Subgroups — C₃×#10615638 #14439652

Order 1920.

1064 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	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₃×#66159	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4097	C₂	1	2	yes	maximal, complemented
4	C₂²×C₃×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65470	C₂	1	2	yes	maximal, complemented
6	C₃×#65456	C₂	1	4	yes	maximal, complemented
7	C₃×#65444	C₂	1	2	yes	maximal, complemented
8	C₃×#65390	C₂	1	1	yes	maximal, characteristic, complemented
9	#10615638	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
12	C₃×C₅×#135	—	2	4	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×#4097	—	2	8	no	—
18	C₃×#4090	C₂²	1	4	yes	—
19	C₂×C₃×#689	C₂²	1	4	yes	—
20	C₃×#4082	C₂²	1	4	yes	—
21	C₃×#4081	—	2	4	no	—
22	C₂×C₃×#687	C₂²	1	4	yes	—
23	C₃×#4072	C₂²	1	1	yes	characteristic
24	C₃×#4070	—	2	4	no	—
25	C₂×C₃×#681	C₂²	1	1	yes	characteristic
26	C₂×C₃×Dic₂₀	—	2	4	no	—
27	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
28	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
29	C₃×#3947	C₂²	1	2	yes	—
30	C₃×C₈×Dic₅	C₂²	1	2	yes	—
31	C₃×#3156	—	5	1	no	maximal, Hall
32	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic
33	#66159	C₂×C₃	1	2	yes	complemented
34	C₂×#4097	C₂×C₃	1	2	yes	complemented
35	C₂²×Dic₂₀	C₂×C₃	1	1	yes	characteristic, complemented
36	#65470	C₂×C₃	1	2	yes	complemented
37	#65456	C₂×C₃	1	4	yes	complemented
38	#65444	C₂×C₃	1	2	yes	complemented
39	#65390	C₂×C₃	1	1	yes	characteristic, complemented
40	C₃×C₅×#41	—	2	4	no	—
41	C₃×C₅×#41	—	2	4	no	—
42	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	2	no	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×Dic₅	—	2	2	no	—
48	C₂×C₃×Dic₁₀	—	2	4	no	—
49	C₂×C₃×Dic₁₀	—	2	4	no	—
50	C₂×C₃×Dic₁₀	—	2	2	no	—
51	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
52	C₃×C₅×Q₁₆	—	2	2	no	—
53	C₃×C₅×SD₁₆	—	2	4	no	—
54	C₃×C₅×D₈	—	2	2	no	—
55	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₃×C₂²⋊Dic₅	—	2	8	no	—
59	C₃×C₂²⋊Dic₅	D₄	1	2	yes	—
60	C₃×#689	—	2	8	no	—
61	C₃×#687	—	2	8	no	—
62	C₃×C₄⋊Dic₅	D₄	1	2	yes	—
63	C₃×#683	—	2	8	no	—
64	C₃×C₄×Dic₅	C₂³	1	2	yes	—
65	C₃×#681	D₄	1	4	yes	—
66	C₂×C₃×#168	C₂³	1	2	yes	—
67	C₃×Dic₂₀	—	2	4	no	—
68	C₃×Dic₂₀	—	2	4	no	—
69	C₂×C₃×#137	—	5	2	no	—
70	C₂×C₃×#135	D₅	1	1	yes	characteristic
71	C₂²×C₃×Q₁₆	—	5	1	no	—
72	C₃×#536	—	5	2	no	—
73	C₃×#497	—	5	4	no	—
74	C₃×#495	—	5	2	no	—
75	C₃×#494	—	5	2	no	—
76	C₃×#405	—	5	1	no	—
77	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
78	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
79	C₅×#135	—	2	4	no	—
80	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
82	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
84	#4097	—	2	8	no	—
85	#4090	C₂²×C₃	1	4	yes	—
86	C₂×#689	C₂²×C₃	1	4	yes	—
87	#4082	C₂²×C₃	1	4	yes	—
88	#4081	—	2	4	no	—
89	C₂×#687	C₂²×C₃	1	4	yes	—
90	#4072	C₂²×C₃	1	1	yes	characteristic
91	#4070	—	2	4	no	—
92	C₂×#681	C₂²×C₃	1	1	yes	characteristic
93	C₂×Dic₂₀	—	2	4	no	—
94	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
95	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
96	#3947	C₂²×C₃	1	2	yes	—
97	C₈×Dic₅	C₂²×C₃	1	2	yes	—
98	#3156	—	5	1	no	Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
