Subgroups — #12963631

Order 1280.

2612 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10619088	C₂	1	1	yes	maximal, characteristic
2	#10619061	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	#10615641	C₂	1	1	yes	maximal, characteristic, complemented
5	#10615523	C₂	1	2	yes	maximal, complemented
6	#10611621	C₂	1	4	yes	maximal, complemented
7	#10611620	C₂	1	4	yes	maximal, complemented
8	#10611619	C₂	1	4	yes	maximal, complemented
9	D₅×#443	C₂	1	4	yes	maximal, complemented
10	#10610983	C₂	1	1	yes	maximal, characteristic, complemented
11	#10610980	C₂	1	1	yes	maximal, characteristic, complemented
12	#10610714	C₂	1	2	yes	maximal, complemented
13	#10610711	C₂	1	2	yes	maximal, complemented
14	C₂×#64989	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#4047	C₂	1	1	yes	maximal, characteristic, complemented
16	#66283	C₂²	1	2	yes	—
17	C₂×C₅×#135	C₂²	1	1	yes	characteristic
18	C₂×C₅×#131	C₂²	1	2	yes	complemented
19	#66156	C₂²	1	2	yes	—
20	#66153	C₂²	1	2	yes	complemented
21	#66105	C₄	1	2	yes	complemented
22	#66104	C₄	1	4	yes	complemented
23	#66103	C₄	1	2	yes	complemented
24	#66102	C₂²	1	4	yes	—
25	D₅×#135	C₂²	1	4	yes	—
26	#66100	C₄	1	2	yes	complemented
27	#66096	C₄	1	4	yes	complemented
28	#66091	C₄	1	2	yes	complemented
29	#66084	—	2	4	no	—
30	#66084	C₂²	1	8	yes	complemented
31	D₅×#131	—	2	4	no	—
32	D₅×#131	C₂²	1	8	yes	complemented
33	#66079	—	2	4	no	—
34	#66079	C₂²	1	2	yes	—
35	#66079	C₂²	1	2	yes	complemented
36	C₂×#4050	C₂²	1	1	yes	characteristic
37	C₂×#4047	—	2	4	no	—
38	C₂×#4047	C₂²	1	1	yes	characteristic
39	C₂×#4047	C₂²	1	1	yes	characteristic
40	C₂×#4047	C₂²	1	2	yes	complemented
41	C₄×#709	C₂²	1	1	yes	characteristic
42	C₅×#443	C₂²	1	2	yes	complemented
43	C₅×#443	C₂²	1	2	yes	complemented
44	C₅×#443	C₂²	1	2	yes	complemented
45	C₅×#443	C₂²	1	2	yes	complemented
46	C₂×C₅×#108	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₅×#104	C₂²	1	2	yes	complemented
48	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
49	#65525	C₂²	1	2	yes	complemented
50	#65486	C₂²	1	4	yes	complemented
51	#65485	C₂²	1	4	yes	complemented
52	#65434	C₂²	1	8	yes	complemented
53	#65433	C₂²	1	8	yes	complemented
54	#65428	C₂²	1	2	yes	complemented
55	#65413	C₂²	1	2	yes	complemented
56	C₂×#3951	C₂²	1	1	yes	characteristic, complemented
57	#65390	C₂²	1	1	yes	characteristic, complemented
58	#65390	C₂²	1	1	yes	characteristic, complemented
59	C₂×#3937	C₂²	1	2	yes	complemented
60	C₄×#681	C₂²	1	1	yes	characteristic, complemented
61	#65184	C₂²	1	4	yes	complemented
62	#65183	C₂²	1	4	yes	complemented
63	#65182	C₂²	1	4	yes	complemented
64	D₅×#108	C₂²	1	4	yes	complemented
65	#65113	C₂²	1	8	yes	complemented
66	#65112	C₂²	1	8	yes	complemented
67	#65110	C₂²	1	8	yes	complemented
68	D₅×#104	C₂²	1	8	yes	complemented
69	#64989	C₂²	1	2	yes	complemented
70	#64989	C₂²	1	2	yes	complemented
71	#64989	C₂²	1	2	yes	complemented
72	#64989	C₂²	1	2	yes	complemented
73	#64978	C₂²	1	2	yes	complemented
74	#64978	C₂²	1	2	yes	complemented
75	C₄×#676	C₂²	1	2	yes	complemented
76	C₄×C₈×D₅	C₂²	1	2	yes	complemented
77	#60183	—	5	1	no	maximal, Sylow
78	C₂×C₅×#41	C₂³	1	2	yes	—
79	#4150	—	2	2	no	—
80	#4150	C₂×C₄	1	4	yes	—
81	#4149	—	2	2	no	—
82	#4149	C₂×C₄	1	4	yes	—
83	D₅×#41	—	2	4	no	—
84	D₅×#41	C₂³	1	8	yes	—
85	#4147	C₂×C₄	1	4	yes	—
86	#4144	—	2	4	no	—
