Subgroups — C₂×C₃×C₄×#700 #14411242

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#700	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4002	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₄×#170	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#700	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄×#700	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×#170	C₂²	1	4	yes	—
11	C₂×C₃×#700	C₄	1	16	yes	direct product factor
12	C₂×C₃×#700	C₂²	1	8	yes	—
13	C₂×C₃×C₄²×C₅	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
17	C₃×C₄²×D₅	C₄	1	4	yes	—
18	C₃×C₄²×D₅	C₂²	1	4	yes	—
19	C₃×#4002	C₂²	1	8	yes	complemented
20	C₃×C₄×#170	C₂²	1	8	yes	complemented
21	C₂×C₃×C₄×M₁₆	—	5	1	no	maximal, Hall
22	C₂²×#700	C₂×C₃	1	2	yes	—
23	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
24	C₂×#4002	C₂×C₃	1	2	yes	complemented
25	C₂×C₄×#170	C₂×C₃	1	2	yes	complemented
26	C₄×#700	C₂×C₃	1	8	yes	direct product factor
27	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
34	C₂×C₃×C₄×D₅	—	2	4	no	—
35	C₂×C₃×C₄×D₅	—	2	4	no	—
36	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
37	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
38	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
39	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
40	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
41	C₂×C₃×#170	C₂×C₄	1	16	yes	complemented
42	C₂×C₃×#170	C₂³	1	8	yes	—
43	C₃×#700	C₂×C₄	1	32	yes	direct product factor
44	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
45	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
46	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
47	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
48	C₃×C₄×Dic₅	C₂³	1	2	yes	—
49	C₃×C₄×Dic₅	C₂³	1	2	yes	—
50	C₂²×C₃×M₁₆	—	5	2	no	—
51	C₂²×C₃×C₄²	—	5	1	no	—
52	C₃×C₄×M₁₆	—	5	8	no	—
53	C₂×C₃×#97	—	5	2	no	—
54	C₂×C₃×C₄×C₈	—	5	2	no	—
55	C₂²×C₄×D₅	C₃×C₄	1	1	yes	characteristic
56	C₂²×C₄×D₅	C₃×C₄	1	1	yes	characteristic
57	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
58	C₂²×#170	C₂²×C₃	1	4	yes	—
59	C₂×#700	C₃×C₄	1	16	yes	direct product factor
60	C₂×#700	C₂²×C₃	1	8	yes	—
61	C₂×C₄²×C₅	C₃×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
65	C₄²×D₅	C₃×C₄	1	4	yes	—
66	C₄²×D₅	C₂²×C₃	1	4	yes	—
67	#4002	C₂²×C₃	1	8	yes	complemented
68	C₄×#170	C₂²×C₃	1	8	yes	complemented
69	C₂×C₄×M₁₆	—	5	1	no	Sylow
70	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₃×D₅	—	2	2	no	—
72	C₂²×C₃×D₅	—	2	2	no	—
73	C₂²×C₃×D₅	C₄²	1	4	yes	—
74	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
77	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
78	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
79	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
80	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
81	C₂×C₃×Dic₅	—	2	2	no	—
82	C₂×C₃×Dic₅	M₁₆	1	4	yes	complemented
83	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
84	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
86	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
87	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
88	C₃×C₄×D₅	—	2	8	no	—
89	C₃×C₄×D₅	—	2	8	no	—
90	C₃×C₄×D₅	C₄²	1	8	yes	—
91	C₃×C₄×D₅	C₂²×C₄	1	8	yes	—
92	C₃×#170	C₂²×C₄	1	16	yes	complemented
93	C₂³×C₃×C₄	—	5	1	no	—
94	C₂³×C₃×C₄	—	5	1	no	—
95	C₂³×C₃×C₄	—	5	1	no	—
96	C₂×C₃×M₁₆	—	5	16	no	—
97	C₂×C₃×M₁₆	—	5	8	no	—
