Subgroups — C₅×#68341 #14283910

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5680	C₂	1	1	yes	maximal, characteristic
2	C₅×#4707	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#329	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4540	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4465	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4465	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1524	—	3	1	no	maximal, Hall
9	C₃×C₅×#124	C₂²	1	1	yes	characteristic
10	C₅×#946	C₄	1	1	yes	characteristic
11	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic
12	C₅×#938	C₄	1	1	yes	characteristic
13	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic
14	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
15	C₂×C₅×D₃×C₈	—	2	1	no	—
16	C₅×#883	—	2	1	no	—
17	C₅×#67⋊C₄	—	2	1	no	—
18	C₅×#879	—	2	1	no	—
19	C₅×#877	—	2	1	no	—
20	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₅×#870	C₂²	1	1	yes	characteristic
22	C₃×C₅×#97	C₂²	1	1	yes	characteristic
23	C₃×C₅×#97	C₂²	1	1	yes	characteristic
24	C₅×#815	—	2	1	no	—
25	C₅×C₈×Dic₃	—	2	1	no	—
26	C₅×#803	C₂²	1	1	yes	characteristic
27	C₅×#803	C₂²	1	1	yes	characteristic
28	#68341	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#529	—	3	1	no	—
30	C₄×C₅×M₁₆	—	3	1	no	—
31	C₂×C₅×#97	—	3	1	no	—
32	C₅×#330	—	3	1	no	—
33	C₅×#330	—	3	1	no	—
34	C₅×#329	—	3	1	no	—
35	C₅×#329	D₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
38	C₂×C₅×#67	—	2	1	no	—
39	C₂²×C₅×Dic₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
48	C₅×#217	—	2	1	no	—
49	C₅×#217	—	2	1	no	—
50	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
51	C₅×C₄⋊Dic₃	—	2	1	no	—
52	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
53	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
54	C₅×Dic₃⋊C₄	—	2	1	no	—
55	C₅×Dic₃⋊C₄	—	2	1	no	—
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
60	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
64	C₅×D₃×C₈	—	2	4	no	—
65	#5680	C₂×C₅	1	1	yes	characteristic
66	#4707	C₂×C₅	1	1	yes	characteristic, complemented
67	D₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
68	C₃×#329	C₂×C₅	1	1	yes	characteristic, complemented
69	#4540	C₂×C₅	1	1	yes	characteristic, complemented
70	#4465	C₂×C₅	1	1	yes	characteristic, complemented
71	#4465	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×C₅×M₁₆	—	6	1	no	—
73	C₂²×C₅×C₈	—	6	1	no	—
74	C₅×#126	—	6	1	no	—
75	C₅×#125	—	3	1	no	—
76	C₅×#124	C₂×D₃	1	1	yes	characteristic
77	C₅×#123	—	6	1	no	—
78	C₅×C₂²⋊Q₈	—	3	1	no	—
79	C₅×#121	—	3	1	no	—
80	C₄×C₅×Q₈	—	3	1	no	—
81	C₄×C₅×D₄	—	3	1	no	—
82	C₄×C₅×D₄	—	6	1	no	—
83	C₅×#117	—	6	1	no	—
84	C₂×C₄²×C₅	—	3	1	no	—
85	C₅×#97	—	3	1	no	—
86	C₅×#97	—	3	1	no	—
87	C₅×#97	—	6	1	no	—
88	C₅×#97	C₂×D₃	1	1	yes	characteristic
89	C₅×#97	C₂×D₃	1	1	yes	characteristic
90	C₄×C₅×C₈	—	6	1	no	—
91	#1524	—	3	1	no	Sylow
92	C₂³×C₃×C₅	—	2	1	no	—
93	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₃×C₅×Q₈	—	4	1	no	—
95	C₃×C₅×D₄	—	4	1	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₅×#67	—	4	2	no	—
