Subgroups — #14281591

Order 1920.

552 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×C₄×#709	C₂	1	1	yes	maximal, characteristic
2	#11751026	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745841	C₂	1	2	yes	maximal, complemented
5	#11745835	C₂	1	2	yes	maximal, complemented
6	#10600527	—	3	1	no	maximal, Hall
7	C₂×C₃×#709	C₄	1	1	yes	characteristic
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
10	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
11	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
12	C₃×#4072	C₄	1	1	yes	characteristic
13	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
14	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
15	C₃×#4018	—	2	1	no	—
16	C₃×C₄²×D₅	—	2	1	no	—
17	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
18	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
19	#91114	—	2	1	no	—
20	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
21	C₄×C₃⋊#168	—	2	1	no	—
22	C₄×C₅×C₃⋊C₈	—	2	1	no	—
23	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	#71638	—	5	1	no	maximal, Hall
25	C₄×#709	D₃	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	—	3	1	no	—
27	#65214	—	3	1	no	—
28	#64679	—	3	2	no	—
29	#64676	—	3	2	no	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
34	C₃×#709	—	2	2	no	—
35	C₃×#709	C₈	1	4	yes	complemented
36	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	—	2	1	no	—
38	C₂×C₃×C₄×D₅	—	2	1	no	—
39	C₂×C₃×C₄×D₅	—	2	1	no	—
40	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
41	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
42	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
43	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₃⋊#168	—	2	2	no	—
46	C₂×C₅×C₃⋊C₈	—	2	4	no	—
47	C₂×C₅×C₃⋊C₈	—	2	2	no	—
48	C₃×C₂²⋊Dic₅	—	2	1	no	—
49	C₃×#685	—	2	1	no	—
50	C₃×#685	—	2	1	no	—
51	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
53	C₃×#683	—	2	1	no	—
54	C₃×#683	—	2	1	no	—
55	C₃×C₄×Dic₅	—	2	1	no	—
56	C₃×C₄×Dic₅	—	2	1	no	—
57	C₃×C₄×Dic₅	—	2	1	no	—
58	C₃×C₄×#41	—	5	1	no	—
59	#4925	—	5	1	no	—
60	C₂×C₄×C₃⋊C₈	D₅	1	1	yes	characteristic, complemented
61	#4535	—	5	2	no	—
62	D₄⋊(C₃⋊C₈)	—	5	2	no	—
63	C₂×#709	Dic₃	1	1	yes	characteristic
64	C₂²×C₅×C₈	—	6	1	no	—
65	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
66	C₄×C₂²⋊D₅	—	2	1	no	—
67	C₄×C₂²⋊D₅	—	2	1	no	—
68	#4072	Dic₃	1	1	yes	characteristic
69	C₄×D₂₀	Dic₃	1	1	yes	characteristic
70	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
71	#4018	—	2	1	no	—
72	C₄²×D₅	—	2	1	no	—
73	C₄×Dic₁₀	Dic₃	1	1	yes	characteristic
74	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
75	C₄×C₅×C₈	—	3	2	no	—
76	C₄×C₅×C₈	—	6	1	no	—
77	C₂²⋊#168	—	6	1	no	—
78	C₄⋊#168	—	3	2	no	—
79	C₄×#168	—	6	1	no	—
80	#1476	—	15	1	no	Sylow
81	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₃×D₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
89	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₃×C₂²⋊D₅	—	2	4	no	—
94	C₂×C₃×Dic₅	—	2	1	no	—
95	C₂×C₃×Dic₅	—	2	1	no	—
96	C₂×C₃×Dic₅	—	2	1	no	—
97	C₃×D₂₀	—	2	1	no	—
98	C₃×D₂₀	C₂×C₈	1	2	yes	complemented