98	C₂²×C₃×C₈	—	5	4	no	—
99	C₂×C₃×C₄²	—	5	1	no	—
100	C₂×C₃×C₄²	—	5	1	no	—
101	C₂×C₃×C₄²	—	5	1	no	—
102	C₂×C₃×C₄²	—	5	4	no	—
103	C₂×C₃×C₄²	—	5	4	no	—
104	C₂×C₃×C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic
105	C₃×#97	—	5	8	no	—
106	C₃×C₄×C₈	—	5	8	no	—
107	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
111	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
112	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
113	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
114	C₂×C₄×D₅	—	2	4	no	—
115	C₂×C₄×D₅	—	2	4	no	—
116	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
117	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
118	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
119	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	—
120	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
121	C₂×#170	C₂×C₃×C₄	1	16	yes	complemented
122	C₂×#170	C₂³×C₃	1	8	yes	—
123	#700	C₂×C₃×C₄	1	32	yes	direct product factor
124	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
125	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
126	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
127	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
128	C₄×Dic₅	C₂³×C₃	1	2	yes	—
129	C₄×Dic₅	C₂³×C₃	1	2	yes	—
130	C₂²×M₁₆	—	5	2	no	—
131	C₂²×C₄²	—	5	1	no	—
132	C₄×M₁₆	—	5	8	no	—
133	C₂×#97	—	5	2	no	—
134	C₂×C₄×C₈	—	5	2	no	—
135	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
136	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
137	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
138	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₃×D₅	—	2	2	no	—
140	C₂×C₃×D₅	—	2	2	no	—
141	C₂×C₃×D₅	—	2	8	no	—
142	C₂×C₃×D₅	C₂×C₄²	1	4	yes	—
143	C₃×C₄×C₅	—	2	2	no	—
144	C₃×C₄×C₅	C₂×C₄²	1	4	yes	—
145	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
146	C₃×Dic₅	—	2	2	no	—
147	C₃×Dic₅	C₂×C₄²	1	2	yes	—
148	C₃×Dic₅	C₂×M₁₆	1	4	yes	complemented
149	C₃×Dic₅	C₂³×C₄	1	2	yes	—
150	C₂⁴×C₃	—	5	1	no	—
151	C₂²×C₃×C₄	—	5	1	no	—
152	C₂²×C₃×C₄	—	5	1	no	—
153	C₂²×C₃×C₄	—	5	8	no	—
154	C₂²×C₃×C₄	—	5	2	no	—
155	C₂²×C₃×C₄	—	5	2	no	—
156	C₂²×C₃×C₄	—	5	1	no	—
157	C₂²×C₃×C₄	—	5	4	no	—
158	C₂²×C₃×C₄	—	5	4	no	—
159	C₂²×C₃×C₄	—	10	4	no	—
160	C₂²×C₃×C₄	—	10	4	no	—
161	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
164	C₃×M₁₆	—	5	32	no	—
165	C₂×C₃×C₈	—	5	8	no	—
166	C₂×C₃×C₈	—	5	16	no	—
167	C₃×C₄²	—	5	2	no	—
168	C₃×C₄²	—	5	2	no	—
169	C₃×C₄²	—	5	4	no	—
170	C₃×C₄²	—	5	2	no	—
171	C₃×C₄²	—	5	2	no	—
172	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	4	yes	—
173	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
174	C₂²×D₅	—	2	2	no	—
175	C₂²×D₅	—	2	2	no	—
176	C₂²×D₅	C₃×C₄²	1	4	yes	—
177	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	C₃×C₄²	1	4	yes	—
180	C₂×C₄×C₅	C₃×M₁₆	1	4	yes	complemented
181	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
182	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
183	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
184	C₂×Dic₅	—	2	2	no	—
185	C₂×Dic₅	C₃×M₁₆	1	4	yes	complemented
186	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
187	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
188	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
189	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
190	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
191	C₄×D₅	—	2	8	no	—
192	C₄×D₅	—	2	8	no	—
