Subgroups — #12101548

Order 1280.

798 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10610908	C₂	1	1	yes	maximal, characteristic
2	D₅×#424	C₂	1	1	yes	maximal, characteristic
3	D₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₅×#1922	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601454	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601327	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600692	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599731	C₂	1	1	yes	maximal, characteristic
9	#10599718	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599546	C₂	1	1	yes	maximal, characteristic
11	#10599546	C₂	1	1	yes	maximal, characteristic
12	#10599536	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599531	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599454	C₂	1	1	yes	maximal, characteristic
15	#10599438	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×D₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×#676	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
20	D₅×#117	C₂²	1	1	yes	characteristic
21	D₅×#117	C₂²	1	1	yes	characteristic
22	C₂×#4018	C₂²	1	1	yes	characteristic
23	C₅×#427	C₂²	1	1	yes	characteristic
24	C₅×#424	C₂²	1	1	yes	characteristic
25	C₅×#405	C₂²	1	1	yes	characteristic
26	#65411	C₂²	1	1	yes	characteristic
27	#65408	C₂²	1	1	yes	characteristic
28	#65395	C₂²	1	1	yes	characteristic
29	#65391	C₂²	1	1	yes	characteristic
30	#65390	C₂²	1	1	yes	characteristic
31	#65288	C₂²	1	1	yes	characteristic
32	#65287	C₂²	1	1	yes	characteristic
33	#65287	C₂²	1	1	yes	characteristic
34	#65286	C₂²	1	1	yes	characteristic
35	#65170	C₄	1	1	yes	characteristic, complemented
36	#65170	C₄	1	1	yes	characteristic, complemented
37	#65170	C₄	1	1	yes	characteristic, complemented
38	#65170	C₄	1	1	yes	characteristic, complemented
39	#65150	C₄	1	1	yes	characteristic, complemented
40	#65150	C₄	1	1	yes	characteristic, complemented
41	#65150	C₄	1	1	yes	characteristic, complemented
42	#65150	C₄	1	1	yes	characteristic, complemented
43	#65128	—	2	1	no	—
44	#65128	—	2	1	no	—
45	D₅×C₄⋊C₈	—	2	1	no	—
46	D₅×C₄⋊C₈	—	2	1	no	—
47	#64997	—	2	1	no	—
48	D₅×#97	—	2	1	no	—
49	#64978	—	2	1	no	—
50	C₄×C₈×D₅	—	2	1	no	—
51	C₅×#341	C₂²	1	1	yes	characteristic
52	C₅×#339	C₂²	1	1	yes	characteristic
53	C₅×#339	C₂²	1	1	yes	characteristic
54	C₅×#336	C₂²	1	1	yes	characteristic
55	#64778	C₂²	1	1	yes	characteristic
56	#64778	C₂²	1	1	yes	characteristic
