Subgroups — #72312607

Order 1024.

At least 6076 conjugacy classes of subgroups; only the 755 normal subgroups are shown.

The subgroup lattice has 471 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10577336	C₂	1	1	yes	maximal, characteristic, complemented
2	#10574854	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#33572	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#33560	C₂	1	1	yes	maximal, characteristic, complemented
5	#6628886	C₂	1	1	yes	maximal, characteristic, complemented
6	#6628885	C₂	1	1	yes	maximal, characteristic, complemented
7	#499888	C₂	1	4	yes	maximal, complemented
8	#499885	C₂	1	4	yes	maximal, complemented
9	#499884	C₂	1	4	yes	maximal, complemented
10	#499881	C₂	1	4	yes	maximal, complemented
11	#498944	C₂	1	1	yes	maximal, characteristic, complemented
12	#498943	C₂	1	1	yes	maximal, characteristic, complemented
13	#498917	C₂	1	1	yes	maximal, characteristic, complemented
14	#498916	C₂	1	1	yes	maximal, characteristic, complemented
15	#494752	C₂	1	1	yes	maximal, characteristic, complemented
16	#494751	C₂	1	1	yes	maximal, characteristic, complemented
17	#494609	C₂	1	1	yes	maximal, characteristic, complemented
18	#494605	C₂	1	1	yes	maximal, characteristic, complemented
19	#493419	C₂	1	1	yes	maximal, characteristic, complemented
20	#63103	C₂²	1	1	yes	characteristic
21	#62812	C₂²	1	1	yes	characteristic
22	C₂×#3551	C₂²	1	1	yes	characteristic, complemented
23	#61676	C₂²	1	2	yes	complemented
24	#61675	C₂²	1	2	yes	complemented
25	#61666	C₂²	1	2	yes	complemented
26	#61663	C₂²	1	2	yes	complemented
27	#60754	C₂²	1	1	yes	characteristic, complemented
28	#60753	C₂²	1	1	yes	characteristic, complemented
29	C₂×#3028	C₂²	1	1	yes	characteristic, complemented
30	C₂×#3027	C₂²	1	1	yes	characteristic, complemented
31	#60391	C₂²	1	2	yes	complemented
32	#60390	C₂²	1	2	yes	complemented
33	#60389	C₂²	1	2	yes	complemented
34	#60388	C₂²	1	2	yes	complemented
35	#60387	C₂²	1	1	yes	characteristic
36	#60387	C₂²	1	1	yes	characteristic
37	C₂×#3022	C₂²	1	1	yes	characteristic, complemented
38	C₂×#3021	C₂²	1	1	yes	characteristic, complemented
39	C₂×#3018	C₂²	1	1	yes	characteristic
40	C₂×#3018	C₂²	1	1	yes	characteristic
41	#60370	C₂²	1	1	yes	characteristic
42	#60369	C₂²	1	1	yes	characteristic
43	#60232	C₂²	1	1	yes	characteristic, complemented
44	#60076	C₂²	1	1	yes	characteristic
45	#33572	C₂²	1	4	yes	complemented
46	#33572	C₂²	1	4	yes	complemented
47	#33560	C₂²	1	4	yes	complemented
48	#33560	C₂²	1	4	yes	complemented
49	C₂×#2135	C₂²	1	1	yes	characteristic, complemented
50	C₂×#2134	C₂²	1	1	yes	characteristic, complemented
51	C₂×#2132	C₂²	1	1	yes	characteristic, complemented
52	C₂×#2126	C₂²	1	1	yes	characteristic, complemented
53	#33347	C₂²	1	1	yes	characteristic, complemented
54	#33347	C₂²	1	1	yes	characteristic, complemented
55	C₂×#2123	C₂²	1	1	yes	characteristic, complemented
56	C₂×#2122	C₂²	1	1	yes	characteristic, complemented
57	#32897	C₂²	1	4	yes	complemented