87	#4144	C₂×C₄	1	4	yes	—
88	C₂×#709	—	2	4	no	—
89	C₂×#709	C₂³	1	2	yes	—
90	C₂×#709	C₂³	1	1	yes	characteristic
91	C₅×#135	C₂×C₄	1	2	yes	complemented
92	C₅×#135	C₂×C₄	1	2	yes	complemented
93	C₅×#135	C₂³	1	2	yes	—
94	C₅×#135	C₂³	1	2	yes	—
95	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
96	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
97	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
98	C₅×#131	—	2	2	no	—
99	C₅×#131	—	2	2	no	—
100	C₅×#131	C₂³	1	4	yes	—
101	C₅×#131	C₂³	1	4	yes	—
102	C₂×C₅×M₁₆	—	2	2	no	—
103	C₂×C₅×M₁₆	C₂³	1	2	yes	—
104	C₂²×C₅×C₈	—	2	2	no	—
105	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	#4097	C₂×C₄	1	4	yes	complemented
109	#4096	C₂³	1	8	yes	—
110	#4095	C₂×C₄	1	4	yes	complemented
111	#4094	—	2	4	no	—
112	#4094	C₂³	1	8	yes	—
113	#4088	C₂×C₄	1	4	yes	complemented
114	#4078	C₂×C₄	1	4	yes	complemented
115	C₄×C₂²⋊D₅	—	2	2	no	—
116	#4072	C₂³	1	1	yes	characteristic
117	C₂×#681	—	2	4	no	—
118	C₂×#681	C₂³	1	2	yes	—
119	C₂×#681	C₂³	1	1	yes	characteristic
120	C₂×#681	C₂³	1	1	yes	characteristic
121	#4065	C₂×C₄	1	4	yes	complemented
122	#4064	C₂×C₄	1	8	yes	complemented
123	D₅×Q₁₆	C₂×C₄	1	4	yes	complemented
124	#4062	C₂×C₄	1	8	yes	complemented
125	#4061	C₂×C₄	1	8	yes	complemented
126	#4060	C₂×C₄	1	8	yes	complemented
127	D₅×SD₁₆	C₂×C₄	1	8	yes	complemented
128	#4058	C₂×C₄	1	4	yes	complemented
129	#4057	C₂×C₄	1	8	yes	complemented
130	D₅×D₈	C₂×C₄	1	4	yes	complemented
131	#4053	—	2	4	no	—
132	#4053	—	2	8	no	—
133	#4053	—	2	8	no	—
134	#4053	C₂³	1	8	yes	—
135	D₅×M₁₆	—	2	4	no	—
136	D₅×M₁₆	—	2	8	no	—
137	D₅×M₁₆	—	2	8	no	—
138	D₅×M₁₆	C₂³	1	8	yes	—
139	C₂×Dic₂₀	C₂×C₄	1	1	yes	characteristic, complemented
140	#4050	C₂×C₄	1	2	yes	complemented
141	#4050	C₂×C₄	1	2	yes	complemented
142	#4050	C₂³	1	2	yes	—
143	#4050	C₂³	1	2	yes	—
144	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic, complemented
145	C₂×#677	C₂×C₄	1	2	yes	complemented
146	#4047	—	2	4	no	—
147	#4047	—	2	2	no	—
148	#4047	—	2	2	no	—
149	#4047	—	2	4	no	—
150	#4047	—	2	8	no	—
151	#4047	—	2	8	no	—
152	#4047	C₂×C₄	1	2	yes	—
153	#4047	C₂×C₄	1	2	yes	—
154	#4047	C₂×C₄	1	2	yes	—
155	#4047	C₂×C₄	1	2	yes	—
156	#4047	D₄	1	2	yes	—
157	#4047	D₄	1	2	yes	—
158	#4047	D₄	1	2	yes	—
159	#4047	D₄	1	2	yes	—
160	#4047	C₂³	1	4	yes	—
161	#4047	C₂³	1	4	yes	—
162	C₂×#676	—	2	2	no	—
163	C₂×#676	—	2	8	no	—
164	C₂×#676	C₂³	1	2	yes	—
165	C₂×#676	C₂³	1	2	yes	—
166	C₂×C₈×D₅	—	2	2	no	—
167	C₂×C₈×D₅	—	2	8	no	—
168	C₂×C₈×D₅	C₂³	1	2	yes	—
169	C₂×C₈×D₅	C₂³	1	2	yes	—
170	C₄×D₂₀	—	2	1	no	—
171	#4018	C₂³	1	2	yes	—
172	C₄²×D₅	C₂³	1	2	yes	—
173	C₄×Dic₁₀	—	2	1	no	—
174	C₅×#108	C₂³	1	2	yes	—
175	C₅×#108	C₂³	1	2	yes	—
176	C₅×#104	C₂³	1	4	yes	—
177	C₅×#104	C₂³	1	4	yes	—
178	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
179	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
180	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
181	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
182	#3969	C₂³	1	8	yes	—
183	#3957	C₂³	1	8	yes	—
184	#3954	C₂³	1	8	yes	—
185	#3951	C₂³	1	2	yes	—
186	#3951	C₂³	1	2	yes	—
187	#3947	C₂³	1	2	yes	—
188	#3947	C₂³	1	2	yes	—
189	C₈×Dic₅	C₂³	1	2	yes	—
190	C₈×Dic₅	C₂³	1	2	yes	—
191	#3937	C₂³	1	4	yes	—
192	#3937	C₂³	1	4	yes	—
193	#3935	C₂³	1	2	yes	—
194	C₄×#168	C₂³	1	2	yes	—
195	#3584	—	5	1	no	—
196	#3573	—	5	2	no	—