57	#64775	C₂²	1	1	yes	characteristic
58	#64775	C₂²	1	1	yes	characteristic
59	#64772	C₂²	1	1	yes	characteristic
60	#64770	C₂²	1	1	yes	characteristic
61	#64770	C₂²	1	1	yes	characteristic
62	#64752	C₂²	1	1	yes	characteristic
63	#64752	C₂²	1	1	yes	characteristic
64	#64744	C₂²	1	1	yes	characteristic
65	#64743	C₂²	1	1	yes	characteristic
66	#64743	C₂²	1	1	yes	characteristic
67	#21041	—	5	1	no	maximal, Sylow
68	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
69	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₅×#117	C₂³	1	1	yes	characteristic
74	C₅×#117	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂×#685	—	2	1	no	—
77	#4072	C₂³	1	1	yes	characteristic
78	#4072	C₂³	1	1	yes	characteristic
79	C₂×#683	—	2	1	no	—
80	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
81	C₂×#681	C₂³	1	1	yes	characteristic
82	C₂×#681	C₂³	1	1	yes	characteristic
83	C₂²×#168	C₂³	1	1	yes	characteristic
84	C₂²×#168	C₂³	1	1	yes	characteristic
85	D₅×M₁₆	—	2	2	no	—
86	D₅×M₁₆	—	2	2	no	—
87	D₅×M₁₆	—	2	2	no	—
88	D₅×M₁₆	Q₈	1	4	yes	—
89	C₂×#676	—	2	1	no	—
90	C₂×#676	—	2	2	no	—
91	C₂×#676	—	2	2	no	—
92	C₂×#676	—	2	1	no	—
93	C₂×#676	C₂×C₄	1	1	yes	characteristic
94	C₂×#676	C₂×C₄	1	1	yes	characteristic
95	C₂×#676	C₂×C₄	1	1	yes	characteristic
96	C₂×#676	C₂×C₄	1	1	yes	characteristic
97	C₂×C₈×D₅	—	2	1	no	—
98	C₂×C₈×D₅	—	2	2	no	—
99	C₂×C₈×D₅	—	2	2	no	—
100	C₂×C₈×D₅	—	2	1	no	—
101	C₂×C₈×D₅	D₄	1	1	yes	characteristic
102	C₂×C₈×D₅	D₄	1	1	yes	characteristic
103	C₂×C₈×D₅	D₄	1	1	yes	characteristic
104	C₂×C₈×D₅	D₄	1	1	yes	characteristic
105	#4038	C₂×C₄	1	1	yes	characteristic
106	#4038	C₂×C₄	1	1	yes	characteristic
107	#4038	C₂×C₄	1	1	yes	characteristic
108	#4038	C₂×C₄	1	1	yes	characteristic
109	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
110	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
111	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
112	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
113	D₅×C₂²⋊C₄	—	2	1	no	—
114	D₅×C₂²⋊C₄	—	2	1	no	—
115	#4023	—	2	1	no	—
116	#4023	—	2	1	no	—
117	#4018	—	2	1	no	—
118	#4018	—	2	1	no	—
119	#4018	—	2	2	no	—
120	#4018	—	2	2	no	—
121	C₄²×D₅	—	2	1	no	—
122	C₄²×D₅	—	2	1	no	—
123	C₅×#107	C₂×C₄	1	1	yes	characteristic
124	C₅×#107	C₂×C₄	1	1	yes	characteristic
125	C₅×#106	C₂×C₄	1	1	yes	characteristic
126	C₅×#106	C₂×C₄	1	1	yes	characteristic
127	C₅×C₄⋊C₈	—	2	1	no	—
128	C₅×C₄⋊C₈	—	2	1	no	—
129	C₅×#97	—	2	1	no	—
130	C₄×C₅×C₈	—	2	1	no	—
