Subgroups — #14281631

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6817	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
4	#11746280	C₂	1	2	yes	maximal, complemented
5	#11746277	C₂	1	2	yes	maximal, complemented
6	#10601548	—	3	1	no	maximal, Hall
7	C₂×#6817	C₄	1	1	yes	characteristic
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₄×#1220	—	2	1	no	—
10	C₄×#1220	—	2	1	no	—
11	#91815	C₄	1	1	yes	characteristic
12	C₂²×C₃⋊#168	—	2	1	no	—
13	C₄×D₆₀	C₄	1	1	yes	characteristic
14	C₄×D₆₀	C₂²	1	1	yes	characteristic
15	#91761	—	2	1	no	—
16	C₄²×D₁₅	—	2	1	no	—
17	C₄×Dic₃₀	C₄	1	1	yes	characteristic
18	C₄×Dic₃₀	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊C₈	—	2	1	no	—
20	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
22	C₄⋊(C₃⋊#168)	—	2	1	no	—
23	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
24	#70755	—	5	1	no	maximal, Hall
25	C₄×#709	—	3	1	no	—
26	C₅×#431	D₃	1	1	yes	characteristic, complemented
27	C₂×C₄⋊#168	—	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×#1220	—	2	1	no	—
34	#6817	—	2	2	no	—
35	#6817	C₈	1	4	yes	complemented
36	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₁₅	—	2	1	no	—
38	C₂×C₄×D₁₅	—	2	1	no	—
39	C₂×C₄×D₁₅	—	2	1	no	—
40	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
46	#6719	—	2	1	no	—
47	#6714	—	2	1	no	—
48	#6714	—	2	1	no	—
49	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
50	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
51	#6712	—	2	1	no	—
52	#6712	—	2	1	no	—
53	C₄×Dic₁₅	—	2	1	no	—
54	C₄×Dic₁₅	—	2	1	no	—
55	C₄×Dic₁₅	—	2	1	no	—
56	C₂×C₃⋊#168	—	2	2	no	—
57	C₂×C₃⋊#168	—	4	2	no	—
58	C₄×#235	—	5	1	no	—
59	C₃×#431	D₅	1	1	yes	characteristic, complemented
60	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
61	#4459	—	5	2	no	—
62	#4456	—	5	2	no	—
63	C₂×#709	—	3	1	no	—
64	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
65	C₄×C₂²⋊D₅	—	6	1	no	—
66	C₄×C₂²⋊D₅	—	6	1	no	—
67	#4072	—	3	1	no	—
68	C₂²×#168	—	6	1	no	—
69	C₄×D₂₀	—	3	1	no	—
70	C₄×D₂₀	—	3	1	no	—
71	#4018	—	6	1	no	—
72	C₄²×D₅	—	6	1	no	—
73	C₄×Dic₁₀	—	3	1	no	—
74	C₄×Dic₁₀	—	3	1	no	—
75	C₅×C₄⋊C₈	—	2	1	no	—
76	C₅×C₂²⋊C₈	—	2	1	no	—
77	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
78	C₄⋊#168	—	3	2	no	—
79	C₄⋊#168	—	6	1	no	—
80	#1477	—	15	1	no	Sylow
81	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×D₁₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
90	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	#1220	—	2	4	no	—
95	C₂×Dic₁₅	—	2	1	no	—
96	C₂×Dic₁₅	—	2	1	no	—
97	C₂×Dic₁₅	—	2	1	no	—
98	D₆₀	—	2	1	no	—
99	D₆₀	C₂×C₈	1	2	yes	complemented
100	C₄×D₁₅	—	2	4	no	—
101	C₄×D₁₅	—	4	2	no	—
102	C₄×D₁₅	—	4	1	no	—
103	C₄×D₁₅	—	4	1	no	—
104	Dic₃₀	—	2	1	no	—
105	Dic₃₀	C₂×C₈	1	2	yes	complemented
106	C₃×C₅×C₈	—	4	2	no	—
107	C₃⋊#168	—	4	2	no	—
108	C₂×#235	—	5	1	no	—
109	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
110	C₄×#67	—	10	1	no	—
111	C₄×#67	—	10	1	no	—
112	#926	—	5	1	no	—
