Subgroups — C₂²×C₅×#823 #14412041

Order 1920.

1984 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	C₂³×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#823	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₅×#100	—	3	1	no	maximal, Hall
6	C₂⁴×C₅×D₃	C₄	1	2	yes	—
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₅×D₁₂	—	2	1	no	—
9	C₂²×C₅×D₁₂	—	2	3	no	—
10	C₂²×C₅×D₁₂	—	2	1	no	—
11	C₂²×C₅×D₁₂	—	2	3	no	—
12	C₂²×C₅×D₁₂	C₄	1	6	yes	—
13	C₂²×C₅×D₁₂	C₂²	1	6	yes	—
14	C₂×C₃×C₅×M₁₆	—	2	3	no	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	6	yes	complemented
16	C₂²×C₃×C₅×C₈	—	2	1	no	—
17	C₂×C₅×#208	—	2	3	no	—
18	C₂×C₅×#208	C₂²	1	6	yes	complemented
19	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
20	C₅×#823	C₂²	1	16	yes	direct product factor
21	C₂²×#823	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂³×C₅×D₄	—	3	1	no	—
23	C₂²×C₅×M₁₆	—	3	1	no	—
24	C₂²×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
25	C₂×C₅×#100	—	3	12	no	—
26	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₅×D₃	—	2	6	no	—
28	C₂³×C₅×D₃	—	2	2	no	—
29	C₂³×C₅×D₃	—	4	8	no	—
30	C₂³×C₅×D₃	C₂×C₄	1	12	yes	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	3	yes	—
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	D₄	1	3	yes	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	3	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
37	C₂×C₅×D₁₂	—	2	12	no	—
38	C₂×C₅×D₁₂	—	2	6	no	—
39	C₂×C₅×D₁₂	—	2	6	no	—
40	C₂×C₅×D₁₂	—	2	6	no	—
41	C₂×C₅×D₁₂	—	2	6	no	—
42	C₂×C₅×D₁₂	—	2	6	no	—
43	C₂×C₅×D₁₂	—	2	6	no	—
44	C₂×C₅×D₁₂	C₂×C₄	1	12	yes	—
45	C₂×C₅×D₁₂	C₂³	1	4	yes	—
46	C₃×C₅×M₁₆	—	2	6	no	—
47	C₃×C₅×M₁₆	C₂³	1	4	yes	complemented
48	C₂×C₃×C₅×C₈	—	2	6	no	—
49	C₅×#208	—	2	6	no	—
50	C₅×#208	C₂³	1	4	yes	complemented
51	C₂×C₅×C₃⋊C₈	—	2	6	no	—
52	C₂³×D₁₂	C₂×C₅	1	1	yes	characteristic
53	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂²×#208	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂×#823	C₂×C₅	1	12	yes	direct product factor
56	C₂⁵×C₅	—	3	2	no	—
57	C₂²×C₅×D₄	—	3	6	no	—
58	C₂²×C₅×D₄	—	3	6	no	—
59	C₂²×C₅×D₄	—	6	3	no	—
60	C₂²×C₅×D₄	—	6	1	no	—
61	C₂²×C₅×D₄	—	6	3	no	—
62	C₂²×C₅×D₄	—	6	1	no	—
63	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
64	C₂×C₅×M₁₆	—	2	3	no	—
65	C₂×C₅×M₁₆	—	3	6	no	—
66	C₂×C₅×M₁₆	—	6	3	no	—
67	C₂×C₅×M₁₆	C₂×D₃	1	6	yes	complemented
68	C₂²×C₅×C₈	—	2	1	no	—
69	C₂²×C₅×C₈	—	6	1	no	—
70	C₅×#100	—	3	16	no	—
71	C₂²×#100	—	3	1	no	Sylow
72	C₂³×C₃×C₅	—	2	4	no	—
73	C₂³×C₃×C₅	C₂²⋊C₄	1	3	yes	—
74	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
75	C₂³×C₃×C₅	C₂²×C₄	1	3	yes	—
76	C₂²×C₅×D₃	—	2	12	no	—
77	C₂²×C₅×D₃	—	2	12	no	—
78	C₂²×C₅×D₃	—	4	24	no	—
79	C₂²×C₅×D₃	—	4	8	no	—
80	C₂²×C₅×D₃	—	4	24	no	—