131	#3950	C₂×C₄	1	1	yes	characteristic
132	#3950	C₂×C₄	1	1	yes	characteristic
133	#3949	C₂×C₄	1	1	yes	characteristic
134	#3949	C₂×C₄	1	1	yes	characteristic
135	#3947	—	2	1	no	—
136	#3947	—	2	1	no	—
137	#3946	—	2	1	no	—
138	#3946	—	2	1	no	—
139	#3946	—	2	1	no	—
140	#3946	—	2	1	no	—
141	C₈×Dic₅	—	2	1	no	—
142	C₈×Dic₅	—	2	1	no	—
143	#3940	C₂×C₄	1	1	yes	characteristic
144	#3940	C₂×C₄	1	1	yes	characteristic
145	#3940	C₂×C₄	1	1	yes	characteristic
146	#3940	C₂×C₄	1	1	yes	characteristic
147	#3939	C₂×C₄	1	1	yes	characteristic
148	#3939	C₂×C₄	1	1	yes	characteristic
149	#3939	C₂×C₄	1	1	yes	characteristic
150	#3939	C₂×C₄	1	1	yes	characteristic
151	C₄⋊#168	—	2	1	no	—
152	C₄⋊#168	—	2	1	no	—
153	#3935	—	2	1	no	—
154	C₄×#168	—	2	1	no	—
155	#2911	—	5	1	no	—
156	C₂×#424	—	5	1	no	—
157	C₂×#405	—	5	1	no	—
158	#1922	—	5	1	no	—
159	#1922	—	5	1	no	—
160	#1922	—	5	1	no	—
161	#1922	—	5	1	no	—
162	#1922	—	5	1	no	—
163	#1922	—	5	1	no	—
164	#1922	—	5	1	no	—
165	#1922	D₅	1	1	yes	characteristic, complemented
166	#1738	—	5	1	no	—
167	#1733	—	5	1	no	—
168	#1733	—	5	1	no	—
169	#1729	—	5	1	no	—
170	C₂³×D₅	#41	1	1	yes	characteristic
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
173	C₂²×Dic₅	—	2	1	no	—
174	C₂²×Dic₅	#41	1	1	yes	characteristic
175	C₂×C₄×D₅	—	2	1	no	—
176	C₂×C₄×D₅	—	2	1	no	—
177	C₂×C₄×D₅	—	2	1	no	—
178	C₂×C₄×D₅	—	2	1	no	—
179	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
182	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
183	C₂×C₄×D₅	C₂×Q₈	1	2	yes	—
184	C₂×C₄×D₅	#41	1	2	yes	—
185	C₂×C₄×D₅	#41	1	2	yes	—
186	C₂×C₄×D₅	#41	1	2	yes	—
187	C₅×M₁₆	—	2	1	no	—
188	C₅×M₁₆	—	2	1	no	—
189	C₅×M₁₆	—	2	1	no	—
190	C₅×M₁₆	C₂×Q₈	1	2	yes	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
200	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
201	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
202	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
203	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
204	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
205	C₅×C₂²⋊C₄	—	2	1	no	—
206	C₅×C₂²⋊C₄	—	2	1	no	—
207	C₄²×C₅	—	2	1	no	—
208	C₄²×C₅	—	2	1	no	—
209	C₄²×C₅	—	2	1	no	—
210	C₄²×C₅	—	2	1	no	—
211	C₂²⋊Dic₅	—	2	1	no	—
212	C₂²⋊Dic₅	—	2	1	no	—
213	#685	—	2	1	no	—
214	#685	—	2	1	no	—
215	#685	—	2	1	no	—
216	#685	—	2	1	no	—
217	#685	—	4	2	no	—
218	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
219	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
