Subgroups — C₅×#22235 #11944955

Order 1280.

686 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3135	C₂	1	1	yes	maximal, characteristic
2	C₅×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2931	C₂	1	1	yes	maximal, characteristic
4	C₅×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1963	C₂	1	1	yes	maximal, characteristic
6	C₅×#1929	C₂	1	4	yes	maximal, complemented
7	C₅×#1866	C₂	1	4	yes	maximal, complemented
8	C₅×#1849	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1746	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#131	C₂²	1	2	yes	—
11	C₅×#533	C₂²	1	1	yes	characteristic
12	C₅×#532	C₂²	1	1	yes	characteristic
13	C₅×#491	C₄	1	2	yes	complemented
14	C₅×#490	C₄	1	2	yes	complemented
15	C₅×#489	C₄	1	2	yes	complemented
16	C₅×#489	C₄	1	2	yes	complemented
17	C₅×#446	—	2	1	no	—
18	C₅×#446	—	2	1	no	—
19	C₅×C₈×Q₈	—	2	1	no	—
20	C₅×C₈×Q₈	—	2	1	no	—
21	C₅×#436	—	2	1	no	—
22	C₅×#436	—	2	1	no	—
23	C₅×C₈×D₄	—	2	1	no	—
24	C₅×C₈×D₄	—	2	1	no	—
25	C₂×C₅×#108	C₂²	1	4	yes	—
26	C₅×#424	C₂²	1	2	yes	—
27	C₅×#423	C₂²	1	1	yes	characteristic
28	C₅×#423	C₂²	1	1	yes	characteristic
29	C₂×C₅×#104	C₂²	1	4	yes	—
30	C₅×#416	C₂²	1	4	yes	—
31	C₅×#408	C₂²	1	2	yes	—
32	C₅×#405	C₂²	1	2	yes	—
33	C₂×C₅×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×#376	C₂²	1	1	yes	characteristic
36	C₅×#339	C₂²	1	4	yes	—
37	C₅×#336	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	#22235	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×C₅×#41	C₂³	1	2	yes	—
41	C₅×#131	—	4	4	no	—
42	C₂×C₅×M₁₆	—	2	2	no	—
43	C₂×C₅×M₁₆	C₂³	1	2	yes	—
44	C₂×C₅×M₁₆	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	—	2	2	no	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₅×#127	C₂×C₄	1	1	yes	characteristic
53	C₅×#125	C₂×C₄	1	2	yes	—
54	C₅×#124	C₂×C₄	1	2	yes	—
55	C₅×C₂²⋊Q₈	—	2	1	no	—
56	C₅×C₂²⋊Q₈	—	2	1	no	—
57	C₅×#121	—	2	1	no	—
58	C₅×#121	—	2	1	no	—
59	C₄×C₅×Q₈	—	2	1	no	—
60	C₄×C₅×Q₈	—	2	1	no	—
61	C₄×C₅×D₄	—	2	1	no	—
62	C₄×C₅×D₄	—	2	1	no	—
63	C₅×#117	C₂³	1	2	yes	—
64	C₂×C₄²×C₅	C₂³	1	2	yes	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₅×#108	—	4	4	no	—
67	C₅×C₄⋊C₈	—	2	2	no	—
68	C₅×C₄⋊C₈	—	2	2	no	—
69	C₅×C₄⋊C₈	—	2	1	no	—
70	C₅×C₄⋊C₈	—	2	1	no	—
71	C₅×C₄⋊C₈	—	2	1	no	—
72	C₅×C₄⋊C₈	—	2	1	no	—
73	C₅×#104	—	4	4	no	—
74	C₅×#103	C₂×C₄	1	4	yes	—
75	C₅×#103	C₂×C₄	1	4	yes	—
76	C₅×#102	C₂×C₄	1	4	yes	—
77	C₅×#102	C₂×C₄	1	4	yes	—
78	C₅×C₂²⋊C₈	—	2	2	no	—
79	C₅×C₂²⋊C₈	—	2	2	no	—
80	C₅×#97	—	2	2	no	—
81	C₅×#97	C₂×C₄	1	2	yes	—
82	C₅×#97	C₂×C₄	1	2	yes	—
83	C₄×C₅×C₈	—	2	2	no	—
84	C₄×C₅×C₈	D₄	1	1	yes	characteristic
85	C₄×C₅×C₈	D₄	1	1	yes	characteristic
86	C₄×C₅×C₈	D₄	1	1	yes	characteristic
87	C₄×C₅×C₈	D₄	1	1	yes	characteristic
88	C₅×#95	—	2	1	no	—
89	C₅×#95	—	2	1	no	—
90	#3135	C₂×C₅	1	1	yes	characteristic
91	#2960	C₂×C₅	1	1	yes	characteristic, complemented
92	#2931	C₂×C₅	1	1	yes	characteristic
93	#1995	C₂×C₅	1	1	yes	characteristic, complemented
94	#1963	C₂×C₅	1	1	yes	characteristic
95	#1929	C₂×C₅	1	4	yes	complemented
96	#1866	C₂×C₅	1	4	yes	complemented
97	#1849	C₂×C₅	1	1	yes	characteristic, complemented
98	#1746	C₂×C₅	1	1	yes	characteristic, complemented
99	C₅×#41	—	2	4	no	—
100	C₅×#41	—	2	4	no	—
101	C₂×C₅×Q₈	—	2	1	no	—
102	C₂×C₅×Q₈	—	2	1	no	—
103	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	—	2	1	no	—
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	#41	1	1	yes	characteristic
