Subgroups — C₅×#19583 #11942303

Order 1280.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3248	C₂	1	1	yes	maximal, characteristic
2	C₅×#3239	C₂	1	1	yes	maximal, characteristic
3	C₅×#3209	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2994	C₂	1	1	yes	maximal, characteristic
5	C₅×#1700	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1690	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1689	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1680	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1679	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1670	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1669	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1573	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1552	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#533	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₅×#529	C₂²	1	1	yes	characteristic
19	C₅×#501	—	2	1	no	—
20	C₅×#494	C₂²	1	1	yes	characteristic
21	C₅×#494	C₂²	1	1	yes	characteristic
22	C₅×#489	—	2	1	no	—
23	C₅×#487	C₂²	1	1	yes	characteristic
24	C₅×#487	C₂²	1	1	yes	characteristic
25	C₅×#484	—	2	1	no	—
26	C₅×#481	—	2	1	no	—
27	C₅×#479	—	2	1	no	—
28	C₅×#475	C₂²	1	1	yes	characteristic
29	C₅×#475	C₂²	1	1	yes	characteristic
30	C₅×#475	C₂²	1	1	yes	characteristic
31	C₅×#474	C₂²	1	1	yes	characteristic
32	C₅×#474	C₂²	1	1	yes	characteristic
33	C₅×#474	C₂²	1	1	yes	characteristic
34	C₅×#467	—	2	1	no	—
35	C₅×#465	—	2	1	no	—
36	C₅×#464	—	2	1	no	—
37	C₅×#462	—	2	1	no	—
38	C₅×#462	—	2	1	no	—
39	C₅×#462	C₂²	1	1	yes	characteristic
40	C₅×#461	C₂²	1	1	yes	characteristic
41	C₅×#451	—	2	1	no	—
42	C₅×#451	—	2	1	no	—
43	C₅×#446	C₂²	1	1	yes	characteristic
44	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
45	C₅×#436	C₂²	1	1	yes	characteristic
46	C₅×#435	—	2	1	no	—
47	C₅×C₈×D₄	—	2	1	no	—
48	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
49	C₅×#433	—	2	1	no	—
50	C₅×#432	C₂²	1	1	yes	characteristic
51	C₅×#431	C₂²	1	1	yes	characteristic
52	C₅×#424	—	2	1	no	—
53	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₅×#335	C₂²	1	1	yes	characteristic
56	C₅×#335	C₂²	1	1	yes	characteristic
57	C₅×#334	C₂²	1	1	yes	characteristic
58	C₅×#334	C₂²	1	1	yes	characteristic
59	C₅×#332	C₂²	1	1	yes	characteristic
60	C₅×#332	C₂²	1	1	yes	characteristic
61	C₅×#332	C₂²	1	1	yes	characteristic
62	C₅×#332	C₂²	1	1	yes	characteristic
63	C₅×#332	C₂²	1	1	yes	characteristic
64	C₅×#332	C₂²	1	1	yes	characteristic
65	C₅×#332	C₂²	1	1	yes	characteristic
66	C₅×#332	C₂²	1	1	yes	characteristic
67	#19583	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂²×C₅×Q₈	—	2	1	no	—
69	C₂×C₅×Q₁₆	—	2	1	no	—
70	C₂×C₅×Q₁₆	—	2	1	no	—
71	C₂×C₅×Q₁₆	—	2	1	no	—
72	C₂×C₅×Q₁₆	—	2	1	no	—
73	C₂×C₅×Q₁₆	—	2	1	no	—
74	C₂×C₅×SD₁₆	—	2	1	no	—
75	C₂×C₅×M₁₆	—	2	1	no	—
76	C₂²×C₅×C₈	—	2	1	no	—
77	C₂²×C₅×C₈	—	2	1	no	—
78	C₂²×C₅×C₈	—	2	1	no	—
79	C₅×C₄⋊Q₈	—	2	1	no	—
80	C₅×C₄⋊Q₈	—	2	1	no	—
81	C₅×C₄⋊Q₈	—	2	1	no	—