58	#32896	C₂²	1	4	yes	complemented
59	#32895	C₂²	1	4	yes	complemented
60	#32894	C₂²	1	4	yes	complemented
61	#20623	C₂²	1	1	yes	characteristic
62	#20623	C₂²	1	1	yes	characteristic
63	#20620	C₂²	1	1	yes	characteristic, complemented
64	#20620	C₂²	1	1	yes	characteristic, complemented
65	#20612	C₂²	1	1	yes	characteristic, complemented
66	#20612	C₂²	1	1	yes	characteristic, complemented
67	#13362	C₂²	1	4	yes	complemented
68	#13361	C₂²	1	4	yes	complemented
69	#13361	C₂²	1	4	yes	complemented
70	#13360	C₂²	1	4	yes	complemented
71	#13356	C₂²	1	4	yes	complemented
72	#13355	C₂²	1	4	yes	complemented
73	#13354	C₂²	1	4	yes	complemented
74	#13353	C₂²	1	4	yes	complemented
75	#13099	C₂²	1	4	yes	complemented
76	#13098	C₂²	1	4	yes	complemented
77	#13097	C₂²	1	4	yes	complemented
78	#13096	C₂²	1	4	yes	complemented
79	#13054	C₂²	1	4	yes	complemented
80	#13053	C₂²	1	4	yes	complemented
81	#13052	C₂²	1	4	yes	complemented
82	#13051	C₂²	1	4	yes	complemented
83	#12718	C₂²	1	2	yes	complemented
84	#12717	C₂²	1	2	yes	complemented
85	#12716	C₂²	1	2	yes	complemented
86	#12715	C₂²	1	2	yes	complemented
87	#12589	C₂²	1	1	yes	characteristic, complemented
88	#12589	C₂²	1	1	yes	characteristic, complemented
89	#12579	C₂²	1	1	yes	characteristic, complemented
90	#12579	C₂²	1	1	yes	characteristic, complemented
91	2₋¹⁺⁶	C₂³	1	2	yes	—
92	H(7,𝔽₂)	C₂³	1	2	yes	—
93	C₂×#585	D₄	1	1	yes	characteristic, complemented
94	C₂×#585	C₂³	1	1	yes	characteristic
95	C₂×#585	C₂³	1	1	yes	characteristic
96	C₂×#585	C₂³	1	1	yes	characteristic
97	C₂²×#137	D₄	1	1	yes	characteristic, complemented
98	C₂²×#137	D₄	1	1	yes	characteristic, complemented
99	C₂²×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
100	C₂²×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
101	#3551	C₂³	1	2	yes	complemented
102	#3551	C₂³	1	2	yes	complemented
103	#3500	D₄	1	1	yes	characteristic, complemented
104	#3500	D₄	1	1	yes	characteristic, complemented
105	#3500	C₂³	1	1	yes	characteristic
106	#3500	C₂³	1	1	yes	characteristic
107	#3499	D₄	1	1	yes	characteristic, complemented
108	#3499	C₂³	1	1	yes	characteristic
109	#3498	D₄	1	1	yes	characteristic, complemented
110	#3498	C₂³	1	1	yes	characteristic
111	#3449	D₄	1	1	yes	characteristic, complemented
112	#3449	C₂³	1	1	yes	characteristic
113	C₂×#536	C₂³	1	1	yes	characteristic
114	C₂×#535	C₂³	1	1	yes	characteristic
115	C₂×#532	D₄	1	1	yes	characteristic, complemented
116	C₂×#532	C₂³	1	1	yes	characteristic
117	C₂×C₄×#41	D₄	1	1	yes	characteristic, complemented
118	#3202	C₂³	1	2	yes	complemented
119	#3200	C₂³	1	2	yes	complemented
120	#3200	C₂³	1	2	yes	complemented
121	#3199	C₂³	1	2	yes	complemented
122	#3028	C₂³	1	4	yes	—
123	#3027	C₂³	1	4	yes	—
124	#3022	C₂³	1	2	yes	—
125	#3022	C₂³	1	2	yes	—
126	#3022	C₂³	1	4	yes	—
127	#3021	C₂³	1	2	yes	—
128	#3021	C₂³	1	2	yes	—
129	#3021	C₂³	1	4	yes	—
130	#3018	D₄	1	2	yes	—
131	#3018	D₄	1	2	yes	—
132	#3018	D₄	1	2	yes	complemented
