Subgroups — C₂×C₃×#65301 #14414823

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#681	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₂²⋊#168	C₂	1	2	yes	maximal, complemented
4	C₃×#65301	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65301	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
10	C₃×C₄×C₅×D₄	C₄	1	4	yes	—
11	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	—	2	8	no	—
16	C₂×C₃×#681	C₂²	1	8	yes	complemented
17	C₂²×C₃×#168	C₂²	1	2	yes	—
18	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₃×C₂²⋊#168	C₂²	1	8	yes	complemented
21	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
22	C₃×C₄×#168	C₂²	1	4	yes	complemented
23	C₂×C₃×#436	—	5	1	no	maximal, Hall
24	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
25	C₂²×#681	C₂×C₃	1	2	yes	complemented
26	C₂×C₂²⋊#168	C₂×C₃	1	2	yes	complemented
27	#65301	C₂×C₃	1	8	yes	direct product factor
28	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
31	C₂×C₃×C₅×D₄	—	2	4	no	—
32	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
33	C₂²×C₃×C₄×C₅	—	2	4	no	—
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
42	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
43	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
44	C₃×C₄²×C₅	C₂³	1	2	yes	—
45	C₃×#681	—	2	16	no	—
46	C₂×C₃×#168	—	2	4	no	—
47	C₂×C₃×#168	—	2	2	no	—
48	C₂×C₃×#168	D₄	1	4	yes	complemented
49	C₂×C₃×#168	C₂³	1	2	yes	—
50	C₂×C₃×#168	C₂³	1	4	yes	—
51	C₂×C₃×#168	C₂³	1	2	yes	—
52	C₂²×C₃×M₁₆	—	5	2	no	—
53	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic
54	C₃×#436	—	5	8	no	—
55	C₂×C₃×C₄⋊C₈	—	5	1	no	—
56	C₂×C₃×C₂²⋊C₈	—	5	2	no	—
57	C₂×C₃×C₄×C₈	—	5	1	no	—
58	C₂²×C₅×D₄	C₃×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
60	C₄×C₅×D₄	C₃×C₄	1	4	yes	—
61	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
62	C₂×C₅×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
63	C₂×C₅×C₂²⋊C₄	C₃×C₄	1	2	yes	—
64	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
65	C₂×#681	—	2	8	no	—
66	C₂×#681	C₂²×C₃	1	8	yes	complemented
67	C₂²×#168	C₂²×C₃	1	2	yes	—
68	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
69	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
70	C₂²⋊#168	C₂²×C₃	1	8	yes	complemented
71	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
72	C₄×#168	C₂²×C₃	1	4	yes	complemented
73	C₂×#436	—	5	1	no	Sylow
74	C₂³×C₃×C₅	—	2	4	no	—
75	C₂³×C₃×C₅	—	2	4	no	—
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
78	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
79	C₃×C₅×D₄	—	2	8	no	—
80	C₂×C₃×C₄×C₅	—	2	4	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	8	no	—
83	C₂×C₃×C₄×C₅	—	2	4	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	#41	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
93	C₃×#168	—	2	4	no	—
94	C₃×#168	—	2	2	no	—
95	C₃×#168	C₂×D₄	1	4	yes	complemented
96	C₂²×C₃×D₄	Dic₅	1	1	yes	characteristic
97	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
98	C₂×C₃×M₁₆	—	5	8	no	—
99	C₂×C₃×M₁₆	—	10	8	no	—
100	C₂²×C₃×C₈	—	5	1	no	—
101	C₂²×C₃×C₈	—	5	2	no	—
102	C₂²×C₃×C₈	—	5	1	no	—
103	C₃×C₄×D₄	Dic₅	1	4	yes	—
104	C₃×C₄×D₄	C₂×D₅	1	4	yes	—
105	C₂×C₃×C₄⋊C₄	Dic₅	1	1	yes	characteristic
106	C₂×C₃×C₂²⋊C₄	Dic₅	1	2	yes	—
107	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