197	#2957	—	5	4	no	—
198	#2957	—	5	1	no	—
199	#2957	—	5	1	no	—
200	#2956	—	5	4	no	—
201	#2956	—	5	2	no	—
202	#2955	—	5	4	no	—
203	#2955	—	5	2	no	—
204	C₂×#443	—	5	4	no	—
205	C₂×#443	—	5	1	no	—
206	C₂×#443	D₅	1	1	yes	characteristic, complemented
207	#2916	—	5	1	no	—
208	#2901	—	5	2	no	—
209	C₄×#131	—	5	1	no	—
210	C₅×#41	—	2	2	no	—
211	C₅×#41	—	2	2	no	—
212	C₅×#41	C₂²×C₄	1	4	yes	—
213	C₅×#41	C₂⁴	1	4	yes	—
214	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
215	C₂×C₅×D₄	—	2	2	no	—
216	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
217	C₂²×C₄×C₅	—	2	2	no	—
218	C₂²×C₄×C₅	—	2	1	no	—
219	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₂×C₂²⋊D₅	—	2	2	no	—
221	C₂×C₂²⋊D₅	—	2	8	no	—
222	C₂×C₂²⋊D₅	#41	1	2	yes	—
223	#713	—	2	4	no	—
224	#713	C₂²×C₄	1	8	yes	—
225	Q₈×D₅	—	2	4	no	—
226	Q₈×D₅	C₂²×C₄	1	8	yes	—
227	#711	—	2	8	no	—
228	#711	—	2	8	no	—
229	#711	—	2	4	no	—
230	#711	C₂²×C₄	1	8	yes	—
231	D₄×D₅	—	2	8	no	—
232	D₄×D₅	—	2	8	no	—
233	D₄×D₅	—	2	4	no	—
234	D₄×D₅	C₂²×C₄	1	8	yes	—
235	#709	—	2	2	no	—
236	#709	—	2	2	no	—
237	#709	—	2	8	no	—
238	#709	—	2	4	no	—
239	#709	—	2	8	no	—
240	#709	—	2	4	no	—
241	#709	C₂²×C₄	1	2	yes	—
242	#709	C₂²×C₄	1	2	yes	—
243	#709	C₂²×C₄	1	4	yes	—
244	#709	C₂×D₄	1	2	yes	—
245	#709	C₂×D₄	1	2	yes	—
246	#709	C₂⁴	1	4	yes	—
247	C₂×D₂₀	—	2	4	no	—
248	C₂×D₂₀	C₂²×C₄	1	2	yes	—
249	C₂×D₂₀	#41	1	1	yes	characteristic
250	C₂×C₄×D₅	—	2	2	no	—
251	C₂×C₄×D₅	—	2	8	no	—
252	C₂×C₄×D₅	—	2	2	no	—
253	C₂×C₄×D₅	C₂⁴	1	2	yes	—
254	C₂×Dic₁₀	—	2	4	no	—
255	C₂×Dic₁₀	C₂²×C₄	1	2	yes	—
256	C₂×Dic₁₀	#41	1	1	yes	characteristic
257	C₅×Q₁₆	C₂²×C₄	1	2	yes	—
258	C₅×Q₁₆	C₂²×C₄	1	2	yes	—
259	C₅×SD₁₆	C₂²×C₄	1	4	yes	—
260	C₅×SD₁₆	C₂²×C₄	1	4	yes	—
261	C₅×D₈	C₂²×C₄	1	2	yes	—
262	C₅×D₈	C₂²×C₄	1	2	yes	—
263	C₅×M₁₆	—	2	2	no	—
264	C₅×M₁₆	—	2	4	no	—
265	C₅×M₁₆	—	2	4	no	—
266	C₅×M₁₆	C₂⁴	1	4	yes	—
267	C₂×C₅×C₈	—	2	2	no	—
268	C₂×C₅×C₈	—	2	4	no	—
269	C₂×C₅×C₈	—	2	4	no	—
270	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
271	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
272	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
273	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
274	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
275	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
276	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
277	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
278	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
279	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
280	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
281	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
282	C₄²×C₅	—	2	1	no	—
283	C₄²×C₅	C₂⁴	1	1	yes	characteristic
284	C₄²×C₅	C₂⁴	1	1	yes	characteristic
285	C₂²⋊Dic₅	—	2	1	no	—
286	#689	C₂²×C₄	1	8	yes	—
287	#688	C₂²×C₄	1	8	yes	—
288	#687	C₂²×C₄	1	8	yes	—
289	#686	C₂²×C₄	1	8	yes	—
290	#685	—	2	2	no	—
291	C₄⋊Dic₅	—	2	1	no	—
292	#683	—	2	2	no	—
293	C₄×Dic₅	—	2	2	no	—
294	C₄×Dic₅	C₂⁴	1	2	yes	—
295	#681	—	2	2	no	—
296	#681	—	2	8	no	—
297	#681	C₂²×C₄	1	2	yes	—
298	#681	C₂²×C₄	1	2	yes	—
299	#681	C₂×D₄	1	2	yes	—
300	#681	C₂×D₄	1	2	yes	—
301	#681	C₂⁴	1	4	yes	—
302	C₂×#168	—	2	2	no	—
303	C₂×#168	—	2	8	no	—
304	C₂×#168	C₂⁴	1	2	yes	—
305	C₂×#168	C₂⁴	1	2	yes	—
306	Dic₂₀	C₂²×C₄	1	2	yes	—
307	Dic₂₀	C₂²×C₄	1	2	yes	—
