Subgroups — C₃×C₄×#4050 #14416222

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4050	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×#709	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65402	C₂	1	2	yes	maximal, complemented
5	C₃×#65395	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄×Dic₂₀	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×D₄₀	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#677	C₂	1	4	yes	maximal, complemented
9	C₄×#4050	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#709	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₃×C₄×C₂²⋊D₅	—	2	4	no	—
15	C₃×#4072	C₂²	1	2	yes	—
16	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
17	C₃×#4050	C₄	1	8	yes	direct product factor
18	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
19	C₂×C₃×#677	C₂²	1	2	yes	—
20	C₃×C₄×D₂₀	C₂²	1	4	yes	—
21	C₃×#4018	—	2	2	no	—
22	C₃×C₄²×D₅	—	2	2	no	—
23	C₃×C₄×Dic₁₀	C₂²	1	4	yes	—
24	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
26	C₃×#3953	C₂²	1	4	yes	—
27	C₃×#3950	C₂²	1	2	yes	—
28	C₃×#3949	C₂²	1	2	yes	—
29	C₃×#3948	C₂²	1	4	yes	—
30	C₃×C₄×#135	—	5	1	no	maximal, Hall
31	C₂×#4050	C₂×C₃	1	1	yes	characteristic
32	C₄×#709	C₂×C₃	1	2	yes	complemented
33	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
34	#65402	C₂×C₃	1	2	yes	complemented
35	#65395	C₂×C₃	1	1	yes	characteristic, complemented
36	C₄×Dic₂₀	C₂×C₃	1	2	yes	complemented
37	C₄×D₄₀	C₂×C₃	1	2	yes	complemented
38	C₄×#677	C₂×C₃	1	4	yes	complemented
39	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
42	C₃×#709	—	2	4	no	—
43	C₃×#709	C₂×C₄	1	8	yes	complemented
44	C₂×C₃×D₂₀	C₂³	1	2	yes	—
45	C₂×C₃×C₄×D₅	—	2	2	no	—
46	C₂×C₃×C₄×D₅	—	2	4	no	—
47	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
48	C₂×C₃×C₅×C₈	—	2	2	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
50	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
51	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂³	1	2	yes	—
56	C₃×C₂²⋊Dic₅	—	2	2	no	—
57	C₃×#685	—	2	4	no	—
58	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
59	C₃×#683	—	2	4	no	—
60	C₃×C₄×Dic₅	—	2	4	no	—
61	C₃×C₄×Dic₅	—	2	2	no	—
62	C₃×Dic₂₀	C₂×C₄	1	4	yes	complemented
63	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
64	C₃×#677	C₂×C₄	1	8	yes	complemented
65	C₂×C₃×#135	—	5	1	no	—
66	C₃×C₄×#41	—	5	2	no	—
67	C₃×C₄×Q₁₆	—	5	2	no	—
68	C₃×C₄×SD₁₆	—	5	4	no	—
69	C₃×C₄×D₈	—	5	2	no	—
70	C₃×#427	—	5	1	no	—
71	C₃×#416	—	5	2	no	—
72	C₂×C₃×C₄×C₈	D₅	1	1	yes	characteristic, complemented
73	C₂×#709	C₂²×C₃	1	2	yes	—
74	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
77	C₄×C₂²⋊D₅	—	2	4	no	—
78	#4072	C₂²×C₃	1	2	yes	—
79	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
80	#4050	C₃×C₄	1	8	yes	direct product factor
81	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
82	C₂×#677	C₂²×C₃	1	2	yes	—
83	C₄×D₂₀	C₂²×C₃	1	4	yes	—
84	#4018	—	2	2	no	—
85	C₄²×D₅	—	2	2	no	—
86	C₄×Dic₁₀	C₂²×C₃	1	4	yes	—
87	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
88	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
89	#3953	C₂²×C₃	1	4	yes	—
90	#3950	C₂²×C₃	1	2	yes	—
91	#3949	C₂²×C₃	1	2	yes	—
92	#3948	C₂²×C₃	1	4	yes	—
93	C₄×#135	—	5	1	no	Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₃×D₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	#41	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