220	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
221	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
222	#683	—	2	1	no	—
223	#683	—	2	1	no	—
224	#683	—	2	1	no	—
225	#683	—	2	1	no	—
226	#683	—	4	2	no	—
227	C₄×Dic₅	—	2	1	no	—
228	C₄×Dic₅	—	2	1	no	—
229	C₄×Dic₅	—	2	1	no	—
230	C₄×Dic₅	—	2	1	no	—
231	C₄×Dic₅	—	2	1	no	—
232	C₄×Dic₅	—	2	1	no	—
233	C₄×Dic₅	—	2	1	no	—
234	C₄×Dic₅	—	2	1	no	—
235	#681	—	2	1	no	—
236	#681	—	2	1	no	—
237	#681	—	2	1	no	—
238	#681	C₂×Q₈	1	2	yes	—
239	C₂×#168	—	2	1	no	—
240	C₂×#168	—	2	1	no	—
241	C₂×#168	—	2	1	no	—
242	C₂×#168	—	2	1	no	—
243	C₂×#168	—	2	1	no	—
244	C₂×#168	—	2	1	no	—
245	C₂×#168	C₂²×C₄	1	1	yes	characteristic
246	C₂×#168	C₂²×C₄	1	1	yes	characteristic
247	C₂×#168	C₂×D₄	1	1	yes	characteristic
248	C₂×#168	C₂×D₄	1	1	yes	characteristic
249	#676	—	2	2	no	—
250	#676	—	2	2	no	—
251	#676	—	2	2	no	—
252	#676	—	2	2	no	—
253	#676	—	2	4	no	—
254	#676	—	4	2	no	—
255	C₈×D₅	—	2	4	no	—
256	C₈×D₅	—	2	2	no	—
257	C₈×D₅	—	2	2	no	—
258	C₈×D₅	—	2	2	no	—
259	C₈×D₅	—	2	2	no	—
260	C₈×D₅	—	4	2	no	—
261	C₂²×M₁₆	—	5	1	no	—
262	C₂²×M₁₆	—	5	1	no	—
263	C₂²×M₁₆	—	5	1	no	—
264	C₂³×C₈	—	5	1	no	—
265	C₂×#117	—	5	1	no	—
266	C₂×#117	—	5	1	no	—
267	C₂×#117	—	5	1	no	—
268	#428	—	5	1	no	—
269	#428	—	5	1	no	—
270	#428	—	5	1	no	—
271	#428	—	5	1	no	—
272	#428	—	5	1	no	—
273	#428	—	5	1	no	—
274	#428	—	5	1	no	—
275	#428	—	5	1	no	—
276	#427	—	5	1	no	—
277	#427	—	5	1	no	—
278	#427	—	5	1	no	—
279	#427	C₂×D₅	1	1	yes	characteristic
280	#424	—	5	1	no	—
281	#424	—	5	1	no	—
282	#424	—	5	1	no	—
283	#424	—	10	1	no	—
284	#424	—	10	1	no	—
285	#424	C₂×D₅	1	1	yes	characteristic
286	C₂×C₄⋊C₈	—	10	1	no	—
287	C₂×C₄⋊C₈	—	10	1	no	—
288	#405	—	5	1	no	—
289	#405	—	5	1	no	—
290	#405	—	5	1	no	—
291	#405	—	10	1	no	—
292	#405	—	10	1	no	—
293	#405	C₂×D₅	1	1	yes	characteristic
294	C₂×#97	—	10	1	no	—
295	C₂×C₄×C₈	—	10	1	no	—
296	#341	—	5	1	no	—
297	#341	—	5	1	no	—
298	#341	—	5	1	no	—
299	#341	C₂×D₅	1	1	yes	characteristic
300	#339	—	5	1	no	—
301	#339	—	5	1	no	—
302	#339	—	5	1	no	—
303	#339	—	5	1	no	—
304	#339	—	5	1	no	—
305	#339	—	5	1	no	—
306	#339	C₂×D₅	1	1	yes	characteristic
307	#339	C₂×D₅	1	1	yes	characteristic
308	#336	—	5	1	no	—
309	#336	—	5	1	no	—
310	#336	—	5	1	no	—
311	#336	C₂×D₅	1	1	yes	characteristic
312	C₂³×C₅	C₂×#41	1	1	yes	characteristic
313	C₂²×D₅	—	4	1	no	—
314	C₂²×D₅	—	4	1	no	—
315	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