133	#3018	D₄	1	2	yes	complemented
134	#3018	C₂³	1	2	yes	—
135	#3018	C₂³	1	2	yes	—
136	#3018	C₂³	1	2	yes	—
137	#3018	C₂³	1	2	yes	—
138	C₂×#456	D₄	1	2	yes	complemented
139	C₂×#454	D₄	1	2	yes	complemented
140	C₂×#455	D₄	1	2	yes	—
141	C₂×#453	D₄	1	2	yes	—
142	#3011	D₄	1	2	yes	complemented
143	#3011	C₂³	1	2	yes	—
144	#3010	D₄	1	2	yes	—
145	#3010	C₂³	1	2	yes	—
146	#3009	D₄	1	2	yes	complemented
147	#3009	C₂³	1	2	yes	—
148	#3008	D₄	1	2	yes	—
149	#3008	C₂³	1	2	yes	—
150	#2980	C₂³	1	2	yes	complemented
151	#2979	C₂³	1	2	yes	complemented
152	#2896	D₄	1	1	yes	characteristic
153	#2896	D₄	1	1	yes	characteristic
154	#2896	D₄	1	1	yes	characteristic, complemented
155	#2896	D₄	1	1	yes	characteristic, complemented
156	#2889	C₂³	1	2	yes	—
157	#2888	C₂³	1	2	yes	—
158	C₂×#413	C₂³	1	1	yes	characteristic
159	C₂×#413	C₂³	1	1	yes	characteristic
160	C₂×#413	C₂³	1	1	yes	characteristic
161	C₂×#413	C₂³	1	1	yes	characteristic
162	C₂×#410	C₂³	1	1	yes	characteristic
163	C₂×#410	C₂³	1	1	yes	characteristic
164	#2879	C₂³	1	1	yes	characteristic
165	#2879	C₂³	1	1	yes	characteristic
166	#2135	C₂³	1	4	yes	complemented
167	#2134	C₂³	1	4	yes	complemented
168	#2132	C₂³	1	2	yes	complemented
169	#2132	C₂³	1	2	yes	complemented
170	#2126	C₂³	1	2	yes	complemented
171	#2126	C₂³	1	2	yes	complemented
172	#2123	C₂³	1	4	yes	complemented
173	#2123	C₂³	1	2	yes	complemented
174	#2123	C₂³	1	2	yes	complemented
175	#2122	C₂³	1	4	yes	complemented
176	#2122	C₂³	1	2	yes	complemented
177	#2122	C₂³	1	2	yes	complemented
178	#1796	C₂³	1	2	yes	—
179	#1796	C₂³	1	2	yes	—
180	#1795	C₂³	1	2	yes	—
181	#1795	C₂³	1	2	yes	—
182	#1794	C₂³	1	4	yes	—
183	#1794	C₂³	1	4	yes	—
184	#1791	C₂³	1	4	yes	—
185	#1791	C₂³	1	4	yes	—
186	#1395	C₂³	1	4	yes	complemented
187	#1395	C₂³	1	4	yes	complemented
188	#1392	C₂³	1	4	yes	complemented
189	#1392	C₂³	1	4	yes	complemented
190	#585	C₂×D₄	1	2	yes	—
191	#585	C₂×D₄	1	2	yes	—
192	#585	C₂⁴	1	2	yes	—
193	#585	C₂⁴	1	2	yes	—
194	C₂×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
195	C₂×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
196	C₂×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
197	C₂×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
198	C₂×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic, complemented
199	C₂×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic, complemented
200	C₂×2₋¹⁺⁴	C₂⁴	1	1	yes	characteristic
201	C₂×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
202	C₂×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
203	C₂×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
204	C₂×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
205	C₂×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
206	C₂×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
207	C₂×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
208	C₂²×#41	C₂×D₄	1	1	yes	characteristic
209	C₂²×#41	C₂×D₄	1	1	yes	characteristic
210	C₂²×#41	C₂×D₄	1	1	yes	characteristic
