Subgroups — C₂×C₅×#5084 #14429862

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×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
3	C₅×#5084	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₅×#809	C₂	1	2	yes	maximal
5	C₂×C₅×#808	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#476	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	—	2	1	no	—
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	—	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×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
19	C₄×C₅×D₁₂	—	2	2	no	—
20	C₄×C₅×D₁₂	C₂²	1	4	yes	—
21	C₅×#809	C₂²	1	8	yes	—
22	C₅×#808	C₂²	1	8	yes	complemented
23	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
24	C₂×#5084	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
26	C₂×C₄×C₅×D₄	—	3	1	no	—
27	C₅×#476	—	3	8	no	—
28	C₂×C₅×#106	—	3	2	no	—
29	C₂×C₅×C₄⋊C₈	—	3	1	no	—
30	C₂×C₅×#102	—	3	2	no	—
31	C₂³×C₅×D₃	—	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×C₅×Dic₃	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	2	no	—
41	C₂×C₅×D₁₂	Q₈	1	4	yes	complemented
42	C₂×C₅×D₁₂	C₂³	1	2	yes	—
43	C₂×C₄×C₅×D₃	—	2	4	no	—
44	C₂×C₄×C₅×D₃	—	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	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
51	C₅×C₄⋊Dic₃	—	2	1	no	—
52	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
53	C₂×C₅×C₃⋊C₈	—	2	4	no	—
54	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
55	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
57	#5084	C₂×C₅	1	8	yes	direct product factor
58	C₂×#809	C₂×C₅	1	2	yes	—
59	C₂×#808	C₂×C₅	1	2	yes	complemented
60	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂²×C₅×Q₈	—	2	1	no	—
62	C₂²×C₅×D₄	—	3	1	no	—
63	C₂³×C₄×C₅	—	6	1	no	—
64	C₂²×C₅×C₈	—	3	2	no	—
65	C₅×C₄⋊Q₈	—	2	2	no	—
66	C₅×C₄⋊Q₈	C₂×D₃	1	4	yes	complemented
67	C₄×C₅×D₄	—	3	4	no	—
68	C₄×C₅×D₄	—	6	2	no	—
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	3	1	no	—
71	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
73	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
74	C₅×#106	—	3	8	no	—
75	C₅×C₄⋊C₈	—	3	4	no	—
76	C₅×#102	—	3	8	no	—
77	C₂×#476	—	3	1	no	Sylow
78	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₅×D₃	—	2	4	no	—
80	C₂²×C₅×D₃	—	2	2	no	—
81	C₂²×C₅×D₃	—	4	2	no	—
82	C₂²×C₅×D₃	—	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×C₅×Dic₃	—	2	2	no	—
95	C₂×C₅×Dic₃	—	4	2	no	—
96	C₅×D₁₂	—	2	4	no	—
97	C₅×D₁₂	—	2	2	no	—
98	C₅×D₁₂	C₂×Q₈	1	4	yes	complemented
99	C₄×C₅×D₃	—	4	8	no	—
100	C₅×C₃⋊C₈	—	2	4	no	—
101	C₂²×C₃×Q₈	—	2	1	no	—
102	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
103	C₂²×C₄×D₃	—	2	1	no	—
104	C₃×C₄⋊Q₈	—	2	2	no	—
105	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	complemented
106	C₂×C₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
108	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
109	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
110	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