82	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₅×#126	—	2	1	no	—
87	C₅×#125	—	2	1	no	—
88	C₅×#125	D₄	1	1	yes	characteristic
89	C₅×#124	D₄	1	1	yes	characteristic
90	C₅×#123	—	2	1	no	—
91	C₅×C₂²⋊Q₈	—	2	1	no	—
92	C₅×C₂²⋊Q₈	—	2	1	no	—
93	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
94	C₅×#121	D₄	1	1	yes	characteristic
95	C₄×C₅×Q₈	—	2	1	no	—
96	C₄×C₅×Q₈	—	2	1	no	—
97	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
98	C₄×C₅×D₄	—	2	1	no	—
99	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
100	C₅×#117	—	2	1	no	—
101	C₅×#117	—	2	1	no	—
102	C₂×C₅×C₄⋊C₄	—	2	1	no	—
103	C₂×C₅×C₄⋊C₄	—	2	1	no	—
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₅×#107	—	2	1	no	—
106	C₅×#107	—	2	1	no	—
107	C₅×#107	—	2	1	no	—
108	C₅×#106	—	2	1	no	—
109	C₅×#106	—	2	1	no	—
110	C₅×#106	—	2	1	no	—
111	C₅×C₄⋊C₈	—	2	1	no	—
112	C₅×C₄⋊C₈	—	2	1	no	—
113	C₅×C₄⋊C₈	—	2	1	no	—
114	C₅×C₄⋊C₈	—	2	1	no	—
115	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
116	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
117	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₅×#103	—	2	1	no	—
124	C₅×#103	—	2	1	no	—
125	C₅×#103	—	2	1	no	—
126	C₅×#103	—	2	1	no	—
127	C₅×#103	—	2	1	no	—
128	C₅×#103	—	2	1	no	—
129	C₅×#103	—	2	1	no	—
130	C₅×#103	—	2	1	no	—
131	C₅×#103	—	2	1	no	—
132	C₅×#102	—	2	1	no	—
133	C₅×#102	—	2	1	no	—
134	C₅×#102	—	2	1	no	—
135	C₅×C₂²⋊C₈	—	2	1	no	—
136	C₅×C₂²⋊C₈	—	2	1	no	—
137	C₅×C₂²⋊C₈	—	2	1	no	—
138	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
139	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
140	C₅×#97	—	2	1	no	—
141	C₅×#97	—	2	1	no	—
142	C₄×C₅×C₈	—	2	1	no	—
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	#3248	C₂×C₅	1	1	yes	characteristic
146	#3239	C₂×C₅	1	1	yes	characteristic
147	#3209	C₂×C₅	1	1	yes	characteristic, complemented
148	#2994	C₂×C₅	1	1	yes	characteristic
149	#1700	C₂×C₅	1	1	yes	characteristic, complemented
150	#1699	C₂×C₅	1	1	yes	characteristic, complemented
151	#1690	C₂×C₅	1	1	yes	characteristic, complemented
152	#1689	C₂×C₅	1	1	yes	characteristic, complemented
153	#1680	C₂×C₅	1	1	yes	characteristic, complemented
154	#1679	C₂×C₅	1	1	yes	characteristic, complemented
155	#1670	C₂×C₅	1	1	yes	characteristic, complemented
156	#1669	C₂×C₅	1	1	yes	characteristic, complemented
157	#1573	C₂×C₅	1	1	yes	characteristic, complemented
158	#1552	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂×#332	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	4	1	no	—
165	C₂×C₅×Q₈	—	8	1	no	—
166	C₂×C₅×Q₈	—	8	1	no	—
167	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	4	1	no	—
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	#41	1	1	yes	characteristic
175	C₅×Q₁₆	—	8	1	no	—
176	C₅×Q₁₆	—	8	1	no	—
177	C₅×Q₁₆	—	8	1	no	—
178	C₅×Q₁₆	—	8	1	no	—
179	C₅×Q₁₆	—	8	1	no	—
180	C₅×SD₁₆	—	8	1	no	—
181	C₅×M₁₆	—	8	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	8	1	no	—
189	C₂×C₅×C₈	—	8	1	no	—
190	C₂×C₅×C₈	—	8	1	no	—
191	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	4	1	no	—