103	C₃×C₂²⋊D₅	—	2	8	no	—
104	C₂×C₃×Dic₅	—	2	2	no	—
105	C₂×C₃×Dic₅	—	2	4	no	—
106	C₃×D₂₀	—	2	2	no	—
107	C₃×D₂₀	C₂²×C₄	1	4	yes	—
108	C₃×C₄×D₅	—	2	8	no	—
109	C₃×C₄×D₅	—	4	8	no	—
110	C₃×Dic₁₀	—	2	2	no	—
111	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
112	C₃×C₅×C₈	—	2	2	no	—
113	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
115	C₂×C₃×#41	—	5	2	no	—
116	C₃×#135	—	5	8	no	—
117	C₂×C₃×Q₁₆	—	5	1	no	—
118	C₂×C₃×SD₁₆	—	5	2	no	—
119	C₂×C₃×D₈	—	5	1	no	—
120	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
121	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
122	C₃×C₄×Q₈	—	5	4	no	—
123	C₃×C₄×D₄	—	5	4	no	—
124	C₃×C₄×D₄	—	10	4	no	—
125	C₃×#117	—	5	2	no	—
126	C₃×#117	—	10	2	no	—
127	C₂×C₃×C₄²	—	10	2	no	—
128	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
129	C₃×#107	—	5	2	no	—
130	C₃×#106	—	5	2	no	—
131	C₃×#103	—	5	4	no	—
132	C₃×#102	—	5	4	no	—
133	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
134	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
135	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
137	C₂×C₂²⋊D₅	—	2	2	no	—
138	#709	—	2	4	no	—
139	#709	C₂×C₃×C₄	1	8	yes	complemented
140	C₂×D₂₀	C₂³×C₃	1	2	yes	—
141	C₂×C₄×D₅	—	2	2	no	—
142	C₂×C₄×D₅	—	2	4	no	—
143	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
146	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
147	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
149	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
150	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
151	C₄²×C₅	C₂³×C₃	1	2	yes	—
152	C₂²⋊Dic₅	—	2	2	no	—
153	#685	—	2	4	no	—
154	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
155	#683	—	2	4	no	—
156	C₄×Dic₅	—	2	4	no	—
157	C₄×Dic₅	—	2	2	no	—
158	Dic₂₀	C₂×C₃×C₄	1	4	yes	complemented
159	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
160	#677	C₂×C₃×C₄	1	8	yes	complemented
161	C₂×#135	—	5	1	no	—
162	C₄×#41	—	5	2	no	—
163	C₄×Q₁₆	—	5	2	no	—
164	C₄×SD₁₆	—	5	4	no	—
165	C₄×D₈	—	5	2	no	—
166	#427	—	5	1	no	—
167	#416	—	5	2	no	—
168	C₂×C₄×C₈	C₃×D₅	1	1	yes	characteristic, complemented
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₃×D₅	—	2	4	no	—
173	C₂×C₃×D₅	—	4	4	no	—
174	C₃×C₄×C₅	—	2	2	no	—
175	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
176	C₃×C₄×C₅	#135	1	4	yes	complemented
177	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
179	C₃×Dic₅	—	2	4	no	—
180	C₃×Dic₅	—	4	4	no	—
181	C₃×#41	—	5	8	no	—
182	C₃×#41	—	10	4	no	—
183	C₂×C₃×Q₈	—	5	2	no	—
184	C₂×C₃×D₄	—	5	2	no	—
185	C₂×C₃×D₄	—	10	2	no	—
186	C₂²×C₃×C₄	—	10	2	no	—
187	C₂²×C₃×C₄	—	10	4	no	—
188	C₂²×C₃×C₄	D₂₀	1	2	yes	—
189	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
190	C₃×Q₁₆	—	5	4	no	—
191	C₃×SD₁₆	—	5	8	no	—
192	C₃×D₈	—	5	4	no	—
193	C₂×C₃×C₈	—	2	2	no	—
194	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
195	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
196	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
197	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
198	C₃×C₄⋊C₄	—	5	4	no	—
199	C₃×C₄⋊C₄	—	10	4	no	—
200	C₃×C₂²⋊C₄	—	10	2	no	—
201	C₃×C₂²⋊C₄	—	10	4	no	—
202	C₃×C₄²	—	10	2	no	—
203	C₃×C₄²	—	10	4	no	—
204	C₃×C₄²	D₂₀	1	1	yes	characteristic
205	C₃×C₄²	D₂₀	1	1	yes	characteristic
206	C₃×C₄²	C₂²×D₅	1	2	yes	—
207	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂²×D₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