316	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
317	C₂²×D₅	#125	1	2	yes	—
318	C₂²×D₅	#126	1	2	yes	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	4	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
332	C₂×Dic₅	—	2	1	no	—
333	C₂×Dic₅	—	2	1	no	—
334	C₂×Dic₅	—	2	1	no	—
335	C₂×Dic₅	—	2	1	no	—
336	C₂×Dic₅	—	4	1	no	—
337	C₂×Dic₅	—	4	1	no	—
338	C₂×Dic₅	—	4	1	no	—
339	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
340	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
341	C₂×Dic₅	#125	1	2	yes	—
342	C₂×Dic₅	#126	1	2	yes	—
343	C₄×D₅	—	4	2	no	—
344	C₄×D₅	—	4	2	no	—
345	C₄×D₅	—	4	2	no	—
346	C₄×D₅	—	4	2	no	—
347	C₄×D₅	#117	1	2	yes	—
348	C₄×D₅	#117	1	2	yes	—
349	C₄×D₅	C₄×Q₈	1	2	yes	—
350	C₄×D₅	C₄×Q₈	1	2	yes	—
351	C₄×D₅	C₂²⋊Q₈	1	2	yes	—
352	C₄×D₅	C₂²⋊Q₈	1	2	yes	—
353	C₄×D₅	#123	1	2	yes	—
354	C₄×D₅	#123	1	2	yes	—
355	C₅×C₈	—	2	1	no	—
356	C₅×C₈	—	2	1	no	—
357	C₅×C₈	—	2	2	no	—
358	C₅×C₈	—	2	1	no	—
359	C₅×C₈	—	2	1	no	—
360	C₅×C₈	—	4	1	no	—
361	#168	—	2	1	no	—
362	#168	—	2	1	no	—
363	#168	—	2	2	no	—
364	#168	—	2	1	no	—
365	#168	—	2	1	no	—
366	#168	—	4	1	no	—
367	C₂³×C₄	—	5	1	no	—
368	C₂×M₁₆	—	5	1	no	—
369	C₂×M₁₆	—	5	1	no	—
370	C₂×M₁₆	—	5	1	no	—
371	C₂×M₁₆	—	5	1	no	—
372	C₂×M₁₆	—	5	1	no	—
373	C₂×M₁₆	—	5	4	no	—
374	C₂×M₁₆	—	5	1	no	—
375	C₂×M₁₆	—	10	1	no	—
376	C₂×M₁₆	—	10	2	no	—
377	C₂×M₁₆	—	10	2	no	—
378	C₂×M₁₆	—	10	1	no	—
379	C₂×M₁₆	—	10	2	no	—
380	C₂×M₁₆	—	10	2	no	—
381	C₂×M₁₆	—	10	2	no	—
382	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
383	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
384	C₂²×C₈	—	5	1	no	—
385	C₂²×C₈	—	5	1	no	—
386	C₂²×C₈	—	5	1	no	—
387	C₂²×C₈	—	5	1	no	—
388	C₂²×C₈	—	5	1	no	—
389	C₂²×C₈	—	5	1	no	—
390	C₂²×C₈	—	10	2	no	—
391	C₂²×C₈	—	10	2	no	—
392	C₂²×C₈	—	10	1	no	—
393	C₂²×C₈	—	10	1	no	—
394	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
395	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
396	#117	—	5	1	no	—
397	#117	—	5	1	no	—
398	#117	—	5	1	no	—
399	#117	—	5	1	no	—
400	#117	—	5	1	no	—
401	#117	—	5	1	no	—
402	#117	—	10	1	no	—
403	#117	—	10	1	no	—
404	#117	—	10	2	no	—
405	#117	—	10	2	no	—
406	#117	—	10	1	no	—
407	#117	—	10	1	no	—
408	#117	C₂²×D₅	1	1	yes	characteristic
409	#117	C₂²×D₅	1	1	yes	characteristic
410	C₂×C₄⋊C₄	—	5	1	no	—
411	C₂×C₄⋊C₄	—	5	1	no	—
412	C₂×C₄⋊C₄	—	5	1	no	—
413	C₂×C₄⋊C₄	—	5	1	no	—
414	C₂×C₄⋊C₄	—	10	1	no	—
415	C₂×C₂²⋊C₄	—	10	1	no	—
416	C₂×C₂²⋊C₄	—	10	1	no	—
417	C₂×C₂²⋊C₄	—	10	1	no	—