81	C₂²×C₅×D₃	C₂²×C₄	1	8	yes	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	6	yes	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	3	yes	—
84	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	3	yes	—
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
86	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
90	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
91	C₅×D₁₂	—	2	12	no	—
92	C₅×D₁₂	—	2	12	no	—
93	C₅×D₁₂	—	2	4	no	—
94	C₅×D₁₂	—	2	4	no	—
95	C₃×C₅×C₈	—	2	4	no	—
96	C₅×C₃⋊C₈	—	2	4	no	—
97	C₂⁴×D₃	C₄×C₅	1	2	yes	—
98	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
99	C₂²×D₁₂	—	2	1	no	—
100	C₂²×D₁₂	—	2	3	no	—
101	C₂²×D₁₂	—	2	1	no	—
102	C₂²×D₁₂	—	2	3	no	—
103	C₂²×D₁₂	C₄×C₅	1	6	yes	—
104	C₂²×D₁₂	C₂²×C₅	1	6	yes	—
105	C₂×C₃×M₁₆	—	2	3	no	—
106	C₂×C₃×M₁₆	C₂²×C₅	1	6	yes	complemented
107	C₂²×C₃×C₈	—	2	1	no	—
108	C₂×#208	—	2	3	no	—
109	C₂×#208	C₂²×C₅	1	6	yes	complemented
110	C₂²×C₃⋊C₈	—	2	1	no	—
111	#823	C₂²×C₅	1	16	yes	direct product factor
112	C₂⁴×C₅	—	3	12	no	—
113	C₂⁴×C₅	—	6	6	no	—
114	C₂⁴×C₅	—	6	2	no	—
115	C₂⁴×C₅	—	12	8	no	—
116	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
117	C₂×C₅×D₄	—	3	12	no	—
118	C₂×C₅×D₄	—	3	4	no	—
119	C₂×C₅×D₄	—	6	12	no	—
120	C₂×C₅×D₄	—	6	6	no	—
121	C₂×C₅×D₄	—	6	6	no	—
122	C₂×C₅×D₄	—	6	6	no	—
123	C₂×C₅×D₄	—	6	6	no	—
124	C₂×C₅×D₄	—	6	6	no	—
125	C₂×C₅×D₄	—	6	6	no	—
126	C₂²×C₄×C₅	C₄×D₃	1	3	yes	—
127	C₂²×C₄×C₅	D₁₂	1	3	yes	—
128	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
129	C₂²×C₄×C₅	#67	1	3	yes	—
130	C₂²×C₄×C₅	#67	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
132	C₅×M₁₆	—	2	6	no	—
133	C₅×M₁₆	—	3	4	no	—
134	C₅×M₁₆	—	6	6	no	—
135	C₅×M₁₆	C₂²×D₃	1	4	yes	complemented
136	C₂×C₅×C₈	—	2	6	no	—
137	C₂×C₅×C₈	—	6	6	no	—
138	C₂³×D₄	—	3	1	no	—
139	C₂²×M₁₆	—	3	1	no	—
140	C₂²×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
141	C₂×#100	—	3	12	no	—
142	C₂²×C₃×C₅	—	2	6	no	—
143	C₂²×C₃×C₅	—	2	6	no	—
144	C₂²×C₃×C₅	#100	1	4	yes	complemented
145	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	3	yes	—
146	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	3	yes	—
147	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₅×D₃	—	2	8	no	—
149	C₂×C₅×D₃	—	4	24	no	—
150	C₂×C₅×D₃	—	4	24	no	—
151	C₂×C₅×D₃	—	4	8	no	—
152	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	3	yes	—
153	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	3	yes	—
154	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
156	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
157	C₂³×D₃	—	2	6	no	—
158	C₂³×D₃	—	2	2	no	—
159	C₂³×D₃	—	4	8	no	—
160	C₂³×D₃	C₂×C₄×C₅	1	12	yes	—
161	C₂²×C₃×C₄	C₂×C₄×C₅	1	3	yes	—
162	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₅×D₄	1	3	yes	—
164	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₅×D₄	1	3	yes	—
166	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