211	C₂²×#41	C₂×D₄	1	1	yes	characteristic
212	C₂²×#41	C₂×D₄	1	1	yes	characteristic
213	C₂²×#41	C₂×D₄	1	1	yes	characteristic
214	C₂²×#41	C₂×D₄	1	1	yes	characteristic
215	C₂²×#41	C₂×D₄	1	1	yes	characteristic
216	C₂²×#41	C₂⁴	1	1	yes	characteristic
217	C₂³×Q₈	C₂×D₄	1	1	yes	characteristic
218	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
219	C₂×#137	C₂×D₄	1	2	yes	complemented
220	C₂×#137	C₂×D₄	1	2	yes	complemented
221	C₂×AGL(1,ℤ/8)	C₂×D₄	1	2	yes	—
222	C₂×AGL(1,ℤ/8)	C₂×D₄	1	2	yes	—
223	C₂²×Q₁₆	C₂×D₄	1	2	yes	complemented
224	C₂²×SD₁₆	C₂×D₄	1	2	yes	—
225	C₂²×SD₁₆	C₂×D₄	1	2	yes	complemented
226	C₂²×D₈	C₂×D₄	1	2	yes	—
227	C₂²×M₁₆	C₂×D₄	1	1	yes	characteristic
228	C₂²×M₁₆	C₂×D₄	1	1	yes	characteristic
229	C₂²×M₁₆	C₂×D₄	1	1	yes	characteristic
230	C₂²×M₁₆	C₂×D₄	1	1	yes	characteristic
231	#536	C₂×D₄	1	2	yes	—
232	#536	C₂×D₄	1	1	yes	characteristic
233	#536	C₂×D₄	1	1	yes	characteristic, complemented
234	#536	C₂×D₄	1	1	yes	characteristic, complemented
235	#536	C₂⁴	1	1	yes	characteristic
236	#536	C₂⁴	1	2	yes	—
237	#535	C₂×D₄	1	2	yes	—
238	#535	C₂×D₄	1	1	yes	characteristic
239	#535	C₂×D₄	1	1	yes	characteristic, complemented
240	#535	C₂×D₄	1	1	yes	characteristic, complemented
241	#535	C₂⁴	1	1	yes	characteristic
242	#535	C₂⁴	1	2	yes	—
243	#532	C₂×D₄	1	1	yes	characteristic
244	#532	C₂×D₄	1	1	yes	characteristic
245	#532	C₂×D₄	1	1	yes	characteristic
246	#532	C₂×D₄	1	1	yes	characteristic
247	#532	C₂×D₄	1	1	yes	characteristic
248	#532	C₂×D₄	1	1	yes	characteristic
249	#532	C₂⁴	1	1	yes	characteristic
250	#532	C₂⁴	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
253	C₂×#127	C₂×D₄	1	1	yes	characteristic
254	C₂×#127	C₂×D₄	1	1	yes	characteristic, complemented
255	C₂×#124	C₂×D₄	1	1	yes	characteristic
256	C₂×#124	C₂×D₄	1	1	yes	characteristic
257	C₂×#124	C₂×D₄	1	1	yes	characteristic, complemented
258	C₂×#124	C₂×D₄	1	1	yes	characteristic, complemented
259	C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
260	C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
261	C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
262	C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
263	C₂×#117	C₂×D₄	1	1	yes	characteristic
264	C₂×#117	C₂×D₄	1	1	yes	characteristic
265	C₂×#117	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄²	C₂×D₄	1	1	yes	characteristic
267	#456	C₂×D₄	1	4	yes	complemented
268	#456	C₂×D₄	1	4	yes	complemented
269	#455	C₂×D₄	1	4	yes	—
270	#455	C₂×D₄	1	4	yes	—
271	#454	C₂×D₄	1	4	yes	complemented
272	#454	C₂×D₄	1	4	yes	complemented
273	#453	C₂×D₄	1	4	yes	—
274	#453	C₂×D₄	1	4	yes	—
275	#419	C₂×D₄	1	2	yes	—
276	#419	C₂×D₄	1	2	yes	complemented
277	#418	C₂×D₄	1	2	yes	—
278	#418	C₂×D₄	1	2	yes	complemented
279	#416	C₂×D₄	1	2	yes	—
280	#416	C₂×D₄	1	2	yes	—
281	#416	C₂×D₄	1	2	yes	complemented
282	#416	C₂×D₄	1	2	yes	complemented
283	#413	C₂×D₄	1	2	yes	—
284	#413	C₂×D₄	1	2	yes	—
285	#413	C₂⁴	1	2	yes	—
286	#413	C₂⁴	1	2	yes	—
287	#413	C₂⁴	1	2	yes	—
288	#413	C₂⁴	1	2	yes	—
