159. C₂²×#117	C₂×D₄	semidirect
160. C₂³×C₄²	C₂×D₄	semidirect
161. C₂×#458	C₂×D₄	semidirect
162. C₂×#458	C₂×D₄	semidirect
163. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
164. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
165. C₂×#421	C₂×D₄	semidirect
166. C₂²×#104	C₂×D₄	semidirect
180. #2296	C₂×D₄	semidirect
181. #2296	C₂×D₄	semidirect
182. #2280	C₂×D₄	semidirect
183. #2280	C₂×D₄	semidirect
184. C₄×#117	C₂×D₄	semidirect
185. C₄×#117	C₂×D₄	semidirect
186. #2120	C₂×D₄	semidirect
187. #2120	C₂×D₄	semidirect
188. #2120	C₂×D₄	semidirect
189. #2120	C₂×D₄	semidirect
190. #1733	C₂×D₄	semidirect
191. C₂×#339	C₂×D₄	semidirect
194. C₂²×#41	#121	semidirect
214. C₂³×Q₈	#121	semidirect
216. C₂³×D₄	#121	semidirect
236. #536	#121	semidirect
237. #536	#121	semidirect
240. #535	#121	semidirect
241. #535	#121	semidirect
318. C₂×#117	#121	semidirect
319. C₂×#117	#121	semidirect
320. C₂×#117	#121	semidirect

Maximal subgroups

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

subgroup	index
#72282405	2
#72282332	2
#72282288	2
#72282225	2
#72280868	2
#72280769	2
#72280748	2
#72280532	2
#72280513	2
C₂×#494587	2
C₂×#7622868	2