Subgroups — C₅×#60612 #11983332

Order 1280.

2050 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3449	C₂	1	1	yes	maximal, characteristic
3	C₅×#3137	C₂	1	8	yes	maximal, complemented
4	C₅×#3136	C₂	1	8	yes	maximal, complemented
5	C₅×#3135	C₂	1	4	yes	maximal, complemented
6	C₅×#3131	C₂	1	4	yes	maximal, complemented
7	C₅×#2896	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#416	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×#544	—	2	2	no	—
14	C₅×#544	C₂²	1	8	yes	complemented
15	C₅×#543	—	2	2	no	—
16	C₅×#537	—	2	2	no	—
17	C₅×#536	C₂²	1	4	yes	—
18	C₅×#535	C₂²	1	4	yes	—
19	C₅×#534	—	2	2	no	—
20	C₅×#533	—	2	4	no	—
21	C₅×#533	C₂²	1	4	yes	complemented
22	C₅×#532	C₂²	1	4	yes	—
23	C₅×#525	—	2	4	no	—
24	C₂×C₅×#117	C₂²	1	2	yes	—
25	C₂×C₅×#117	C₂²	1	1	yes	characteristic
26	C₅×#491	C₂²	1	8	yes	complemented
27	C₅×#490	C₂²	1	8	yes	complemented
28	C₅×#489	C₂²	1	16	yes	complemented
29	C₅×#488	C₂²	1	16	yes	complemented
30	C₅×#487	C₂²	1	8	yes	complemented
31	C₅×#486	C₂²	1	8	yes	complemented
32	C₅×#419	C₂²	1	4	yes	complemented
33	C₅×#418	C₂²	1	4	yes	complemented
34	C₅×#417	C₂²	1	8	yes	—
35	C₅×#416	C₂²	1	8	yes	—
36	C₅×#416	C₂²	1	4	yes	complemented
37	C₅×#416	C₂²	1	8	yes	complemented
38	C₅×#416	C₂²	1	4	yes	complemented
39	C₂×C₅×#103	C₂²	1	4	yes	complemented
40	C₂×C₅×#102	C₂²	1	4	yes	complemented
41	C₅×#405	C₂²	1	8	yes	complemented
42	C₂×C₅×#97	C₂²	1	2	yes	complemented
43	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
44	#60612	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×C₅×#41	—	2	2	no	—
46	C₂×C₅×#41	—	2	2	no	—
47	C₂×C₅×#41	—	2	8	no	—
48	C₂×C₅×#41	—	2	8	no	—
49	C₂×C₅×#41	C₂³	1	4	yes	—
50	C₂×C₅×#41	C₂³	1	4	yes	—
51	C₂²×C₅×Q₈	C₂³	1	2	yes	—
52	C₂²×C₅×D₄	—	2	2	no	—
53	C₂²×C₅×D₄	C₂³	1	2	yes	—
54	C₂³×C₄×C₅	—	2	2	no	—
55	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₅×M₁₆	—	2	4	no	—
57	C₂×C₅×M₁₆	C₂³	1	4	yes	—
58	C₂²×C₅×C₈	—	2	4	no	—
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂³	1	2	yes	—
61	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	4	yes	—
63	C₅×C₄⋊Q₈	—	2	8	no	—
64	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
65	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
66	C₅×#127	C₂³	1	4	yes	—
67	C₅×#125	—	2	8	no	—
68	C₅×#125	C₂³	1	8	yes	—
69	C₅×#124	C₂³	1	8	yes	—
70	C₅×#123	—	2	8	no	—
71	C₅×C₂²⋊Q₈	—	2	8	no	—
72	C₅×C₂²⋊Q₈	—	2	8	no	—
73	C₅×C₂²⋊Q₈	—	2	16	no	—
74	C₅×#121	—	2	8	no	—
75	C₅×#121	—	2	8	no	—
76	C₅×#120	—	2	8	no	—
77	C₄×C₅×Q₈	—	2	8	no	—
78	C₄×C₅×D₄	—	2	8	no	—
79	C₅×#117	—	2	2	no	—
80	C₅×#117	—	2	2	no	—
81	C₅×#117	D₄	1	4	yes	—
82	C₅×#117	C₂³	1	4	yes	—
83	C₅×#117	C₂³	1	4	yes	—
84	C₅×#117	C₂³	1	4	yes	—
85	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