108	C₃×C₄⋊C₈	—	5	4	no	—
109	C₃×C₂²⋊C₈	—	5	8	no	—
110	C₃×C₄×C₈	—	5	4	no	—
111	C₂⁴×C₅	C₂×C₃×C₄	1	2	yes	—
112	C₂×C₅×D₄	—	2	4	no	—
113	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	2	4	no	—
116	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
118	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
119	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
121	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
122	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
123	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
124	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
125	C₄²×C₅	C₂³×C₃	1	2	yes	—
126	#681	—	2	16	no	—
127	C₂×#168	—	2	4	no	—
128	C₂×#168	—	2	2	no	—
129	C₂×#168	C₃×D₄	1	4	yes	complemented
130	C₂×#168	C₂³×C₃	1	2	yes	—
131	C₂×#168	C₂³×C₃	1	4	yes	—
132	C₂×#168	C₂³×C₃	1	2	yes	—
133	C₂²×M₁₆	—	5	2	no	—
134	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic
135	#436	—	5	8	no	—
136	C₂×C₄⋊C₈	—	5	1	no	—
137	C₂×C₂²⋊C₈	—	5	2	no	—
138	C₂×C₄×C₈	—	5	1	no	—
139	C₂²×C₃×C₅	—	2	4	no	—
140	C₂²×C₃×C₅	—	2	4	no	—
141	C₂²×C₃×C₅	—	2	4	no	—
142	C₂²×C₃×C₅	—	4	8	no	—
143	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
144	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
145	C₂²×C₃×C₅	#131	1	2	yes	—
146	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
147	C₃×C₄×C₅	—	2	4	no	—
148	C₃×C₄×C₅	—	2	2	no	—
149	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
150	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
151	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
152	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
153	C₂⁴×C₃	C₂×Dic₅	1	2	yes	—
154	C₂×C₃×D₄	—	2	4	no	—
155	C₂×C₃×D₄	C₂×Dic₅	1	4	yes	—
156	C₂²×C₃×C₄	—	2	4	no	—
157	C₂²×C₃×C₄	—	2	4	no	—
158	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
160	C₂²×C₃×C₄	C₂×Dic₅	1	4	yes	—
161	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
163	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
164	C₃×M₁₆	—	10	16	no	—
165	C₂×C₃×C₈	—	5	4	no	—
166	C₂×C₃×C₈	—	5	2	no	—
167	C₂×C₃×C₈	—	5	2	no	—
168	C₂×C₃×C₈	—	5	4	no	—
169	C₂×C₃×C₈	—	10	4	no	—
170	C₂×C₃×C₈	—	10	2	no	—
171	C₃×C₄⋊C₄	C₂×Dic₅	1	4	yes	—
172	C₃×C₂²⋊C₄	C₂×Dic₅	1	8	yes	—
173	C₃×C₄²	C₂×Dic₅	1	2	yes	—
174	C₃×C₄²	C₂²×D₅	1	2	yes	—
175	C₂³×C₅	—	2	4	no	—
176	C₂³×C₅	—	2	4	no	—
177	C₂³×C₅	—	2	4	no	—
178	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
179	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
180	C₅×D₄	—	2	8	no	—
181	C₂×C₄×C₅	—	2	4	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	8	no	—
184	C₂×C₄×C₅	—	2	4	no	—
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	C₃×M₁₆	1	4	yes	complemented
187	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
188	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
189	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
191	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
192	C₂×C₄×C₅	C₃×#41	1	2	yes	—
193	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
194	#168	—	2	4	no	—
195	#168	—	2	2	no	—
196	#168	C₂×C₃×D₄	1	4	yes	complemented
197	C₂²×D₄	C₃×Dic₅	1	1	yes	characteristic
198	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
199	C₂×M₁₆	—	5	8	no	—
200	C₂×M₁₆	—	10	8	no	—
201	C₂²×C₈	—	5	1	no	—
