Subgroups — C₅×#71712 #14301993

Order 1920.

716 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#837	C₂	1	2	yes	maximal, complemented
4	C₅×#5207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4532	C₂	1	2	yes	maximal, complemented
6	C₅×#1897	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₃×C₅×#123	—	2	1	no	—
10	C₃×C₅×C₂²⋊Q₈	C₄	1	2	yes	complemented
11	C₃×C₅×#121	C₄	1	2	yes	complemented
12	C₃×C₅×#120	—	2	1	no	—
13	C₃×C₄×C₅×D₄	—	2	2	no	—
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×C₅×#217	—	2	1	no	—
16	C₅×#926	—	2	4	no	—
17	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
18	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
19	C₂×C₅×#208	C₂²	1	2	yes	—
20	C₅×#837	—	2	4	no	—
21	C₅×#830	—	2	2	no	—
22	#71712	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₅×#525	D₃	1	1	yes	characteristic
24	C₂×C₅×#117	—	3	1	no	—
25	C₂×C₅×#104	—	3	2	no	—
26	C₅×#407	—	3	1	no	—
27	C₅×#339	—	3	2	no	—
28	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
29	C₃×C₅×#41	—	2	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	2	1	no	—
34	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	—	2	2	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
48	C₃×C₄²×C₅	—	2	1	no	—
49	C₅×#217	—	2	4	no	—
50	C₅×C₄⋊Dic₃	—	2	4	no	—
51	C₄×C₅×Dic₃	—	2	2	no	—
52	C₄×C₅×Dic₃	D₄	1	4	yes	complemented
53	C₅×#208	—	2	2	no	—
54	C₅×#208	—	2	2	no	—
55	C₂×C₅×C₃⋊C₈	—	2	2	no	—
56	C₃×#525	C₂×C₅	1	1	yes	characteristic
57	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×#837	C₂×C₅	1	2	yes	complemented
59	#5207	C₂×C₅	1	1	yes	characteristic, complemented
60	#4532	C₂×C₅	1	2	yes	complemented
61	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
62	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
63	C₂×C₅×M₁₆	—	3	2	no	—
64	C₅×#123	—	2	1	no	—
65	C₅×C₂²⋊Q₈	Dic₃	1	2	yes	complemented
66	C₅×#121	Dic₃	1	2	yes	complemented
67	C₅×#120	—	2	1	no	—
68	C₄×C₅×D₄	—	2	2	no	—
69	C₅×#117	—	6	4	no	—
70	C₅×#117	C₂×D₃	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	—	6	1	no	—
72	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
73	C₂×C₄²×C₅	—	3	2	no	—
74	C₅×#104	—	6	4	no	—
75	C₅×C₂²⋊C₈	—	6	2	no	—
76	#1897	—	3	1	no	Sylow
77	C₂³×C₃×C₅	—	2	1	no	—
78	C₂³×C₃×C₅	—	2	1	no	—
79	C₂³×C₃×C₅	—	2	1	no	—
80	C₂³×C₃×C₅	—	4	2	no	—
81	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
82	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
83	C₃×C₅×Q₈	—	2	2	no	—
84	C₃×C₅×D₄	—	2	2	no	—
85	C₃×C₅×D₄	—	4	4	no	—
86	C₃×C₅×D₄	—	4	1	no	—
87	C₃×C₅×D₄	—	4	1	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	2	yes	—
100	C₂×C₅×Dic₃	—	2	4	no	—
101	C₂×C₅×Dic₃	—	4	4	no	—
102	C₅×C₃⋊C₈	—	4	2	no	—
103	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
104	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
105	C₃×#123	—	2	1	no	—
106	C₃×C₂²⋊Q₈	C₄×C₅	1	2	yes	complemented
107	C₃×#121	C₄×C₅	1	2	yes	complemented
108	C₃×#120	—	2	1	no	—
109	C₃×C₄×D₄	—	2	2	no	—
110	C₃×#117	C₂²×C₅	1	1	yes	characteristic
111	C₂×#217	—	2	1	no	—
112	#926	—	2	4	no	—
113	C₂×C₄⋊Dic₃	—	2	1	no	—
114	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
115	C₂×#208	C₂²×C₅	1	2	yes	—
116	#837	—	2	4	no	—
117	#830	—	2	2	no	—
118	C₂⁴×C₅	#67	1	1	yes	characteristic
119	C₅×#41	—	2	2	no	—
120	C₅×#41	—	2	2	no	—
121	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
122	C₂×C₅×D₄	—	2	2	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	6	2	no	—
129	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
130	C₂²×C₄×C₅	#67	1	1	yes	characteristic
131	C₂²×C₄×C₅	#67	1	2	yes	—
132	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₅×M₁₆	—	6	2	no	—
134	C₅×M₁₆	—	6	2	no	—
135	C₂×C₅×C₈	—	6	2	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	6	4	no	—
138	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
139	C₅×C₂²⋊C₄	—	2	2	no	—
140	C₅×C₂²⋊C₄	—	2	1	no	—
