Subgroups — C₂×C₅×#5132 #14412100

Order 1920.

1512 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	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×#824	C₂	1	2	yes	maximal, complemented
5	C₅×#5132	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#823	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#413	—	3	1	no	maximal, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₅×#67	C₄	1	2	yes	—
10	C₂×C₅×#235	—	2	1	no	—
11	C₂×C₅×#235	—	2	1	no	—
12	C₂×C₅×#235	—	2	2	no	—
13	C₂×C₅×#235	—	2	1	no	—
14	C₂×C₅×#235	—	2	1	no	—
15	C₂×C₅×#235	—	2	2	no	—
16	C₂×C₅×#235	C₄	1	4	yes	—
17	C₂×C₅×#235	C₂²	1	4	yes	—
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₄	1	2	yes	—
20	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×M₁₆	—	2	1	no	—
22	C₂×C₃×C₅×M₁₆	—	2	2	no	—
23	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
24	C₂×C₃×C₅×M₁₆	C₂²	1	4	yes	complemented
25	C₂²×C₃×C₅×C₈	—	2	1	no	—
26	C₂×C₅×#208	—	2	1	no	—
27	C₂×C₅×#208	—	2	2	no	—
28	C₂×C₅×#208	C₂²	1	2	yes	—
29	C₂×C₅×#208	C₂²	1	4	yes	complemented
30	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
31	C₅×#824	C₂²	1	8	yes	complemented
32	C₅×#823	C₂²	1	8	yes	complemented
33	C₂×#5132	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂²×C₅×#41	—	3	1	no	—
35	C₂²×C₅×M₁₆	—	3	1	no	—
36	C₂²×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
37	C₅×#413	—	3	8	no	—
38	C₂×C₅×#101	—	3	2	no	—
39	C₂×C₅×#100	—	3	2	no	—
40	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₅×D₃	C₂×C₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂×C₅×#67	—	2	2	no	—
53	C₂×C₅×#67	—	2	2	no	—
54	C₂×C₅×#67	—	2	4	no	—
55	C₂×C₅×#67	C₂×C₄	1	8	yes	—
56	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
57	C₅×#235	—	2	4	no	—
58	C₅×#235	—	2	4	no	—
59	C₅×#235	—	2	4	no	—
60	C₅×#235	—	2	4	no	—
61	C₅×#235	—	2	4	no	—
62	C₅×#235	—	2	4	no	—
63	C₅×#235	—	2	4	no	—
64	C₅×#235	—	2	4	no	—
65	C₂×C₅×D₁₂	—	2	1	no	—
66	C₂×C₅×D₁₂	—	2	1	no	—
67	C₂×C₅×D₁₂	—	2	1	no	—
68	C₂×C₅×D₁₂	—	2	1	no	—
69	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
70	C₂×C₅×D₁₂	C₂³	1	2	yes	—
71	C₂×C₄×C₅×D₃	—	2	4	no	—
72	C₂×C₄×C₅×D₃	—	2	2	no	—
73	C₂×C₄×C₅×D₃	—	2	2	no	—
74	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
75	C₂×C₅×Dic₆	—	2	1	no	—
76	C₂×C₅×Dic₆	—	2	1	no	—
77	C₂×C₅×Dic₆	—	2	1	no	—
78	C₂×C₅×Dic₆	—	2	1	no	—
79	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
80	C₂×C₅×Dic₆	C₂³	1	2	yes	—
81	C₃×C₅×M₁₆	—	2	2	no	—
82	C₃×C₅×M₁₆	—	2	4	no	—
83	C₃×C₅×M₁₆	C₂³	1	4	yes	—
84	C₂×C₃×C₅×C₈	—	2	2	no	—
85	C₂×C₃×C₅×C₈	—	2	4	no	—
86	C₅×#208	—	2	2	no	—
87	C₅×#208	—	2	4	no	—
88	C₅×#208	C₂³	1	4	yes	—
89	C₂×C₅×C₃⋊C₈	—	2	2	no	—
90	C₂×C₅×C₃⋊C₈	—	2	4	no	—
91	C₂²×#235	C₂×C₅	1	1	yes	characteristic
92	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂²×#208	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#824	C₂×C₅	1	2	yes	complemented
95	#5132	C₂×C₅	1	8	yes	direct product factor
96	C₂×#823	C₂×C₅	1	2	yes	complemented
97	C₂×C₅×#41	—	3	4	no	—
98	C₂×C₅×#41	—	3	4	no	—
99	C₂×C₅×#41	—	6	1	no	—
100	C₂×C₅×#41	—	6	2	no	—
101	C₂×C₅×#41	—	6	1	no	—
