Subgroups — #12066797

Order 1280.

1042 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×#65226	C₂	1	1	yes	maximal, characteristic, complemented
3	#10613780	C₂	1	1	yes	maximal, characteristic, complemented
4	#10602630	C₂	1	2	yes	maximal, complemented
5	#10602606	C₂	1	2	yes	maximal, complemented
6	#10602550	C₂	1	4	yes	maximal, complemented
7	#10602501	C₂	1	4	yes	maximal, complemented
8	C₅×#533	C₄	1	1	yes	characteristic, complemented
9	C₅×#533	C₄	1	1	yes	characteristic, complemented
10	C₅×#533	C₂²	1	1	yes	characteristic
11	C₅×#532	C₄	1	1	yes	characteristic, complemented
12	C₅×#532	C₄	1	1	yes	characteristic, complemented
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₅×#529	—	2	1	no	—
15	C₅×#529	—	2	1	no	—
16	C₅×#529	—	2	1	no	—
17	C₅×#529	—	2	1	no	—
18	C₅×#529	C₄	1	2	yes	complemented
19	C₅×#529	C₂²	1	2	yes	—
20	C₅×#525	—	2	1	no	—
21	C₅×#525	—	2	1	no	—
22	C₅×#525	C₂²	1	2	yes	—
23	C₄×C₅×#41	—	2	1	no	—
24	C₄×C₅×#41	—	2	1	no	—
25	C₄×C₅×#41	C₄	1	2	yes	complemented
26	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂×#3963	—	2	1	no	—
28	C₂×#3963	—	2	1	no	—
29	C₂×#3963	C₂²	1	2	yes	—
30	#65496	C₂²	1	2	yes	—
31	#65226	—	2	1	no	—
32	#65226	—	2	1	no	—
33	#65226	C₂²	1	2	yes	—
34	#65226	C₂²	1	2	yes	—
35	#65215	—	2	1	no	—
36	#65215	C₂²	1	2	yes	—
37	#65214	—	2	1	no	—
38	#65214	C₂²	1	2	yes	—
39	#65213	—	2	1	no	—
40	C₄×#681	—	2	1	no	—
41	#64758	C₂²	1	8	yes	—
42	#64757	C₂²	1	8	yes	—
43	#17593	—	5	1	no	maximal, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂×C₅×#41	—	2	1	no	—
46	C₂×C₅×#41	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂³×Dic₅	—	2	2	no	—
51	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
52	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
53	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
54	C₅×#127	C₂×C₄	1	1	yes	characteristic, complemented
55	C₅×#126	—	2	2	no	—
56	C₅×#126	—	2	2	no	—
57	C₅×#125	—	2	1	no	—
58	C₅×#125	—	2	1	no	—
59	C₅×#125	C₂×C₄	1	2	yes	complemented
60	C₅×#124	—	2	1	no	—
61	C₅×#124	—	2	1	no	—
62	C₅×#124	C₂×C₄	1	2	yes	complemented
63	C₅×#123	—	2	2	no	—
64	C₅×#123	—	2	2	no	—
65	C₅×#123	—	2	2	no	—
66	C₅×C₂²⋊Q₈	—	2	1	no	—
67	C₅×C₂²⋊Q₈	—	2	1	no	—
68	C₅×C₂²⋊Q₈	—	2	1	no	—
69	C₅×C₂²⋊Q₈	—	2	1	no	—
70	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
71	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
72	C₅×#121	—	2	1	no	—
73	C₅×#121	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₅×#121	—	2	1	no	—
76	C₅×#121	C₂×C₄	1	2	yes	—
77	C₅×#121	C₂³	1	2	yes	—
78	C₅×#120	—	2	2	no	—
79	C₄×C₅×Q₈	—	2	1	no	—
80	C₄×C₅×Q₈	—	2	1	no	—
81	C₄×C₅×Q₈	—	2	1	no	—
82	C₄×C₅×Q₈	—	2	1	no	—
83	C₄×C₅×Q₈	C₂×C₄	1	2	yes	complemented
84	C₄×C₅×Q₈	C₂×C₄	1	2	yes	complemented
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	2	2	no	—
87	C₄×C₅×D₄	—	2	2	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₄×C₅×D₄	—	2	2	no	—
90	C₄×C₅×D₄	—	2	2	no	—
91	C₄×C₅×D₄	—	2	1	no	—
92	C₄×C₅×D₄	—	2	1	no	—
93	C₄×C₅×D₄	—	2	1	no	—
94	C₄×C₅×D₄	—	2	1	no	—
95	C₄×C₅×D₄	C₂×C₄	1	2	yes	complemented
96	C₄×C₅×D₄	C₂×C₄	1	2	yes	complemented
97	C₅×#117	—	2	1	no	—