111	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
112	C₄×D₁₂	—	2	2	no	—
113	C₄×D₁₂	C₂²×C₅	1	4	yes	—
114	#809	C₂²×C₅	1	8	yes	—
115	#808	C₂²×C₅	1	8	yes	complemented
116	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
117	C₂⁴×C₅	—	6	1	no	—
118	C₂×C₅×Q₈	—	2	4	no	—
119	C₂×C₅×Q₈	—	4	4	no	—
120	C₂×C₅×D₄	—	3	4	no	—
121	C₂×C₅×D₄	—	3	2	no	—
122	C₂×C₅×D₄	—	6	2	no	—
123	C₂×C₅×D₄	—	6	1	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	6	1	no	—
126	C₂²×C₄×C₅	—	6	4	no	—
127	C₂²×C₄×C₅	—	12	4	no	—
128	C₂²×C₄×C₅	#67	1	1	yes	characteristic
129	C₂²×C₄×C₅	#67	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
131	C₂×C₅×C₈	—	3	4	no	—
132	C₂×C₅×C₈	—	6	4	no	—
133	C₅×C₄⋊C₄	—	2	4	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	3	2	no	—
136	C₅×C₄⋊C₄	—	6	1	no	—
137	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
138	C₅×C₂²⋊C₄	—	6	4	no	—
139	C₄²×C₅	#67	1	2	yes	—
140	C₄²×C₅	C₂²×D₃	1	2	yes	—
141	C₂×C₄⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
142	C₂×C₄×D₄	—	3	1	no	—
143	#476	—	3	8	no	—
144	C₂×#106	—	3	2	no	—
145	C₂×C₄⋊C₈	—	3	1	no	—
146	C₂×#102	—	3	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×C₅×D₃	—	2	4	no	—
152	C₂×C₅×D₃	—	4	2	no	—
153	C₂×C₅×D₃	—	4	2	no	—
154	C₂×C₅×D₃	—	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	C₅×Dic₃	—	4	2	no	—
162	C₂³×D₃	—	2	1	no	—
163	C₂×C₃×Q₈	—	2	4	no	—
164	C₂×C₃×Q₈	—	4	4	no	—
165	C₂²×C₃×C₄	—	2	2	no	—
166	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
169	C₂²×Dic₃	—	2	1	no	—
170	C₂×D₁₂	—	2	1	no	—
171	C₂×D₁₂	—	2	2	no	—
172	C₂×D₁₂	C₅×Q₈	1	4	yes	complemented
173	C₂×D₁₂	C₂³×C₅	1	2	yes	—
174	C₂×C₄×D₃	—	2	4	no	—
175	C₂×C₄×D₃	—	4	4	no	—
176	C₃×C₄⋊C₄	—	2	4	no	—
177	C₃×C₄⋊C₄	—	2	2	no	—
178	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
179	C₃×C₄²	C₅×D₄	1	2	yes	—
180	C₃×C₄²	C₂³×C₅	1	2	yes	—
181	(C₂×D₃)⋊C₄	—	2	4	no	—
182	C₄⋊Dic₃	—	2	1	no	—
183	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
184	C₂×C₃⋊C₈	—	2	4	no	—
185	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
186	C₂³×C₅	—	6	4	no	—
187	C₂³×C₅	—	6	2	no	—
188	C₂³×C₅	—	12	2	no	—
189	C₂³×C₅	—	12	2	no	—
190	C₂³×C₅	C₂×#67	1	1	yes	characteristic
191	C₅×Q₈	—	4	8	no	—
192	C₅×D₄	—	3	4	no	—
193	C₅×D₄	—	6	4	no	—
194	C₅×D₄	—	6	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	4	no	—
197	C₂×C₄×C₅	—	4	4	no	—
198	C₂×C₄×C₅	—	6	2	no	—
199	C₂×C₄×C₅	—	12	2	no	—
200	C₂×C₄×C₅	—	12	8	no	—
201	C₂×C₄×C₅	#215	1	4	yes	—
202	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
203	C₂×C₄×C₅	#239	1	2	yes	—
204	C₂×C₄×C₅	C₂×#67	1	2	yes	—
205	C₂×C₄×C₅	C₂×#67	1	2	yes	—
206	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
208	C₅×C₈	—	6	4	no	—
209	C₂²×Q₈	—	2	1	no	—
210	C₂²×D₄	—	3	1	no	—
211	C₂³×C₄	—	6	1	no	—
212	C₂²×C₈	—	3	2	no	—
213	C₄⋊Q₈	—	2	2	no	—
214	C₄⋊Q₈	C₂×C₅×D₃	1	4	yes	complemented
215	C₄×D₄	—	3	4	no	—
216	C₄×D₄	—	6	2	no	—
217	C₂×C₄⋊C₄	—	2	1	no	—
218	C₂×C₄⋊C₄	—	3	1	no	—
219	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
220	C₂×C₂²⋊C₄	—	6	1	no	—
221	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