113	C₂²×C₃⋊C₈	—	10	1	no	—
114	C₄×D₁₂	—	5	1	no	—
115	C₄×D₁₂	—	5	1	no	—
116	#872	—	10	1	no	—
117	C₄²×D₃	—	10	1	no	—
118	C₄×Dic₆	—	5	1	no	—
119	C₄×Dic₆	—	5	1	no	—
120	C₃×C₄⋊C₈	—	2	1	no	—
121	C₃×C₂²⋊C₈	—	2	1	no	—
122	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
123	C₄⋊(C₃⋊C₈)	—	5	2	no	—
124	C₄⋊(C₃⋊C₈)	—	10	1	no	—
125	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
126	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
127	C₂²×C₄×C₅	#67	1	1	yes	characteristic
128	C₂×C₂²⋊D₅	—	6	1	no	—
129	#709	—	3	4	no	—
130	#709	—	6	2	no	—
131	C₂×D₂₀	—	3	1	no	—
132	C₂×C₄×D₅	—	6	1	no	—
133	C₂×C₄×D₅	—	6	1	no	—
134	C₂×C₄×D₅	—	6	1	no	—
135	C₂×Dic₁₀	—	3	1	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
138	C₄²×C₅	D₁₂	1	1	yes	characteristic
139	C₄²×C₅	#67	1	1	yes	characteristic
140	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
141	C₂²⋊Dic₅	—	6	1	no	—
142	#685	—	6	1	no	—
143	#685	—	6	1	no	—
144	C₄⋊Dic₅	—	3	1	no	—
145	C₄⋊Dic₅	—	3	1	no	—
146	#683	—	6	1	no	—
147	#683	—	6	1	no	—
148	C₄×Dic₅	—	6	1	no	—
149	C₄×Dic₅	—	6	1	no	—
150	C₄×Dic₅	—	6	1	no	—
151	C₂×#168	—	6	2	no	—
152	C₂×#168	—	12	2	no	—
153	C₄×#41	—	15	1	no	—
154	#431	D₁₅	1	1	yes	characteristic, complemented
155	C₂×C₄⋊C₈	—	15	1	no	—
156	Q₈⋊C₈	—	15	2	no	—
157	D₄⋊C₈	—	15	2	no	—
158	C₂²×C₃×C₅	—	2	1	no	—
159	C₂²×C₃×C₅	—	2	1	no	—
160	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
161	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×D₁₅	—	2	2	no	—
163	C₂×D₁₅	—	4	1	no	—
164	C₂×D₁₅	—	4	1	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	2	1	no	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
169	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
170	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
171	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₃×C₄×C₅	#137	1	1	yes	characteristic
173	Dic₁₅	—	2	2	no	—
174	Dic₁₅	—	4	1	no	—
175	Dic₁₅	—	4	1	no	—
176	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
179	C₂×#67	—	10	1	no	—
180	#235	—	5	4	no	—
181	#235	—	10	2	no	—
182	C₂×D₁₂	—	5	1	no	—
183	C₂×C₄×D₃	—	10	1	no	—
184	C₂×C₄×D₃	—	10	1	no	—
185	C₂×C₄×D₃	—	10	1	no	—
186	C₂×Dic₆	—	5	1	no	—
187	C₂×C₃×C₈	—	2	2	no	—
188	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
189	C₃×C₄²	D₂₀	1	1	yes	characteristic
190	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
191	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
192	#217	—	10	1	no	—
193	(C₂×D₃)⋊C₄	—	10	1	no	—
194	(C₂×D₃)⋊C₄	—	10	1	no	—
195	C₄⋊Dic₃	—	5	1	no	—
196	C₄⋊Dic₃	—	5	1	no	—
197	Dic₃⋊C₄	—	10	1	no	—
198	Dic₃⋊C₄	—	10	1	no	—
199	C₄×Dic₃	—	10	1	no	—
200	C₄×Dic₃	—	10	1	no	—
201	C₄×Dic₃	—	10	1	no	—
202	C₂×C₃⋊C₈	—	10	2	no	—
203	C₂×C₃⋊C₈	—	20	2	no	—
204	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
205	C₂²×D₅	—	6	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	D₃×C₈	1	2	yes	—
210	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	2	yes	—
211	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