98	C₅×#117	—	2	1	no	—
99	C₅×#117	—	2	2	no	—
100	C₅×#117	—	2	2	no	—
101	C₅×#117	—	2	2	no	—
102	C₅×#117	C₂×C₄	1	2	yes	—
103	C₂×C₄²×C₅	—	2	2	no	—
104	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
116	C₂×#681	—	2	2	no	—
117	#3963	—	2	2	no	—
118	#3963	—	2	2	no	—
119	#3963	—	2	2	no	—
120	#3963	—	2	2	no	—
121	#3963	—	2	2	no	—
122	#3963	C₂³	1	4	yes	—
123	C₂²⋊#168	—	2	2	no	—
124	C₂²⋊#168	C₂³	1	4	yes	—
125	C₄⋊#168	—	2	2	no	—
126	C₄⋊#168	—	2	2	no	—
127	#3935	—	2	2	no	—
128	C₄×#168	—	2	2	no	—
129	#3444	D₅	1	1	yes	characteristic
130	#2920	—	5	1	no	—
131	C₂×#383	—	5	1	no	—
132	#1521	—	5	4	no	—
133	#1515	—	5	2	no	—
134	#1514	—	5	2	no	—
135	#1504	—	5	4	no	—
136	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
137	C₅×#41	—	4	4	no	—
138	C₅×#41	—	4	4	no	—
139	C₅×#41	—	4	4	no	—
140	C₂×C₅×Q₈	—	2	1	no	—
141	C₂×C₅×Q₈	—	2	1	no	—
142	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
143	C₂×C₅×D₄	—	2	2	no	—
144	C₂×C₅×D₄	—	2	2	no	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	2	2	no	—
152	C₂²×C₄×C₅	—	4	2	no	—
153	C₂²×C₄×C₅	—	4	2	no	—
154	C₂²×C₄×C₅	—	4	2	no	—
155	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
173	C₂²×Dic₅	—	2	4	no	—
174	C₂²×Dic₅	—	4	4	no	—
175	C₂²×Dic₅	—	4	4	no	—
176	C₂²×Dic₅	—	4	4	no	—
177	C₅×C₄⋊C₄	—	2	1	no	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	2	1	no	—
180	C₅×C₄⋊C₄	—	2	1	no	—
181	C₅×C₄⋊C₄	—	2	2	no	—
182	C₅×C₄⋊C₄	—	2	2	no	—
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	—	2	2	no	—
185	C₅×C₄⋊C₄	—	2	2	no	—
186	C₅×C₄⋊C₄	—	2	2	no	—
187	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
188	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
189	C₅×C₂²⋊C₄	—	2	2	no	—
190	C₅×C₂²⋊C₄	—	2	2	no	—
191	C₅×C₂²⋊C₄	—	2	2	no	—
192	C₅×C₂²⋊C₄	—	2	2	no	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	2	2	no	—
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	2	2	no	—
198	C₄²×C₅	—	2	2	no	—
199	C₄²×C₅	—	2	2	no	—
200	C₄²×C₅	—	2	2	no	—
201	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
217	#681	—	4	4	no	—
218	C₂×#168	—	2	4	no	—
219	#533	Dic₅	1	1	yes	characteristic, complemented
220	#533	Dic₅	1	1	yes	characteristic, complemented
221	#533	C₂×D₅	1	1	yes	characteristic
222	#532	Dic₅	1	1	yes	characteristic, complemented
223	#532	Dic₅	1	1	yes	characteristic, complemented
224	#532	C₂×D₅	1	1	yes	characteristic
225	#529	—	2	1	no	—
226	#529	—	2	1	no	—
227	#529	—	2	1	no	—
228	#529	—	2	1	no	—
229	#529	Dic₅	1	2	yes	complemented
230	#529	C₂×D₅	1	2	yes	—
231	#525	—	2	1	no	—
232	#525	—	2	1	no	—
233	#525	C₂×D₅	1	2	yes	—
234	C₄×#41	—	2	1	no	—
235	C₄×#41	—	2	1	no	—
236	C₄×#41	Dic₅	1	2	yes	complemented
237	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
238	#432	—	5	2	no	—
239	#432	—	10	1	no	—
240	#431	—	5	2	no	—
241	#431	—	10	1	no	—
242	#423	—	10	1	no	—
243	#407	—	5	2	no	—
244	C₄×M₁₆	—	10	1	no	—
245	#383	—	5	2	no	—
246	#383	—	5	2	no	—
247	#383	—	10	1	no	—
248	#383	—	10	1	no	—
249	C₂×#95	—	5	2	no	—
250	C₂×#95	—	10	1	no	—
251	C₂×#95	—	10	1	no	—
252	#328	—	5	8	no	—
253	#327	—	5	8	no	—
254	C₂³×C₅	—	2	2	no	—
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	2	2	no	—