167	C₂×D₁₂	—	2	12	no	—
168	C₂×D₁₂	—	2	6	no	—
169	C₂×D₁₂	—	2	6	no	—
170	C₂×D₁₂	—	2	6	no	—
171	C₂×D₁₂	—	2	6	no	—
172	C₂×D₁₂	—	2	6	no	—
173	C₂×D₁₂	—	2	6	no	—
174	C₂×D₁₂	C₂×C₄×C₅	1	12	yes	—
175	C₂×D₁₂	C₂³×C₅	1	4	yes	—
176	C₃×M₁₆	—	2	6	no	—
177	C₃×M₁₆	C₂³×C₅	1	4	yes	complemented
178	C₂×C₃×C₈	—	2	6	no	—
179	#208	—	2	6	no	—
180	#208	C₂³×C₅	1	4	yes	complemented
181	C₂×C₃⋊C₈	—	2	6	no	—
182	C₂³×C₅	—	2	4	no	—
183	C₂³×C₅	—	3	8	no	—
184	C₂³×C₅	—	6	12	no	—
185	C₂³×C₅	—	6	12	no	—
186	C₂³×C₅	—	12	24	no	—
187	C₂³×C₅	—	12	24	no	—
188	C₂³×C₅	—	12	8	no	—
189	C₂³×C₅	(C₂×D₃)⋊C₄	1	3	yes	—
190	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
191	C₂³×C₅	C₂×C₄×D₃	1	3	yes	—
192	C₅×D₄	—	6	12	no	—
193	C₅×D₄	—	6	12	no	—
194	C₅×D₄	—	6	4	no	—
195	C₅×D₄	—	6	4	no	—
196	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	6	yes	—
197	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	3	yes	—
198	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	3	yes	—
199	C₂×C₄×C₅	C₂×C₄×D₃	1	3	yes	—
200	C₂×C₄×C₅	C₂×D₁₂	1	3	yes	—
201	C₂×C₄×C₅	C₂×D₁₂	1	3	yes	—
202	C₂×C₄×C₅	C₂×#67	1	3	yes	—
203	C₂×C₄×C₅	C₂×#67	1	3	yes	—
204	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
205	C₅×C₈	—	2	4	no	—
206	C₅×C₈	—	6	4	no	—
207	C₂⁵	—	3	2	no	—
208	C₂²×D₄	—	3	6	no	—
209	C₂²×D₄	—	3	6	no	—
210	C₂²×D₄	—	6	1	no	—
211	C₂²×D₄	—	6	3	no	—
212	C₂²×D₄	—	6	1	no	—
213	C₂²×D₄	—	6	3	no	—
214	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
215	C₂×M₁₆	—	2	3	no	—
216	C₂×M₁₆	—	3	6	no	—
217	C₂×M₁₆	—	6	3	no	—
218	C₂×M₁₆	C₂×C₅×D₃	1	6	yes	complemented
219	C₂²×C₈	—	2	1	no	—
220	C₂²×C₈	—	6	1	no	—
221	#100	—	3	16	no	—
222	C₂×C₃×C₅	—	2	3	no	—
223	C₂×C₃×C₅	—	2	1	no	—
224	C₂×C₃×C₅	C₂×#100	1	6	yes	complemented
225	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
226	C₅×D₃	—	4	8	no	—
227	C₂³×C₃	—	2	4	no	—
228	C₂³×C₃	C₅×C₂²⋊C₄	1	3	yes	—
229	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×C₃	C₂²×C₄×C₅	1	3	yes	—
231	C₂²×D₃	—	2	12	no	—
232	C₂²×D₃	—	2	12	no	—
233	C₂²×D₃	—	4	24	no	—
234	C₂²×D₃	—	4	8	no	—
235	C₂²×D₃	—	4	24	no	—
236	C₂²×D₃	C₂²×C₄×C₅	1	8	yes	—
237	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	6	yes	—
238	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	3	yes	—
239	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	3	yes	—
240	C₂×C₃×C₄	C₂²×C₄×C₅	1	3	yes	—
241	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
242	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
243	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
244	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
245	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
246	D₁₂	—	2	12	no	—
247	D₁₂	—	2	12	no	—
248	D₁₂	—	2	4	no	—
249	D₁₂	—	2	4	no	—
250	C₃×C₈	—	2	4	no	—
251	C₃⋊C₈	—	2	4	no	—
252	C₂²×C₅	—	2	6	no	—