193	C₄×D₅	C₃×C₄²	1	8	yes	—
194	C₄×D₅	C₂²×C₃×C₄	1	8	yes	—
195	#170	C₂²×C₃×C₄	1	16	yes	complemented
196	C₂³×C₄	—	5	1	no	—
197	C₂³×C₄	—	5	1	no	—
198	C₂³×C₄	—	5	1	no	—
199	C₂×M₁₆	—	5	16	no	—
200	C₂×M₁₆	—	5	8	no	—
201	C₂²×C₈	—	5	4	no	—
202	C₂×C₄²	—	5	1	no	—
203	C₂×C₄²	—	5	1	no	—
204	C₂×C₄²	—	5	1	no	—
205	C₂×C₄²	—	5	4	no	—
206	C₂×C₄²	—	5	4	no	—
207	C₂×C₄²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
208	#97	—	5	8	no	—
209	C₄×C₈	—	5	8	no	—
210	C₂×C₃×C₅	C₄×M₁₆	1	4	yes	complemented
211	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
212	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
213	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
214	C₃×D₅	—	2	4	no	—
215	C₂³×C₃	—	5	4	no	—
216	C₂³×C₃	—	5	2	no	—
217	C₂³×C₃	—	10	2	no	—
218	C₂³×C₃	—	10	2	no	—
219	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	5	4	no	—
222	C₂×C₃×C₄	—	5	4	no	—
223	C₂×C₃×C₄	—	5	2	no	—
224	C₂×C₃×C₄	—	5	1	no	—
225	C₂×C₃×C₄	—	5	1	no	—
226	C₂×C₃×C₄	—	5	8	no	—
227	C₂×C₃×C₄	—	5	8	no	—
228	C₂×C₃×C₄	—	5	2	no	—
229	C₂×C₃×C₄	—	10	8	no	—
230	C₂×C₃×C₄	—	10	2	no	—
231	C₂×C₃×C₄	—	10	8	no	—
232	C₂×C₃×C₄	#700	1	4	yes	direct product factor
233	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	4	yes	—
234	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
235	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
236	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
237	C₃×C₈	—	5	16	no	—
238	C₂²×C₅	C₂×C₃×C₄²	1	2	yes	—
239	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
240	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
241	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
242	C₂×D₅	—	2	2	no	—
243	C₂×D₅	—	2	2	no	—
244	C₂×D₅	—	2	8	no	—
245	C₂×D₅	C₂×C₃×C₄²	1	4	yes	—
246	C₄×C₅	—	2	2	no	—
247	C₄×C₅	C₂×C₃×C₄²	1	4	yes	—
248	C₄×C₅	C₂×C₃×M₁₆	1	4	yes	complemented
249	Dic₅	—	2	2	no	—
250	Dic₅	C₂×C₃×C₄²	1	2	yes	—
251	Dic₅	C₂×C₃×M₁₆	1	4	yes	complemented
252	Dic₅	C₂³×C₃×C₄	1	2	yes	—
253	C₂⁴	—	5	1	no	—
254	C₂²×C₄	—	5	1	no	—
255	C₂²×C₄	—	5	1	no	—
256	C₂²×C₄	—	5	8	no	—
257	C₂²×C₄	—	5	2	no	—
258	C₂²×C₄	—	5	2	no	—
259	C₂²×C₄	—	5	1	no	—
260	C₂²×C₄	—	5	4	no	—
261	C₂²×C₄	—	5	4	no	—
262	C₂²×C₄	—	10	4	no	—
263	C₂²×C₄	—	10	4	no	—
264	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
267	M₁₆	—	5	32	no	—
268	C₂×C₈	—	5	8	no	—
269	C₂×C₈	—	5	16	no	—
270	C₄²	—	5	2	no	—
271	C₄²	—	5	2	no	—
272	C₄²	—	5	2	no	—
273	C₄²	—	5	2	no	—
274	C₄²	—	5	4	no	—
275	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	—
276	C₃×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic, complemented, Hall
277	C₂²×C₃	—	5	4	no	—
278	C₂²×C₃	—	10	8	no	—
279	C₂²×C₃	—	10	2	no	—
280	C₂²×C₃	—	10	2	no	—
281	C₂²×C₃	C₂×#700	1	2	yes	—
282	C₂²×C₃	D₅⋊M₁₆	1	2	yes	—
283	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
284	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
285	C₃×C₄	—	2	2	no	—
286	C₃×C₄	—	5	4	no	—
287	C₃×C₄	—	5	2	no	—
288	C₃×C₄	—	5	2	no	—
289	C₃×C₄	—	10	2	no	—
290	C₃×C₄	C₂×#700	1	4	yes	direct product factor
291	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	4	yes	—
292	C₂×C₅	C₃×C₄×M₁₆	1	4	yes	complemented
293	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
294	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
295	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
296	D₅	—	2	4	no	—
297	C₂³	—	5	4	no	—
298	C₂³	—	5	2	no	—
299	C₂³	—	10	2	no	—
300	C₂³	—	10	2	no	—