141	C₅×C₂²⋊C₄	—	2	2	no	—
142	C₅×C₂²⋊C₄	—	6	4	no	—
143	C₄²×C₅	—	2	1	no	—
144	C₄²×C₅	—	3	4	no	—
145	C₄²×C₅	—	6	2	no	—
146	#525	C₅×D₃	1	1	yes	characteristic
147	C₂×#117	—	3	1	no	—
148	C₂×#104	—	3	2	no	—
149	#407	—	3	1	no	—
150	#339	—	3	2	no	—
151	C₂²×C₃×C₅	—	2	2	no	—
152	C₂²×C₃×C₅	—	2	2	no	—
153	C₂²×C₃×C₅	—	2	2	no	—
154	C₂²×C₃×C₅	—	2	2	no	—
155	C₂²×C₃×C₅	—	4	2	no	—
156	C₂²×C₃×C₅	—	4	2	no	—
157	C₂²×C₃×C₅	—	4	1	no	—
158	C₂²×C₃×C₅	—	4	2	no	—
159	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₃×C₅	#120	1	1	yes	characteristic
161	C₂²×C₃×C₅	#123	1	1	yes	characteristic
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	—	4	1	no	—
164	C₃×C₄×C₅	—	4	2	no	—
165	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
166	C₃×C₄×C₅	#121	1	2	yes	—
167	C₅×Dic₃	—	4	4	no	—
168	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
169	C₃×#41	—	2	2	no	—
170	C₃×#41	—	2	2	no	—
171	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
172	C₂×C₃×D₄	—	2	2	no	—
173	C₂×C₃×D₄	—	2	1	no	—
174	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	2	2	no	—
177	C₂²×C₃×C₄	—	2	1	no	—
178	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
179	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
180	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₂²×Dic₃	—	2	2	no	—
183	C₃×C₄⋊C₄	—	2	2	no	—
184	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
185	C₃×C₂²⋊C₄	—	2	2	no	—
186	C₃×C₂²⋊C₄	—	2	1	no	—
187	C₃×C₂²⋊C₄	—	2	2	no	—
188	C₃×C₄²	—	2	1	no	—
189	#217	—	2	4	no	—
190	C₄⋊Dic₃	—	2	4	no	—
191	C₄×Dic₃	—	2	2	no	—
192	C₄×Dic₃	C₅×D₄	1	4	yes	complemented
193	#208	—	2	2	no	—
194	#208	—	2	2	no	—
195	C₂×C₃⋊C₈	—	2	2	no	—
196	C₂³×C₅	—	2	1	no	—
197	C₂³×C₅	—	2	1	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	—	4	2	no	—
200	C₂³×C₅	#217	1	2	yes	—
201	C₂³×C₅	C₂×#67	1	1	yes	characteristic
202	C₅×Q₈	—	2	2	no	—
203	C₅×D₄	—	2	2	no	—
204	C₅×D₄	—	4	4	no	—
205	C₅×D₄	—	4	1	no	—
206	C₅×D₄	—	4	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	6	4	no	—
215	C₂×C₄×C₅	—	12	4	no	—
216	C₂×C₄×C₅	#217	1	2	yes	—
217	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
218	C₂×C₄×C₅	#237	1	2	yes	—
219	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
221	C₅×C₈	—	12	2	no	—
222	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
223	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
224	C₂×M₁₆	—	3	2	no	—
225	#123	—	2	1	no	—
226	C₂²⋊Q₈	C₅×Dic₃	1	2	yes	complemented
227	#121	C₅×Dic₃	1	2	yes	complemented
228	#120	—	2	1	no	—
229	C₄×D₄	—	2	2	no	—
230	#117	—	6	4	no	—
231	#117	C₂×C₅×D₃	1	1	yes	characteristic
232	C₂×C₄⋊C₄	—	6	1	no	—
233	C₂×C₂²⋊C₄	—	6	1	no	—
234	C₂×C₄²	—	3	2	no	—
235	#104	—	6	4	no	—
236	C₂²⋊C₈	—	6	2	no	—
237	C₂×C₃×C₅	—	2	1	no	—
238	C₂×C₃×C₅	—	2	1	no	—
239	C₂×C₃×C₅	—	4	2	no	—
240	C₂×C₃×C₅	—	8	1	no	—
241	C₂×C₃×C₅	#386	1	1	yes	characteristic
242	C₂×C₃×C₅	#421	1	2	yes	—
243	C₂³×C₃	—	2	1	no	—
244	C₂³×C₃	—	2	1	no	—
245	C₂³×C₃	—	2	1	no	—
246	C₂³×C₃	—	4	2	no	—
247	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
248	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
249	C₃×Q₈	—	2	2	no	—
250	C₃×D₄	—	2	2	no	—
251	C₃×D₄	—	4	4	no	—
252	C₃×D₄	—	4	1	no	—
253	C₃×D₄	—	4	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	4	2	no	—
261	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
262	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
264	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₅×#41	1	2	yes	—
266	C₂×Dic₃	—	2	4	no	—
267	C₂×Dic₃	—	4	4	no	—
268	C₃⋊C₈	—	4	2	no	—
269	C₂²×C₅	—	2	2	no	—
270	C₂²×C₅	—	2	2	no	—
271	C₂²×C₅	—	2	2	no	—
272	C₂²×C₅	—	2	2	no	—
273	C₂²×C₅	—	4	2	no	—
274	C₂²×C₅	—	4	2	no	—
275	C₂²×C₅	—	4	1	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	#935	1	1	yes	characteristic
278	C₂²×C₅	#937	1	1	yes	characteristic
279	C₂²×C₅	C₂×#217	1	1	yes	characteristic