253	C₂²×C₅	—	2	6	no	—
254	C₂²×C₅	—	6	8	no	—
255	C₂²×C₅	—	12	8	no	—
256	C₂²×C₅	—	12	24	no	—
257	C₂²×C₅	—	12	24	no	—
258	C₂²×C₅	#823	1	4	yes	direct product factor
259	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	3	yes	—
260	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	3	yes	—
261	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
262	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	3	yes	—
263	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	3	yes	—
264	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
265	C₄×C₅	C₂²×#67	1	1	yes	characteristic
266	C₂⁴	—	3	12	no	—
267	C₂⁴	—	6	6	no	—
268	C₂⁴	—	6	2	no	—
269	C₂⁴	—	12	8	no	—
270	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
271	C₂×D₄	—	3	12	no	—
272	C₂×D₄	—	3	4	no	—
273	C₂×D₄	—	6	12	no	—
274	C₂×D₄	—	6	6	no	—
275	C₂×D₄	—	6	6	no	—
276	C₂×D₄	—	6	6	no	—
277	C₂×D₄	—	6	6	no	—
278	C₂×D₄	—	6	6	no	—
279	C₂×D₄	—	6	6	no	—
280	C₂²×C₄	C₄×C₅×D₃	1	3	yes	—
281	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
282	C₂²×C₄	C₅×D₁₂	1	3	yes	—
283	C₂²×C₄	C₅×#67	1	1	yes	characteristic
284	C₂²×C₄	C₅×#67	1	3	yes	—
285	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	—
286	M₁₆	—	2	6	no	—
287	M₁₆	—	3	4	no	—
288	M₁₆	—	6	6	no	—
289	M₁₆	C₂²×C₅×D₃	1	4	yes	complemented
290	C₂×C₈	—	2	6	no	—
291	C₂×C₈	—	6	6	no	—
292	C₃×C₅	C₂²×#100	1	1	yes	characteristic, complemented, Hall
293	C₂²×C₃	—	2	6	no	—
294	C₂²×C₃	—	2	6	no	—
295	C₂²×C₃	C₅×#100	1	4	yes	complemented
296	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	3	yes	—
297	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	3	yes	—
298	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
299	C₂×D₃	—	2	8	no	—
300	C₂×D₃	—	4	24	no	—
301	C₂×D₃	—	4	24	no	—
302	C₂×D₃	—	4	8	no	—
303	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	3	yes	—
304	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	3	yes	—
305	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
306	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
307	C₂×C₅	—	2	3	no	—
308	C₂×C₅	—	2	1	no	—
309	C₂×C₅	—	12	8	no	—
310	C₂×C₅	C₂×#823	1	6	yes	direct product factor
311	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
312	C₂³	—	2	4	no	—
313	C₂³	—	3	8	no	—
314	C₂³	—	6	12	no	—
315	C₂³	—	6	12	no	—
316	C₂³	—	12	24	no	—
317	C₂³	—	12	24	no	—
318	C₂³	—	12	8	no	—
319	C₂³	C₅×(C₂×D₃)⋊C₄	1	3	yes	—
320	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
321	C₂³	C₂×C₄×C₅×D₃	1	3	yes	—
322	D₄	—	6	12	no	—
323	D₄	—	6	12	no	—
324	D₄	—	6	4	no	—
325	D₄	—	6	4	no	—
326	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	6	yes	—
327	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	3	yes	—
328	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	3	yes	—
329	C₂×C₄	C₂×C₄×C₅×D₃	1	3	yes	—
330	C₂×C₄	C₂×C₅×D₁₂	1	3	yes	—