111	C₂²×C₄×C₅	#41	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
113	C₅×M₁₆	—	2	4	no	—
114	C₅×M₁₆	—	2	4	no	—
115	C₅×M₁₆	—	4	4	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	4	4	no	—
123	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
124	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
126	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
128	C₅×C₄⋊C₄	—	2	1	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
135	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
136	C₅×C₂²⋊C₄	—	2	2	no	—
137	C₅×C₂²⋊C₄	—	2	2	no	—
138	C₅×C₂²⋊C₄	—	2	2	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×#131	C₂²×C₅	1	2	yes	—
147	#533	C₂²×C₅	1	1	yes	characteristic
148	#532	C₂²×C₅	1	1	yes	characteristic
149	#491	C₄×C₅	1	2	yes	complemented
150	#490	C₄×C₅	1	2	yes	complemented
151	#489	C₄×C₅	1	2	yes	complemented
152	#489	C₄×C₅	1	2	yes	complemented
153	#446	—	2	1	no	—
154	#446	—	2	1	no	—
155	C₈×Q₈	—	2	1	no	—
156	C₈×Q₈	—	2	1	no	—
157	#436	—	2	1	no	—
158	#436	—	2	1	no	—
159	C₈×D₄	—	2	1	no	—
160	C₈×D₄	—	2	1	no	—
161	C₂×#108	C₂²×C₅	1	4	yes	—
162	#424	C₂²×C₅	1	2	yes	—
163	#423	C₂²×C₅	1	1	yes	characteristic
164	#423	C₂²×C₅	1	1	yes	characteristic
165	C₂×#104	C₂²×C₅	1	4	yes	—
166	#416	C₂²×C₅	1	4	yes	—
167	#408	C₂²×C₅	1	2	yes	—
168	#405	C₂²×C₅	1	2	yes	—
169	C₂×#97	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
171	#376	C₂²×C₅	1	1	yes	characteristic
172	#339	C₂²×C₅	1	4	yes	—
173	#336	C₂²×C₅	1	2	yes	—
174	#336	C₂²×C₅	1	2	yes	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	C₂×#41	1	1	yes	characteristic
177	C₅×Q₈	—	2	4	no	—
178	C₅×Q₈	—	4	2	no	—
179	C₅×Q₈	—	4	2	no	—
180	C₅×D₄	—	2	4	no	—
181	C₅×D₄	—	4	2	no	—
182	C₅×D₄	—	4	2	no	—
183	C₅×D₄	—	4	4	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	4	1	no	—
188	C₂×C₄×C₅	—	4	1	no	—
189	C₂×C₄×C₅	—	4	2	no	—
190	C₂×C₄×C₅	—	4	2	no	—
191	C₂×C₄×C₅	—	4	2	no	—
192	C₂×C₄×C₅	—	4	2	no	—
193	C₂×C₄×C₅	—	4	2	no	—
194	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
201	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
202	C₅×C₈	—	2	4	no	—
203	C₅×C₈	—	2	1	no	—
204	C₅×C₈	—	2	1	no	—
205	C₅×C₈	—	2	1	no	—
206	C₅×C₈	—	2	1	no	—
207	C₅×C₈	—	4	2	no	—
208	C₅×C₈	—	4	2	no	—
209	C₂×#41	C₂³×C₅	1	2	yes	—
210	#131	—	4	4	no	—
211	C₂×M₁₆	—	2	2	no	—
212	C₂×M₁₆	C₂³×C₅	1	2	yes	—
213	C₂×M₁₆	C₂³×C₅	1	2	yes	—
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	C₂³×C₅	1	2	yes	—
216	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
218	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
219	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
220	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
221	#127	C₂×C₄×C₅	1	1	yes	characteristic
222	#125	C₂×C₄×C₅	1	2	yes	—
223	#124	C₂×C₄×C₅	1	2	yes	—
224	C₂²⋊Q₈	—	2	1	no	—
225	C₂²⋊Q₈	—	2	1	no	—
226	#121	—	2	1	no	—
227	#121	—	2	1	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	#117	C₂³×C₅	1	2	yes	—
233	C₂×C₄²	C₂³×C₅	1	2	yes	—
234	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
235	#108	—	4	4	no	—
236	C₄⋊C₈	—	2	2	no	—
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	1	no	—
239	C₄⋊C₈	—	2	1	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	—	2	1	no	—
242	#104	—	4	4	no	—
243	#103	C₂×C₄×C₅	1	4	yes	—
244	#103	C₂×C₄×C₅	1	4	yes	—
245	#102	C₂×C₄×C₅	1	4	yes	—
246	#102	C₂×C₄×C₅	1	4	yes	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	2	2	no	—
249	#97	—	2	2	no	—
250	#97	C₂×C₄×C₅	1	2	yes	—
