Subgroups — C₃×C₄×C₅×C₄⋊Q₈ #14275341

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 320 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
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	2	yes	maximal
3	C₃×C₅×#391	C₂	1	2	yes	maximal
4	C₃×C₅×#389	C₂	1	4	yes	maximal
5	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	4	yes	maximal
7	C₃×C₄³×C₅	C₂	1	1	yes	maximal, characteristic
8	C₄×C₅×C₄⋊Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
10	C₃×C₅×C₄⋊Q₈	C₄	1	8	yes	direct product factor
11	C₃×C₄×C₅×Q₈	—	2	8	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	8	yes	—
23	C₃×C₄×C₄⋊Q₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
25	C₂×C₄×C₅×Q₈	C₂×C₃	1	2	yes	—
26	C₅×#391	C₂×C₃	1	2	yes	—
27	C₅×#389	C₂×C₃	1	4	yes	—
28	C₅×#384	C₂×C₃	1	1	yes	characteristic
29	C₄×C₅×C₄⋊C₄	C₂×C₃	1	4	yes	—
30	C₄³×C₅	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×C₅×Q₈	—	2	4	no	—
32	C₂×C₃×C₅×Q₈	—	2	4	no	—
33	C₂×C₃×C₅×Q₈	C₂×C₄	1	8	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₃×C₅×C₄⋊C₄	—	2	8	no	—
42	C₃×C₅×C₄⋊C₄	—	2	4	no	—
43	C₃×C₅×C₄⋊C₄	—	2	8	no	—
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	16	yes	—
45	C₃×C₄²×C₅	—	2	8	no	—
46	C₃×C₄²×C₅	—	2	2	no	—
47	C₃×C₄²×C₅	—	2	4	no	—
48	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
49	C₃×C₄²×C₅	D₄	1	4	yes	—
50	C₃×C₄²×C₅	Q₈	1	8	yes	complemented
51	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
52	C₂×C₃×C₄×Q₈	C₂×C₅	1	2	yes	—
53	C₃×#391	C₂×C₅	1	2	yes	—
54	C₃×#389	C₂×C₅	1	4	yes	—
55	C₃×#384	C₂×C₅	1	1	yes	characteristic
56	C₃×C₄×C₄⋊C₄	C₂×C₅	1	4	yes	—
57	C₃×C₄³	C₂×C₅	1	1	yes	characteristic
58	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
59	C₅×C₄⋊Q₈	C₃×C₄	1	8	yes	direct product factor
60	C₄×C₅×Q₈	—	2	8	no	—
61	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
65	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
66	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
68	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
71	C₅×#95	C₂²×C₃	1	8	yes	—
72	C₄×C₄⋊Q₈	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
73	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
74	C₃×C₅×Q₈	—	2	16	no	—
75	C₂×C₃×C₄×C₅	—	2	4	no	—
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	2	2	no	—
79	C₂×C₃×C₄×C₅	—	2	4	no	—
80	C₂×C₃×C₄×C₅	—	2	4	no	—
81	C₂×C₃×C₄×C₅	—	2	8	no	—
82	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
83	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
85	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
89	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
90	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
91	C₂×C₃×C₄×C₅	#41	1	2	yes	—
92	C₂×C₃×C₄×C₅	#41	1	4	yes	—
93	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
94	C₃×C₄⋊Q₈	C₄×C₅	1	8	yes	direct product factor
95	C₃×C₄×Q₈	—	2	8	no	—
96	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
97	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
98	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
99	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
100	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
101	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
103	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
104	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
105	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
106	C₃×#95	C₂²×C₅	1	8	yes	—
107	C₂×C₅×Q₈	—	2	4	no	—
108	C₂×C₅×Q₈	—	2	4	no	—
109	C₂×C₅×Q₈	C₂×C₃×C₄	1	8	yes	—
110	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
111	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
112	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
114	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
116	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
117	C₅×C₄⋊C₄	—	2	8	no	—
118	C₅×C₄⋊C₄	—	2	4	no	—
119	C₅×C₄⋊C₄	—	2	8	no	—
120	C₅×C₄⋊C₄	C₂×C₃×C₄	1	16	yes	—
121	C₄²×C₅	—	2	8	no	—
122	C₄²×C₅	—	2	2	no	—
123	C₄²×C₅	—	2	4	no	—
124	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
125	C₄²×C₅	C₃×D₄	1	4	yes	—
126	C₄²×C₅	C₃×Q₈	1	8	yes	complemented
127	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
128	C₂×C₄×Q₈	C₂×C₃×C₅	1	2	yes	—
129	#391	C₂×C₃×C₅	1	2	yes	—
130	#389	C₂×C₃×C₅	1	4	yes	—
131	#384	C₂×C₃×C₅	1	1	yes	characteristic
132	C₄×C₄⋊C₄	C₂×C₃×C₅	1	4	yes	—
133	C₄³	C₂×C₃×C₅	1	1	yes	characteristic
134	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
135	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