101	C₃×C₅×Q₈	—	2	2	no	—
102	C₃×C₅×Q₈	—	2	2	no	—
103	C₃×C₅×D₄	—	2	2	no	—
104	C₃×C₅×D₄	—	2	2	no	—
105	C₃×C₅×D₄	—	4	4	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	4	4	no	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₂×C₃×Dic₅	—	2	4	no	—
113	C₂×C₃×Dic₅	—	4	4	no	—
114	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
115	C₃×Dic₁₀	—	2	4	no	—
116	C₃×Dic₁₀	—	2	4	no	—
117	C₃×Dic₁₀	—	4	4	no	—
118	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
119	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
120	C₃×#168	C₂×D₄	1	4	yes	—
121	C₂×C₃×#41	C₂×D₅	1	2	yes	—
122	C₂²×C₃×Q₈	—	5	2	no	—
123	C₃×#137	—	10	8	no	—
124	C₃×#135	—	2	4	no	—
125	C₂×C₃×Q₁₆	—	5	4	no	—
126	C₂×C₃×Q₁₆	—	5	2	no	—
127	C₂×C₃×Q₁₆	—	5	2	no	—
128	C₂×C₃×Q₁₆	—	10	4	no	—
129	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
130	C₂×C₃×SD₁₆	—	5	4	no	—
131	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
132	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
133	C₂×C₃×M₁₆	—	5	1	no	—
134	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
135	C₃×C₄⋊Q₈	—	5	4	no	—
136	C₃×#124	—	5	4	no	—
137	C₃×#123	—	10	4	no	—
138	C₃×C₂²⋊Q₈	—	10	4	no	—
139	C₃×#117	—	5	1	no	—
140	C₃×#97	—	5	2	no	—
141	C₃×C₄×C₈	—	5	2	no	—
142	C₅×#41	—	2	4	no	—
143	C₅×#41	—	2	4	no	—
144	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂²×Dic₅	—	2	2	no	—
150	C₂×Dic₁₀	—	2	4	no	—
151	C₂×Dic₁₀	—	2	4	no	—
152	C₂×Dic₁₀	—	2	2	no	—
153	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
154	C₅×Q₁₆	—	2	2	no	—
155	C₅×SD₁₆	—	2	4	no	—
156	C₅×D₈	—	2	2	no	—
157	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
158	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
159	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
160	C₂²⋊Dic₅	—	2	8	no	—
161	C₂²⋊Dic₅	C₃×D₄	1	2	yes	—
162	#689	—	2	8	no	—
163	#687	—	2	8	no	—
164	C₄⋊Dic₅	C₃×D₄	1	2	yes	—
165	#683	—	2	8	no	—
166	C₄×Dic₅	C₂³×C₃	1	2	yes	—
167	#681	C₃×D₄	1	4	yes	—
168	C₂×#168	C₂³×C₃	1	2	yes	—
169	Dic₂₀	—	2	4	no	—
170	Dic₂₀	—	2	4	no	—
171	C₂×#137	—	5	2	no	—
172	C₂×#135	C₃×D₅	1	1	yes	characteristic
173	C₂²×Q₁₆	—	5	1	no	—
174	#536	—	5	2	no	—
175	#497	—	5	4	no	—
176	#495	—	5	2	no	—
177	#494	—	5	2	no	—
178	#405	—	5	1	no	—
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	4	2	no	—
181	C₂²×C₃×C₅	—	4	4	no	—
182	C₂²×C₃×C₅	#127	1	2	yes	—
183	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₃×C₄×C₅	—	4	2	no	—
185	C₃×C₄×C₅	#127	1	2	yes	—
186	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₃×Dic₅	—	2	4	no	—
189	C₃×Dic₅	—	4	4	no	—
190	C₃×#41	—	2	4	no	—
191	C₃×#41	—	2	4	no	—
192	C₂×C₃×Q₈	—	5	4	no	—
193	C₂×C₃×Q₈	—	10	2	no	—
194	C₂×C₃×Q₈	—	10	4	no	—
195	C₂×C₃×Q₈	—	10	4	no	—
196	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
197	C₂×C₃×D₄	—	2	2	no	—
198	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
199	C₂²×C₃×C₄	—	2	2	no	—
200	C₂²×C₃×C₄	—	10	2	no	—
201	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
202	C₃×Q₁₆	—	2	2	no	—
203	C₃×Q₁₆	—	10	8	no	—
204	C₃×Q₁₆	—	10	4	no	—
205	C₃×Q₁₆	—	10	4	no	—
206	C₃×SD₁₆	—	2	4	no	—
207	C₃×SD₁₆	—	10	8	no	—
208	C₃×D₈	—	2	2	no	—
209	C₃×M₁₆	—	5	4	no	—
210	C₂×C₃×C₈	—	5	2	no	—
211	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	—