217	C₂²⋊D₅	—	6	4	no	—
218	C₂×Dic₅	—	6	1	no	—
219	C₂×Dic₅	—	6	1	no	—
220	C₂×Dic₅	—	6	1	no	—
221	D₂₀	—	3	2	no	—
222	D₂₀	—	6	1	no	—
223	C₄×D₅	—	6	4	no	—
224	C₄×D₅	—	12	2	no	—
225	C₄×D₅	—	12	1	no	—
226	C₄×D₅	—	12	1	no	—
227	Dic₁₀	—	3	2	no	—
228	Dic₁₀	—	6	1	no	—
229	C₅×C₈	—	4	2	no	—
230	#168	—	12	2	no	—
231	C₂×#41	—	15	1	no	—
232	C₂²×C₈	—	30	1	no	—
233	C₄×Q₈	—	15	1	no	—
234	C₄×Q₈	—	15	1	no	—
235	C₄×D₄	—	15	1	no	—
236	C₄×D₄	—	15	1	no	—
237	C₄×D₄	—	30	1	no	—
238	C₄×D₄	—	30	1	no	—
239	#117	—	15	1	no	—
240	#117	—	30	1	no	—
241	C₂×C₄²	—	30	1	no	—
242	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	15	2	no	—
245	C₄⋊C₈	—	30	1	no	—
246	C₂²⋊C₈	—	2	1	no	—
247	C₄×C₈	C₂×D₁₅	1	2	yes	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
250	C₂×C₃×C₅	#417	1	1	yes	characteristic
251	C₂×C₃×C₅	#421	1	1	yes	characteristic
252	D₁₅	—	4	2	no	—
253	C₂³×C₃	#685	1	1	yes	characteristic
254	C₂²×D₃	—	10	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	C₈×D₅	1	2	yes	—
259	C₂×C₃×C₄	#676	1	2	yes	—
260	C₂×C₃×C₄	#685	1	1	yes	characteristic
261	C₂×C₃×C₄	#685	1	1	yes	characteristic
262	C₂×C₃×C₄	#685	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
266	#67	—	10	4	no	—
267	C₂×Dic₃	—	10	1	no	—
268	C₂×Dic₃	—	10	1	no	—
269	C₂×Dic₃	—	10	1	no	—
270	D₁₂	—	5	2	no	—
271	D₁₂	—	10	1	no	—
272	C₄×D₃	—	10	4	no	—
273	C₄×D₃	—	20	2	no	—
274	C₄×D₃	—	20	1	no	—
275	C₄×D₃	—	20	1	no	—
276	Dic₆	—	5	2	no	—
277	Dic₆	—	10	1	no	—
278	C₃×C₈	—	4	2	no	—
279	C₃⋊C₈	—	20	2	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	(C₂×D₃)⋊C₈	1	2	yes	—
283	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
284	C₂×D₅	—	6	2	no	—
285	C₂×D₅	—	12	1	no	—
286	C₂×D₅	—	12	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	(C₂×D₃)⋊C₈	1	2	yes	—
291	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
292	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
293	C₄×C₅	#908	1	1	yes	characteristic
294	C₄×C₅	#909	1	1	yes	characteristic
295	Dic₅	—	6	2	no	—
296	Dic₅	—	12	1	no	—
297	Dic₅	—	12	1	no	—
298	#41	—	15	4	no	—
299	#41	—	30	2	no	—
300	C₂×Q₈	—	15	1	no	—
301	C₂×D₄	—	15	1	no	—
302	C₂×D₄	—	30	1	no	—
303	C₂²×C₄	—	30	1	no	—
304	C₂²×C₄	—	30	1	no	—
305	C₂²×C₄	—	30	1	no	—
306	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
307	C₂²×C₄	D₆₀	1	1	yes	characteristic
308	C₂²×C₄	#1220	1	1	yes	characteristic
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	30	2	no	—
311	C₂×C₈	—	60	2	no	—
312	C₄⋊C₄	—	15	1	no	—
313	C₄⋊C₄	—	15	1	no	—
314	C₄⋊C₄	—	30	1	no	—
315	C₄⋊C₄	—	30	1	no	—
316	C₂²⋊C₄	—	30	1	no	—
317	C₂²⋊C₄	—	30	1	no	—
318	C₂²⋊C₄	—	30	1	no	—
319	C₄²	—	30	1	no	—
320	C₄²	—	30	1	no	—
321	C₄²	—	30	1	no	—
322	C₄²	C₄×D₁₅	1	1	yes	characteristic
323	C₄²	D₆₀	1	1	yes	characteristic
324	C₄²	#1220	1	1	yes	characteristic
325	C₄²	C₂²×D₁₅	1	1	yes	characteristic
326	C₃×C₅	#1477	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	#3952	1	2	yes	—
330	C₂²×C₃	C₂×#685	1	1	yes	characteristic