289	C₂×#101	C₂×D₄	1	2	yes	—
290	C₂×#100	C₂×D₄	1	2	yes	—
291	#410	C₂⁴	1	2	yes	—
292	#410	C₂⁴	1	2	yes	—
293	#408	C₂×D₄	1	2	yes	—
294	#408	C₂×D₄	1	2	yes	—
295	#408	C₂⁴	1	2	yes	—
296	#408	C₂⁴	1	2	yes	—
297	2₋¹⁺⁴	C₂²×D₄	1	4	yes	—
298	H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
299	C₂×#41	#120	1	1	yes	characteristic
300	C₂×#41	#120	1	1	yes	characteristic
301	C₂×#41	#120	1	1	yes	characteristic
302	C₂×#41	#120	1	1	yes	characteristic
303	C₂×#41	#120	1	1	yes	characteristic
304	C₂×#41	#120	1	1	yes	characteristic
305	C₂×#41	#120	1	1	yes	characteristic
306	C₂×#41	#120	1	1	yes	characteristic
307	C₂×#41	#120	1	1	yes	characteristic
308	C₂×#41	#120	1	1	yes	characteristic
309	C₂×#41	#120	1	1	yes	characteristic
310	C₂×#41	#120	1	1	yes	characteristic
311	C₂×#41	C₂²×D₄	1	1	yes	characteristic
312	C₂×#41	C₂²×D₄	1	1	yes	characteristic
313	C₂×#41	C₂²×D₄	1	1	yes	characteristic
314	C₂×#41	C₂²×D₄	1	1	yes	characteristic
315	C₂×#41	C₂²×D₄	1	1	yes	characteristic
316	C₂×#41	C₂²×D₄	1	1	yes	characteristic
317	C₂×#41	C₂²×D₄	1	1	yes	characteristic
318	C₂×#41	C₂²×D₄	1	1	yes	characteristic
319	C₂×#41	C₂²×D₄	1	1	yes	characteristic
320	C₂×#41	C₂²×D₄	1	1	yes	characteristic
321	C₂×#41	C₂²×D₄	1	1	yes	characteristic
322	C₂×#41	C₂²×D₄	1	1	yes	characteristic
323	C₂×#41	C₂²×D₄	1	1	yes	characteristic
324	C₂×#41	H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×#41	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×#41	C₂⁵	1	1	yes	characteristic
327	C₂²×Q₈	#120	1	1	yes	characteristic
328	C₂²×Q₈	#120	1	1	yes	characteristic
329	C₂²×Q₈	#120	1	1	yes	characteristic
330	C₂²×Q₈	#120	1	1	yes	characteristic
331	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
332	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
333	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
334	C₂²×Q₈	C₂²×D₄	1	2	yes	—
335	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
336	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
337	C₂²×D₄	#120	1	1	yes	characteristic
338	C₂²×D₄	#120	1	1	yes	characteristic
339	C₂²×D₄	#120	1	1	yes	characteristic
340	C₂²×D₄	#120	1	1	yes	characteristic
341	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
342	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
343	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
344	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
345	C₂²×D₄	C₂²×D₄	1	2	yes	—
346	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
347	C₂²×D₄	H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²×D₄	H(5,𝔽₂)	1	1	yes	characteristic
349	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
350	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
351	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
352	C₂×M₁₆	C₂²×D₄	1	2	yes	—
353	C₂×M₁₆	C₂²×D₄	1	2	yes	—
354	C₂²×C₈	C₂²×D₄	1	2	yes	—
355	C₂²×C₈	C₂²×D₄	1	2	yes	—
356	C₄⋊Q₈	#120	1	1	yes	characteristic
357	C₄⋊Q₈	#120	1	1	yes	characteristic
358	C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