99	C₃×C₄×D₅	—	2	4	no	—
100	C₃×C₄×D₅	—	4	2	no	—
101	C₃×C₄×D₅	—	4	2	no	—
102	C₃×Dic₁₀	—	2	1	no	—
103	C₃×Dic₁₀	C₂×C₈	1	2	yes	complemented
104	C₃⋊#168	—	4	2	no	—
105	C₅×C₃⋊C₈	—	2	4	no	—
106	C₂×C₃×#41	—	5	1	no	—
107	C₃×C₄×Q₈	—	5	1	no	—
108	C₃×C₄×Q₈	—	5	1	no	—
109	C₃×C₄×D₄	—	5	1	no	—
110	C₃×C₄×D₄	—	5	1	no	—
111	C₃×C₄×D₄	—	10	1	no	—
112	C₃×C₄×D₄	—	10	1	no	—
113	C₃×#117	—	5	1	no	—
114	C₃×#117	—	10	1	no	—
115	C₂×C₃×C₄²	—	10	1	no	—
116	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
117	C₂²×C₃⋊C₈	—	2	1	no	—
118	#830	—	10	1	no	—
119	C₄⋊(C₃⋊C₈)	—	5	2	no	—
120	C₄×C₃⋊C₈	—	2	1	no	—
121	C₄×C₃⋊C₈	—	10	1	no	—
122	C₄×C₃⋊C₈	C₂×D₅	1	2	yes	—
123	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	#67	1	1	yes	characteristic
125	C₂²×C₄×C₅	#67	1	1	yes	characteristic
126	C₂×C₂²⋊D₅	—	2	1	no	—
127	#709	—	2	2	no	—
128	#709	C₃⋊C₈	1	4	yes	complemented
129	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
130	C₂×C₄×D₅	—	2	1	no	—
131	C₂×C₄×D₅	—	2	1	no	—
132	C₂×C₄×D₅	—	2	1	no	—
133	C₂×Dic₁₀	C₂×Dic₃	1	1	yes	characteristic
134	C₂×C₅×C₈	—	6	4	no	—
135	C₂×C₅×C₈	—	6	2	no	—
136	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
137	C₄²×C₅	#67	1	1	yes	characteristic
138	C₄²×C₅	#67	1	1	yes	characteristic
139	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
140	C₂²⋊Dic₅	—	2	1	no	—
141	#685	—	2	1	no	—
142	#685	—	2	1	no	—
143	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
144	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
145	#683	—	2	1	no	—
146	#683	—	2	1	no	—
147	C₄×Dic₅	—	2	1	no	—
148	C₄×Dic₅	—	2	1	no	—
149	C₄×Dic₅	—	2	1	no	—
150	C₂×#168	—	6	2	no	—
151	C₄×#41	—	5	1	no	—
152	#431	—	15	1	no	—
153	C₂×C₄×C₈	—	3	1	no	—
154	Q₈⋊C₈	—	15	2	no	—
155	D₄⋊C₈	—	15	2	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	—	2	1	no	—
158	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
159	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₃×D₅	—	2	2	no	—
161	C₂×C₃×D₅	—	4	1	no	—
162	C₂×C₃×D₅	—	4	1	no	—
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	2	1	no	—
165	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
166	C₃×C₄×C₅	#104	1	2	yes	—
167	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
169	C₃×C₄×C₅	#135	1	2	yes	—
170	C₃×Dic₅	—	2	2	no	—
171	C₃×Dic₅	—	4	1	no	—
172	C₃×Dic₅	—	4	1	no	—
173	C₃×#41	—	5	4	no	—
174	C₃×#41	—	10	2	no	—
175	C₂×C₃×Q₈	—	5	1	no	—
176	C₂×C₃×D₄	—	5	1	no	—
177	C₂×C₃×D₄	—	10	1	no	—
178	C₂²×C₃×C₄	—	10	1	no	—
179	C₂²×C₃×C₄	—	10	1	no	—
180	C₂²×C₃×C₄	—	10	1	no	—
181	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
184	C₃×C₄⋊C₄	—	5	1	no	—
185	C₃×C₄⋊C₄	—	5	1	no	—
186	C₃×C₄⋊C₄	—	10	1	no	—
187	C₃×C₄⋊C₄	—	10	1	no	—
188	C₃×C₂²⋊C₄	—	10	1	no	—
189	C₃×C₂²⋊C₄	—	10	1	no	—
190	C₃×C₂²⋊C₄	—	10	1	no	—
191	C₃×C₄²	—	10	1	no	—
192	C₃×C₄²	—	10	1	no	—
193	C₃×C₄²	—	10	1	no	—
194	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
195	C₃×C₄²	D₂₀	1	1	yes	characteristic
196	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
197	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
198	C₂×C₃⋊C₈	—	2	4	no	—
199	C₂×C₃⋊C₈	—	2	2	no	—