308	D₄₀	C₂²×C₄	1	2	yes	—
309	D₄₀	C₂²×C₄	1	2	yes	—
310	#677	C₂²×C₄	1	4	yes	—
311	#677	C₂²×C₄	1	4	yes	—
312	#676	—	2	8	no	—
313	#676	—	2	4	no	—
314	#676	—	2	4	no	—
315	#676	—	2	8	no	—
316	#676	C₂²×C₄	1	4	yes	—
317	#676	C₂²×C₄	1	4	yes	—
318	#676	C₂×D₄	1	4	yes	—
319	#676	C₂×D₄	1	4	yes	—
320	C₈×D₅	—	2	8	no	—
321	C₈×D₅	—	2	4	no	—
322	C₈×D₅	—	2	4	no	—
323	C₈×D₅	—	2	8	no	—
324	C₈×D₅	C₂²×C₄	1	4	yes	—
325	C₈×D₅	C₂²×C₄	1	4	yes	—
326	C₈×D₅	C₂×D₄	1	4	yes	—
327	C₈×D₅	C₂×D₄	1	4	yes	—
328	#585	—	5	2	no	—
329	#578	—	5	2	no	—
330	#578	—	5	2	no	—
331	#577	—	5	4	no	—
332	#577	—	5	4	no	—
333	#576	—	5	2	no	—
334	#576	—	5	2	no	—
335	#575	—	5	2	no	—
336	#575	—	5	4	no	—
337	C₂×#135	—	5	4	no	—
338	C₂×#135	—	5	1	no	—
339	C₂×#135	C₂×D₅	1	1	yes	characteristic
340	#568	—	5	2	no	—
341	#568	—	5	2	no	—
342	#568	—	5	8	no	—
343	#568	—	5	2	no	—
344	#568	—	10	4	no	—
345	#568	—	10	4	no	—
346	C₂×#131	—	5	1	no	—
347	C₂×#131	—	5	1	no	—
348	C₂×#131	—	5	8	no	—
349	C₂×#131	—	5	2	no	—
350	C₂×#131	—	10	4	no	—
351	C₂×#131	—	10	4	no	—
352	C₂×#131	C₂×D₅	1	2	yes	complemented
353	C₄×#41	—	5	1	no	—
354	#444	—	5	4	no	—
355	#444	—	5	8	no	—
356	#444	—	5	4	no	—
357	#444	—	5	8	no	—
358	#443	—	5	4	no	—
359	#443	—	5	8	no	—
360	#443	—	5	4	no	—
361	#443	—	5	8	no	—
362	#443	—	5	2	no	—
363	#443	—	5	2	no	—
364	#443	—	5	2	no	—
365	#443	—	5	2	no	—
366	#443	C₂×D₅	1	2	yes	complemented
367	#443	C₂×D₅	1	2	yes	complemented
368	#443	C₂×D₅	1	2	yes	complemented
369	#443	C₂×D₅	1	2	yes	complemented
370	#430	—	5	2	no	—
371	#430	—	5	4	no	—
372	C₂×#108	—	5	1	no	—
373	C₂×#108	—	5	4	no	—
374	C₂×#108	C₂×D₅	1	1	yes	characteristic, complemented
375	#421	—	5	2	no	—
376	#421	—	5	2	no	—
377	#421	—	5	8	no	—
378	C₂×#104	—	5	2	no	—
379	C₂×#104	—	5	8	no	—
380	C₂×#104	C₂×D₅	1	2	yes	complemented
381	#405	—	5	1	no	—
382	#405	—	5	1	no	—
383	#405	—	5	2	no	—
384	#405	—	5	2	no	—
385	C₄×M₁₆	—	5	1	no	—
386	C₄×M₁₆	—	5	2	no	—
387	C₂×C₄×C₈	—	5	2	no	—
388	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
389	C₂³×C₅	—	2	2	no	—
390	C₂³×C₅	C₂×#41	1	1	yes	characteristic
391	C₂²×D₅	—	2	2	no	—
392	C₂²×D₅	—	2	8	no	—
393	C₂²×D₅	C₂×#41	1	2	yes	—
394	C₅×Q₈	—	2	2	no	—
395	C₅×Q₈	C₂³×C₄	1	4	yes	—
396	C₅×D₄	—	2	4	no	—
397	C₅×D₄	—	2	4	no	—
398	C₅×D₄	—	2	2	no	—
399	C₅×D₄	C₂³×C₄	1	4	yes	—
400	C₂×C₄×C₅	—	2	2	no	—
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	4	no	—
403	C₂×C₄×C₅	—	2	4	no	—
404	C₂×C₄×C₅	—	2	1	no	—
405	C₂×C₄×C₅	—	4	2	no	—
406	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
407	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
408	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
411	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
412	C₂²⋊D₅	—	2	4	no	—
413	C₂²⋊D₅	—	2	4	no	—
414	C₂²⋊D₅	—	2	8	no	—
415	C₂²⋊D₅	—	2	8	no	—
416	C₂²⋊D₅	C₄×D₄	1	4	yes	—
417	C₂²⋊D₅	C₄×D₄	1	4	yes	—
418	C₂×Dic₅	—	2	2	no	—
419	C₂×Dic₅	—	2	8	no	—
420	C₂×Dic₅	—	2	2	no	—
421	C₂×Dic₅	C₂×#41	1	2	yes	—
422	D₂₀	—	2	8	no	—
423	D₂₀	—	2	2	no	—
424	D₂₀	C₄×D₄	1	2	yes	—
425	D₂₀	C₄×D₄	1	2	yes	—
426	D₂₀	C₂³×C₄	1	4	yes	—
427	C₄×D₅	—	2	8	no	—
428	C₄×D₅	—	2	4	no	—
429	C₄×D₅	—	2	4	no	—
430	C₄×D₅	—	2	8	no	—
431	C₄×D₅	—	4	4	no	—
432	C₄×D₅	C₂³×C₄	1	4	yes	—
433	C₄×D₅	C₂²×D₄	1	4	yes	—
434	Dic₁₀	—	2	2	no	—
435	Dic₁₀	—	2	8	no	—
436	Dic₁₀	C₄×D₄	1	2	yes	—
437	Dic₁₀	C₄×D₄	1	2	yes	—
438	Dic₁₀	C₂³×C₄	1	4	yes	—