257	C₂³×C₅	—	2	2	no	—
258	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₅×Q₈	—	4	2	no	—
262	C₅×Q₈	—	4	2	no	—
263	C₅×Q₈	—	4	2	no	—
264	C₅×D₄	—	4	2	no	—
265	C₅×D₄	—	4	2	no	—
266	C₅×D₄	—	4	2	no	—
267	C₅×D₄	—	4	4	no	—
268	C₅×D₄	—	4	4	no	—
269	C₅×D₄	—	4	4	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	4	1	no	—
280	C₂×C₄×C₅	—	4	1	no	—
281	C₂×C₄×C₅	—	4	1	no	—
282	C₂×C₄×C₅	—	4	1	no	—
283	C₂×C₄×C₅	—	4	1	no	—
284	C₂×C₄×C₅	—	4	1	no	—
285	C₂×C₄×C₅	—	4	1	no	—
286	C₂×C₄×C₅	—	4	1	no	—
287	C₂×C₄×C₅	—	4	1	no	—
288	C₂×C₄×C₅	—	4	1	no	—
289	C₂×C₄×C₅	—	4	1	no	—
290	C₂×C₄×C₅	—	4	1	no	—
291	C₂×C₄×C₅	—	4	4	no	—
292	C₂×C₄×C₅	—	4	4	no	—
293	C₂×C₄×C₅	—	4	4	no	—
294	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
306	C₂×Dic₅	—	4	4	no	—
307	C₂×Dic₅	—	4	4	no	—
308	C₂×Dic₅	—	4	4	no	—
309	C₂×Dic₅	—	8	8	no	—
310	#168	—	4	4	no	—
311	C₂×#41	—	2	1	no	—
312	C₂×#41	—	2	1	no	—
313	C₂×#41	C₂×Dic₅	1	2	yes	—
314	C₂³×C₄	—	10	2	no	—
315	C₂³×C₄	C₂²⋊D₅	1	1	yes	characteristic
316	C₂³×C₄	C₂²⋊D₅	1	1	yes	characteristic
317	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
318	C₂×M₁₆	—	10	2	no	—
319	C₄⋊Q₈	C₂×Dic₅	1	1	yes	characteristic, complemented
320	C₄⋊Q₈	C₂×Dic₅	1	1	yes	characteristic, complemented
321	C₄⋊Q₈	C₂×Dic₅	1	1	yes	characteristic, complemented
322	#127	C₂×Dic₅	1	1	yes	characteristic, complemented
323	#126	—	2	2	no	—
324	#126	—	2	2	no	—
325	#125	—	2	1	no	—
326	#125	—	2	1	no	—
327	#125	C₂×Dic₅	1	2	yes	complemented
328	#124	—	2	1	no	—
329	#124	—	2	1	no	—
330	#124	C₂×Dic₅	1	2	yes	complemented
331	#123	—	2	2	no	—
332	#123	—	2	2	no	—
333	#123	—	2	2	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	—	2	1	no	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	C₂×Dic₅	1	2	yes	—
339	C₂²⋊Q₈	C₂²×D₅	1	2	yes	—
340	#121	—	2	1	no	—
341	#121	—	2	1	no	—
342	#121	—	2	1	no	—
343	#121	—	2	1	no	—
344	#121	C₂×Dic₅	1	2	yes	—
345	#121	C₂²×D₅	1	2	yes	—
346	#120	—	2	2	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	C₂×Dic₅	1	2	yes	complemented
352	C₄×Q₈	C₂×Dic₅	1	2	yes	complemented
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	C₂×Dic₅	1	2	yes	complemented
364	C₄×D₄	C₂×Dic₅	1	2	yes	complemented
365	#117	—	2	1	no	—
366	#117	—	2	1	no	—
367	#117	—	2	2	no	—
368	#117	—	2	2	no	—
369	#117	—	2	2	no	—
370	#117	C₂×Dic₅	1	2	yes	—
371	C₂×C₄²	—	2	2	no	—
372	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
373	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
374	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
375	C₂×C₄²	C₂×Dic₅	1	1	yes	characteristic
376	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
377	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
378	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
379	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
380	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
381	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
382	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
383	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
384	C₄⋊C₈	—	10	2	no	—
385	C₄⋊C₈	—	10	2	no	—