208	C₅×C₄⋊C₄	—	4	1	no	—
209	C₅×C₄⋊C₄	—	4	1	no	—
210	C₅×C₄⋊C₄	—	4	1	no	—
211	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
212	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
213	C₅×C₂²⋊C₄	—	2	1	no	—
214	C₅×C₂²⋊C₄	—	2	1	no	—
215	C₅×C₂²⋊C₄	—	2	1	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₅×C₂²⋊C₄	—	2	1	no	—
218	C₅×C₂²⋊C₄	—	4	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	4	1	no	—
221	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₅	#41	1	1	yes	characteristic
224	C₄²×C₅	C₂⁴	1	1	yes	characteristic
225	#533	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
227	#529	C₂²×C₅	1	1	yes	characteristic
228	#501	—	2	1	no	—
229	#494	C₂²×C₅	1	1	yes	characteristic
230	#494	C₂²×C₅	1	1	yes	characteristic
231	#489	—	2	1	no	—
232	#487	C₂²×C₅	1	1	yes	characteristic
233	#487	C₂²×C₅	1	1	yes	characteristic
234	#484	—	2	1	no	—
235	#481	—	2	1	no	—
236	#479	—	2	1	no	—
237	#475	C₂²×C₅	1	1	yes	characteristic
238	#475	C₂²×C₅	1	1	yes	characteristic
239	#475	C₂²×C₅	1	1	yes	characteristic
240	#474	C₂²×C₅	1	1	yes	characteristic
241	#474	C₂²×C₅	1	1	yes	characteristic
242	#474	C₂²×C₅	1	1	yes	characteristic
243	#467	—	2	1	no	—
244	#465	—	2	1	no	—
245	#464	—	2	1	no	—
246	#462	—	2	1	no	—
247	#462	—	2	1	no	—
248	#462	C₂²×C₅	1	1	yes	characteristic
249	#461	C₂²×C₅	1	1	yes	characteristic
250	#451	—	2	1	no	—
251	#451	—	2	1	no	—
252	#446	C₂²×C₅	1	1	yes	characteristic
253	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
254	#436	C₂²×C₅	1	1	yes	characteristic
255	#435	—	2	1	no	—
256	C₈×D₄	—	2	1	no	—
257	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
258	#433	—	2	1	no	—
259	#432	C₂²×C₅	1	1	yes	characteristic
260	#431	C₂²×C₅	1	1	yes	characteristic
261	#424	—	2	1	no	—
262	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	#335	C₂²×C₅	1	1	yes	characteristic
265	#335	C₂²×C₅	1	1	yes	characteristic
266	#334	C₂²×C₅	1	1	yes	characteristic
267	#334	C₂²×C₅	1	1	yes	characteristic
268	#332	C₂²×C₅	1	1	yes	characteristic
269	#332	C₂²×C₅	1	1	yes	characteristic
270	#332	C₂²×C₅	1	1	yes	characteristic
271	#332	C₂²×C₅	1	1	yes	characteristic
272	#332	C₂²×C₅	1	1	yes	characteristic
273	#332	C₂²×C₅	1	1	yes	characteristic
274	#332	C₂²×C₅	1	1	yes	characteristic
275	#332	C₂²×C₅	1	1	yes	characteristic
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	#121	1	1	yes	characteristic
278	C₅×Q₈	—	2	1	no	—
279	C₅×Q₈	—	2	1	no	—
280	C₅×Q₈	—	4	1	no	—
281	C₅×Q₈	—	4	1	no	—
282	C₅×Q₈	—	4	1	no	—
283	C₅×Q₈	—	4	1	no	—
284	C₅×Q₈	—	4	1	no	—
285	C₅×Q₈	—	4	1	no	—
286	C₅×Q₈	—	4	1	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×Q₈	—	8	2	no	—
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	2	1	no	—
291	C₅×D₄	—	4	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	1	no	—
302	C₂×C₄×C₅	—	4	1	no	—
303	C₂×C₄×C₅	—	4	1	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	—	4	1	no	—
306	C₂×C₄×C₅	—	8	2	no	—
307	C₂×C₄×C₅	#121	1	1	yes	characteristic
