Subgroups — C₂×C₃×#65373 #14429863

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₃×#65373	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#3941	C₂	1	2	yes	maximal
5	C₂×C₃×#3940	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#65373	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	—	2	1	no	—
9	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄×D₅	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	complemented
13	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×#685	—	2	1	no	—
17	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
18	C₂²×C₃×#168	C₂²	1	2	yes	—
19	C₃×C₄×D₂₀	—	2	2	no	—
20	C₃×C₄×D₂₀	C₂²	1	4	yes	—
21	C₃×#3941	C₂²	1	8	yes	—
22	C₃×#3940	C₂²	1	8	yes	complemented
23	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
24	C₂×C₃×#476	—	5	1	no	maximal, Hall
25	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic
27	#65373	C₂×C₃	1	8	yes	direct product factor
28	C₂×#3941	C₂×C₃	1	2	yes	—
29	C₂×#3940	C₂×C₃	1	2	yes	complemented
30	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂³×C₃×D₅	—	2	1	no	—
32	C₂×C₃×C₅×Q₈	—	2	4	no	—
33	C₂×C₃×C₅×Q₈	—	4	4	no	—
34	C₂²×C₃×C₄×C₅	—	2	2	no	—
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₃×Dic₅	—	2	1	no	—
39	C₂×C₃×D₂₀	—	2	1	no	—
40	C₂×C₃×D₂₀	—	2	2	no	—
41	C₂×C₃×D₂₀	Q₈	1	4	yes	complemented
42	C₂×C₃×D₂₀	C₂³	1	2	yes	—
43	C₂×C₃×C₄×D₅	—	2	4	no	—
44	C₂×C₃×C₄×D₅	—	4	4	no	—
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₅×C₄⋊C₄	—	2	2	no	—
47	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
48	C₃×C₄²×C₅	D₄	1	2	yes	—
49	C₃×C₄²×C₅	C₂³	1	2	yes	—
50	C₃×#685	—	2	4	no	—
51	C₃×C₄⋊Dic₅	—	2	1	no	—
52	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
53	C₂×C₃×#168	—	2	4	no	—
54	C₂×C₃×#168	C₂³	1	4	yes	—
55	C₂×C₃×C₄⋊Q₈	D₅	1	1	yes	characteristic, complemented
56	C₂×C₃×C₄×D₄	—	5	1	no	—
57	C₃×#476	—	5	8	no	—
58	C₂×C₃×#106	—	5	2	no	—
59	C₂×C₃×C₄⋊C₈	—	5	1	no	—
60	C₂×C₃×#102	—	5	2	no	—
61	C₂²×C₅×Q₈	—	2	1	no	—
62	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
63	C₂²×C₄×D₅	—	2	1	no	—
64	C₅×C₄⋊Q₈	—	2	2	no	—
65	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	complemented
66	C₂×C₅×C₄⋊C₄	—	2	1	no	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
69	C₂×#685	—	2	1	no	—
70	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
71	C₂²×#168	C₂²×C₃	1	2	yes	—
72	C₄×D₂₀	—	2	2	no	—
73	C₄×D₂₀	C₂²×C₃	1	4	yes	—
74	#3941	C₂²×C₃	1	8	yes	—
75	#3940	C₂²×C₃	1	8	yes	complemented
76	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
77	C₂×#476	—	5	1	no	Sylow
78	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₃×D₅	—	2	4	no	—
80	C₂²×C₃×D₅	—	2	2	no	—
81	C₂²×C₃×D₅	—	4	2	no	—
82	C₂²×C₃×D₅	—	4	2	no	—
83	C₃×C₅×Q₈	—	4	8	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	4	4	no	—
87	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
92	C₂×C₃×C₄×C₅	#41	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
94	C₂×C₃×Dic₅	—	2	2	no	—
95	C₂×C₃×Dic₅	—	4	2	no	—
96	C₃×D₂₀	—	2	4	no	—
97	C₃×D₂₀	—	2	2	no	—
98	C₃×D₂₀	C₂×Q₈	1	4	yes	complemented
99	C₃×C₄×D₅	—	4	8	no	—
100	C₃×#168	—	2	4	no	—
101	C₂²×C₃×Q₈	—	2	1	no	—
102	C₂²×C₃×D₄	—	5	1	no	—
103	C₂³×C₃×C₄	—	10	1	no	—
104	C₂²×C₃×C₈	—	5	2	no	—