386	C₂²⋊C₈	—	5	4	no	—
387	C₂²⋊C₈	—	10	2	no	—
388	#97	—	10	2	no	—
389	C₄×C₈	—	10	2	no	—
390	#95	—	5	4	no	—
391	#95	—	10	2	no	—
392	#95	—	10	2	no	—
393	#95	—	10	2	no	—
394	#95	—	10	2	no	—
395	#95	—	10	2	no	—
396	C₂²×C₅	—	2	8	no	—
397	C₂²×C₅	—	2	1	no	—
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	4	2	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	4	2	no	—
406	C₂²×C₅	#410	1	2	yes	—
407	C₂²×C₅	#421	1	2	yes	—
408	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
409	C₂²×C₅	#575	1	2	yes	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	2	1	no	—
412	C₄×C₅	—	2	1	no	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	1	no	—
421	C₄×C₅	—	2	1	no	—
422	C₄×C₅	—	4	2	no	—
423	C₄×C₅	—	4	2	no	—
424	C₄×C₅	—	4	2	no	—
425	Dic₅	—	8	4	no	—
426	C₂⁴	C₂×C₂²⋊D₅	1	1	yes	characteristic
427	#41	—	4	4	no	—
428	#41	—	4	4	no	—
429	#41	—	4	4	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	C₂²×Dic₅	1	2	yes	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	C₂²×Dic₅	1	2	yes	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	10	4	no	—
446	C₂²×C₄	—	20	4	no	—
447	C₂²×C₄	—	20	4	no	—
448	C₂²×C₄	—	20	4	no	—
449	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
450	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
451	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
452	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
453	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
454	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
455	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
456	C₂²×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
457	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
458	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
466	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
467	M₁₆	—	20	4	no	—
468	C₂×C₈	—	10	4	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	C₂²×Dic₅	1	2	yes	—
480	C₄⋊C₄	C₂²×Dic₅	1	2	yes	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
494	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
495	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
496	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
497	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
498	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
499	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
500	C₄²	C₂²⋊Dic₅	1	1	yes	characteristic
501	C₄²	C₂²×Dic₅	1	1	yes	characteristic
502	C₄²	C₂²×Dic₅	1	1	yes	characteristic
503	C₄²	C₂²×Dic₅	1	1	yes	characteristic
504	C₄²	C₂²×Dic₅	1	1	yes	characteristic
505	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
506	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
507	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
508	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
509	C₂×C₅	—	2	2	no	—
510	C₂×C₅	—	2	2	no	—
511	C₂×C₅	—	2	2	no	—
512	C₂×C₅	—	8	2	no	—
513	C₂×C₅	C₂×#410	1	1	yes	characteristic
514	C₂×C₅	#2896	1	1	yes	characteristic
515	C₂×C₅	C₂×#421	1	1	yes	characteristic
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