212	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
213	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
214	C₃×C₄⋊C₄	—	5	2	no	—
215	C₃×C₄⋊C₄	—	10	8	no	—
216	C₃×C₂²⋊C₄	—	5	2	no	—
217	C₃×C₂²⋊C₄	—	10	8	no	—
218	C₃×C₄²	—	5	2	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
221	C₅×Q₈	—	2	2	no	—
222	C₅×Q₈	—	2	2	no	—
223	C₅×D₄	—	2	2	no	—
224	C₅×D₄	—	2	2	no	—
225	C₅×D₄	—	4	4	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	4	4	no	—
228	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
230	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
231	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
232	C₂×Dic₅	—	2	4	no	—
233	C₂×Dic₅	—	4	4	no	—
234	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
235	Dic₁₀	—	2	4	no	—
236	Dic₁₀	—	2	4	no	—
237	Dic₁₀	—	4	4	no	—
238	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
239	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
240	#168	C₂×C₃×D₄	1	4	yes	—
241	C₂×#41	C₂×C₃×D₅	1	2	yes	—
242	C₂²×Q₈	—	5	2	no	—
243	#137	—	10	8	no	—
244	#135	—	2	4	no	—
245	C₂×Q₁₆	—	5	4	no	—
246	C₂×Q₁₆	—	5	2	no	—
247	C₂×Q₁₆	—	5	2	no	—
248	C₂×Q₁₆	—	10	4	no	—
249	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
250	C₂×SD₁₆	—	5	4	no	—
251	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
252	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
253	C₂×M₁₆	—	5	1	no	—
254	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
255	C₄⋊Q₈	—	5	4	no	—
256	#124	—	5	4	no	—
257	#123	—	10	4	no	—
258	C₂²⋊Q₈	—	10	4	no	—
259	#117	—	5	1	no	—
260	#97	—	5	2	no	—
261	C₄×C₈	—	5	2	no	—
262	C₂×C₃×C₅	—	2	2	no	—
263	C₂×C₃×C₅	—	8	2	no	—
264	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
265	C₂×C₃×C₅	#578	1	2	yes	—
266	C₂³×C₃	—	2	2	no	—
267	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
268	C₃×Q₈	—	2	2	no	—
269	C₃×Q₈	—	2	2	no	—
270	C₃×Q₈	—	10	4	no	—
271	C₃×Q₈	—	10	4	no	—
272	C₃×Q₈	—	20	4	no	—
273	C₃×D₄	—	2	2	no	—
274	C₃×D₄	—	2	2	no	—
275	C₃×D₄	—	4	4	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	4	4	no	—
278	C₂×C₃×C₄	—	5	4	no	—
279	C₂×C₃×C₄	—	10	4	no	—
280	C₂×C₃×C₄	—	20	4	no	—
281	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
282	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
284	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
285	C₃×C₈	—	5	4	no	—
286	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
287	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	4	4	no	—
290	C₂²×C₅	—	4	2	no	—
291	C₂²×C₅	C₃×#127	1	2	yes	—
292	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
293	C₄×C₅	—	4	2	no	—
294	C₄×C₅	C₃×#127	1	2	yes	—
295	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
296	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
297	Dic₅	—	2	4	no	—
298	Dic₅	—	4	4	no	—
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	C₂×Q₈	—	5	4	no	—
302	C₂×Q₈	—	10	2	no	—
303	C₂×Q₈	—	10	4	no	—
304	C₂×Q₈	—	10	4	no	—
305	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	10	2	no	—
310	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	10	8	no	—
313	Q₁₆	—	10	4	no	—
314	Q₁₆	—	10	4	no	—
315	SD₁₆	—	2	4	no	—
316	SD₁₆	—	10	8	no	—
317	D₈	—	2	2	no	—
318	M₁₆	—	5	4	no	—
319	C₂×C₈	—	5	2	no	—
320	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	—