102	C₂×C₅×#41	—	6	1	no	—
103	C₂×C₅×#41	—	6	2	no	—
104	C₂×C₅×#41	—	6	1	no	—
105	C₂²×C₅×Q₈	—	3	1	no	—
106	C₂²×C₅×D₄	—	3	2	no	—
107	C₂²×C₅×D₄	—	3	1	no	—
108	C₂³×C₄×C₅	—	3	2	no	—
109	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
110	C₂×C₅×M₁₆	—	2	1	no	—
111	C₂×C₅×M₁₆	—	2	2	no	—
112	C₂×C₅×M₁₆	—	3	2	no	—
113	C₂×C₅×M₁₆	—	3	4	no	—
114	C₂×C₅×M₁₆	—	6	1	no	—
115	C₂×C₅×M₁₆	—	6	2	no	—
116	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
117	C₂×C₅×M₁₆	C₂×D₃	1	4	yes	complemented
118	C₂²×C₅×C₈	—	2	1	no	—
119	C₂²×C₅×C₈	—	6	1	no	—
120	C₅×#101	—	3	8	no	—
121	C₅×#100	—	3	8	no	—
122	C₂×#413	—	3	1	no	Sylow
123	C₂³×C₃×C₅	—	4	2	no	—
124	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
126	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
127	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
129	C₂²×C₅×D₃	—	2	2	no	—
130	C₂²×C₅×D₃	—	2	2	no	—
131	C₂²×C₅×D₃	—	4	4	no	—
132	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
133	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
151	C₅×#67	—	2	8	no	—
152	C₅×#67	—	2	8	no	—
153	C₂×C₅×Dic₃	—	2	2	no	—
154	C₂×C₅×Dic₃	—	2	2	no	—
155	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
156	C₅×D₁₂	—	2	2	no	—
157	C₅×D₁₂	—	2	2	no	—
158	C₅×D₁₂	—	2	2	no	—
159	C₅×D₁₂	—	2	2	no	—
160	C₄×C₅×D₃	—	2	8	no	—
161	C₄×C₅×D₃	—	2	8	no	—
162	C₅×Dic₆	—	2	2	no	—
163	C₅×Dic₆	—	2	2	no	—
164	C₅×Dic₆	—	2	2	no	—
165	C₅×Dic₆	—	2	2	no	—
166	C₃×C₅×C₈	—	2	4	no	—
167	C₅×C₃⋊C₈	—	2	4	no	—
168	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
169	C₂²×#67	C₄×C₅	1	2	yes	—
170	C₂×#235	—	2	1	no	—
171	C₂×#235	—	2	1	no	—
172	C₂×#235	—	2	2	no	—
173	C₂×#235	—	2	1	no	—
174	C₂×#235	—	2	1	no	—
175	C₂×#235	—	2	2	no	—
176	C₂×#235	C₄×C₅	1	4	yes	—
177	C₂×#235	C₂²×C₅	1	4	yes	—
178	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
179	C₂²×C₄×D₃	C₄×C₅	1	2	yes	—
180	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₃×M₁₆	—	2	1	no	—
182	C₂×C₃×M₁₆	—	2	2	no	—
183	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
184	C₂×C₃×M₁₆	C₂²×C₅	1	4	yes	complemented
185	C₂²×C₃×C₈	—	2	1	no	—
186	C₂×#208	—	2	1	no	—
187	C₂×#208	—	2	2	no	—
188	C₂×#208	C₂²×C₅	1	2	yes	—
189	C₂×#208	C₂²×C₅	1	4	yes	complemented
190	C₂²×C₃⋊C₈	—	2	1	no	—
191	#824	C₂²×C₅	1	8	yes	complemented
192	#823	C₂²×C₅	1	8	yes	complemented
193	C₂⁴×C₅	—	3	2	no	—
194	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
195	C₅×#41	—	6	4	no	—
196	C₅×#41	—	6	4	no	—
197	C₅×#41	—	6	4	no	—
198	C₅×#41	—	6	4	no	—
199	C₅×#41	—	6	4	no	—
200	C₅×#41	—	6	4	no	—
201	C₅×#41	—	6	4	no	—
202	C₅×#41	—	6	4	no	—
203	C₂×C₅×Q₈	—	3	2	no	—
204	C₂×C₅×Q₈	—	3	2	no	—
205	C₂×C₅×Q₈	—	6	1	no	—
206	C₂×C₅×Q₈	—	6	1	no	—
207	C₂×C₅×Q₈	—	6	1	no	—
208	C₂×C₅×Q₈	—	6	1	no	—
209	C₂×C₅×D₄	—	3	8	no	—
210	C₂×C₅×D₄	—	3	2	no	—
211	C₂×C₅×D₄	—	3	2	no	—
212	C₂×C₅×D₄	—	6	2	no	—
213	C₂×C₅×D₄	—	6	2	no	—
214	C₂×C₅×D₄	—	6	4	no	—
215	C₂×C₅×D₄	—	6	1	no	—
216	C₂×C₅×D₄	—	6	1	no	—
217	C₂×C₅×D₄	—	6	1	no	—
218	C₂×C₅×D₄	—	6	1	no	—
219	C₂²×C₄×C₅	—	3	2	no	—
220	C₂²×C₄×C₅	—	3	8	no	—
221	C₂²×C₄×C₅	—	6	4	no	—
222	C₂²×C₄×C₅	—	6	2	no	—
223	C₂²×C₄×C₅	—	6	2	no	—