101	C₂×C₅×Dic₃	—	2	1	no	—
102	C₂×C₅×Dic₃	—	2	1	no	—
103	C₂×C₅×Dic₃	—	4	2	no	—
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₄×C₅×D₃	—	2	2	no	—
108	C₄×C₅×D₃	—	2	2	no	—
109	C₄×C₅×D₃	—	4	1	no	—
110	C₃×C₅×C₈	—	2	2	no	—
111	C₃×C₅×C₈	—	2	2	no	—
112	C₅×C₃⋊C₈	—	2	2	no	—
113	C₅×C₃⋊C₈	—	2	2	no	—
114	C₃×#124	C₂²×C₅	1	1	yes	characteristic
115	#946	C₄×C₅	1	1	yes	characteristic
116	Q₈×Dic₃	C₄×C₅	1	1	yes	characteristic
117	#938	C₄×C₅	1	1	yes	characteristic
118	D₄×Dic₃	C₄×C₅	1	1	yes	characteristic
119	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
120	C₂×D₃×C₈	—	2	1	no	—
121	#883	—	2	1	no	—
122	#67⋊C₄	—	2	1	no	—
123	#879	—	2	1	no	—
124	#877	—	2	1	no	—
125	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
126	#870	C₂²×C₅	1	1	yes	characteristic
127	C₃×#97	C₂²×C₅	1	1	yes	characteristic
128	C₃×#97	C₂²×C₅	1	1	yes	characteristic
129	#815	—	2	1	no	—
130	C₈×Dic₃	—	2	1	no	—
131	#803	C₂²×C₅	1	1	yes	characteristic
132	#803	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
134	C₂×C₅×D₄	—	6	1	no	—
135	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	—	3	1	no	—
137	C₂²×C₄×C₅	—	3	1	no	—
138	C₂²×C₄×C₅	—	3	1	no	—
139	C₂²×C₄×C₅	—	6	1	no	—
140	C₅×M₁₆	—	6	4	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	6	4	no	—
144	C₂×C₅×C₈	—	6	1	no	—
145	C₂×C₅×C₈	—	6	1	no	—
146	C₅×C₄⋊C₄	—	3	1	no	—
147	C₅×C₄⋊C₄	—	3	1	no	—
148	C₅×C₄⋊C₄	—	6	1	no	—
149	C₅×C₄⋊C₄	—	6	1	no	—
150	C₅×C₄⋊C₄	—	6	1	no	—
151	C₅×C₄⋊C₄	—	6	1	no	—
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₅×C₂²⋊C₄	—	2	1	no	—
154	C₅×C₂²⋊C₄	—	6	1	no	—
155	C₅×C₂²⋊C₄	—	6	1	no	—
156	C₅×C₂²⋊C₄	—	6	1	no	—
157	C₄²×C₅	—	3	1	no	—
158	C₄²×C₅	—	3	1	no	—
159	C₄²×C₅	—	3	1	no	—
160	C₄²×C₅	—	6	1	no	—
161	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
162	#529	—	3	1	no	—
163	C₄×M₁₆	—	3	1	no	—
164	C₂×#97	—	3	1	no	—
165	#330	—	3	1	no	—
166	#330	—	3	1	no	—
167	#329	—	3	1	no	—
168	#329	C₅×D₃	1	1	yes	characteristic, complemented
169	C₂²×C₃×C₅	—	4	1	no	—
170	C₂²×C₃×C₅	—	4	1	no	—
171	C₂²×C₃×C₅	—	4	1	no	—
172	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₅×D₃	—	2	1	no	—
174	C₂×C₅×D₃	—	2	1	no	—
175	C₂×C₅×D₃	#104	1	2	yes	—
176	C₃×C₄×C₅	—	2	1	no	—
177	C₃×C₄×C₅	—	2	1	no	—
178	C₃×C₄×C₅	—	2	1	no	—
179	C₃×C₄×C₅	—	4	1	no	—
180	C₅×Dic₃	—	2	1	no	—
181	C₅×Dic₃	—	2	1	no	—
182	C₅×Dic₃	—	4	1	no	—
183	C₅×Dic₃	—	4	1	no	—
184	C₅×Dic₃	#104	1	2	yes	—
185	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
186	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
187	C₂×#67	—	2	1	no	—
188	C₂²×Dic₃	—	2	1	no	—
189	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
190	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
191	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	2	1	no	—
194	C₃×C₂²⋊C₄	—	2	1	no	—
195	C₃×C₂²⋊C₄	—	2	1	no	—
196	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
197	#217	—	2	1	no	—
198	#217	—	2	1	no	—
199	(C₂×D₃)⋊C₄	—	2	1	no	—
200	C₄⋊Dic₃	—	2	1	no	—
201	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
202	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