331	C₂×C₄	C₂×C₅×D₁₂	1	3	yes	—
332	C₂×C₄	C₂×C₅×#67	1	3	yes	—
333	C₂×C₄	C₂×C₅×#67	1	3	yes	—
334	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
335	C₈	—	2	4	no	—
336	C₈	—	6	4	no	—
337	C₂×C₃	—	2	3	no	—
338	C₂×C₃	—	2	1	no	—
339	C₂×C₃	C₂×C₅×#100	1	6	yes	complemented
340	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
341	D₃	—	4	8	no	—
342	C₅	C₂²×#823	1	1	yes	characteristic, direct product factor, Sylow
343	C₂²	—	2	6	no	—
344	C₂²	—	2	6	no	—
345	C₂²	—	6	8	no	—
346	C₂²	—	12	8	no	—
347	C₂²	—	12	24	no	—
348	C₂²	—	12	24	no	—
349	C₂²	C₅×#823	1	4	yes	direct product factor
350	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	3	yes	—
351	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	3	yes	—
352	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
353	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	3	yes	—
354	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	3	yes	—
355	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
356	C₄	C₂²×C₅×#67	1	1	yes	characteristic
357	C₃	C₂²×C₅×#100	1	1	yes	characteristic, complemented, Sylow
358	C₂	—	2	3	no	—
359	C₂	—	2	1	no	—
360	C₂	—	12	8	no	—
361	C₂	C₂×C₅×#823	1	6	yes	direct product factor
362	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂³×C₃×C₅	C₂²⋊C₄
prime radical	C₂³×C₅×D₁₂	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×M₁₆	D₃
hypocenter	C₃	C₂²×C₅×#100
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂²×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₂²×C₅×#208	C₂	semidirect
4. C₂×C₅×#823	C₂	direct (N × H)
15. C₂×C₃×C₅×M₁₆	C₂²	semidirect
18. C₂×C₅×#208	C₂²	semidirect
20. C₅×#823	C₂²	direct (N × H)
21. C₂²×#823	C₅	direct (N × H)
24. C₂²×C₅×M₁₆	D₃	semidirect
47. C₃×C₅×M₁₆	C₂³	semidirect
50. C₅×#208	C₂³	semidirect
53. C₂²×C₃×M₁₆	C₂×C₅	semidirect
54. C₂²×#208	C₂×C₅	semidirect
55. C₂×#823	C₂×C₅	direct (N × H)
67. C₂×C₅×M₁₆	C₂×D₃	semidirect
106. C₂×C₃×M₁₆	C₂²×C₅	semidirect
109. C₂×#208	C₂²×C₅	semidirect
111. #823	C₂²×C₅	direct (N × H)
135. C₅×M₁₆	C₂²×D₃	semidirect
140. C₂²×M₁₆	C₅×D₃	semidirect
144. C₂²×C₃×C₅	#100	semidirect
177. C₃×M₁₆	C₂³×C₅	semidirect
180. #208	C₂³×C₅	semidirect
218. C₂×M₁₆	C₂×C₅×D₃	semidirect
224. C₂×C₃×C₅	C₂×#100	semidirect
258. C₂²×C₅	#823	direct (N × H)
289. M₁₆	C₂²×C₅×D₃	semidirect
292. C₃×C₅	C₂²×#100	semidirect
295. C₂²×C₃	C₅×#100	semidirect
310. C₂×C₅	C₂×#823	direct (N × H)
339. C₂×C₃	C₂×C₅×#100	semidirect
342. C₅	C₂²×#823	direct (N × H)
349. C₂²	C₅×#823	direct (N × H)
357. C₃	C₂²×C₅×#100	semidirect
361. C₂	C₂×C₅×#823	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×D₁₂	2
C₂²×C₃×C₅×M₁₆	2
C₂²×C₅×#208	2
C₂×C₅×#823	2
C₂²×C₅×#100	3
C₂²×#823	5

Subgroups — C22×C5×#823 #14412041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×#823 #14412041