105	C₃×C₄⋊Q₈	—	2	2	no	—
106	C₃×C₄⋊Q₈	C₂×D₅	1	4	yes	complemented
107	C₃×C₄×D₄	—	5	4	no	—
108	C₃×C₄×D₄	—	10	2	no	—
109	C₂×C₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₃×C₄⋊C₄	—	5	1	no	—
111	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
112	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
113	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
114	C₃×#106	—	5	8	no	—
115	C₃×C₄⋊C₈	—	5	4	no	—
116	C₃×#102	—	5	8	no	—
117	C₂³×D₅	—	2	1	no	—
118	C₂×C₅×Q₈	—	2	4	no	—
119	C₂×C₅×Q₈	—	4	4	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
124	C₂²×Dic₅	—	2	1	no	—
125	C₂×D₂₀	—	2	1	no	—
126	C₂×D₂₀	—	2	2	no	—
127	C₂×D₂₀	C₃×Q₈	1	4	yes	complemented
128	C₂×D₂₀	C₂³×C₃	1	2	yes	—
129	C₂×C₄×D₅	—	2	4	no	—
130	C₂×C₄×D₅	—	4	4	no	—
131	C₅×C₄⋊C₄	—	2	4	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
134	C₄²×C₅	C₃×D₄	1	2	yes	—
135	C₄²×C₅	C₂³×C₃	1	2	yes	—
136	#685	—	2	4	no	—
137	C₄⋊Dic₅	—	2	1	no	—
138	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
139	C₂×#168	—	2	4	no	—
140	C₂×#168	C₂³×C₃	1	4	yes	—
141	C₂×C₄⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
142	C₂×C₄×D₄	—	5	1	no	—
143	#476	—	5	8	no	—
144	C₂×#106	—	5	2	no	—
145	C₂×C₄⋊C₈	—	5	1	no	—
146	C₂×#102	—	5	2	no	—
147	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
148	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
149	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
150	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₃×D₅	—	2	4	no	—
152	C₂×C₃×D₅	—	4	2	no	—
153	C₂×C₃×D₅	—	4	2	no	—
154	C₂×C₃×D₅	—	4	8	no	—
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	—	4	4	no	—
157	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
158	C₃×C₄×C₅	C₂×SD₁₆	1	4	yes	—
159	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
160	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
161	C₃×Dic₅	—	4	2	no	—
162	C₂⁴×C₃	—	10	1	no	—
163	C₂×C₃×Q₈	—	2	4	no	—
164	C₂×C₃×Q₈	—	4	4	no	—
165	C₂×C₃×D₄	—	5	4	no	—
166	C₂×C₃×D₄	—	5	2	no	—
167	C₂×C₃×D₄	—	10	2	no	—
168	C₂×C₃×D₄	—	10	1	no	—
169	C₂²×C₃×C₄	—	2	2	no	—
170	C₂²×C₃×C₄	—	10	1	no	—
171	C₂²×C₃×C₄	—	10	4	no	—
172	C₂²×C₃×C₄	—	20	4	no	—
173	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
176	C₂×C₃×C₈	—	5	4	no	—
177	C₂×C₃×C₈	—	10	4	no	—
178	C₃×C₄⋊C₄	—	2	4	no	—
179	C₃×C₄⋊C₄	—	2	2	no	—
180	C₃×C₄⋊C₄	—	5	2	no	—
181	C₃×C₄⋊C₄	—	10	1	no	—
182	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
183	C₃×C₂²⋊C₄	—	10	4	no	—
184	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
185	C₃×C₄²	C₂²×D₅	1	2	yes	—
186	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
187	C₂²×D₅	—	2	4	no	—
188	C₂²×D₅	—	2	2	no	—
189	C₂²×D₅	—	4	2	no	—
190	C₂²×D₅	—	4	2	no	—
191	C₅×Q₈	—	4	8	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	4	4	no	—
195	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	—
196	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
197	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
200	C₂×C₄×C₅	C₃×#41	1	2	yes	—
201	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
202	C₂×Dic₅	—	2	2	no	—
203	C₂×Dic₅	—	4	2	no	—
204	D₂₀	—	2	4	no	—
205	D₂₀	—	2	2	no	—
206	D₂₀	C₂×C₃×Q₈	1	4	yes	complemented
207	C₄×D₅	—	4	8	no	—
208	#168	—	2	4	no	—