301	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	5	4	no	—
304	C₂×C₄	—	5	4	no	—
305	C₂×C₄	—	5	1	no	—
306	C₂×C₄	—	5	2	no	—
307	C₂×C₄	—	5	1	no	—
308	C₂×C₄	—	5	8	no	—
309	C₂×C₄	—	5	8	no	—
310	C₂×C₄	—	5	2	no	—
311	C₂×C₄	—	10	8	no	—
312	C₂×C₄	—	10	2	no	—
313	C₂×C₄	—	10	8	no	—
314	C₂×C₄	C₃×#700	1	4	yes	direct product factor
315	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	4	yes	—
316	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
317	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
318	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
319	C₈	—	5	16	no	—
320	C₂×C₃	—	10	4	no	—
321	C₂×C₃	C₄×#700	1	4	yes	direct product factor
322	C₂×C₃	C₂²×#700	1	1	yes	characteristic
323	C₂×C₃	C₂×D₅⋊M₁₆	1	1	yes	characteristic
324	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
325	C₅	C₂×C₃×C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
326	C₂²	—	5	4	no	—
327	C₂²	—	10	8	no	—
328	C₂²	—	10	2	no	—
329	C₂²	—	10	2	no	—
330	C₂²	C₂×C₃×#700	1	2	yes	—
331	C₂²	C₃×D₅⋊M₁₆	1	2	yes	—
332	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
333	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
334	C₄	—	2	2	no	—
335	C₄	—	5	4	no	—
336	C₄	—	5	2	no	—
337	C₄	—	5	2	no	—
338	C₄	—	10	2	no	—
339	C₄	C₂×C₃×#700	1	4	yes	direct product factor
340	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	4	yes	—
341	C₃	C₂×C₄×#700	1	1	yes	characteristic, direct product factor, Sylow
342	C₂	—	10	4	no	—
343	C₂	C₃×C₄×#700	1	4	yes	direct product factor
344	C₂	C₂²×C₃×#700	1	1	yes	characteristic
345	C₂	C₂×C₃×D₅⋊M₁₆	1	1	yes	characteristic
346	C₂	C₂²×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₄²×C₅	C₄
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄²	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×C₄×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄²

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×#4002	C₂	semidirect
4. C₂×C₃×C₄×#170	C₂	semidirect
5. C₃×C₄×#700	C₂	direct (N × H)
6. C₂×C₄×#700	C₃	direct (N × H)
11. C₂×C₃×#700	C₄	direct (N × H)
19. C₃×#4002	C₂²	semidirect
20. C₃×C₄×#170	C₂²	semidirect
24. C₂×#4002	C₂×C₃	semidirect
25. C₂×C₄×#170	C₂×C₃	semidirect
26. C₄×#700	C₂×C₃	direct (N × H)
41. C₂×C₃×#170	C₂×C₄	semidirect
43. C₃×#700	C₂×C₄	direct (N × H)
59. C₂×#700	C₃×C₄	direct (N × H)
67. #4002	C₂²×C₃	semidirect
68. C₄×#170	C₂²×C₃	semidirect
77. C₂×C₃×C₄×C₅	M₁₆	semidirect
82. C₂×C₃×Dic₅	M₁₆	semidirect
92. C₃×#170	C₂²×C₄	semidirect
121. C₂×#170	C₂×C₃×C₄	semidirect
123. #700	C₂×C₃×C₄	direct (N × H)
145. C₃×C₄×C₅	C₂×M₁₆	semidirect
148. C₃×Dic₅	C₂×M₁₆	semidirect
180. C₂×C₄×C₅	C₃×M₁₆	semidirect
185. C₂×Dic₅	C₃×M₁₆	semidirect
195. #170	C₂²×C₃×C₄	semidirect
210. C₂×C₃×C₅	C₄×M₁₆	semidirect
232. C₂×C₃×C₄	#700	direct (N × H)
248. C₄×C₅	C₂×C₃×M₁₆	semidirect
251. Dic₅	C₂×C₃×M₁₆	semidirect
276. C₃×C₅	C₂×C₄×M₁₆	semidirect
290. C₃×C₄	C₂×#700	direct (N × H)
292. C₂×C₅	C₃×C₄×M₁₆	semidirect
314. C₂×C₄	C₃×#700	direct (N × H)
321. C₂×C₃	C₄×#700	direct (N × H)
325. C₅	C₂×C₃×C₄×M₁₆	semidirect
339. C₄	C₂×C₃×#700	direct (N × H)
341. C₃	C₂×C₄×#700	direct (N × H)
343. C₂	C₃×C₄×#700	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×#700	2
C₂×C₃×C₄²×D₅	2
C₂×C₃×#4002	2
C₂×C₃×C₄×#170	2
C₃×C₄×#700	2
C₂×C₄×#700	3
C₂×C₃×C₄×M₁₆	5

Subgroups — C2×C3×C4×#700 #14411242

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×#700 #14411242