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	—	4	1	no	—
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	—	12	4	no	—
284	C₄×C₅	D₄×Dic₃	1	2	yes	—
285	C₄×C₅	#939	1	2	yes	—
286	C₂⁴	C₅×#67	1	1	yes	characteristic
287	#41	—	2	2	no	—
288	#41	—	2	2	no	—
289	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	6	2	no	—
297	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
298	C₂²×C₄	C₅×#67	1	1	yes	characteristic
299	C₂²×C₄	C₅×#67	1	2	yes	—
300	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
301	M₁₆	—	6	2	no	—
302	M₁₆	—	6	2	no	—
303	C₂×C₈	—	6	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	6	4	no	—
306	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	1	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	6	4	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	3	4	no	—
313	C₄²	—	6	2	no	—
314	C₃×C₅	#1897	1	1	yes	characteristic, complemented, Hall
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	—	2	2	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	2	no	—
319	C₂²×C₃	—	4	2	no	—
320	C₂²×C₃	—	4	2	no	—
321	C₂²×C₃	—	4	1	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
324	C₂²×C₃	C₅×#120	1	1	yes	characteristic
325	C₂²×C₃	C₅×#123	1	1	yes	characteristic
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	—	4	2	no	—
329	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
330	C₃×C₄	C₅×#121	1	2	yes	—
331	Dic₃	—	4	4	no	—
332	C₂×C₅	—	2	1	no	—
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	—	4	2	no	—
335	C₂×C₅	—	8	1	no	—
336	C₂×C₅	#5220	1	1	yes	characteristic
337	C₂×C₅	#5236	1	2	yes	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	C₅×#217	1	2	yes	—
343	C₂³	C₂×C₅×#67	1	1	yes	characteristic
344	Q₈	—	2	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	6	4	no	—
357	C₂×C₄	—	12	4	no	—
358	C₂×C₄	C₅×#217	1	2	yes	—
359	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
360	C₂×C₄	C₅×#237	1	2	yes	—
361	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
363	C₈	—	12	2	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	4	2	no	—
367	C₂×C₃	—	8	1	no	—
368	C₂×C₃	C₅×#386	1	1	yes	characteristic
369	C₂×C₃	C₅×#421	1	2	yes	—
370	C₅	#71712	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	C₅×#935	1	1	yes	characteristic
380	C₂²	C₅×#937	1	1	yes	characteristic
381	C₂²	C₂×C₅×#217	1	1	yes	characteristic
382	C₄	—	2	2	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	12	4	no	—
386	C₄	C₅×D₄×Dic₃	1	2	yes	—
387	C₄	C₅×#939	1	2	yes	—
388	C₃	C₅×#1897	1	1	yes	characteristic, complemented, Sylow
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	4	2	no	—
392	C₂	—	8	1	no	—
393	C₂	C₅×#5220	1	1	yes	characteristic
394	C₂	C₅×#5236	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting, prime radical	C₃×C₅×#525	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#525	D₃
hypocenter	C₃	C₅×#1897
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₅×#525

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#926	C₂	semidirect
3. C₂×C₅×#837	C₂	semidirect
4. C₅×#5207	C₂	semidirect
5. C₅×#4532	C₂	semidirect
10. C₃×C₅×C₂²⋊Q₈	C₄	semidirect
11. C₃×C₅×#121	C₄	semidirect
22. #71712	C₅	direct (N × H)
52. C₄×C₅×Dic₃	D₄	semidirect
57. C₂×#926	C₂×C₅	semidirect
58. C₂×#837	C₂×C₅	semidirect
59. #5207	C₂×C₅	semidirect
60. #4532	C₂×C₅	semidirect
65. C₅×C₂²⋊Q₈	Dic₃	semidirect
66. C₅×#121	Dic₃	semidirect
106. C₃×C₂²⋊Q₈	C₄×C₅	semidirect
107. C₃×#121	C₄×C₅	semidirect
192. C₄×Dic₃	C₅×D₄	semidirect
226. C₂²⋊Q₈	C₅×Dic₃	semidirect
227. #121	C₅×Dic₃	semidirect
314. C₃×C₅	#1897	semidirect
370. C₅	#71712	direct (N × H)
388. C₃	C₅×#1897	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#525	2
C₂×C₅×#926	2
C₂×C₅×#837	2
C₅×#5207	2
C₅×#4532	2
C₅×#1897	3
#71712	5

Subgroups — C5×#71712 #14301993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71712 #14301993