439	C₅×C₈	—	2	4	no	—
440	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
441	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
442	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
443	C₅×C₈	C₂³×C₄	1	1	yes	characteristic
444	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
445	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
446	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
447	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
448	#168	—	2	4	no	—
449	#168	C₂³×C₄	1	4	yes	—
450	#168	C₂²×D₄	1	4	yes	—
451	2₋¹⁺⁴	—	5	4	no	—
452	2₋¹⁺⁴	—	5	4	no	—
453	2₋¹⁺⁴	—	10	2	no	—
454	H(5,𝔽₂)	—	5	4	no	—
455	H(5,𝔽₂)	—	5	4	no	—
456	H(5,𝔽₂)	—	10	4	no	—
457	H(5,𝔽₂)	—	10	2	no	—
458	C₂×#41	—	5	1	no	—
459	C₂×#41	—	5	8	no	—
460	C₂×#41	—	5	2	no	—
461	C₂×#41	—	10	4	no	—
462	C₂×#41	—	10	4	no	—
463	C₂×#41	C₂²×D₅	1	2	yes	—
464	#137	—	5	4	no	—
465	#137	—	5	4	no	—
466	#137	—	5	8	no	—
467	#137	—	5	8	no	—
468	AGL(1,ℤ/8)	—	5	4	no	—
469	AGL(1,ℤ/8)	—	5	4	no	—
470	AGL(1,ℤ/8)	—	5	8	no	—
471	AGL(1,ℤ/8)	—	5	8	no	—
472	#135	—	5	8	no	—
473	#135	—	5	4	no	—
474	#135	—	5	8	no	—
475	#135	—	5	4	no	—
476	#135	—	5	2	no	—
477	#135	—	5	2	no	—
478	#135	—	5	2	no	—
479	#135	—	5	2	no	—
480	#135	C₄×D₅	1	2	yes	complemented
481	#135	C₄×D₅	1	2	yes	complemented
482	#135	C₂²×D₅	1	2	yes	—
483	#135	C₂²×D₅	1	2	yes	—
484	C₂×Q₁₆	—	5	4	no	—
485	C₂×Q₁₆	—	5	1	no	—
486	C₂×Q₁₆	C₄×D₅	1	1	yes	characteristic, complemented
487	C₂×SD₁₆	—	5	8	no	—
488	C₂×SD₁₆	—	5	2	no	—
489	C₂×SD₁₆	C₄×D₅	1	2	yes	complemented
490	C₂×D₈	—	5	4	no	—
491	C₂×D₈	—	5	1	no	—
492	C₂×D₈	C₄×D₅	1	1	yes	characteristic, complemented
493	#131	—	2	2	no	—
494	#131	—	2	2	no	—
495	#131	—	5	2	no	—
496	#131	—	5	2	no	—
497	#131	—	5	2	no	—
498	#131	—	5	2	no	—
499	#131	—	5	2	no	—
500	#131	—	5	2	no	—
501	#131	—	5	2	no	—
502	#131	—	5	2	no	—
503	#131	—	5	8	no	—
504	#131	—	5	8	no	—
505	#131	—	5	4	no	—
506	#131	—	5	4	no	—
507	#131	—	10	8	no	—
508	#131	—	10	4	no	—
509	#131	—	10	8	no	—
510	#131	—	10	4	no	—
511	#131	—	10	8	no	—
512	#131	—	10	8	no	—
513	#131	—	10	4	no	—
514	#131	—	10	4	no	—
515	#131	—	10	2	no	—
516	#131	—	10	2	no	—
517	#131	C₂²×D₅	1	4	yes	—
518	#131	C₂²×D₅	1	4	yes	—
519	C₂×M₁₆	—	2	2	no	—
520	C₂×M₁₆	—	5	1	no	—
521	C₂×M₁₆	—	5	1	no	—
522	C₂×M₁₆	—	5	2	no	—
523	C₂×M₁₆	—	5	2	no	—
524	C₂×M₁₆	—	5	2	no	—
525	C₂×M₁₆	—	5	8	no	—
526	C₂×M₁₆	—	10	8	no	—
527	C₂×M₁₆	—	10	8	no	—
528	C₂×M₁₆	—	10	4	no	—
529	C₂×M₁₆	—	10	8	no	—
530	C₂×M₁₆	—	10	4	no	—
531	C₂×M₁₆	—	10	2	no	—
532	C₂×M₁₆	C₂²×D₅	1	2	yes	—
533	C₂²×C₈	—	2	2	no	—
534	C₂²×C₈	—	5	2	no	—
535	C₂²×C₈	—	5	2	no	—
536	C₂²×C₈	—	10	8	no	—
537	C₂²×C₈	—	10	2	no	—
538	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
539	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
540	C₄×Q₈	—	10	1	no	—
541	C₄×D₄	—	10	1	no	—
542	C₄×D₄	—	10	2	no	—
543	#117	—	5	1	no	—
544	#117	—	5	2	no	—
545	C₂×C₄²	—	5	2	no	—
546	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
547	#108	—	5	8	no	—
548	#108	—	5	2	no	—
549	#108	—	5	2	no	—
550	#108	C₂²×D₅	1	2	yes	—
551	#108	C₂²×D₅	1	2	yes	—
552	#104	—	5	8	no	—
553	#104	—	5	8	no	—
554	#104	—	5	4	no	—
555	#104	—	5	4	no	—
556	#104	C₂²×D₅	1	4	yes	—
557	#104	C₂²×D₅	1	4	yes	—
558	#97	—	5	2	no	—
559	#97	—	5	2	no	—
560	#97	—	5	2	no	—
561	C₄×C₈	—	5	2	no	—
562	C₄×C₈	—	5	2	no	—
563	C₄×C₈	—	5	2	no	—