203	Dic₃⋊C₄	—	2	1	no	—
204	Dic₃⋊C₄	—	2	1	no	—
205	Dic₃⋊C₄	—	2	1	no	—
206	C₄×Dic₃	—	2	1	no	—
207	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
208	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
209	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
210	C₂×C₃⋊C₈	—	2	1	no	—
211	C₂×C₃⋊C₈	—	2	1	no	—
212	ΓL(1,𝔽₂₅)	—	2	4	no	—
213	D₃×C₈	—	2	4	no	—
214	C₂³×C₅	—	2	1	no	—
215	C₂³×C₅	—	3	1	no	—
216	C₅×Q₈	—	4	1	no	—
217	C₅×D₄	—	4	1	no	—
218	C₅×D₄	—	12	2	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	3	1	no	—
221	C₂×C₄×C₅	—	3	1	no	—
222	C₂×C₄×C₅	—	3	1	no	—
223	C₂×C₄×C₅	—	6	2	no	—
224	C₂×C₄×C₅	—	6	2	no	—
225	C₂×C₄×C₅	—	6	1	no	—
226	C₂×C₄×C₅	—	6	1	no	—
227	C₂×C₄×C₅	—	12	1	no	—
228	C₂×C₄×C₅	—	12	2	no	—
229	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
232	C₅×C₈	—	2	2	no	—
233	C₅×C₈	—	2	2	no	—
234	C₅×C₈	—	6	2	no	—
235	C₅×C₈	—	6	2	no	—
236	C₂×M₁₆	—	6	1	no	—
237	C₂²×C₈	—	6	1	no	—
238	#126	—	6	1	no	—
239	#125	—	3	1	no	—
240	#124	C₂×C₅×D₃	1	1	yes	characteristic
241	#123	—	6	1	no	—
242	C₂²⋊Q₈	—	3	1	no	—
243	#121	—	3	1	no	—
244	C₄×Q₈	—	3	1	no	—
245	C₄×D₄	—	3	1	no	—
246	C₄×D₄	—	6	1	no	—
247	#117	—	6	1	no	—
248	C₂×C₄²	—	3	1	no	—
249	#97	—	3	1	no	—
250	#97	—	3	1	no	—
251	#97	—	6	1	no	—
252	#97	C₂×C₅×D₃	1	1	yes	characteristic
253	#97	C₂×C₅×D₃	1	1	yes	characteristic
254	C₄×C₈	—	6	1	no	—
255	C₂×C₃×C₅	—	8	1	no	—
256	C₂×C₃×C₅	#413	1	1	yes	characteristic
257	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
258	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
259	C₅×D₃	—	2	2	no	—
260	C₂³×C₃	—	2	1	no	—
261	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
262	C₃×Q₈	—	4	1	no	—
263	C₃×D₄	—	4	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	#67	—	4	2	no	—
269	C₂×Dic₃	—	2	1	no	—
270	C₂×Dic₃	—	2	1	no	—
271	C₂×Dic₃	—	4	2	no	—
272	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
275	C₄×D₃	—	2	2	no	—
276	C₄×D₃	—	2	2	no	—
277	C₄×D₃	—	4	1	no	—
278	C₃×C₈	—	2	2	no	—
279	C₃×C₈	—	2	2	no	—
280	C₃⋊C₈	—	2	2	no	—
281	C₃⋊C₈	—	2	2	no	—
282	C₂²×C₅	—	3	2	no	—
283	C₂²×C₅	—	4	1	no	—
284	C₂²×C₅	—	4	1	no	—
285	C₂²×C₅	—	4	1	no	—
286	C₂²×C₅	—	6	1	no	—
287	C₂²×C₅	—	6	1	no	—
288	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	3	2	no	—
293	C₄×C₅	—	4	1	no	—
294	C₄×C₅	—	6	1	no	—
295	C₄×C₅	—	6	1	no	—
296	C₄×C₅	—	12	1	no	—
297	C₄×C₅	—	12	1	no	—
298	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
299	C₂×D₄	—	6	1	no	—
300	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
301	C₂²×C₄	—	3	1	no	—
302	C₂²×C₄	—	3	1	no	—
303	C₂²×C₄	—	3	1	no	—
304	C₂²×C₄	—	6	1	no	—
305	M₁₆	—	6	4	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	6	4	no	—
309	C₂×C₈	—	6	1	no	—
310	C₂×C₈	—	6	1	no	—
311	C₄⋊C₄	—	3	1	no	—
312	C₄⋊C₄	—	3	1	no	—
313	C₄⋊C₄	—	6	1	no	—
314	C₄⋊C₄	—	6	1	no	—
315	C₄⋊C₄	—	6	1	no	—
316	C₄⋊C₄	—	6	1	no	—
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	6	1	no	—
320	C₂²⋊C₄	—	6	1	no	—
321	C₂²⋊C₄	—	6	1	no	—
322	C₄²	—	3	1	no	—
323	C₄²	—	3	1	no	—
324	C₄²	—	3	1	no	—
325	C₄²	—	6	1	no	—