136	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
137	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
138	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
139	C₃×C₄×C₅	—	2	8	no	—
140	C₃×C₄×C₅	—	2	2	no	—
141	C₃×C₄×C₅	—	2	4	no	—
142	C₃×C₄×C₅	—	4	4	no	—
143	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
144	C₃×C₄×C₅	C₄×Q₈	1	8	yes	complemented
145	C₃×C₄×C₅	C₄⋊Q₈	1	4	yes	direct product factor
146	C₂×C₃×Q₈	—	2	4	no	—
147	C₂×C₃×Q₈	—	2	4	no	—
148	C₂×C₃×Q₈	C₂×C₄×C₅	1	8	yes	—
149	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
150	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
151	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
153	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
155	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
156	C₃×C₄⋊C₄	—	2	8	no	—
157	C₃×C₄⋊C₄	—	2	4	no	—
158	C₃×C₄⋊C₄	—	2	8	no	—
159	C₃×C₄⋊C₄	C₂×C₄×C₅	1	16	yes	—
160	C₃×C₄²	—	2	8	no	—
161	C₃×C₄²	—	2	2	no	—
162	C₃×C₄²	—	2	4	no	—
163	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
164	C₃×C₄²	C₅×D₄	1	4	yes	—
165	C₃×C₄²	C₅×Q₈	1	8	yes	complemented
166	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
167	C₅×Q₈	—	2	16	no	—
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	2	4	no	—
174	C₂×C₄×C₅	—	2	8	no	—
175	C₂×C₄×C₅	C₂²×C₃×C₄	1	8	yes	—
176	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
177	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
178	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
179	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
180	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
181	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
182	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
183	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
184	C₂×C₄×C₅	C₃×#41	1	2	yes	—
185	C₂×C₄×C₅	C₃×#41	1	4	yes	—
186	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
187	C₄⋊Q₈	C₃×C₄×C₅	1	8	yes	direct product factor
188	C₄×Q₈	—	2	8	no	—
189	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
190	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
191	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
192	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
193	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
194	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
195	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
196	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
197	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
198	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
199	#95	C₂²×C₃×C₅	1	8	yes	—
200	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂×C₃×C₅	C₂×C₄×Q₈	1	2	yes	—
202	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
203	C₂×C₃×C₅	#532	1	1	yes	characteristic
204	C₂×C₃×C₅	#533	1	2	yes	—
205	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
206	C₃×Q₈	—	2	16	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	2	2	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	2	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	4	no	—
213	C₂×C₃×C₄	—	2	8	no	—
214	C₂×C₃×C₄	C₂²×C₄×C₅	1	8	yes	—
215	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
216	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
217	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
218	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
219	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
220	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
221	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
222	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
223	C₂×C₃×C₄	C₅×#41	1	2	yes	—
224	C₂×C₃×C₄	C₅×#41	1	4	yes	—
225	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
226	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
227	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
228	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
229	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
230	C₄×C₅	—	2	8	no	—
231	C₄×C₅	—	2	2	no	—
232	C₄×C₅	—	2	4	no	—
233	C₄×C₅	—	4	4	no	—
234	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
235	C₄×C₅	C₃×C₄×Q₈	1	8	yes	complemented
236	C₄×C₅	C₃×C₄⋊Q₈	1	4	yes	direct product factor
237	C₂×Q₈	—	2	4	no	—
238	C₂×Q₈	—	2	4	no	—
239	C₂×Q₈	C₂×C₃×C₄×C₅	1	8	yes	—
240	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
241	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