564	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
565	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
566	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
567	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
568	C₂²×C₅	—	2	4	no	—
569	C₂²×C₅	—	4	1	no	—
570	C₂²×C₅	—	8	2	no	—
571	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
572	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
573	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
574	C₂×D₅	—	2	4	no	—
575	C₂×D₅	—	4	2	no	—
576	C₂×D₅	—	8	8	no	—
577	C₂×D₅	—	8	2	no	—
578	C₂×D₅	C₂×C₄×D₄	1	4	yes	—
579	C₄×C₅	—	2	2	no	—
580	C₄×C₅	—	2	4	no	—
581	C₄×C₅	—	4	1	no	—
582	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
583	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
584	C₄×C₅	C₂⁴×C₄	1	1	yes	characteristic
585	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
586	Dic₅	—	2	4	no	—
587	Dic₅	—	4	2	no	—
588	Dic₅	C₂×C₄×D₄	1	4	yes	—
589	#41	—	2	2	no	—
590	#41	—	2	2	no	—
591	#41	—	5	2	no	—
592	#41	—	5	2	no	—
593	#41	—	5	2	no	—
594	#41	—	5	2	no	—
595	#41	—	5	8	no	—
596	#41	—	5	8	no	—
597	#41	—	5	4	no	—
598	#41	—	5	4	no	—
599	#41	—	10	8	no	—
600	#41	—	10	8	no	—
601	#41	—	10	4	no	—
602	#41	—	10	4	no	—
603	#41	—	10	8	no	—
604	#41	—	10	8	no	—
605	#41	—	10	4	no	—
606	#41	—	10	4	no	—
607	#41	—	10	2	no	—
608	#41	—	10	2	no	—
609	#41	C₂×C₄×D₅	1	4	yes	—
610	#41	C₂³×D₅	1	4	yes	—
611	C₂×Q₈	—	5	1	no	—
612	C₂×Q₈	—	5	8	no	—
613	C₂×Q₈	—	5	2	no	—
614	C₂×Q₈	—	10	4	no	—
615	C₂×Q₈	—	10	4	no	—
616	C₂×Q₈	C₂×C₄×D₅	1	2	yes	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	5	2	no	—
619	C₂×D₄	—	5	8	no	—
620	C₂×D₄	—	5	2	no	—
621	C₂×D₄	—	5	1	no	—
622	C₂×D₄	—	10	4	no	—
623	C₂×D₄	—	10	8	no	—
624	C₂×D₄	—	10	4	no	—
625	C₂×D₄	—	10	8	no	—
626	C₂×D₄	—	10	8	no	—
627	C₂×D₄	—	10	2	no	—
628	C₂×D₄	C₂×C₄×D₅	1	2	yes	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	5	2	no	—
632	C₂²×C₄	—	10	8	no	—
633	C₂²×C₄	—	10	2	no	—
634	C₂²×C₄	—	10	2	no	—
635	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
636	Q₁₆	—	5	8	no	—
637	Q₁₆	—	5	2	no	—
638	Q₁₆	—	5	2	no	—
639	Q₁₆	C₂×C₄×D₅	1	2	yes	—
640	Q₁₆	C₂×C₄×D₅	1	2	yes	—
641	SD₁₆	—	5	8	no	—
642	SD₁₆	—	5	8	no	—
643	SD₁₆	—	5	4	no	—
644	SD₁₆	—	5	4	no	—
645	SD₁₆	C₂×C₄×D₅	1	4	yes	—
646	SD₁₆	C₂×C₄×D₅	1	4	yes	—
647	D₈	—	5	8	no	—
648	D₈	—	5	2	no	—
649	D₈	—	5	2	no	—
650	D₈	C₂×C₄×D₅	1	2	yes	—
651	D₈	C₂×C₄×D₅	1	2	yes	—
652	M₁₆	—	2	2	no	—
653	M₁₆	—	2	4	no	—
654	M₁₆	—	2	4	no	—
655	M₁₆	—	5	2	no	—
656	M₁₆	—	5	2	no	—
657	M₁₆	—	5	2	no	—
658	M₁₆	—	5	2	no	—
659	M₁₆	—	5	4	no	—
660	M₁₆	—	5	4	no	—
661	M₁₆	—	5	4	no	—
662	M₁₆	—	5	4	no	—
663	M₁₆	—	5	4	no	—
664	M₁₆	—	10	8	no	—
665	M₁₆	—	10	8	no	—
666	M₁₆	—	10	8	no	—
667	M₁₆	—	10	2	no	—
668	M₁₆	—	10	4	no	—
669	M₁₆	—	10	4	no	—
670	M₁₆	C₂³×D₅	1	4	yes	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	2	4	no	—
673	C₂×C₈	—	2	4	no	—
674	C₂×C₈	—	5	2	no	—
675	C₂×C₈	—	5	2	no	—
676	C₂×C₈	—	5	4	no	—
677	C₂×C₈	—	5	4	no	—
678	C₂×C₈	—	5	4	no	—
679	C₂×C₈	—	5	4	no	—
680	C₂×C₈	—	10	8	no	—
681	C₂×C₈	—	10	8	no	—
682	C₂×C₈	—	10	8	no	—
683	C₂×C₈	—	10	2	no	—
684	C₂×C₈	—	10	4	no	—
685	C₂×C₈	—	10	4	no	—
686	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
687	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
688	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
689	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