521	C₂³	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
522	C₂³	C₂²×C₂²⋊D₅	1	1	yes	characteristic
523	Q₈	—	4	2	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	4	no	—
530	D₄	—	4	4	no	—
531	D₄	—	4	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	20	4	no	—
557	C₂×C₄	—	20	4	no	—
558	C₂×C₄	—	20	4	no	—
559	C₂×C₄	—	40	8	no	—
560	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
561	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
562	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
563	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
564	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
565	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
566	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
567	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
568	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
569	C₂×C₄	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
570	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
571	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
572	C₈	—	20	4	no	—
573	C₅	#17593	1	1	yes	characteristic, complemented, Sylow
574	C₂²	—	2	8	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	#65525	1	2	yes	—
585	C₂²	#65529	1	2	yes	—
586	C₂²	#66156	1	2	yes	—
587	C₂²	C₂²×C₂²⋊Dic₅	1	1	yes	characteristic
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	40	4	no	—
604	C₂	—	2	2	no	—
605	C₂	—	2	2	no	—
606	C₂	—	2	2	no	—
607	C₂	—	8	2	no	—
608	C₂	#10615803	1	1	yes	characteristic
609	C₂	C₂×#65525	1	1	yes	characteristic
610	C₂	C₂×#65529	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting, prime radical	C₅×#3444	C₂
socle	C₂²×C₅	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#3444	D₅
hypocenter	C₅	#17593
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
2. C₂×#65226	C₂	semidirect
3. #10613780	C₂	semidirect
4. #10602630	C₂	semidirect
5. #10602606	C₂	semidirect
6. #10602550	C₂	semidirect
7. #10602501	C₂	semidirect
8. C₅×#533	C₄	semidirect
9. C₅×#533	C₄	semidirect
11. C₅×#532	C₄	semidirect
12. C₅×#532	C₄	semidirect
18. C₅×#529	C₄	semidirect
25. C₄×C₅×#41	C₄	semidirect
51. C₅×C₄⋊Q₈	C₂×C₄	semidirect
52. C₅×C₄⋊Q₈	C₂×C₄	semidirect
53. C₅×C₄⋊Q₈	C₂×C₄	semidirect
54. C₅×#127	C₂×C₄	semidirect
59. C₅×#125	C₂×C₄	semidirect
62. C₅×#124	C₂×C₄	semidirect
83. C₄×C₅×Q₈	C₂×C₄	semidirect
84. C₄×C₅×Q₈	C₂×C₄	semidirect
95. C₄×C₅×D₄	C₂×C₄	semidirect
96. C₄×C₅×D₄	C₂×C₄	semidirect
219. #533	Dic₅	semidirect
220. #533	Dic₅	semidirect
222. #532	Dic₅	semidirect
223. #532	Dic₅	semidirect
229. #529	Dic₅	semidirect
236. C₄×#41	Dic₅	semidirect
319. C₄⋊Q₈	C₂×Dic₅	semidirect
320. C₄⋊Q₈	C₂×Dic₅	semidirect
321. C₄⋊Q₈	C₂×Dic₅	semidirect
322. #127	C₂×Dic₅	semidirect
327. #125	C₂×Dic₅	semidirect
330. #124	C₂×Dic₅	semidirect
351. C₄×Q₈	C₂×Dic₅	semidirect
352. C₄×Q₈	C₂×Dic₅	semidirect
363. C₄×D₄	C₂×Dic₅	semidirect
364. C₄×D₄	C₂×Dic₅	semidirect
573. C₅	#17593	semidirect

Maximal subgroups

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

subgroup	index
C₅×#3444	2
C₂×#65226	2
#10613780	2
#10602630	2
#10602606	2
#10602550	2
#10602501	2
#17593	5