331	C₂×D₃	—	10	2	no	—
332	C₂×D₃	—	20	1	no	—
333	C₂×D₃	—	20	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	#3952	1	2	yes	—
338	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
339	C₃×C₄	C₂×#676	1	1	yes	characteristic
340	C₃×C₄	#4054	1	1	yes	characteristic
341	C₃×C₄	#4055	1	1	yes	characteristic
342	Dic₃	—	10	2	no	—
343	Dic₃	—	20	1	no	—
344	Dic₃	—	20	1	no	—
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	#5005	1	1	yes	characteristic
347	C₂×C₅	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
348	C₂×C₅	#5133	1	1	yes	characteristic
349	D₅	—	12	2	no	—
350	C₂³	—	30	1	no	—
351	C₂³	#6714	1	1	yes	characteristic
352	Q₈	—	15	2	no	—
353	Q₈	—	30	1	no	—
354	D₄	—	15	2	no	—
355	D₄	—	30	4	no	—
356	D₄	—	30	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	30	1	no	—
361	C₂×C₄	—	30	4	no	—
362	C₂×C₄	—	30	1	no	—
363	C₂×C₄	—	30	1	no	—
364	C₂×C₄	—	60	2	no	—
365	C₂×C₄	—	60	1	no	—
366	C₂×C₄	—	60	1	no	—
367	C₂×C₄	C₈×D₁₅	1	2	yes	—
368	C₂×C₄	#6705	1	2	yes	—
369	C₂×C₄	#6714	1	1	yes	characteristic
370	C₂×C₄	#6714	1	1	yes	characteristic
371	C₂×C₄	#6714	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
373	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
374	C₂×C₄	C₂×#1220	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	60	2	no	—
377	C₂×C₃	—	2	2	no	—
378	C₂×C₃	#65294	1	1	yes	characteristic
379	C₂×C₃	C₂×#3952	1	1	yes	characteristic
380	C₂×C₃	#65422	1	1	yes	characteristic
381	D₃	—	20	2	no	—
382	C₅	#70755	1	1	yes	characteristic, complemented, Sylow
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	30	2	no	—
386	C₂²	—	60	1	no	—
387	C₂²	—	60	1	no	—
388	C₂²	#91104	1	2	yes	—
389	C₂²	C₂×#6714	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	30	2	no	—
394	C₄	—	60	1	no	—
395	C₄	—	60	1	no	—
396	C₄	#91104	1	2	yes	—
397	C₄	C₂×C₈×D₁₅	1	1	yes	characteristic
398	C₄	C₂×#6705	1	1	yes	characteristic
399	C₄	#91797	1	1	yes	characteristic
400	C₄	#91798	1	1	yes	characteristic
401	C₃	#10601548	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	60	2	no	—
404	C₂	#11751106	1	1	yes	characteristic
405	C₂	C₂×#91104	1	1	yes	characteristic
406	C₂	#11751234	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₆₀
commutator	C₃×C₄×C₅	C₂²×C₈
Frattini	C₄²	C₂²×D₁₅
Fitting	C₃×C₅×#431	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×#6817	C₄
cosocle	C₃×C₄²×C₅	C₂³
hypercenter	#431	D₁₅
hypocenter	C₃×C₅	#1477
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#431	C₂	semidirect
3. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
4. #11746280	C₂	semidirect
5. #11746277	C₂	semidirect
26. C₅×#431	D₃	semidirect
35. #6817	C₈	semidirect
59. C₃×#431	D₅	semidirect
99. D₆₀	C₂×C₈	semidirect
105. Dic₃₀	C₂×C₈	semidirect
154. #431	D₁₅	semidirect
326. C₃×C₅	#1477	semidirect
382. C₅	#70755	semidirect
401. C₃	#10601548	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6817	2
C₃×C₅×#431	2
C₂×C₄⋊(C₃⋊#168)	2
#11746280	2
#11746277	2
#10601548	3
#70755	5