308	C₂×C₄×C₅	#121	1	1	yes	characteristic
309	C₂×C₄×C₅	#121	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	—	2	1	no	—
315	C₅×C₈	—	2	1	no	—
316	C₅×C₈	—	2	1	no	—
317	C₅×C₈	—	4	1	no	—
318	C₅×C₈	—	4	1	no	—
319	C₅×C₈	—	4	1	no	—
320	C₅×C₈	—	4	1	no	—
321	C₅×C₈	—	4	1	no	—
322	C₅×C₈	—	4	1	no	—
323	C₂²×Q₈	—	2	1	no	—
324	C₂×Q₁₆	—	2	1	no	—
325	C₂×Q₁₆	—	2	1	no	—
326	C₂×Q₁₆	—	2	1	no	—
327	C₂×Q₁₆	—	2	1	no	—
328	C₂×Q₁₆	—	2	1	no	—
329	C₂×SD₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	—	2	1	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₄⋊Q₈	—	2	1	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
338	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
339	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
340	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
341	#126	—	2	1	no	—
342	#125	—	2	1	no	—
343	#125	C₅×D₄	1	1	yes	characteristic
344	#124	C₅×D₄	1	1	yes	characteristic
345	#123	—	2	1	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
349	#121	C₅×D₄	1	1	yes	characteristic
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
355	#117	—	2	1	no	—
356	#117	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
360	#107	—	2	1	no	—
361	#107	—	2	1	no	—
362	#107	—	2	1	no	—
363	#106	—	2	1	no	—
364	#106	—	2	1	no	—
365	#106	—	2	1	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
371	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
372	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
373	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
374	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
375	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
376	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
377	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
378	#103	—	2	1	no	—
379	#103	—	2	1	no	—
380	#103	—	2	1	no	—
381	#103	—	2	1	no	—
382	#103	—	2	1	no	—
383	#103	—	2	1	no	—
384	#103	—	2	1	no	—
385	#103	—	2	1	no	—
386	#103	—	2	1	no	—
387	#102	—	2	1	no	—
388	#102	—	2	1	no	—
389	#102	—	2	1	no	—
390	C₂²⋊C₈	—	2	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
394	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
395	#97	—	2	1	no	—
396	#97	—	2	1	no	—
397	C₄×C₈	—	2	1	no	—
398	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	4	1	no	—
403	C₂²×C₅	—	4	1	no	—
404	C₂²×C₅	—	4	1	no	—
405	C₂²×C₅	#473	1	2	yes	—
406	C₂²×C₅	C₂×#121	1	1	yes	characteristic
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	1	no	—
413	C₄×C₅	—	4	1	no	—
414	C₄×C₅	—	8	1	no	—
415	C₄×C₅	—	8	1	no	—
416	C₄×C₅	—	8	1	no	—
417	C₄×C₅	—	8	1	no	—
418	C₄×C₅	#576	1	1	yes	characteristic
419	C₄×C₅	#577	1	1	yes	characteristic
420	C₄×C₅	#577	1	1	yes	characteristic
421	C₄×C₅	#578	1	1	yes	characteristic
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	4	1	no	—
427	C₂×Q₈	—	8	1	no	—
428	C₂×Q₈	—	8	1	no	—
429	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	4	1	no	—
434	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
436	C₂²×C₄	C₅×#41	1	1	yes	characteristic