224	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
225	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
226	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
227	C₂²×C₄×C₅	D₁₂	1	2	yes	—
228	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
229	C₂²×C₄×C₅	#67	1	1	yes	characteristic
230	C₂²×C₄×C₅	#67	1	2	yes	—
231	C₂²×C₄×C₅	#67	1	1	yes	characteristic
232	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
233	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
234	C₅×M₁₆	—	2	2	no	—
235	C₅×M₁₆	—	2	4	no	—
236	C₅×M₁₆	—	3	4	no	—
237	C₅×M₁₆	—	6	2	no	—
238	C₅×M₁₆	—	6	4	no	—
239	C₅×M₁₆	C₂²×D₃	1	4	yes	—
240	C₂×C₅×C₈	—	2	2	no	—
241	C₂×C₅×C₈	—	2	4	no	—
242	C₂×C₅×C₈	—	6	2	no	—
243	C₂×C₅×C₈	—	6	4	no	—
244	C₂²×#41	—	3	1	no	—
245	C₂²×M₁₆	—	3	1	no	—
246	C₂²×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
247	#413	—	3	8	no	—
248	C₂×#101	—	3	2	no	—
249	C₂×#100	—	3	2	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	—	4	2	no	—
254	C₂²×C₃×C₅	—	4	2	no	—
255	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₅×D₃	—	2	4	no	—
261	C₂×C₅×D₃	—	4	4	no	—
262	C₂×C₅×D₃	—	4	4	no	—
263	C₂×C₅×D₃	—	4	4	no	—
264	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
267	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
268	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
269	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₅×Dic₃	—	2	4	no	—
271	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
272	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
273	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
275	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
278	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
279	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
280	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
281	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
283	C₂×#67	—	2	2	no	—
284	C₂×#67	—	2	2	no	—
285	C₂×#67	—	2	4	no	—
286	C₂×#67	C₂×C₄×C₅	1	8	yes	—
287	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
288	#235	—	2	4	no	—
289	#235	—	2	4	no	—
290	#235	—	2	4	no	—
291	#235	—	2	4	no	—
292	#235	—	2	4	no	—
293	#235	—	2	4	no	—
294	#235	—	2	4	no	—
295	#235	—	2	4	no	—
296	C₂×D₁₂	—	2	1	no	—
297	C₂×D₁₂	—	2	1	no	—
298	C₂×D₁₂	—	2	1	no	—
299	C₂×D₁₂	—	2	1	no	—
300	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
301	C₂×D₁₂	C₂³×C₅	1	2	yes	—
302	C₂×C₄×D₃	—	2	4	no	—
303	C₂×C₄×D₃	—	2	2	no	—
304	C₂×C₄×D₃	—	2	2	no	—
305	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
306	C₂×Dic₆	—	2	1	no	—
307	C₂×Dic₆	—	2	1	no	—
308	C₂×Dic₆	—	2	1	no	—
309	C₂×Dic₆	—	2	1	no	—
310	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
311	C₂×Dic₆	C₂³×C₅	1	2	yes	—
312	C₃×M₁₆	—	2	2	no	—
313	C₃×M₁₆	—	2	4	no	—
314	C₃×M₁₆	C₂³×C₅	1	4	yes	—
315	C₂×C₃×C₈	—	2	2	no	—
316	C₂×C₃×C₈	—	2	4	no	—
317	#208	—	2	2	no	—
318	#208	—	2	4	no	—
319	#208	C₂³×C₅	1	4	yes	—
320	C₂×C₃⋊C₈	—	2	2	no	—
321	C₂×C₃⋊C₈	—	2	4	no	—
322	C₂³×C₅	—	3	4	no	—
323	C₂³×C₅	—	4	2	no	—
324	C₂³×C₅	—	6	2	no	—
325	C₂³×C₅	—	6	2	no	—
326	C₂³×C₅	—	12	4	no	—