418	C₂×C₄²	—	5	1	no	—
419	C₂×C₄²	—	10	1	no	—
420	C₂×C₄²	—	10	1	no	—
421	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
422	#107	—	5	1	no	—
423	#107	—	5	1	no	—
424	#107	—	5	1	no	—
425	#107	—	5	1	no	—
426	#107	—	5	1	no	—
427	#107	—	5	1	no	—
428	#107	C₄×D₅	1	1	yes	characteristic
429	#107	C₄×D₅	1	1	yes	characteristic
430	#106	—	5	1	no	—
431	#106	—	5	1	no	—
432	#106	—	5	1	no	—
433	#106	—	5	1	no	—
434	#106	—	5	1	no	—
435	#106	—	5	1	no	—
436	#106	C₄×D₅	1	1	yes	characteristic
437	#106	C₄×D₅	1	1	yes	characteristic
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	—	2	1	no	—
440	C₄⋊C₈	—	10	1	no	—
441	C₄⋊C₈	—	10	1	no	—
442	C₄⋊C₈	—	10	1	no	—
443	C₄⋊C₈	—	10	1	no	—
444	C₄⋊C₈	—	10	1	no	—
445	C₄⋊C₈	—	10	1	no	—
446	#97	—	2	1	no	—
447	#97	—	10	1	no	—
448	#97	—	10	1	no	—
449	#97	—	10	1	no	—
450	C₄×C₈	—	2	1	no	—
451	C₄×C₈	—	10	1	no	—
452	C₄×C₈	—	10	1	no	—
453	C₄×C₈	—	10	1	no	—
454	C₂²×C₅	—	2	1	no	—
455	C₂²×C₅	—	2	1	no	—
456	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
457	C₂²×C₅	C₂×#125	1	1	yes	characteristic
458	C₂²×C₅	C₂×#126	1	1	yes	characteristic
459	C₂×D₅	—	2	1	no	—
460	C₂×D₅	—	2	1	no	—
461	C₂×D₅	—	2	1	no	—
462	C₂×D₅	—	2	1	no	—
463	C₂×D₅	—	4	2	no	—
464	C₂×D₅	—	4	2	no	—
465	C₂×D₅	#387	1	2	yes	—
466	C₂×D₅	#387	1	2	yes	—
467	C₄×C₅	—	4	1	no	—
468	C₄×C₅	—	4	1	no	—
469	C₄×C₅	—	4	1	no	—
470	C₄×C₅	—	4	1	no	—
471	C₄×C₅	—	8	1	no	—
472	C₄×C₅	C₂×#117	1	1	yes	characteristic
473	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
474	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
475	C₄×C₅	C₂×#123	1	1	yes	characteristic
476	Dic₅	—	4	1	no	—
477	Dic₅	—	4	1	no	—
478	Dic₅	—	4	1	no	—
479	Dic₅	—	4	1	no	—
480	Dic₅	—	8	1	no	—
481	Dic₅	#387	1	2	yes	—
482	Dic₅	#387	1	2	yes	—
483	C₂⁴	—	5	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	5	1	no	—
486	C₂²×C₄	—	5	1	no	—
487	C₂²×C₄	—	5	1	no	—
488	C₂²×C₄	—	5	1	no	—
489	C₂²×C₄	—	5	1	no	—
490	C₂²×C₄	—	5	2	no	—
491	C₂²×C₄	—	5	2	no	—
492	C₂²×C₄	—	5	2	no	—
493	C₂²×C₄	—	5	2	no	—
494	C₂²×C₄	—	10	1	no	—
495	C₂²×C₄	—	10	1	no	—
496	C₂²×C₄	—	10	1	no	—
497	C₂²×C₄	—	10	1	no	—
498	C₂²×C₄	—	10	1	no	—
499	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
500	M₁₆	—	2	1	no	—
501	M₁₆	—	2	1	no	—
502	M₁₆	—	2	1	no	—
503	M₁₆	—	5	2	no	—
504	M₁₆	—	10	2	no	—
505	M₁₆	—	10	2	no	—
506	M₁₆	—	10	2	no	—
507	M₁₆	—	10	2	no	—
508	M₁₆	—	10	4	no	—
509	M₁₆	—	10	1	no	—
510	M₁₆	—	10	1	no	—
511	M₁₆	—	10	1	no	—
512	M₁₆	—	20	2	no	—