211	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
212	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
214	C₂×C₄×C₅	C₃×#41	1	2	yes	—
215	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
216	C₂²⋊D₅	—	2	8	no	—
217	C₂×Dic₅	—	2	2	no	—
218	C₂×Dic₅	—	2	4	no	—
219	D₂₀	—	2	2	no	—
220	D₂₀	C₂²×C₃×C₄	1	4	yes	—
221	C₄×D₅	—	2	8	no	—
222	C₄×D₅	—	4	8	no	—
223	Dic₁₀	—	2	2	no	—
224	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
227	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
228	C₂×#41	—	5	2	no	—
229	#135	—	5	8	no	—
230	C₂×Q₁₆	—	5	1	no	—
231	C₂×SD₁₆	—	5	2	no	—
232	C₂×D₈	—	5	1	no	—
233	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
234	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
235	C₄×Q₈	—	5	4	no	—
236	C₄×D₄	—	5	4	no	—
237	C₄×D₄	—	10	4	no	—
238	#117	—	5	2	no	—
239	#117	—	10	2	no	—
240	C₂×C₄²	—	10	2	no	—
241	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
242	#107	—	5	2	no	—
243	#106	—	5	2	no	—
244	#103	—	5	4	no	—
245	#102	—	5	4	no	—
246	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
247	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×#135	1	2	yes	—
251	C₃×D₅	—	4	4	no	—
252	C₂³×C₃	—	10	2	no	—
253	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
254	C₃×Q₈	—	5	4	no	—
255	C₃×Q₈	—	10	2	no	—
256	C₃×D₄	—	5	4	no	—
257	C₃×D₄	—	10	8	no	—
258	C₃×D₄	—	10	2	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	10	2	no	—
261	C₂×C₃×C₄	—	10	8	no	—
262	C₂×C₃×C₄	—	10	4	no	—
263	C₂×C₃×C₄	—	20	8	no	—
264	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
265	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
266	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
268	C₂×C₃×C₄	#709	1	2	yes	—
269	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
270	C₃×C₈	—	2	2	no	—
271	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
272	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
275	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
276	C₂×D₅	—	2	4	no	—
277	C₂×D₅	—	4	4	no	—
278	C₄×C₅	—	2	2	no	—
279	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
280	C₄×C₅	C₃×#135	1	4	yes	complemented
281	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
282	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
283	Dic₅	—	2	4	no	—
284	Dic₅	—	4	4	no	—
285	#41	—	5	8	no	—
286	#41	—	10	4	no	—
287	C₂×Q₈	—	5	2	no	—
288	C₂×D₄	—	5	2	no	—
289	C₂×D₄	—	10	2	no	—
290	C₂²×C₄	—	10	2	no	—
291	C₂²×C₄	—	10	4	no	—
292	C₂²×C₄	C₃×D₂₀	1	2	yes	—
293	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
294	Q₁₆	—	5	4	no	—
295	SD₁₆	—	5	8	no	—
296	D₈	—	5	4	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	C₃×C₄×D₅	1	4	yes	complemented
299	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
300	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
302	C₄⋊C₄	—	5	4	no	—
303	C₄⋊C₄	—	10	4	no	—
304	C₂²⋊C₄	—	10	2	no	—
305	C₂²⋊C₄	—	10	4	no	—
306	C₄²	—	10	2	no	—
307	C₄²	—	10	4	no	—
308	C₄²	C₃×D₂₀	1	1	yes	characteristic
309	C₄²	C₃×D₂₀	1	1	yes	characteristic
310	C₄²	C₂²×C₃×D₅	1	2	yes	—
311	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	10	4	no	—
314	C₂²×C₃	—	20	4	no	—
315	C₂²×C₃	C₄×D₂₀	1	2	yes	—
316	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	—	10	4	no	—
319	C₃×C₄	—	20	4	no	—
320	C₃×C₄	C₄×D₂₀	1	2	yes	—
321	C₃×C₄	#4050	1	4	yes	direct product factor
322	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