242	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
243	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
244	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
245	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
246	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
247	C₄⋊C₄	—	2	8	no	—
248	C₄⋊C₄	—	2	4	no	—
249	C₄⋊C₄	—	2	8	no	—
250	C₄⋊C₄	C₂×C₃×C₄×C₅	1	16	yes	—
251	C₄²	—	2	8	no	—
252	C₄²	—	2	2	no	—
253	C₄²	—	2	4	no	—
254	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
255	C₄²	C₃×C₅×D₄	1	4	yes	—
256	C₄²	C₃×C₅×Q₈	1	8	yes	complemented
257	C₃×C₅	C₄×C₄⋊Q₈	1	1	yes	characteristic, direct product factor, Hall
258	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
259	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
260	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
261	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
262	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
263	C₃×C₄	—	2	8	no	—
264	C₃×C₄	—	2	2	no	—
265	C₃×C₄	—	2	4	no	—
266	C₃×C₄	—	4	4	no	—
267	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
268	C₃×C₄	C₄×C₅×Q₈	1	8	yes	complemented
269	C₃×C₄	C₅×C₄⋊Q₈	1	4	yes	direct product factor
270	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
271	C₂×C₅	C₂×C₃×C₄×Q₈	1	2	yes	—
272	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
273	C₂×C₅	C₃×#532	1	1	yes	characteristic
274	C₂×C₅	C₃×#533	1	2	yes	—
275	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
276	Q₈	—	2	16	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	2	4	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	C₂²×C₃×C₄×C₅	1	8	yes	—
285	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
286	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
287	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
288	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
289	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
290	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
291	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
292	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
293	C₂×C₄	C₃×C₅×#41	1	2	yes	—
294	C₂×C₄	C₃×C₅×#41	1	4	yes	—
295	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
296	C₂×C₃	C₂×C₄×C₅×Q₈	1	2	yes	—
297	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
298	C₂×C₃	C₅×#532	1	1	yes	characteristic
299	C₂×C₃	C₅×#533	1	2	yes	—
300	C₅	C₃×C₄×C₄⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
301	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
302	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
303	C₂²	C₂²×C₃×C₅×Q₈	1	2	yes	—
304	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
305	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
306	C₄	—	2	8	no	—
307	C₄	—	2	2	no	—
308	C₄	—	2	4	no	—
309	C₄	—	4	4	no	—
310	C₄	C₃×C₄×C₅×D₄	1	4	yes	—
311	C₄	C₃×C₄×C₅×Q₈	1	8	yes	complemented
312	C₄	C₃×C₅×C₄⋊Q₈	1	4	yes	direct product factor
313	C₃	C₄×C₅×C₄⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
314	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
315	C₂	C₂×C₃×C₄×C₅×Q₈	1	2	yes	—
316	C₂	C₂×C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
317	C₂	C₃×C₅×#532	1	1	yes	characteristic
318	C₂	C₃×C₅×#533	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄×C₅	C₂³
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
socle, prime radical	C₂³×C₃×C₅	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₄×C₅×C₄⋊Q₈	C₃	direct (N × H)
10. C₃×C₅×C₄⋊Q₈	C₄	direct (N × H)
23. C₃×C₄×C₄⋊Q₈	C₅	direct (N × H)
50. C₃×C₄²×C₅	Q₈	semidirect
59. C₅×C₄⋊Q₈	C₃×C₄	direct (N × H)
72. C₄×C₄⋊Q₈	C₃×C₅	direct (N × H)
94. C₃×C₄⋊Q₈	C₄×C₅	direct (N × H)
126. C₄²×C₅	C₃×Q₈	semidirect
144. C₃×C₄×C₅	C₄×Q₈	semidirect
145. C₃×C₄×C₅	C₄⋊Q₈	direct (N × H)
165. C₃×C₄²	C₅×Q₈	semidirect
187. C₄⋊Q₈	C₃×C₄×C₅	direct (N × H)
235. C₄×C₅	C₃×C₄×Q₈	semidirect
236. C₄×C₅	C₃×C₄⋊Q₈	direct (N × H)
256. C₄²	C₃×C₅×Q₈	semidirect
257. C₃×C₅	C₄×C₄⋊Q₈	direct (N × H)
268. C₃×C₄	C₄×C₅×Q₈	semidirect
269. C₃×C₄	C₅×C₄⋊Q₈	direct (N × H)
300. C₅	C₃×C₄×C₄⋊Q₈	direct (N × H)
311. C₄	C₃×C₄×C₅×Q₈	semidirect
312. C₄	C₃×C₅×C₄⋊Q₈	direct (N × H)
313. C₃	C₄×C₅×C₄⋊Q₈	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×C₅×Q₈	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#384	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄³×C₅	2
C₄×C₅×C₄⋊Q₈	3
C₃×C₄×C₄⋊Q₈	5

Subgroups — C3×C4×C5×C4⋊Q8 #14275341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₅×C₄⋊Q₈ #14275341