513	M₁₆	Q₈×D₅	1	2	yes	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	5	1	no	—
521	C₂×C₈	—	5	1	no	—
522	C₂×C₈	—	5	1	no	—
523	C₂×C₈	—	5	1	no	—
524	C₂×C₈	—	10	2	no	—
525	C₂×C₈	—	10	2	no	—
526	C₂×C₈	—	10	2	no	—
527	C₂×C₈	—	10	2	no	—
528	C₂×C₈	—	10	4	no	—
529	C₂×C₈	—	10	1	no	—
530	C₂×C₈	—	10	1	no	—
531	C₂×C₈	—	10	1	no	—
532	C₂×C₈	—	10	1	no	—
533	C₂×C₈	—	10	1	no	—
534	C₂×C₈	—	10	1	no	—
535	C₂×C₈	—	20	2	no	—
536	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
537	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
538	C₂×C₈	D₄×D₅	1	1	yes	characteristic
539	C₂×C₈	D₄×D₅	1	1	yes	characteristic
540	C₄⋊C₄	—	5	1	no	—
541	C₄⋊C₄	—	5	1	no	—
542	C₄⋊C₄	—	5	1	no	—
543	C₄⋊C₄	—	5	1	no	—
544	C₄⋊C₄	—	10	1	no	—
545	C₄⋊C₄	—	10	1	no	—
546	C₄⋊C₄	—	10	1	no	—
547	C₄⋊C₄	—	10	1	no	—
548	C₄⋊C₄	—	20	2	no	—
549	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
550	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
551	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
552	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	1	no	—
555	C₂²⋊C₄	—	10	1	no	—
556	C₂²⋊C₄	—	10	1	no	—
557	C₂²⋊C₄	—	10	1	no	—
558	C₂²⋊C₄	—	10	1	no	—
559	C₂²⋊C₄	—	10	1	no	—
560	C₂²⋊C₄	—	10	1	no	—
561	C₂²⋊C₄	—	20	2	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	10	1	no	—
567	C₄²	—	10	1	no	—
568	C₄²	—	10	1	no	—
569	C₄²	—	10	1	no	—
570	C₄²	—	10	1	no	—
571	C₄²	—	10	1	no	—
572	C₄²	—	10	1	no	—
573	C₄²	—	10	1	no	—
574	C₂×C₅	—	2	1	no	—
575	C₂×C₅	—	2	1	no	—
576	C₂×C₅	C₂×#387	1	1	yes	characteristic
577	C₂×C₅	#2955	1	1	yes	characteristic
578	C₂×C₅	#2955	1	1	yes	characteristic
579	D₅	—	2	2	no	—
580	D₅	—	2	2	no	—
581	C₂³	—	5	1	no	—
582	C₂³	—	5	1	no	—
583	C₂³	—	5	2	no	—
584	C₂³	—	5	2	no	—
585	C₂³	—	20	1	no	—
586	C₂³	—	20	1	no	—
587	C₂³	D₅×#41	1	1	yes	characteristic
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	5	1	no	—
596	C₂×C₄	—	5	1	no	—
597	C₂×C₄	—	5	2	no	—
598	C₂×C₄	—	5	2	no	—
599	C₂×C₄	—	5	2	no	—
600	C₂×C₄	—	5	2	no	—
601	C₂×C₄	—	5	2	no	—
602	C₂×C₄	—	5	2	no	—
603	C₂×C₄	—	5	2	no	—
604	C₂×C₄	—	5	2	no	—
605	C₂×C₄	—	5	2	no	—
606	C₂×C₄	—	5	2	no	—
607	C₂×C₄	—	10	1	no	—
608	C₂×C₄	—	10	1	no	—
609	C₂×C₄	—	10	1	no	—
610	C₂×C₄	—	10	1	no	—
611	C₂×C₄	—	20	2	no	—
612	C₂×C₄	—	20	2	no	—
613	C₂×C₄	—	20	2	no	—
614	C₂×C₄	—	20	2	no	—
615	C₂×C₄	—	20	1	no	—
616	C₂×C₄	—	20	1	no	—
617	C₂×C₄	—	20	1	no	—
618	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
619	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