251	#97	C₂×C₄×C₅	1	2	yes	—
252	C₄×C₈	—	2	2	no	—
253	C₄×C₈	C₅×D₄	1	1	yes	characteristic
254	C₄×C₈	C₅×D₄	1	1	yes	characteristic
255	C₄×C₈	C₅×D₄	1	1	yes	characteristic
256	C₄×C₈	C₅×D₄	1	1	yes	characteristic
257	#95	—	2	1	no	—
258	#95	—	2	1	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	2	1	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	4	2	no	—
263	C₂²×C₅	—	4	2	no	—
264	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
265	C₂²×C₅	#542	1	2	yes	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	—	4	2	no	—
271	C₄×C₅	—	4	2	no	—
272	C₄×C₅	—	4	2	no	—
273	C₄×C₅	—	8	2	no	—
274	C₄×C₅	#520	1	2	yes	—
275	C₄×C₅	#535	1	1	yes	characteristic
276	C₄×C₅	#536	1	1	yes	characteristic
277	#41	—	2	4	no	—
278	#41	—	2	4	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	C₅×#41	1	1	yes	characteristic
289	C₂²×C₄	C₅×#41	1	1	yes	characteristic
290	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
291	M₁₆	—	2	4	no	—
292	M₁₆	—	2	4	no	—
293	M₁₆	—	4	4	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
302	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
313	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
321	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
322	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
323	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	—	8	2	no	—
326	C₂×C₅	#2326	1	1	yes	characteristic
327	C₂×C₅	#2955	1	1	yes	characteristic
328	C₂×C₅	#2955	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	C₂×C₅×#41	1	1	yes	characteristic
331	Q₈	—	2	4	no	—
332	Q₈	—	4	2	no	—
333	Q₈	—	4	2	no	—
334	D₄	—	2	4	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
349	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
350	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
351	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
352	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
354	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
355	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
356	C₈	—	2	4	no	—
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	4	2	no	—
362	C₈	—	4	2	no	—
363	C₅	#22235	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
370	C₂²	C₅×#542	1	2	yes	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	C₅×#520	1	2	yes	—
380	C₄	C₅×#535	1	1	yes	characteristic
381	C₄	C₅×#536	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	8	2	no	—
384	C₂	C₅×#2326	1	1	yes	characteristic
385	C₂	C₅×#2955	1	1	yes	characteristic
386	C₂	C₅×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2960	C₂	semidirect
4. C₅×#1995	C₂	semidirect
6. C₅×#1929	C₂	semidirect
7. C₅×#1866	C₂	semidirect
8. C₅×#1849	C₂	semidirect
9. C₅×#1746	C₂	semidirect
13. C₅×#491	C₄	semidirect
14. C₅×#490	C₄	semidirect
15. C₅×#489	C₄	semidirect
16. C₅×#489	C₄	semidirect
39. #22235	C₅	direct (N × H)
91. #2960	C₂×C₅	semidirect
93. #1995	C₂×C₅	semidirect
95. #1929	C₂×C₅	semidirect
96. #1866	C₂×C₅	semidirect
97. #1849	C₂×C₅	semidirect
98. #1746	C₂×C₅	semidirect
149. #491	C₄×C₅	semidirect
150. #490	C₄×C₅	semidirect
151. #489	C₄×C₅	semidirect
152. #489	C₄×C₅	semidirect
363. C₅	#22235	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×#3135	2
C₅×#2960	2
C₅×#2931	2
C₅×#1995	2
C₅×#1963	2
C₅×#1929	2
C₅×#1866	2
C₅×#1849	2
C₅×#1746	2
#22235	5

Subgroups — C5×#22235 #11944955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22235 #11944955