321	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
322	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
323	C₄⋊C₄	—	5	2	no	—
324	C₄⋊C₄	—	10	8	no	—
325	C₂²⋊C₄	—	5	2	no	—
326	C₂²⋊C₄	—	10	8	no	—
327	C₄²	—	5	2	no	—
328	C₃×C₅	#3156	1	1	yes	characteristic, complemented, Hall
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	4	4	no	—
331	C₂²×C₃	—	4	2	no	—
332	C₂²×C₃	#4086	1	2	yes	—
333	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
334	C₃×C₄	—	4	2	no	—
335	C₃×C₄	—	10	4	no	—
336	C₃×C₄	—	20	4	no	—
337	C₃×C₄	#4086	1	2	yes	—
338	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
339	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
340	C₂×C₅	—	2	2	no	—
341	C₂×C₅	—	8	2	no	—
342	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
343	C₂×C₅	C₃×#578	1	2	yes	—
344	C₂³	—	2	2	no	—
345	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
346	Q₈	—	2	2	no	—
347	Q₈	—	2	2	no	—
348	Q₈	—	10	4	no	—
349	Q₈	—	10	4	no	—
350	Q₈	—	20	4	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	4	4	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	5	4	no	—
357	C₂×C₄	—	10	4	no	—
358	C₂×C₄	—	20	4	no	—
359	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
360	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
361	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
362	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
363	C₈	—	5	4	no	—
364	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
365	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	8	2	no	—
368	C₂×C₃	#66105	1	2	yes	—
369	C₂×C₃	C₂×#4086	1	1	yes	characteristic
370	C₅	C₃×#3156	1	1	yes	characteristic, complemented, Sylow
371	C₂²	—	2	2	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	4	2	no	—
374	C₂²	C₃×#4086	1	2	yes	—
375	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
376	C₄	—	4	2	no	—
377	C₄	—	10	4	no	—
378	C₄	—	20	4	no	—
379	C₄	C₃×#4086	1	2	yes	—
380	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
381	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
382	C₃	#10615638	1	1	yes	characteristic, direct product factor, Sylow
383	C₂	—	2	2	no	—
384	C₂	—	8	2	no	—
385	C₂	C₃×#66105	1	2	yes	—
386	C₂	C₂×C₃×#4086	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting, prime radical	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×#135	D₅
hypocenter	C₅	C₃×#3156
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
2. C₃×#66159	C₂	semidirect
3. C₂×C₃×#4097	C₂	semidirect
4. C₂²×C₃×Dic₂₀	C₂	semidirect
5. C₃×#65470	C₂	semidirect
6. C₃×#65456	C₂	semidirect
7. C₃×#65444	C₂	semidirect
8. C₃×#65390	C₂	semidirect
9. #10615638	C₃	direct (N × H)
33. #66159	C₂×C₃	semidirect
34. C₂×#4097	C₂×C₃	semidirect
35. C₂²×Dic₂₀	C₂×C₃	semidirect
36. #65470	C₂×C₃	semidirect
37. #65456	C₂×C₃	semidirect
38. #65444	C₂×C₃	semidirect
39. #65390	C₂×C₃	semidirect
328. C₃×C₅	#3156	semidirect
370. C₅	C₃×#3156	semidirect
382. C₃	#10615638	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#135	2
C₃×#66159	2
C₂×C₃×#4097	2
C₂²×C₃×Dic₂₀	2
C₃×#65470	2
C₃×#65456	2
C₃×#65444	2
C₃×#65390	2
#10615638	3
C₃×#3156	5

Subgroups — C3×#10615638 #14439652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615638 #14439652