437	Q₁₆	—	8	1	no	—
438	Q₁₆	—	8	1	no	—
439	Q₁₆	—	8	1	no	—
440	Q₁₆	—	8	1	no	—
441	Q₁₆	—	8	1	no	—
442	SD₁₆	—	8	1	no	—
443	M₁₆	—	8	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	8	1	no	—
451	C₂×C₈	—	8	1	no	—
452	C₂×C₈	—	8	1	no	—
453	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
454	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
455	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
456	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
474	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	4	1	no	—
483	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
484	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
485	C₄²	C₅×#41	1	1	yes	characteristic
486	C₄²	C₂⁴×C₅	1	1	yes	characteristic
487	C₂×C₅	—	2	2	no	—
488	C₂×C₅	—	8	1	no	—
489	C₂×C₅	#3045	1	1	yes	characteristic
490	C₂×C₅	#3063	1	1	yes	characteristic
491	C₂×C₅	C₂×#473	1	1	yes	characteristic
492	C₂³	—	2	1	no	—
493	C₂³	C₅×#121	1	1	yes	characteristic
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	8	2	no	—
505	D₄	—	2	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	4	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	C₅×#121	1	1	yes	characteristic
524	C₂×C₄	C₅×#121	1	1	yes	characteristic
525	C₂×C₄	C₅×#121	1	1	yes	characteristic
526	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₅	#19583	1	1	yes	characteristic, direct product factor, Sylow
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	C₅×#473	1	2	yes	—
546	C₂²	C₂×C₅×#121	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	C₅×#576	1	1	yes	characteristic
559	C₄	C₅×#577	1	1	yes	characteristic
560	C₄	C₅×#577	1	1	yes	characteristic
561	C₄	C₅×#578	1	1	yes	characteristic
562	C₂	—	2	2	no	—
563	C₂	—	8	1	no	—
564	C₂	C₅×#3045	1	1	yes	characteristic
565	C₂	C₅×#3063	1	1	yes	characteristic
566	C₂	C₂×C₅×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#121	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#3209	C₂	semidirect
5. C₅×#1700	C₂	semidirect
6. C₅×#1699	C₂	semidirect
7. C₅×#1690	C₂	semidirect
8. C₅×#1689	C₂	semidirect
9. C₅×#1680	C₂	semidirect
10. C₅×#1679	C₂	semidirect
11. C₅×#1670	C₂	semidirect
12. C₅×#1669	C₂	semidirect
13. C₅×#1573	C₂	semidirect
14. C₅×#1552	C₂	semidirect
15. C₂×C₅×#332	C₂	semidirect
67. #19583	C₅	direct (N × H)
147. #3209	C₂×C₅	semidirect
149. #1700	C₂×C₅	semidirect
150. #1699	C₂×C₅	semidirect
151. #1690	C₂×C₅	semidirect
152. #1689	C₂×C₅	semidirect
153. #1680	C₂×C₅	semidirect
154. #1679	C₂×C₅	semidirect
155. #1670	C₂×C₅	semidirect
156. #1669	C₂×C₅	semidirect
157. #1573	C₂×C₅	semidirect
158. #1552	C₂×C₅	semidirect
159. C₂×#332	C₂×C₅	semidirect
539. C₅	#19583	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3248	2
C₅×#3239	2
C₅×#3209	2
C₅×#2994	2
C₅×#1700	2
C₅×#1699	2
C₅×#1690	2
C₅×#1689	2
C₅×#1680	2
C₅×#1679	2
C₅×#1670	2
C₅×#1669	2
C₅×#1573	2
C₅×#1552	2
C₂×C₅×#332	2
#19583	5

Subgroups — C5×#19583 #11942303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19583 #11942303