620	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
621	C₂×C₄	D₅×#41	1	1	yes	characteristic
622	C₂×C₄	D₅×#41	1	1	yes	characteristic
623	C₂×C₄	D₅×#41	1	1	yes	characteristic
624	C₈	—	2	1	no	—
625	C₈	—	2	1	no	—
626	C₈	—	2	2	no	—
627	C₈	—	2	1	no	—
628	C₈	—	2	1	no	—
629	C₈	—	4	1	no	—
630	C₈	—	10	1	no	—
631	C₈	—	10	1	no	—
632	C₈	—	10	2	no	—
633	C₈	—	10	1	no	—
634	C₈	—	10	1	no	—
635	C₈	—	20	1	no	—
636	C₅	#21041	1	1	yes	characteristic, complemented, Sylow
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	5	2	no	—
640	C₂²	—	5	2	no	—
641	C₂²	—	10	1	no	—
642	C₂²	—	10	1	no	—
643	C₂²	—	10	1	no	—
644	C₂²	—	10	1	no	—
645	C₂²	—	20	2	no	—
646	C₂²	—	20	2	no	—
647	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
648	C₂²	D₅×#125	1	1	yes	characteristic
649	C₂²	D₅×#126	1	1	yes	characteristic
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	5	2	no	—
655	C₄	—	5	2	no	—
656	C₄	—	8	1	no	—
657	C₄	—	20	1	no	—
658	C₄	—	20	1	no	—
659	C₄	—	20	1	no	—
660	C₄	—	20	1	no	—
661	C₄	—	40	1	no	—
662	C₄	D₅×#117	1	1	yes	characteristic
663	C₄	C₄×Q₈×D₅	1	1	yes	characteristic
664	C₄	D₅×C₂²⋊Q₈	1	1	yes	characteristic
665	C₄	D₅×#123	1	1	yes	characteristic
666	C₂	—	2	1	no	—
667	C₂	—	2	1	no	—
668	C₂	—	10	2	no	—
669	C₂	—	10	2	no	—
670	C₂	D₅×#387	1	1	yes	characteristic
671	C₂	#10611619	1	1	yes	characteristic
672	C₂	#10611628	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#1922	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂³×D₅	#41
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1922	D₅
hypocenter	C₅	#21041
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1922

Complements

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

N	H ≅ G/N	type
4. C₅×#1922	C₂	semidirect
5. #10601454	C₂	semidirect
6. #10601327	C₂	semidirect
7. #10600692	C₂	semidirect
9. #10599718	C₂	semidirect
12. #10599536	C₂	semidirect
13. #10599531	C₂	semidirect
15. #10599438	C₂	semidirect
35. #65170	C₄	semidirect
36. #65170	C₄	semidirect
37. #65170	C₄	semidirect
38. #65170	C₄	semidirect
39. #65150	C₄	semidirect
40. #65150	C₄	semidirect
41. #65150	C₄	semidirect
42. #65150	C₄	semidirect
165. #1922	D₅	semidirect
636. C₅	#21041	semidirect

Maximal subgroups

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

subgroup	index
#10610908	2
D₅×#424	2
D₅×#405	2
C₅×#1922	2
#10601454	2
#10601327	2
#10600692	2
#10599731	2
#10599718	2
#10599546	2
#10599536	2
#10599531	2
#10599454	2
#10599438	2
#21041	5