202	C₂²×C₈	—	5	2	no	—
203	C₂²×C₈	—	5	1	no	—
204	C₄×D₄	C₃×Dic₅	1	4	yes	—
205	C₄×D₄	C₂×C₃×D₅	1	4	yes	—
206	C₂×C₄⋊C₄	C₃×Dic₅	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	C₃×Dic₅	1	2	yes	—
208	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
209	C₄⋊C₈	—	5	4	no	—
210	C₂²⋊C₈	—	5	8	no	—
211	C₄×C₈	—	5	4	no	—
212	C₂×C₃×C₅	—	4	4	no	—
213	C₂×C₃×C₅	#436	1	4	yes	complemented
214	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
216	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
217	C₂³×C₃	—	2	4	no	—
218	C₂³×C₃	—	2	4	no	—
219	C₂³×C₃	—	2	4	no	—
220	C₂³×C₃	C₂²×Dic₅	1	4	yes	—
221	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
222	C₃×D₄	—	2	8	no	—
223	C₂×C₃×C₄	—	2	4	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	4	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	2	8	no	—
228	C₂×C₃×C₄	#681	1	4	yes	complemented
229	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
230	C₂×C₃×C₄	#711	1	2	yes	—
231	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
232	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
233	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
234	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
236	C₃×C₈	—	5	4	no	—
237	C₃×C₈	—	10	4	no	—
238	C₃×C₈	—	10	2	no	—
239	C₂²×C₅	—	2	4	no	—
240	C₂²×C₅	—	2	4	no	—
241	C₂²×C₅	—	2	4	no	—
242	C₂²×C₅	—	4	8	no	—
243	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
244	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
245	C₂²×C₅	C₃×#131	1	2	yes	—
246	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
247	C₄×C₅	—	2	2	no	—
248	C₄×C₅	—	2	4	no	—
249	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
250	C₄×C₅	C₂×C₃×M₁₆	1	4	yes	complemented
251	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
252	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
253	C₂⁴	C₂×C₃×Dic₅	1	2	yes	—
254	C₂×D₄	—	2	4	no	—
255	C₂×D₄	C₂×C₃×Dic₅	1	4	yes	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
260	C₂²×C₄	C₂×C₃×Dic₅	1	4	yes	—
261	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
263	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
264	M₁₆	—	10	16	no	—
265	C₂×C₈	—	5	4	no	—
266	C₂×C₈	—	5	2	no	—
267	C₂×C₈	—	5	2	no	—
268	C₂×C₈	—	5	4	no	—
269	C₂×C₈	—	10	4	no	—
270	C₂×C₈	—	10	2	no	—
271	C₄⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
272	C₂²⋊C₄	C₂×C₃×Dic₅	1	8	yes	—
273	C₄²	C₂×C₃×Dic₅	1	2	yes	—
274	C₄²	C₂²×C₃×D₅	1	2	yes	—
275	C₃×C₅	C₂×#436	1	1	yes	characteristic, complemented, Hall
276	C₂²×C₃	—	2	4	no	—
277	C₂²×C₃	—	2	4	no	—
278	C₂²×C₃	—	2	4	no	—
279	C₂²×C₃	—	4	8	no	—
280	C₂²×C₃	C₂×#681	1	2	yes	—
281	C₂²×C₃	D₄×Dic₅	1	2	yes	—
282	C₂²×C₃	#4094	1	2	yes	—
283	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
284	C₃×C₄	—	2	4	no	—
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	C₂×#681	1	4	yes	complemented
287	C₃×C₄	D₄×Dic₅	1	2	yes	—
288	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
289	C₃×C₄	C₂×#711	1	1	yes	characteristic
290	C₂×C₅	—	4	4	no	—
291	C₂×C₅	C₃×#436	1	4	yes	complemented
292	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
293	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
294	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
295	C₂³	—	2	4	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	2	4	no	—