327	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
328	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
329	C₂³×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
330	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
331	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
332	C₅×Q₈	—	6	2	no	—
333	C₅×Q₈	—	6	2	no	—
334	C₅×Q₈	—	6	2	no	—
335	C₅×Q₈	—	6	2	no	—
336	C₅×D₄	—	6	8	no	—
337	C₅×D₄	—	6	8	no	—
338	C₅×D₄	—	6	2	no	—
339	C₅×D₄	—	6	2	no	—
340	C₅×D₄	—	6	2	no	—
341	C₅×D₄	—	6	2	no	—
342	C₂×C₄×C₅	—	3	4	no	—
343	C₂×C₄×C₅	—	6	2	no	—
344	C₂×C₄×C₅	—	6	2	no	—
345	C₂×C₄×C₅	—	6	8	no	—
346	C₂×C₄×C₅	—	6	8	no	—
347	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
348	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
349	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
350	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
351	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
352	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
353	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
355	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
356	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
358	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
359	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
360	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
361	C₂×C₄×C₅	C₂×#67	1	2	yes	—
362	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
363	C₂×C₄×C₅	C₂×#67	1	2	yes	—
364	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
365	C₅×C₈	—	2	4	no	—
366	C₅×C₈	—	6	4	no	—
367	C₂×#41	—	3	4	no	—
368	C₂×#41	—	3	4	no	—
369	C₂×#41	—	6	1	no	—
370	C₂×#41	—	6	1	no	—
371	C₂×#41	—	6	2	no	—
372	C₂×#41	—	6	1	no	—
373	C₂×#41	—	6	1	no	—
374	C₂×#41	—	6	2	no	—
375	C₂²×Q₈	—	3	1	no	—
376	C₂²×D₄	—	3	2	no	—
377	C₂²×D₄	—	3	1	no	—
378	C₂³×C₄	—	3	2	no	—
379	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	2	no	—
382	C₂×M₁₆	—	3	2	no	—
383	C₂×M₁₆	—	3	4	no	—
384	C₂×M₁₆	—	6	1	no	—
385	C₂×M₁₆	—	6	2	no	—
386	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
387	C₂×M₁₆	C₂×C₅×D₃	1	4	yes	complemented
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	—	6	1	no	—
390	#101	—	3	8	no	—
391	#100	—	3	8	no	—
392	C₂×C₃×C₅	—	2	1	no	—
393	C₂×C₃×C₅	—	2	1	no	—
394	C₂×C₃×C₅	—	2	2	no	—
395	C₂×C₃×C₅	—	2	2	no	—
396	C₂×C₃×C₅	#413	1	2	yes	complemented
397	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
398	C₅×D₃	—	4	4	no	—
399	C₂³×C₃	—	4	2	no	—
400	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
401	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
402	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
403	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
404	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
405	C₂²×D₃	—	2	2	no	—
406	C₂²×D₃	—	2	2	no	—
407	C₂²×D₃	—	4	4	no	—
408	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
409	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
410	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
411	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