86	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
89	C₂×C₄²×C₅	—	2	2	no	—
90	C₂×C₄²×C₅	C₂³	1	2	yes	—
91	C₅×#103	C₂³	1	8	yes	—
92	C₅×#103	C₂³	1	8	yes	—
93	C₅×#103	C₂³	1	16	yes	—
94	C₅×#102	C₂³	1	8	yes	—
95	C₅×#102	C₂³	1	8	yes	—
96	C₅×#102	C₂³	1	16	yes	—
97	C₅×#97	C₂³	1	8	yes	—
98	C₄×C₅×C₈	C₂³	1	8	yes	—
99	#3458	C₂×C₅	1	1	yes	characteristic, complemented
100	#3449	C₂×C₅	1	1	yes	characteristic
101	#3137	C₂×C₅	1	8	yes	complemented
102	#3136	C₂×C₅	1	8	yes	complemented
103	#3135	C₂×C₅	1	4	yes	complemented
104	#3131	C₂×C₅	1	4	yes	complemented
105	#2896	C₂×C₅	1	2	yes	complemented
106	C₂×#416	C₂×C₅	1	2	yes	complemented
107	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂⁴×C₅	—	2	2	no	—
109	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
110	C₅×#41	—	2	8	no	—
111	C₅×#41	—	2	8	no	—
112	C₅×#41	—	2	8	no	—
113	C₅×#41	—	2	8	no	—
114	C₅×#41	—	4	8	no	—
115	C₅×#41	—	4	8	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	—	2	8	no	—
118	C₂×C₅×Q₈	—	2	4	no	—
119	C₂×C₅×Q₈	—	2	4	no	—
120	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
121	C₂×C₅×D₄	—	2	4	no	—
122	C₂×C₅×D₄	—	2	4	no	—
123	C₂×C₅×D₄	—	2	2	no	—
124	C₂×C₅×D₄	—	2	8	no	—
125	C₂×C₅×D₄	—	2	4	no	—
126	C₂×C₅×D₄	—	2	4	no	—
127	C₂×C₅×D₄	—	4	8	no	—
128	C₂×C₅×D₄	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	4	no	—
131	C₂²×C₄×C₅	—	2	4	no	—
132	C₂²×C₄×C₅	—	2	4	no	—
133	C₂²×C₄×C₅	—	4	8	no	—
134	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₅	#41	1	4	yes	—
138	C₂²×C₄×C₅	#41	1	4	yes	—
139	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₅×M₁₆	—	2	8	no	—
142	C₂×C₅×C₈	—	2	8	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	4	no	—
146	C₂×C₅×C₈	C₂⁴	1	2	yes	—
147	C₂×C₅×C₈	C₂⁴	1	2	yes	—
148	C₂×C₅×C₈	C₂⁴	1	4	yes	—
149	C₅×C₄⋊C₄	—	2	4	no	—
150	C₅×C₄⋊C₄	—	2	8	no	—
151	C₅×C₄⋊C₄	—	2	8	no	—
152	C₅×C₄⋊C₄	—	2	16	no	—
153	C₅×C₄⋊C₄	C₂×D₄	1	8	yes	—
154	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
155	C₅×C₂²⋊C₄	—	2	4	no	—
156	C₅×C₂²⋊C₄	—	2	4	no	—
157	C₅×C₂²⋊C₄	—	2	16	no	—
158	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
159	C₄²×C₅	—	2	4	no	—
160	C₄²×C₅	—	2	4	no	—
161	C₄²×C₅	C₂×D₄	1	4	yes	—
162	C₄²×C₅	C₂⁴	1	4	yes	—
163	C₂²×#41	C₂²×C₅	1	2	yes	—
164	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
165	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
166	#544	—	2	2	no	—
167	#544	C₂²×C₅	1	8	yes	complemented
168	#543	—	2	2	no	—
169	#537	—	2	2	no	—
170	#536	C₂²×C₅	1	4	yes	—
171	#535	C₂²×C₅	1	4	yes	—
172	#534	—	2	2	no	—
173	#533	—	2	4	no	—
174	#533	C₂²×C₅	1	4	yes	complemented
175	#532	C₂²×C₅	1	4	yes	—
176	#525	—	2	4	no	—
177	C₂×#117	C₂²×C₅	1	2	yes	—
178	C₂×#117	C₂²×C₅	1	1	yes	characteristic
179	#491	C₂²×C₅	1	8	yes	complemented