690	C₂×C₈	D₄×D₅	1	1	yes	characteristic
691	C₂×C₈	D₄×D₅	1	1	yes	characteristic
692	C₂×C₈	D₄×D₅	1	1	yes	characteristic
693	C₂×C₈	D₄×D₅	1	1	yes	characteristic
694	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
695	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
696	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
697	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
698	C₄⋊C₄	—	10	2	no	—
699	C₄⋊C₄	—	10	1	no	—
700	C₂²⋊C₄	—	10	2	no	—
701	C₂²⋊C₄	—	10	1	no	—
702	C₄²	—	2	1	no	—
703	C₄²	—	5	2	no	—
704	C₄²	—	10	2	no	—
705	C₄²	C₂³×D₅	1	1	yes	characteristic
706	C₄²	C₂³×D₅	1	1	yes	characteristic
707	C₂×C₅	—	2	1	no	—
708	C₂×C₅	—	2	1	no	—
709	C₂×C₅	—	2	1	no	—
710	C₂×C₅	—	4	4	no	—
711	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
712	D₅	—	2	4	no	—
713	D₅	—	4	4	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	5	2	no	—
716	C₂³	—	10	8	no	—
717	C₂³	—	10	2	no	—
718	C₂³	D₅×#41	1	1	yes	characteristic
719	Q₈	—	2	2	no	—
720	Q₈	—	5	2	no	—
721	Q₈	—	5	2	no	—
722	Q₈	—	5	4	no	—
723	Q₈	—	10	8	no	—
724	Q₈	—	10	2	no	—
725	Q₈	C₂²×C₄×D₅	1	4	yes	—
726	D₄	—	2	4	no	—
727	D₄	—	2	4	no	—
728	D₄	—	2	2	no	—
729	D₄	—	5	4	no	—
730	D₄	—	5	4	no	—
731	D₄	—	5	2	no	—
732	D₄	—	5	2	no	—
733	D₄	—	5	4	no	—
734	D₄	—	10	8	no	—
735	D₄	—	10	8	no	—
736	D₄	—	10	8	no	—
737	D₄	—	10	4	no	—
738	D₄	—	10	4	no	—
739	D₄	—	10	2	no	—
740	D₄	C₂²×C₄×D₅	1	4	yes	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	5	2	no	—
748	C₂×C₄	—	5	4	no	—
749	C₂×C₄	—	5	4	no	—
750	C₂×C₄	—	10	8	no	—
751	C₂×C₄	—	10	8	no	—
752	C₂×C₄	—	10	8	no	—
753	C₂×C₄	—	10	2	no	—
754	C₂×C₄	—	10	4	no	—
755	C₂×C₄	—	10	4	no	—
756	C₂×C₄	—	10	2	no	—
757	C₂×C₄	—	20	4	no	—
758	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
759	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
760	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
761	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
762	C₂×C₄	D₅×#41	1	1	yes	characteristic
763	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
764	C₈	—	2	4	no	—
765	C₈	—	5	4	no	—
766	C₈	—	5	4	no	—
767	C₈	—	10	4	no	—
768	C₈	C₂²×C₄×D₅	1	1	yes	characteristic
769	C₈	C₂²×C₄×D₅	1	1	yes	characteristic
770	C₈	C₂²×C₄×D₅	1	1	yes	characteristic
771	C₈	C₂²×C₄×D₅	1	1	yes	characteristic
772	C₈	C₂×D₄×D₅	1	1	yes	characteristic
773	C₈	C₂×D₄×D₅	1	1	yes	characteristic
774	C₈	C₂×D₄×D₅	1	1	yes	characteristic
775	C₈	C₂×D₄×D₅	1	1	yes	characteristic
776	C₅	#60183	1	1	yes	characteristic, complemented, Sylow
777	C₂²	—	2	4	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	5	4	no	—
780	C₂²	—	8	2	no	—
781	C₂²	—	10	4	no	—
782	C₂²	—	20	2	no	—
783	C₂²	—	40	2	no	—
784	C₂²	—	40	8	no	—
785	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
786	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
787	C₂²	C₂×D₅×#41	1	1	yes	characteristic
788	C₄	—	2	2	no	—
789	C₄	—	2	4	no	—
790	C₄	—	4	1	no	—
791	C₄	—	5	4	no	—
792	C₄	—	10	4	no	—
793	C₄	—	20	2	no	—
794	C₄	C₄×D₄×D₅	1	1	yes	characteristic
795	C₄	C₄×D₄×D₅	1	1	yes	characteristic
796	C₄	C₂³×C₄×D₅	1	1	yes	characteristic
797	C₄	C₂²×D₄×D₅	1	1	yes	characteristic
798	C₂	—	2	1	no	—
799	C₂	—	2	1	no	—
800	C₂	—	2	1	no	—
801	C₂	—	4	4	no	—
802	C₂	—	10	4	no	—
803	C₂	—	20	4	no	—
804	C₂	C₂×C₄×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₅
commutator	C₄×C₅	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₅