359	C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic
360	#127	#120	1	1	yes	characteristic
361	#127	#120	1	1	yes	characteristic
362	#127	C₂²×D₄	1	1	yes	characteristic
363	#127	C₂²×D₄	1	1	yes	characteristic
364	#124	#120	1	1	yes	characteristic
365	#124	#120	1	1	yes	characteristic
366	#124	#120	1	1	yes	characteristic
367	#124	#120	1	1	yes	characteristic
368	#124	C₂²×D₄	1	1	yes	characteristic
369	#124	C₂²×D₄	1	1	yes	characteristic
370	#124	C₂²×D₄	1	1	yes	characteristic
371	#124	C₂²×D₄	1	1	yes	characteristic
372	#117	C₂²×D₄	1	1	yes	characteristic
373	#117	C₂²×D₄	1	1	yes	characteristic
374	#117	C₂²×D₄	1	2	yes	—
375	#117	C₂²×D₄	1	2	yes	—
376	C₂×C₄²	#120	1	1	yes	characteristic
377	C₂×C₄²	#120	1	1	yes	characteristic
378	C₂×C₄²	#120	1	1	yes	characteristic
379	C₂×C₄²	#120	1	1	yes	characteristic
380	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
382	#101	C₂²×D₄	1	4	yes	—
383	#100	C₂²×D₄	1	4	yes	—
384	C₂⁴	#534	1	1	yes	characteristic
385	C₂⁴	D₄²	1	1	yes	characteristic
386	C₂⁴	D₄²	1	1	yes	characteristic
387	#41	B(4,𝔽₂)	1	2	yes	—
388	#41	B(4,𝔽₂)	1	2	yes	—
389	#41	B(4,𝔽₂)	1	2	yes	—
390	#41	B(4,𝔽₂)	1	2	yes	—
391	C₂×Q₈	C₂×#120	1	1	yes	characteristic
392	C₂×Q₈	C₂×#120	1	1	yes	characteristic
393	C₂×Q₈	C₂×#120	1	1	yes	characteristic
394	C₂×Q₈	C₂×#120	1	1	yes	characteristic
395	C₂×Q₈	C₂×#120	1	1	yes	characteristic
396	C₂×Q₈	C₂×#120	1	1	yes	characteristic
397	C₂×Q₈	C₂×#120	1	1	yes	characteristic
398	C₂×Q₈	D₄²	1	1	yes	characteristic
399	C₂×Q₈	D₄²	1	1	yes	characteristic
400	C₂×Q₈	C₂³×D₄	1	1	yes	characteristic
401	C₂×D₄	C₂×#120	1	1	yes	characteristic
402	C₂×D₄	C₂×#120	1	1	yes	characteristic
403	C₂×D₄	C₂×#120	1	1	yes	characteristic
404	C₂×D₄	C₂×#120	1	1	yes	characteristic
405	C₂×D₄	C₂×#120	1	1	yes	characteristic
406	C₂×D₄	C₂×#120	1	1	yes	characteristic
407	C₂×D₄	C₂×#120	1	1	yes	characteristic
408	C₂×D₄	#534	1	1	yes	characteristic
409	C₂×D₄	#534	1	1	yes	characteristic
410	C₂×D₄	D₄²	1	1	yes	characteristic
411	C₂×D₄	D₄²	1	1	yes	characteristic
412	C₂×D₄	D₄²	1	1	yes	characteristic
413	C₂×D₄	D₄²	1	1	yes	characteristic
414	C₂×D₄	D₄²	1	1	yes	characteristic
415	C₂×D₄	D₄²	1	1	yes	characteristic
416	C₂×D₄	C₂³×D₄	1	1	yes	characteristic
417	C₂×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂×D₄	C₂×H(5,𝔽₂)	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	#534	1	1	yes	characteristic
426	C₂²×C₄	D₄²	1	1	yes	characteristic
427	C₂²×C₄	D₄²	1	1	yes	characteristic
428	C₂²×C₄	D₄²	1	1	yes	characteristic
429	C₂²×C₄	D₄²	1	1	yes	characteristic
430	C₂²×C₄	D₄²	1	1	yes	characteristic
431	C₂²×C₄	D₄²	1	1	yes	characteristic
432	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
433	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
434	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
435	C₄²	C₂×#120	1	1	yes	characteristic
436	C₄²	C₂×#120	1	1	yes	characteristic
437	C₄²	C₂×#120	1	1	yes	characteristic
438	C₄²	C₂×#120	1	1	yes	characteristic