200	C₂×C₃⋊C₈	—	10	2	no	—
201	C₂³×C₅	#217	1	1	yes	characteristic
202	C₂²×D₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
206	C₂×C₄×C₅	#208	1	2	yes	—
207	C₂×C₄×C₅	#217	1	1	yes	characteristic
208	C₂×C₄×C₅	#217	1	1	yes	characteristic
209	C₂×C₄×C₅	#217	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
213	C₂²⋊D₅	—	2	4	no	—
214	C₂×Dic₅	—	2	1	no	—
215	C₂×Dic₅	—	2	1	no	—
216	C₂×Dic₅	—	2	1	no	—
217	D₂₀	—	2	1	no	—
218	D₂₀	C₂×C₃⋊C₈	1	2	yes	complemented
219	C₄×D₅	—	2	4	no	—
220	C₄×D₅	—	4	2	no	—
221	C₄×D₅	—	4	2	no	—
222	Dic₁₀	—	2	1	no	—
223	Dic₁₀	C₂×C₃⋊C₈	1	2	yes	complemented
224	C₅×C₈	—	6	4	no	—
225	#168	—	12	2	no	—
226	C₂×#41	—	5	1	no	—
227	C₂²×C₈	—	6	1	no	—
228	C₄×Q₈	—	5	1	no	—
229	C₄×Q₈	—	5	1	no	—
230	C₄×D₄	—	5	1	no	—
231	C₄×D₄	—	5	1	no	—
232	C₄×D₄	—	10	1	no	—
233	C₄×D₄	—	10	1	no	—
234	#117	—	5	1	no	—
235	#117	—	10	1	no	—
236	C₂×C₄²	—	10	1	no	—
237	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
238	C₄⋊C₈	—	15	2	no	—
239	C₂²⋊C₈	—	30	1	no	—
240	C₄×C₈	—	3	2	no	—
241	C₄×C₈	—	6	1	no	—
242	C₄×C₈	—	30	1	no	—
243	C₂×C₃×C₅	—	2	2	no	—
244	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
245	C₂×C₃×C₅	#416	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
247	C₃×D₅	—	4	2	no	—
248	C₂³×C₃	—	10	1	no	—
249	C₂³×C₃	#685	1	1	yes	characteristic
250	C₃×Q₈	—	5	2	no	—
251	C₃×Q₈	—	10	1	no	—
252	C₃×D₄	—	5	2	no	—
253	C₃×D₄	—	10	4	no	—
254	C₃×D₄	—	10	1	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	10	1	no	—
258	C₂×C₃×C₄	—	10	4	no	—
259	C₂×C₃×C₄	—	10	1	no	—
260	C₂×C₃×C₄	—	10	1	no	—
261	C₂×C₃×C₄	—	20	2	no	—
262	C₂×C₃×C₄	—	20	2	no	—
263	C₂×C₃×C₄	C₈×D₅	1	2	yes	—
264	C₂×C₃×C₄	#676	1	2	yes	—
265	C₂×C₃×C₄	#685	1	1	yes	characteristic
266	C₂×C₃×C₄	#685	1	1	yes	characteristic
267	C₂×C₃×C₄	#685	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
271	C₃⋊C₈	—	2	4	no	—
272	C₃⋊C₈	—	20	2	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	#830	1	2	yes	—
276	C₂²×C₅	C₂×#217	1	1	yes	characteristic
277	C₂×D₅	—	2	2	no	—
278	C₂×D₅	—	4	1	no	—
279	C₂×D₅	—	4	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	#830	1	2	yes	—
283	C₄×C₅	#837	1	2	yes	—
284	C₄×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
285	C₄×C₅	C₂×#208	1	1	yes	characteristic
286	C₄×C₅	#950	1	2	yes	—
287	Dic₅	—	2	2	no	—
288	Dic₅	—	4	1	no	—
289	Dic₅	—	4	1	no	—
290	#41	—	5	4	no	—
291	#41	—	10	2	no	—
292	C₂×Q₈	—	5	1	no	—
293	C₂×D₄	—	5	1	no	—
294	C₂×D₄	—	10	1	no	—
295	C₂²×C₄	—	10	1	no	—
296	C₂²×C₄	—	10	1	no	—
297	C₂²×C₄	—	10	1	no	—
298	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
299	C₂²×C₄	#1201	1	1	yes	characteristic
300	C₂²×C₄	#1202	1	1	yes	characteristic
301	C₂×C₈	—	6	4	no	—
302	C₂×C₈	—	6	2	no	—
303	C₂×C₈	—	30	2	no	—
304	C₄⋊C₄	—	5	1	no	—
305	C₄⋊C₄	—	5	1	no	—
306	C₄⋊C₄	—	10	1	no	—
307	C₄⋊C₄	—	10	1	no	—
308	C₂²⋊C₄	—	10	1	no	—
309	C₂²⋊C₄	—	10	1	no	—
310	C₂²⋊C₄	—	10	1	no	—
311	C₄²	—	10	1	no	—
312	C₄²	—	10	1	no	—
313	C₄²	—	10	1	no	—
314	C₄²	D₅×Dic₃	1	1	yes	characteristic
315	C₄²	#1201	1	1	yes	characteristic
316	C₄²	#1202	1	1	yes	characteristic
317	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