222	#106	—	3	8	no	—
223	C₄⋊C₈	—	3	4	no	—
224	#102	—	3	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	C₅×D₃	—	4	4	no	—
230	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
231	C₂²×D₃	—	2	4	no	—
232	C₂²×D₃	—	2	2	no	—
233	C₂²×D₃	—	4	2	no	—
234	C₂²×D₃	—	4	2	no	—
235	C₃×Q₈	—	4	8	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	4	4	no	—
239	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	—
240	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
241	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
243	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
244	C₂×C₃×C₄	C₅×#41	1	2	yes	—
245	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
246	C₂×Dic₃	—	2	2	no	—
247	C₂×Dic₃	—	4	2	no	—
248	D₁₂	—	2	4	no	—
249	D₁₂	—	2	2	no	—
250	D₁₂	C₂×C₅×Q₈	1	4	yes	complemented
251	C₄×D₃	—	4	8	no	—
252	C₃⋊C₈	—	2	4	no	—
253	C₂²×C₅	—	6	4	no	—
254	C₂²×C₅	—	12	2	no	—
255	C₂²×C₅	—	12	2	no	—
256	C₂²×C₅	—	12	8	no	—
257	C₂²×C₅	#932	1	2	yes	—
258	C₂²×C₅	C₂×#215	1	2	yes	—
259	C₂²×C₅	#946	1	2	yes	—
260	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
261	C₄×C₅	—	2	2	no	—
262	C₄×C₅	—	4	4	no	—
263	C₄×C₅	—	12	2	no	—
264	C₄×C₅	C₂×#215	1	4	yes	—
265	C₄×C₅	#946	1	2	yes	—
266	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
267	C₄×C₅	C₂×#239	1	1	yes	characteristic
268	C₂⁴	—	6	1	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂×D₄	—	3	4	no	—
272	C₂×D₄	—	3	2	no	—
273	C₂×D₄	—	6	2	no	—
274	C₂×D₄	—	6	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	6	1	no	—
277	C₂²×C₄	—	6	4	no	—
278	C₂²×C₄	—	12	4	no	—
279	C₂²×C₄	C₅×#67	1	1	yes	characteristic
280	C₂²×C₄	C₅×#67	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
282	C₂×C₈	—	3	4	no	—
283	C₂×C₈	—	6	4	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	3	2	no	—
287	C₄⋊C₄	—	6	1	no	—
288	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
289	C₂²⋊C₄	—	6	4	no	—
290	C₄²	C₅×#67	1	2	yes	—
291	C₄²	C₂²×C₅×D₃	1	2	yes	—
292	C₃×C₅	C₂×#476	1	1	yes	characteristic, complemented, Hall
293	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
294	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
295	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
296	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
297	C₂×D₃	—	2	4	no	—
298	C₂×D₃	—	4	8	no	—
299	C₂×D₃	—	4	2	no	—
300	C₂×D₃	—	4	2	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	4	4	no	—
303	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
304	C₃×C₄	C₂×C₅×SD₁₆	1	4	yes	—
305	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
306	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
307	Dic₃	—	4	2	no	—
308	C₂×C₅	—	12	4	no	—
309	C₂×C₅	#5084	1	4	yes	direct product factor
310	C₂×C₅	C₂×#932	1	1	yes	characteristic
311	C₂×C₅	C₂²×#215	1	1	yes	characteristic
312	C₂×C₅	C₂×#946	1	1	yes	characteristic
313	C₂³	—	6	4	no	—
314	C₂³	—	6	2	no	—
315	C₂³	—	12	2	no	—
316	C₂³	—	12	2	no	—
317	C₂³	C₂×C₅×#67	1	1	yes	characteristic
318	Q₈	—	4	8	no	—
319	D₄	—	3	4	no	—