439	C₂³	#2403	1	1	yes	characteristic
440	C₂³	#2403	1	1	yes	characteristic
441	C₂³	#2403	1	1	yes	characteristic
442	C₂³	#2403	1	1	yes	characteristic
443	C₂³	C₂×#534	1	1	yes	characteristic
444	C₂³	C₂×D₄²	1	1	yes	characteristic
445	C₂³	C₂×D₄²	1	1	yes	characteristic
446	Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
447	Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
448	D₄	C₂×B(4,𝔽₂)	1	2	yes	—
449	D₄	C₂×B(4,𝔽₂)	1	2	yes	—
450	C₂×C₄	#2403	1	1	yes	characteristic
451	C₂×C₄	#2403	1	1	yes	characteristic
452	C₂×C₄	#2403	1	1	yes	characteristic
453	C₂×C₄	#2403	1	1	yes	characteristic
454	C₂×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
455	C₂×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
456	C₂×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
457	C₂×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
458	C₂×C₄	C₂²×#120	1	1	yes	characteristic
459	C₂×C₄	C₂²×#120	1	1	yes	characteristic
460	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
461	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
462	C₂²	#23900	1	1	yes	characteristic
463	C₂²	#23900	1	1	yes	characteristic
464	C₂²	C₂×#2403	1	1	yes	characteristic
465	C₄	#23900	1	1	yes	characteristic
466	C₄	#23900	1	1	yes	characteristic
467	C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
468	C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
469	C₂	C₂×#23900	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#23900
commutator, Frattini, cosocle	C₂×#41	C₂⁵
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#585 ◁ G
LECS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #10577336	C₂	semidirect
2. #10574854	C₂	semidirect
3. C₂×#33572	C₂	semidirect
4. C₂×#33560	C₂	semidirect
5. #6628886	C₂	semidirect
6. #6628885	C₂	semidirect
7. #499888	C₂	semidirect
8. #499885	C₂	semidirect
9. #499884	C₂	semidirect
10. #499881	C₂	semidirect
11. #498944	C₂	semidirect
12. #498943	C₂	semidirect
13. #498917	C₂	semidirect
14. #498916	C₂	semidirect
15. #494752	C₂	semidirect
16. #494751	C₂	semidirect
17. #494609	C₂	semidirect
18. #494605	C₂	semidirect
19. #493419	C₂	semidirect
22. C₂×#3551	C₂²	semidirect
23. #61676	C₂²	semidirect
24. #61675	C₂²	semidirect
25. #61666	C₂²	semidirect
26. #61663	C₂²	semidirect
27. #60754	C₂²	semidirect
28. #60753	C₂²	semidirect
29. C₂×#3028	C₂²	semidirect
30. C₂×#3027	C₂²	semidirect
31. #60391	C₂²	semidirect
32. #60390	C₂²	semidirect
33. #60389	C₂²	semidirect
34. #60388	C₂²	semidirect
37. C₂×#3022	C₂²	semidirect
38. C₂×#3021	C₂²	semidirect
43. #60232	C₂²	semidirect
45. #33572	C₂²	semidirect
46. #33572	C₂²	semidirect
47. #33560	C₂²	semidirect
48. #33560	C₂²	semidirect
49. C₂×#2135	C₂²	semidirect
50. C₂×#2134	C₂²	semidirect
51. C₂×#2132	C₂²	semidirect
52. C₂×#2126	C₂²	semidirect
53. #33347	C₂²	semidirect
54. #33347	C₂²	semidirect
55. C₂×#2123	C₂²	semidirect
56. C₂×#2122	C₂²	semidirect
57. #32897	C₂²	semidirect
58. #32896	C₂²	semidirect
59. #32895	C₂²	semidirect