298	C₂³	C₂²×C₃×Dic₅	1	4	yes	—
299	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
300	D₄	—	2	8	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	C₃×#681	1	4	yes	complemented
307	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
308	C₂×C₄	C₃×#711	1	2	yes	—
309	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
310	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	—
311	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
312	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
313	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
314	C₈	—	5	4	no	—
315	C₈	—	10	4	no	—
316	C₈	—	10	2	no	—
317	C₂×C₃	—	4	4	no	—
318	C₂×C₃	#65301	1	4	yes	direct product factor
319	C₂×C₃	C₂²×#681	1	1	yes	characteristic
320	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
321	C₂×C₃	C₂×#4094	1	1	yes	characteristic
322	C₅	C₂×C₃×#436	1	1	yes	characteristic, complemented, Sylow
323	C₂²	—	2	4	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	4	8	no	—
327	C₂²	C₂×C₃×#681	1	2	yes	—
328	C₂²	C₃×D₄×Dic₅	1	2	yes	—
329	C₂²	C₃×#4094	1	2	yes	—
330	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
331	C₄	—	2	4	no	—
332	C₄	—	2	2	no	—
333	C₄	C₂×C₃×#681	1	4	yes	complemented
334	C₄	C₃×D₄×Dic₅	1	2	yes	—
335	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
336	C₄	C₂×C₃×#711	1	1	yes	characteristic
337	C₃	C₂×#65301	1	1	yes	characteristic, direct product factor, Sylow
338	C₂	—	4	4	no	—
339	C₂	C₃×#65301	1	4	yes	direct product factor
340	C₂	C₂²×C₃×#681	1	1	yes	characteristic
341	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic
342	C₂	C₂×C₃×#4094	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₃×C₅×D₄	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₂×C₃×#436
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×#681	C₂	semidirect
3. C₂×C₃×C₂²⋊#168	C₂	semidirect
4. C₃×#65301	C₂	direct (N × H)
5. C₂×C₃×C₄⋊#168	C₂	semidirect
6. C₂×C₃×C₄×#168	C₂	semidirect
7. C₂×#65301	C₃	direct (N × H)
16. C₂×C₃×#681	C₂²	semidirect
20. C₃×C₂²⋊#168	C₂²	semidirect
21. C₃×C₄⋊#168	C₂²	semidirect
22. C₃×C₄×#168	C₂²	semidirect
25. C₂²×#681	C₂×C₃	semidirect
26. C₂×C₂²⋊#168	C₂×C₃	semidirect
27. #65301	C₂×C₃	direct (N × H)
28. C₂×C₄⋊#168	C₂×C₃	semidirect
29. C₂×C₄×#168	C₂×C₃	semidirect
48. C₂×C₃×#168	D₄	semidirect
66. C₂×#681	C₂²×C₃	semidirect
70. C₂²⋊#168	C₂²×C₃	semidirect
71. C₄⋊#168	C₂²×C₃	semidirect
72. C₄×#168	C₂²×C₃	semidirect
85. C₂×C₃×C₄×C₅	M₁₆	semidirect
95. C₃×#168	C₂×D₄	semidirect
129. C₂×#168	C₃×D₄	semidirect
150. C₃×C₄×C₅	C₂×M₁₆	semidirect
186. C₂×C₄×C₅	C₃×M₁₆	semidirect
196. #168	C₂×C₃×D₄	semidirect
213. C₂×C₃×C₅	#436	semidirect
228. C₂×C₃×C₄	#681	semidirect
250. C₄×C₅	C₂×C₃×M₁₆	semidirect
275. C₃×C₅	C₂×#436	semidirect
286. C₃×C₄	C₂×#681	semidirect
291. C₂×C₅	C₃×#436	semidirect
306. C₂×C₄	C₃×#681	semidirect
318. C₂×C₃	#65301	direct (N × H)
322. C₅	C₂×C₃×#436	semidirect
333. C₄	C₂×C₃×#681	semidirect
337. C₃	C₂×#65301	direct (N × H)
339. C₂	C₃×#65301	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×C₄×C₅×D₄	2
C₂²×C₃×#681	2
C₂×C₃×C₂²⋊#168	2
C₃×#65301	2
C₂×C₃×C₄⋊#168	2
C₂×C₃×C₄×#168	2
C₂×#65301	3
C₂×C₃×#436	5

Subgroups — C2×C3×#65301 #14414823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65301 #14414823