180	#490	C₂²×C₅	1	8	yes	complemented
181	#489	C₂²×C₅	1	16	yes	complemented
182	#488	C₂²×C₅	1	16	yes	complemented
183	#487	C₂²×C₅	1	8	yes	complemented
184	#486	C₂²×C₅	1	8	yes	complemented
185	#419	C₂²×C₅	1	4	yes	complemented
186	#418	C₂²×C₅	1	4	yes	complemented
187	#417	C₂²×C₅	1	8	yes	—
188	#416	C₂²×C₅	1	8	yes	—
189	#416	C₂²×C₅	1	4	yes	complemented
190	#416	C₂²×C₅	1	8	yes	complemented
191	#416	C₂²×C₅	1	4	yes	complemented
192	C₂×#103	C₂²×C₅	1	4	yes	complemented
193	C₂×#102	C₂²×C₅	1	4	yes	complemented
194	#405	C₂²×C₅	1	8	yes	complemented
195	C₂×#97	C₂²×C₅	1	2	yes	complemented
196	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
197	C₂³×C₅	—	2	4	no	—
198	C₂³×C₅	—	4	2	no	—
199	C₂³×C₅	—	4	4	no	—
200	C₂³×C₅	—	8	4	no	—
201	C₂³×C₅	#124	1	4	yes	—
202	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
203	C₂³×C₅	C₂²×D₄	1	2	yes	—
204	C₅×Q₈	—	2	4	no	—
205	C₅×Q₈	—	2	4	no	—
206	C₅×Q₈	—	4	4	no	—
207	C₅×Q₈	—	8	8	no	—
208	C₅×D₄	—	2	4	no	—
209	C₅×D₄	—	2	4	no	—
210	C₅×D₄	—	4	8	no	—
211	C₅×D₄	—	4	8	no	—
212	C₅×D₄	—	4	4	no	—
213	C₅×D₄	—	8	8	no	—
214	C₂×C₄×C₅	—	2	8	no	—
215	C₂×C₄×C₅	—	2	4	no	—
216	C₂×C₄×C₅	—	4	4	no	—
217	C₂×C₄×C₅	—	4	4	no	—
218	C₂×C₄×C₅	—	4	8	no	—
219	C₂×C₄×C₅	—	4	8	no	—
220	C₂×C₄×C₅	—	8	4	no	—
221	C₂×C₄×C₅	#124	1	8	yes	—
222	C₂×C₄×C₅	#124	1	4	yes	—
223	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
224	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×#41	1	4	yes	—
227	C₂×C₄×C₅	C₂×#41	1	2	yes	—
228	C₂×C₄×C₅	C₂×#41	1	2	yes	—
229	C₂×C₄×C₅	C₂×#41	1	4	yes	—
230	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
231	C₅×C₈	—	2	2	no	—
232	C₅×C₈	—	2	2	no	—
233	C₅×C₈	—	2	4	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	8	no	—
237	C₂×#41	—	2	8	no	—
238	C₂×#41	C₂³×C₅	1	4	yes	—
239	C₂×#41	C₂³×C₅	1	4	yes	—
240	C₂²×Q₈	C₂³×C₅	1	2	yes	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	C₂³×C₅	1	2	yes	—
243	C₂³×C₄	—	2	2	no	—
244	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
245	C₂×M₁₆	—	2	4	no	—
246	C₂×M₁₆	C₂³×C₅	1	4	yes	—
247	C₂²×C₈	—	2	4	no	—
248	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₅	1	4	yes	—
251	C₂²×C₈	C₂³×C₅	1	2	yes	—
252	C₄⋊Q₈	—	2	8	no	—
253	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
254	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
255	#127	C₂³×C₅	1	4	yes	—
256	#125	—	2	8	no	—
257	#125	C₂³×C₅	1	8	yes	—
258	#124	C₂³×C₅	1	8	yes	—
259	#123	—	2	8	no	—
260	C₂²⋊Q₈	—	2	8	no	—
261	C₂²⋊Q₈	—	2	8	no	—
262	C₂²⋊Q₈	—	2	16	no	—
263	#121	—	2	8	no	—
264	#121	—	2	8	no	—
265	#120	—	2	8	no	—
266	C₄×Q₈	—	2	8	no	—
267	C₄×D₄	—	2	8	no	—
268	#117	—	2	2	no	—
269	#117	—	2	2	no	—
270	#117	C₅×D₄	1	4	yes	—
271	#117	C₂³×C₅	1	4	yes	—
272	#117	C₂³×C₅	1	4	yes	—