318	C₃×C₅	#1476	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	10	2	no	—
322	C₂²×C₃	—	20	1	no	—
323	C₂²×C₃	—	20	1	no	—
324	C₂²×C₃	#3952	1	2	yes	—
325	C₂²×C₃	C₂×#685	1	1	yes	characteristic
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	10	2	no	—
329	C₃×C₄	—	20	1	no	—
330	C₃×C₄	—	20	1	no	—
331	C₃×C₄	#3937	1	2	yes	—
332	C₃×C₄	#3952	1	2	yes	—
333	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
334	C₃×C₄	C₂×#676	1	1	yes	characteristic
335	C₃×C₄	#4050	1	2	yes	—
336	C₂×C₅	—	2	2	no	—
337	C₂×C₅	C₂×#830	1	1	yes	characteristic
338	C₂×C₅	#5233	1	1	yes	characteristic
339	C₂×C₅	C₂×#837	1	1	yes	characteristic
340	D₅	—	4	2	no	—
341	C₂³	—	10	1	no	—
342	C₂³	#6665	1	1	yes	characteristic
343	Q₈	—	5	2	no	—
344	Q₈	—	10	1	no	—
345	D₄	—	5	2	no	—
346	D₄	—	10	4	no	—
347	D₄	—	10	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	10	1	no	—
351	C₂×C₄	—	10	4	no	—
352	C₂×C₄	—	10	1	no	—
353	C₂×C₄	—	10	1	no	—
354	C₂×C₄	—	20	2	no	—
355	C₂×C₄	—	20	2	no	—
356	C₂×C₄	D₅×C₃⋊C₈	1	2	yes	—
357	C₂×C₄	#6649	1	2	yes	—
358	C₂×C₄	#6665	1	1	yes	characteristic
359	C₂×C₄	#6665	1	1	yes	characteristic
360	C₂×C₄	#6665	1	1	yes	characteristic
361	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
362	C₂×C₄	C₂×#1201	1	1	yes	characteristic
363	C₂×C₄	C₂×#1202	1	1	yes	characteristic
364	C₈	—	6	4	no	—
365	C₈	—	60	2	no	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	20	2	no	—
368	C₂×C₃	C₂×#3937	1	1	yes	characteristic
369	C₂×C₃	C₂×#3952	1	1	yes	characteristic
370	C₂×C₃	#65402	1	1	yes	characteristic
371	C₅	#71638	1	1	yes	characteristic, complemented, Sylow
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	10	2	no	—
375	C₂²	—	20	1	no	—
376	C₂²	—	20	1	no	—
377	C₂²	#90955	1	2	yes	—
378	C₂²	C₂×#6665	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	10	2	no	—
382	C₄	—	20	1	no	—
383	C₄	—	20	1	no	—
384	C₄	#90955	1	2	yes	—
385	C₄	#90977	1	2	yes	—
386	C₄	C₂×D₅×C₃⋊C₈	1	1	yes	characteristic
387	C₄	C₂×#6649	1	1	yes	characteristic
388	C₄	#91311	1	2	yes	—
389	C₃	#10600527	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	2	2	no	—
391	C₂	—	20	2	no	—
392	C₂	C₂×#90955	1	1	yes	characteristic
393	C₂	#11748365	1	1	yes	characteristic
394	C₂	C₂×#90977	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	#1202
commutator	C₃×C₄×C₅	C₂²×C₈
Frattini	C₄²	C₂×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#709	C₄
cosocle	C₃×C₄²×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#1476
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #11751026	C₂	semidirect
3. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
4. #11745841	C₂	semidirect
5. #11745835	C₂	semidirect
35. C₃×#709	C₈	semidirect
60. C₂×C₄×C₃⋊C₈	D₅	semidirect
98. C₃×D₂₀	C₂×C₈	semidirect
103. C₃×Dic₁₀	C₂×C₈	semidirect
128. #709	C₃⋊C₈	semidirect
218. D₂₀	C₂×C₃⋊C₈	semidirect
223. Dic₁₀	C₂×C₃⋊C₈	semidirect
318. C₃×C₅	#1476	semidirect
371. C₅	#71638	semidirect
389. C₃	#10600527	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#709	2
#11751026	2
C₂×C₄×C₅×C₃⋊C₈	2
#11745841	2
#11745835	2
#10600527	3
#71638	5