323	C₃×C₄	C₂×#709	1	1	yes	characteristic
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
326	C₂×C₅	C₂×C₃×#135	1	2	yes	—
327	D₅	—	4	4	no	—
328	C₂³	—	10	2	no	—
329	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
330	Q₈	—	5	4	no	—
331	Q₈	—	10	2	no	—
332	D₄	—	5	4	no	—
333	D₄	—	10	8	no	—
334	D₄	—	10	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	10	2	no	—
337	C₂×C₄	—	10	8	no	—
338	C₂×C₄	—	10	4	no	—
339	C₂×C₄	—	20	8	no	—
340	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
341	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
342	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
344	C₂×C₄	C₃×#709	1	2	yes	—
345	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
346	C₈	—	2	2	no	—
347	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
348	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	—	20	4	no	—
351	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
352	C₂×C₃	C₂×#4050	1	2	yes	—
353	C₅	C₃×C₄×#135	1	1	yes	characteristic, complemented, Sylow
354	C₂²	—	2	2	no	—
355	C₂²	—	10	4	no	—
356	C₂²	—	20	4	no	—
357	C₂²	C₃×C₄×D₂₀	1	2	yes	—
358	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	10	4	no	—
361	C₄	—	20	4	no	—
362	C₄	C₃×C₄×D₂₀	1	2	yes	—
363	C₄	C₃×#4050	1	4	yes	direct product factor
364	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
365	C₄	C₂×C₃×#709	1	1	yes	characteristic
366	C₃	C₄×#4050	1	1	yes	characteristic, direct product factor, Sylow
367	C₂	—	2	2	no	—
368	C₂	—	20	4	no	—
369	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic
370	C₂	C₂×C₃×#4050	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4050	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×C₈	D₅
hypocenter	C₅	C₃×C₄×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄² ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×#709	C₂	semidirect
3. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
4. C₃×#65402	C₂	semidirect
5. C₃×#65395	C₂	semidirect
6. C₃×C₄×Dic₂₀	C₂	semidirect
7. C₃×C₄×D₄₀	C₂	semidirect
8. C₃×C₄×#677	C₂	semidirect
9. C₄×#4050	C₃	direct (N × H)
17. C₃×#4050	C₄	direct (N × H)
32. C₄×#709	C₂×C₃	semidirect
33. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
34. #65402	C₂×C₃	semidirect
35. #65395	C₂×C₃	semidirect
36. C₄×Dic₂₀	C₂×C₃	semidirect
37. C₄×D₄₀	C₂×C₃	semidirect
38. C₄×#677	C₂×C₃	semidirect
43. C₃×#709	C₂×C₄	semidirect
49. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
62. C₃×Dic₂₀	C₂×C₄	semidirect
63. C₃×D₄₀	C₂×C₄	semidirect
64. C₃×#677	C₂×C₄	semidirect
72. C₂×C₃×C₄×C₈	D₅	semidirect
80. #4050	C₃×C₄	direct (N × H)
139. #709	C₂×C₃×C₄	semidirect
145. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
158. Dic₂₀	C₂×C₃×C₄	semidirect
159. D₄₀	C₂×C₃×C₄	semidirect
160. #677	C₂×C₃×C₄	semidirect
168. C₂×C₄×C₈	C₃×D₅	semidirect
176. C₃×C₄×C₅	#135	semidirect
194. C₂×C₃×C₈	C₄×D₅	semidirect
280. C₄×C₅	C₃×#135	semidirect
298. C₂×C₈	C₃×C₄×D₅	semidirect
311. C₃×C₅	C₄×#135	semidirect
321. C₃×C₄	#4050	direct (N × H)
353. C₅	C₃×C₄×#135	semidirect
363. C₄	C₃×#4050	direct (N × H)
366. C₃	C₄×#4050	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×#4050	2
C₃×C₄×#709	2
C₂×C₃×C₄×C₅×C₈	2
C₃×#65402	2
C₃×#65395	2
C₃×C₄×Dic₂₀	2
C₃×C₄×D₄₀	2
C₃×C₄×#677	2
C₄×#4050	3
C₃×C₄×#135	5

Subgroups — C3×C4×#4050 #14416222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4050 #14416222