273	#117	C₂³×C₅	1	4	yes	—
274	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂³×C₅	1	2	yes	—
280	#103	C₂³×C₅	1	8	yes	—
281	#103	C₂³×C₅	1	8	yes	—
282	#103	C₂³×C₅	1	16	yes	—
283	#102	C₂³×C₅	1	8	yes	—
284	#102	C₂³×C₅	1	8	yes	—
285	#102	C₂³×C₅	1	16	yes	—
286	#97	C₂³×C₅	1	8	yes	—
287	C₄×C₈	C₂³×C₅	1	8	yes	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	2	4	no	—
290	C₂²×C₅	—	4	4	no	—
291	C₂²×C₅	—	4	8	no	—
292	C₂²×C₅	—	4	4	no	—
293	C₂²×C₅	—	8	8	no	—
294	C₂²×C₅	C₂×#124	1	4	yes	—
295	C₂²×C₅	C₂×#124	1	2	yes	—
296	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
297	C₄×C₅	—	2	8	no	—
298	C₄×C₅	—	4	8	no	—
299	C₄×C₅	—	4	4	no	—
300	C₄×C₅	C₂×#124	1	2	yes	—
301	C₄×C₅	C₂×#124	1	4	yes	—
302	C₄×C₅	C₂²×#41	1	1	yes	characteristic
303	C₄×C₅	C₂²×#41	1	1	yes	characteristic
304	C₂⁴	—	2	2	no	—
305	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
306	#41	—	2	8	no	—
307	#41	—	2	8	no	—
308	#41	—	2	8	no	—
309	#41	—	2	8	no	—
310	#41	—	4	8	no	—
311	#41	—	4	8	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	8	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	4	8	no	—
324	C₂×D₄	C₂⁴×C₅	1	4	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	4	8	no	—
330	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
331	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
332	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₅×#41	1	4	yes	—
334	C₂²×C₄	C₅×#41	1	4	yes	—
335	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
337	M₁₆	—	2	8	no	—
338	C₂×C₈	—	2	8	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	C₂⁴×C₅	1	2	yes	—
343	C₂×C₈	C₂⁴×C₅	1	4	yes	—
344	C₂×C₈	C₂⁴×C₅	1	2	yes	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	16	no	—
349	C₄⋊C₄	C₂×C₅×D₄	1	8	yes	—
350	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₂²⋊C₄	—	2	16	no	—
354	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
355	C₄²	—	2	4	no	—
356	C₄²	—	2	4	no	—
357	C₄²	C₂×C₅×D₄	1	4	yes	—
358	C₄²	C₂⁴×C₅	1	4	yes	—
359	C₂×C₅	—	2	4	no	—
360	C₂×C₅	—	2	2	no	—
361	C₂×C₅	—	8	4	no	—
362	C₂×C₅	C₂²×#124	1	1	yes	characteristic
363	C₂×C₅	#3584	1	2	yes	—
364	C₂³	—	2	4	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	8	4	no	—
368	C₂³	C₅×#124	1	4	yes	—
369	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
370	C₂³	C₂²×C₅×D₄	1	2	yes	—
371	Q₈	—	2	4	no	—
372	Q₈	—	2	4	no	—
373	Q₈	—	4	4	no	—
374	Q₈	—	8	8	no	—
375	D₄	—	2	4	no	—
376	D₄	—	2	4	no	—
377	D₄	—	4	8	no	—
378	D₄	—	4	8	no	—
379	D₄	—	4	4	no	—
380	D₄	—	8	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	8	4	no	—
388	C₂×C₄	C₅×#124	1	8	yes	—
389	C₂×C₄	C₅×#124	1	4	yes	—
390	C₂×C₄	C₂²×C₅×D₄	1	8	yes	—
391	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
393	C₂×C₄	C₂×C₅×#41	1	4	yes	—