320	D₄	—	6	4	no	—
321	D₄	—	6	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	6	2	no	—
326	C₂×C₄	—	12	2	no	—
327	C₂×C₄	—	12	8	no	—
328	C₂×C₄	C₅×#215	1	4	yes	—
329	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
330	C₂×C₄	C₅×#239	1	2	yes	—
331	C₂×C₄	C₂×C₅×#67	1	2	yes	—
332	C₂×C₄	C₂×C₅×#67	1	2	yes	—
333	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
334	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
335	C₈	—	6	4	no	—
336	C₂×C₃	C₅×#476	1	4	yes	complemented
337	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
338	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
339	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
340	D₃	—	4	4	no	—
341	C₅	C₂×#5084	1	1	yes	characteristic, direct product factor, Sylow
342	C₂²	—	6	4	no	—
343	C₂²	—	12	2	no	—
344	C₂²	—	12	2	no	—
345	C₂²	—	12	8	no	—
346	C₂²	C₅×#932	1	2	yes	—
347	C₂²	C₂×C₅×#215	1	2	yes	—
348	C₂²	C₅×#946	1	2	yes	—
349	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
350	C₄	—	2	2	no	—
351	C₄	—	4	4	no	—
352	C₄	—	12	2	no	—
353	C₄	C₂×C₅×#215	1	4	yes	—
354	C₄	C₅×#946	1	2	yes	—
355	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
356	C₄	C₂×C₅×#239	1	1	yes	characteristic
357	C₃	C₂×C₅×#476	1	1	yes	characteristic, complemented, Sylow
358	C₂	—	12	4	no	—
359	C₂	C₅×#5084	1	4	yes	direct product factor
360	C₂	C₂×C₅×#932	1	1	yes	characteristic
361	C₂	C₂²×C₅×#215	1	1	yes	characteristic
362	C₂	C₂×C₅×#946	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₅×C₄⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#476
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×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. C₅×#5084	C₂	direct (N × H)
5. C₂×C₅×#808	C₂	semidirect
6. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
12. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
22. C₅×#808	C₂²	semidirect
23. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
24. C₂×#5084	C₅	direct (N × H)
25. C₂×C₅×C₄⋊Q₈	D₃	semidirect
41. C₂×C₅×D₁₂	Q₈	semidirect
55. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
57. #5084	C₂×C₅	direct (N × H)
59. C₂×#808	C₂×C₅	semidirect
60. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
66. C₅×C₄⋊Q₈	C₂×D₃	semidirect
98. C₅×D₁₂	C₂×Q₈	semidirect
105. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
115. #808	C₂²×C₅	semidirect
116. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
141. C₂×C₄⋊Q₈	C₅×D₃	semidirect
172. C₂×D₁₂	C₅×Q₈	semidirect
214. C₄⋊Q₈	C₂×C₅×D₃	semidirect
225. C₂×C₃×C₅	#476	semidirect
250. D₁₂	C₂×C₅×Q₈	semidirect
292. C₃×C₅	C₂×#476	semidirect
309. C₂×C₅	#5084	direct (N × H)
336. C₂×C₃	C₅×#476	semidirect
341. C₅	C₂×#5084	direct (N × H)
357. C₃	C₂×C₅×#476	semidirect
359. C₂	C₅×#5084	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×C₄×C₅×D₁₂	2
C₅×#5084	2
C₂×C₅×#809	2
C₂×C₅×#808	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×#476	3
C₂×#5084	5

Subgroups — C2×C5×#5084 #14429862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5084 #14429862