209	C₂²×Q₈	—	2	1	no	—
210	C₂²×D₄	—	5	1	no	—
211	C₂³×C₄	—	10	1	no	—
212	C₂²×C₈	—	5	2	no	—
213	C₄⋊Q₈	—	2	2	no	—
214	C₄⋊Q₈	C₂×C₃×D₅	1	4	yes	complemented
215	C₄×D₄	—	5	4	no	—
216	C₄×D₄	—	10	2	no	—
217	C₂×C₄⋊C₄	—	2	1	no	—
218	C₂×C₄⋊C₄	—	5	1	no	—
219	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
220	C₂×C₂²⋊C₄	—	10	1	no	—
221	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
222	#106	—	5	8	no	—
223	C₄⋊C₈	—	5	4	no	—
224	#102	—	5	8	no	—
225	C₂×C₃×C₅	#476	1	4	yes	complemented
226	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
228	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₃×D₅	—	4	4	no	—
230	C₂³×C₃	—	10	2	no	—
231	C₂³×C₃	—	10	4	no	—
232	C₂³×C₃	—	20	2	no	—
233	C₂³×C₃	—	20	2	no	—
234	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
235	C₃×Q₈	—	4	8	no	—
236	C₃×D₄	—	5	4	no	—
237	C₃×D₄	—	10	2	no	—
238	C₃×D₄	—	10	4	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	4	4	no	—
242	C₂×C₃×C₄	—	10	2	no	—
243	C₂×C₃×C₄	—	20	2	no	—
244	C₂×C₃×C₄	—	20	8	no	—
245	C₂×C₃×C₄	#688	1	4	yes	—
246	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
247	C₂×C₃×C₄	#713	1	2	yes	—
248	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
249	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
250	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
252	C₃×C₈	—	10	4	no	—
253	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
254	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
255	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
256	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
257	C₂×D₅	—	2	4	no	—
258	C₂×D₅	—	4	2	no	—
259	C₂×D₅	—	4	2	no	—
260	C₂×D₅	—	4	8	no	—
261	C₄×C₅	—	2	2	no	—
262	C₄×C₅	—	4	4	no	—
263	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
264	C₄×C₅	C₂×C₃×SD₁₆	1	4	yes	—
265	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
266	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
267	Dic₅	—	4	2	no	—
268	C₂⁴	—	10	1	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂×D₄	—	5	4	no	—
272	C₂×D₄	—	5	2	no	—
273	C₂×D₄	—	10	2	no	—
274	C₂×D₄	—	10	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	10	1	no	—
277	C₂²×C₄	—	10	4	no	—
278	C₂²×C₄	—	20	4	no	—
279	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
280	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
282	C₂×C₈	—	5	4	no	—
283	C₂×C₈	—	10	4	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	5	2	no	—
287	C₄⋊C₄	—	10	1	no	—
288	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
289	C₂²⋊C₄	—	10	4	no	—
290	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
291	C₄²	C₂²×C₃×D₅	1	2	yes	—
292	C₃×C₅	C₂×#476	1	1	yes	characteristic, complemented, Hall
293	C₂²×C₃	—	10	4	no	—
294	C₂²×C₃	—	20	2	no	—
295	C₂²×C₃	—	20	2	no	—
296	C₂²×C₃	—	20	8	no	—
297	C₂²×C₃	#4078	1	2	yes	—
298	C₂²×C₃	C₂×#688	1	2	yes	—
299	C₂²×C₃	#4092	1	2	yes	—
300	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	4	4	no	—
303	C₃×C₄	—	20	2	no	—
304	C₃×C₄	C₂×#688	1	4	yes	—
305	C₃×C₄	#4092	1	2	yes	—
306	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
307	C₃×C₄	C₂×#713	1	1	yes	characteristic
308	C₂×C₅	C₃×#476	1	4	yes	complemented
309	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