60. #32894	C₂²	semidirect
63. #20620	C₂²	semidirect
64. #20620	C₂²	semidirect
65. #20612	C₂²	semidirect
66. #20612	C₂²	semidirect
67. #13362	C₂²	semidirect
68. #13361	C₂²	semidirect
69. #13361	C₂²	semidirect
70. #13360	C₂²	semidirect
71. #13356	C₂²	semidirect
72. #13355	C₂²	semidirect
73. #13354	C₂²	semidirect
74. #13353	C₂²	semidirect
75. #13099	C₂²	semidirect
76. #13098	C₂²	semidirect
77. #13097	C₂²	semidirect
78. #13096	C₂²	semidirect
79. #13054	C₂²	semidirect
80. #13053	C₂²	semidirect
81. #13052	C₂²	semidirect
82. #13051	C₂²	semidirect
83. #12718	C₂²	semidirect
84. #12717	C₂²	semidirect
85. #12716	C₂²	semidirect
86. #12715	C₂²	semidirect
87. #12589	C₂²	semidirect
88. #12589	C₂²	semidirect
89. #12579	C₂²	semidirect
90. #12579	C₂²	semidirect
93. C₂×#585	D₄	semidirect
97. C₂²×#137	D₄	semidirect
98. C₂²×#137	D₄	semidirect
101. #3551	C₂³	semidirect
102. #3551	C₂³	semidirect
103. #3500	D₄	semidirect
104. #3500	D₄	semidirect
107. #3499	D₄	semidirect
109. #3498	D₄	semidirect
111. #3449	D₄	semidirect
115. C₂×#532	D₄	semidirect
117. C₂×C₄×#41	D₄	semidirect
118. #3202	C₂³	semidirect
119. #3200	C₂³	semidirect
120. #3200	C₂³	semidirect
121. #3199	C₂³	semidirect
132. #3018	D₄	semidirect
133. #3018	D₄	semidirect
138. C₂×#456	D₄	semidirect
139. C₂×#454	D₄	semidirect
142. #3011	D₄	semidirect
146. #3009	D₄	semidirect
150. #2980	C₂³	semidirect
151. #2979	C₂³	semidirect
154. #2896	D₄	semidirect
155. #2896	D₄	semidirect
166. #2135	C₂³	semidirect
167. #2134	C₂³	semidirect
168. #2132	C₂³	semidirect
169. #2132	C₂³	semidirect
170. #2126	C₂³	semidirect
171. #2126	C₂³	semidirect
172. #2123	C₂³	semidirect
173. #2123	C₂³	semidirect
174. #2123	C₂³	semidirect
175. #2122	C₂³	semidirect
176. #2122	C₂³	semidirect
177. #2122	C₂³	semidirect
186. #1395	C₂³	semidirect
187. #1395	C₂³	semidirect
188. #1392	C₂³	semidirect
189. #1392	C₂³	semidirect
198. C₂×2₋¹⁺⁴	C₂×D₄	semidirect
199. C₂×2₋¹⁺⁴	C₂×D₄	semidirect
205. C₂×H(5,𝔽₂)	C₂×D₄	semidirect
206. C₂×H(5,𝔽₂)	C₂×D₄	semidirect
219. C₂×#137	C₂×D₄	semidirect
220. C₂×#137	C₂×D₄	semidirect
223. C₂²×Q₁₆	C₂×D₄	semidirect
225. C₂²×SD₁₆	C₂×D₄	semidirect
233. #536	C₂×D₄	semidirect
234. #536	C₂×D₄	semidirect
239. #535	C₂×D₄	semidirect
240. #535	C₂×D₄	semidirect
252. C₂×C₄⋊Q₈	C₂×D₄	semidirect
254. C₂×#127	C₂×D₄	semidirect
257. C₂×#124	C₂×D₄	semidirect
258. C₂×#124	C₂×D₄	semidirect
259. C₄×#41	C₂×D₄	semidirect
260. C₄×#41	C₂×D₄	semidirect
261. C₄×#41	C₂×D₄	semidirect
262. C₄×#41	C₂×D₄	semidirect
267. #456	C₂×D₄	semidirect
268. #456	C₂×D₄	semidirect
271. #454	C₂×D₄	semidirect
272. #454	C₂×D₄	semidirect
276. #419	C₂×D₄	semidirect
278. #418	C₂×D₄	semidirect
281. #416	C₂×D₄	semidirect
282. #416	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#10577336	2
#10574854	2
C₂×#33572	2
C₂×#33560	2
#6628886	2
#6628885	2
#499888	2
#499885	2
#499884	2
#499881	2
#498944	2
#498943	2
#498917	2
#498916	2
#494752	2
#494751	2
#494609	2
#494605	2
#493419	2