Fitting	C₂×C₅×#443	C₂
socle	C₂×C₅	C₂²×C₄×D₄
prime radical	#10619088	C₂
cosocle	C₂×C₄×C₅	C₂⁵
hypercenter	C₂×#443	D₅
hypocenter	C₅	#60183
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. #10619061	C₂	semidirect
3. C₂×C₅×#443	C₂	semidirect
4. #10615641	C₂	semidirect
5. #10615523	C₂	semidirect
6. #10611621	C₂	semidirect
7. #10611620	C₂	semidirect
8. #10611619	C₂	semidirect
9. D₅×#443	C₂	semidirect
10. #10610983	C₂	semidirect
11. #10610980	C₂	semidirect
12. #10610714	C₂	semidirect
13. #10610711	C₂	semidirect
14. C₂×#64989	C₂	semidirect
15. C₄×#4047	C₂	semidirect
18. C₂×C₅×#131	C₂²	semidirect
20. #66153	C₂²	semidirect
21. #66105	C₄	semidirect
22. #66104	C₄	semidirect
23. #66103	C₄	semidirect
26. #66100	C₄	semidirect
27. #66096	C₄	semidirect
28. #66091	C₄	semidirect
30. #66084	C₂²	semidirect
32. D₅×#131	C₂²	semidirect
35. #66079	C₂²	semidirect
40. C₂×#4047	C₂²	semidirect
42. C₅×#443	C₂²	semidirect
43. C₅×#443	C₂²	semidirect
44. C₅×#443	C₂²	semidirect
45. C₅×#443	C₂²	semidirect
46. C₂×C₅×#108	C₂²	semidirect
47. C₂×C₅×#104	C₂²	semidirect
48. C₂×C₄×C₅×C₈	C₂²	semidirect
49. #65525	C₂²	semidirect
50. #65486	C₂²	semidirect
51. #65485	C₂²	semidirect
52. #65434	C₂²	semidirect
53. #65433	C₂²	semidirect
54. #65428	C₂²	semidirect
55. #65413	C₂²	semidirect
56. C₂×#3951	C₂²	semidirect
57. #65390	C₂²	semidirect
58. #65390	C₂²	semidirect
59. C₂×#3937	C₂²	semidirect
60. C₄×#681	C₂²	semidirect
61. #65184	C₂²	semidirect
62. #65183	C₂²	semidirect
63. #65182	C₂²	semidirect
64. D₅×#108	C₂²	semidirect
65. #65113	C₂²	semidirect
66. #65112	C₂²	semidirect
67. #65110	C₂²	semidirect
68. D₅×#104	C₂²	semidirect
69. #64989	C₂²	semidirect
70. #64989	C₂²	semidirect
71. #64989	C₂²	semidirect
72. #64989	C₂²	semidirect
73. #64978	C₂²	semidirect
74. #64978	C₂²	semidirect
75. C₄×#676	C₂²	semidirect
76. C₄×C₈×D₅	C₂²	semidirect
91. C₅×#135	C₂×C₄	semidirect
92. C₅×#135	C₂×C₄	semidirect
95. C₂×C₅×Q₁₆	C₂×C₄	semidirect
96. C₂×C₅×SD₁₆	C₂×C₄	semidirect
97. C₂×C₅×D₈	C₂×C₄	semidirect
108. #4097	C₂×C₄	semidirect
110. #4095	C₂×C₄	semidirect
113. #4088	C₂×C₄	semidirect
114. #4078	C₂×C₄	semidirect
121. #4065	C₂×C₄	semidirect
122. #4064	C₂×C₄	semidirect
123. D₅×Q₁₆	C₂×C₄	semidirect
124. #4062	C₂×C₄	semidirect
125. #4061	C₂×C₄	semidirect
126. #4060	C₂×C₄	semidirect
127. D₅×SD₁₆	C₂×C₄	semidirect
128. #4058	C₂×C₄	semidirect
129. #4057	C₂×C₄	semidirect
130. D₅×D₈	C₂×C₄	semidirect
139. C₂×Dic₂₀	C₂×C₄	semidirect
140. #4050	C₂×C₄	semidirect
141. #4050	C₂×C₄	semidirect
144. C₂×D₄₀	C₂×C₄	semidirect
145. C₂×#677	C₂×C₄	semidirect
206. C₂×#443	D₅	semidirect
352. C₂×#131	C₂×D₅	semidirect
366. #443	C₂×D₅	semidirect
367. #443	C₂×D₅	semidirect
368. #443	C₂×D₅	semidirect
369. #443	C₂×D₅	semidirect
374. C₂×#108	C₂×D₅	semidirect
380. C₂×#104	C₂×D₅	semidirect
388. C₂×C₄×C₈	C₂×D₅	semidirect
480. #135	C₄×D₅	semidirect
481. #135	C₄×D₅	semidirect
486. C₂×Q₁₆	C₄×D₅	semidirect
489. C₂×SD₁₆	C₄×D₅	semidirect
492. C₂×D₈	C₄×D₅	semidirect
776. C₅	#60183	semidirect

Maximal subgroups

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

subgroup	index
#10619088	2
#10619061	2
C₂×C₅×#443	2
#10615641	2
#10615523	2
#10611621	2
#10611620	2
#10611619	2
D₅×#443	2
#10610983	2
#10610980	2
#10610714	2
#10610711	2
C₂×#64989	2
C₄×#4047	2
#60183	5