394	C₂×C₄	C₂×C₅×#41	1	2	yes	—
395	C₂×C₄	C₂×C₅×#41	1	2	yes	—
396	C₂×C₄	C₂×C₅×#41	1	4	yes	—
397	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	—	2	4	no	—
401	C₅	#60612	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	2	2	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	8	no	—
407	C₂²	—	8	8	no	—
408	C₂²	C₂×C₅×#124	1	4	yes	—
409	C₂²	C₂×C₅×#124	1	2	yes	—
410	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
411	C₄	—	2	8	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	8	no	—
414	C₄	C₂×C₅×#124	1	2	yes	—
415	C₄	C₂×C₅×#124	1	4	yes	—
416	C₄	C₂²×C₅×#41	1	1	yes	characteristic
417	C₄	C₂²×C₅×#41	1	1	yes	characteristic
418	C₂	—	2	4	no	—
419	C₂	—	2	2	no	—
420	C₂	—	8	4	no	—
421	C₂	C₂²×C₅×#124	1	1	yes	characteristic
422	C₂	C₅×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂³×D₄
prime radical	C₅×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3458	C₂	semidirect
3. C₅×#3137	C₂	semidirect
4. C₅×#3136	C₂	semidirect
5. C₅×#3135	C₂	semidirect
6. C₅×#3131	C₂	semidirect
7. C₅×#2896	C₂	semidirect
8. C₂×C₅×#416	C₂	semidirect
9. C₂×C₅×#405	C₂	semidirect
14. C₅×#544	C₂²	semidirect
21. C₅×#533	C₂²	semidirect
26. C₅×#491	C₂²	semidirect
27. C₅×#490	C₂²	semidirect
28. C₅×#489	C₂²	semidirect
29. C₅×#488	C₂²	semidirect
30. C₅×#487	C₂²	semidirect
31. C₅×#486	C₂²	semidirect
32. C₅×#419	C₂²	semidirect
33. C₅×#418	C₂²	semidirect
36. C₅×#416	C₂²	semidirect
37. C₅×#416	C₂²	semidirect
38. C₅×#416	C₂²	semidirect
39. C₂×C₅×#103	C₂²	semidirect
40. C₂×C₅×#102	C₂²	semidirect
41. C₅×#405	C₂²	semidirect
42. C₂×C₅×#97	C₂²	semidirect
43. C₂×C₄×C₅×C₈	C₂²	semidirect
44. #60612	C₅	direct (N × H)
99. #3458	C₂×C₅	semidirect
101. #3137	C₂×C₅	semidirect
102. #3136	C₂×C₅	semidirect
103. #3135	C₂×C₅	semidirect
104. #3131	C₂×C₅	semidirect
105. #2896	C₂×C₅	semidirect
106. C₂×#416	C₂×C₅	semidirect
107. C₂×#405	C₂×C₅	semidirect
167. #544	C₂²×C₅	semidirect
174. #533	C₂²×C₅	semidirect
179. #491	C₂²×C₅	semidirect
180. #490	C₂²×C₅	semidirect
181. #489	C₂²×C₅	semidirect
182. #488	C₂²×C₅	semidirect
183. #487	C₂²×C₅	semidirect
184. #486	C₂²×C₅	semidirect
185. #419	C₂²×C₅	semidirect
186. #418	C₂²×C₅	semidirect
189. #416	C₂²×C₅	semidirect
190. #416	C₂²×C₅	semidirect
191. #416	C₂²×C₅	semidirect
192. C₂×#103	C₂²×C₅	semidirect
193. C₂×#102	C₂²×C₅	semidirect
194. #405	C₂²×C₅	semidirect
195. C₂×#97	C₂²×C₅	semidirect
196. C₂×C₄×C₈	C₂²×C₅	semidirect
401. C₅	#60612	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×#3458	2
C₅×#3449	2
C₅×#3137	2
C₅×#3136	2
C₅×#3135	2
C₅×#3131	2
C₅×#2896	2
C₂×C₅×#416	2
C₂×C₅×#405	2
#60612	5

Subgroups — C5×#60612 #11983332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60612 #11983332