326	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
327	C₃×C₅	#1524	1	1	yes	characteristic, complemented, Hall
328	C₂²×C₃	—	4	1	no	—
329	C₂²×C₃	—	4	1	no	—
330	C₂²×C₃	—	4	1	no	—
331	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
332	C₂×D₃	—	2	1	no	—
333	C₂×D₃	—	2	1	no	—
334	C₂×D₃	C₅×#104	1	2	yes	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	4	1	no	—
339	Dic₃	—	2	1	no	—
340	Dic₃	—	2	1	no	—
341	Dic₃	—	4	1	no	—
342	Dic₃	—	4	1	no	—
343	Dic₃	C₅×#104	1	2	yes	—
344	C₂×C₅	—	6	2	no	—
345	C₂×C₅	—	8	1	no	—
346	C₂×C₅	#4745	1	1	yes	characteristic
347	C₂×C₅	D₃×#104	1	1	yes	characteristic
348	C₂×C₅	D₃×#104	1	1	yes	characteristic
349	C₂³	—	2	1	no	—
350	C₂³	—	3	1	no	—
351	Q₈	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	12	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	3	1	no	—
356	C₂×C₄	—	3	1	no	—
357	C₂×C₄	—	3	1	no	—
358	C₂×C₄	—	6	2	no	—
359	C₂×C₄	—	6	2	no	—
360	C₂×C₄	—	6	1	no	—
361	C₂×C₄	—	6	1	no	—
362	C₂×C₄	—	12	1	no	—
363	C₂×C₄	—	12	2	no	—
364	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
365	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
366	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
367	C₈	—	2	2	no	—
368	C₈	—	2	2	no	—
369	C₈	—	6	2	no	—
370	C₈	—	6	2	no	—
371	C₂×C₃	—	8	1	no	—
372	C₂×C₃	C₅×#413	1	1	yes	characteristic
373	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
374	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
375	D₃	—	2	2	no	—
376	C₅	#68341	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²	—	3	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	6	1	no	—
382	C₂²	—	6	1	no	—
383	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	3	2	no	—
388	C₄	—	4	1	no	—
389	C₄	—	6	1	no	—
390	C₄	—	6	1	no	—
391	C₄	—	12	1	no	—
392	C₄	—	12	1	no	—
393	C₃	C₅×#1524	1	1	yes	characteristic, complemented, Sylow
394	C₂	—	6	2	no	—
395	C₂	—	8	1	no	—
396	C₂	C₅×#4745	1	1	yes	characteristic
397	C₂	C₅×D₃×#104	1	1	yes	characteristic
398	C₂	C₅×D₃×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#329	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#938	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#329	D₃
hypocenter	C₃	C₅×#1524
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#329

Complements

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

N	H ≅ G/N	type
2. C₅×#4707	C₂	semidirect
3. C₅×D₃×#97	C₂	semidirect
4. C₃×C₅×#329	C₂	semidirect
5. C₅×#4540	C₂	semidirect
6. C₅×#4465	C₂	semidirect
7. C₅×#4465	C₂	semidirect
28. #68341	C₅	direct (N × H)
35. C₅×#329	D₃	semidirect
66. #4707	C₂×C₅	semidirect
67. D₃×#97	C₂×C₅	semidirect
68. C₃×#329	C₂×C₅	semidirect
69. #4540	C₂×C₅	semidirect
70. #4465	C₂×C₅	semidirect
71. #4465	C₂×C₅	semidirect
168. #329	C₅×D₃	semidirect
327. C₃×C₅	#1524	semidirect
376. C₅	#68341	direct (N × H)
393. C₃	C₅×#1524	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5680	2
C₅×#4707	2
C₅×D₃×#97	2
C₃×C₅×#329	2
C₅×#4540	2
C₅×#4465	2
C₅×#1524	3
#68341	5

Subgroups — C5×#68341 #14283910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68341 #14283910