310	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
311	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
312	D₅	—	4	4	no	—
313	C₂³	—	10	4	no	—
314	C₂³	—	10	2	no	—
315	C₂³	—	20	2	no	—
316	C₂³	—	20	2	no	—
317	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
318	Q₈	—	4	8	no	—
319	D₄	—	5	4	no	—
320	D₄	—	10	4	no	—
321	D₄	—	10	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	10	2	no	—
326	C₂×C₄	—	20	2	no	—
327	C₂×C₄	—	20	8	no	—
328	C₂×C₄	C₃×#688	1	4	yes	—
329	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
330	C₂×C₄	C₃×#713	1	2	yes	—
331	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
332	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
333	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
334	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
335	C₈	—	10	4	no	—
336	C₂×C₃	—	20	4	no	—
337	C₂×C₃	#65373	1	4	yes	direct product factor
338	C₂×C₃	C₂×#4078	1	1	yes	characteristic
339	C₂×C₃	C₂²×#688	1	1	yes	characteristic
340	C₂×C₃	C₂×#4092	1	1	yes	characteristic
341	C₅	C₂×C₃×#476	1	1	yes	characteristic, complemented, Sylow
342	C₂²	—	10	4	no	—
343	C₂²	—	20	2	no	—
344	C₂²	—	20	2	no	—
345	C₂²	—	20	8	no	—
346	C₂²	C₃×#4078	1	2	yes	—
347	C₂²	C₂×C₃×#688	1	2	yes	—
348	C₂²	C₃×#4092	1	2	yes	—
349	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
350	C₄	—	2	2	no	—
351	C₄	—	4	4	no	—
352	C₄	—	20	2	no	—
353	C₄	C₂×C₃×#688	1	4	yes	—
354	C₄	C₃×#4092	1	2	yes	—
355	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
356	C₄	C₂×C₃×#713	1	1	yes	characteristic
357	C₃	C₂×#65373	1	1	yes	characteristic, direct product factor, Sylow
358	C₂	—	20	4	no	—
359	C₂	C₃×#65373	1	4	yes	direct product factor
360	C₂	C₂×C₃×#4078	1	1	yes	characteristic
361	C₂	C₂²×C₃×#688	1	1	yes	characteristic
362	C₂	C₂×C₃×#4092	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
hypercenter	C₂×C₃×C₄⋊Q₈	D₅
hypocenter	C₅	C₂×C₃×#476
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₃×#65373	C₂	direct (N × H)
5. C₂×C₃×#3940	C₂	semidirect
6. C₂×C₃×C₄⋊#168	C₂	semidirect
7. C₂×#65373	C₃	direct (N × H)
12. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
22. C₃×#3940	C₂²	semidirect
23. C₃×C₄⋊#168	C₂²	semidirect
25. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
27. #65373	C₂×C₃	direct (N × H)
29. C₂×#3940	C₂×C₃	semidirect
30. C₂×C₄⋊#168	C₂×C₃	semidirect
41. C₂×C₃×D₂₀	Q₈	semidirect
55. C₂×C₃×C₄⋊Q₈	D₅	semidirect
65. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
75. #3940	C₂²×C₃	semidirect
76. C₄⋊#168	C₂²×C₃	semidirect
98. C₃×D₂₀	C₂×Q₈	semidirect
106. C₃×C₄⋊Q₈	C₂×D₅	semidirect
127. C₂×D₂₀	C₃×Q₈	semidirect
141. C₂×C₄⋊Q₈	C₃×D₅	semidirect
206. D₂₀	C₂×C₃×Q₈	semidirect
214. C₄⋊Q₈	C₂×C₃×D₅	semidirect
225. C₂×C₃×C₅	#476	semidirect
292. C₃×C₅	C₂×#476	semidirect
308. C₂×C₅	C₃×#476	semidirect
337. C₂×C₃	#65373	direct (N × H)
341. C₅	C₂×C₃×#476	semidirect
357. C₃	C₂×#65373	direct (N × H)
359. C₂	C₃×#65373	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×C₄⋊Q₈	2
C₂×C₃×C₄×D₂₀	2
C₃×#65373	2
C₂×C₃×#3941	2
C₂×C₃×#3940	2
C₂×C₃×C₄⋊#168	2
C₂×#65373	3
C₂×C₃×#476	5

Subgroups — C2×C3×#65373 #14429863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65373 #14429863