412	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
413	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
414	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
415	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
416	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
418	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
420	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
422	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
424	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
426	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
427	#67	—	2	8	no	—
428	#67	—	2	8	no	—
429	C₂×Dic₃	—	2	2	no	—
430	C₂×Dic₃	—	2	2	no	—
431	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
432	D₁₂	—	2	2	no	—
433	D₁₂	—	2	2	no	—
434	D₁₂	—	2	2	no	—
435	D₁₂	—	2	2	no	—
436	C₄×D₃	—	2	8	no	—
437	C₄×D₃	—	2	8	no	—
438	Dic₆	—	2	2	no	—
439	Dic₆	—	2	2	no	—
440	Dic₆	—	2	2	no	—
441	Dic₆	—	2	2	no	—
442	C₃×C₈	—	2	4	no	—
443	C₃⋊C₈	—	2	4	no	—
444	C₂²×C₅	—	2	2	no	—
445	C₂²×C₅	—	2	2	no	—
446	C₂²×C₅	—	2	2	no	—
447	C₂²×C₅	—	4	2	no	—
448	C₂²×C₅	—	4	2	no	—
449	C₂²×C₅	—	6	4	no	—
450	C₂²×C₅	—	12	4	no	—
451	C₂²×C₅	—	12	4	no	—
452	C₂²×C₅	—	12	4	no	—
453	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
454	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
455	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
456	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
457	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
458	C₄×C₅	—	6	4	no	—
459	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
460	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
461	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
462	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
463	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
464	C₄×C₅	C₂²×#67	1	1	yes	characteristic
465	C₂⁴	—	3	2	no	—
466	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
467	#41	—	6	4	no	—
468	#41	—	6	4	no	—
469	#41	—	6	4	no	—
470	#41	—	6	4	no	—
471	#41	—	6	4	no	—
472	#41	—	6	4	no	—
473	#41	—	6	4	no	—
474	#41	—	6	4	no	—
475	C₂×Q₈	—	3	2	no	—
476	C₂×Q₈	—	3	2	no	—
477	C₂×Q₈	—	6	1	no	—
478	C₂×Q₈	—	6	1	no	—
479	C₂×Q₈	—	6	1	no	—
480	C₂×Q₈	—	6	1	no	—
481	C₂×D₄	—	3	8	no	—
482	C₂×D₄	—	3	2	no	—
483	C₂×D₄	—	3	2	no	—
484	C₂×D₄	—	6	2	no	—
485	C₂×D₄	—	6	2	no	—
486	C₂×D₄	—	6	4	no	—
487	C₂×D₄	—	6	1	no	—
488	C₂×D₄	—	6	1	no	—
489	C₂×D₄	—	6	1	no	—
490	C₂×D₄	—	6	1	no	—
491	C₂²×C₄	—	3	2	no	—
492	C₂²×C₄	—	3	8	no	—
493	C₂²×C₄	—	6	4	no	—
494	C₂²×C₄	—	6	2	no	—
495	C₂²×C₄	—	6	2	no	—
496	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
497	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
498	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
499	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
500	C₂²×C₄	C₅×D₁₂	1	2	yes	—
501	C₂²×C₄	C₅×#67	1	1	yes	characteristic
502	C₂²×C₄	C₅×#67	1	1	yes	characteristic
503	C₂²×C₄	C₅×#67	1	2	yes	—
504	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
506	M₁₆	—	2	2	no	—
507	M₁₆	—	2	4	no	—
508	M₁₆	—	3	4	no	—
509	M₁₆	—	6	2	no	—
510	M₁₆	—	6	4	no	—
511	M₁₆	C₂²×C₅×D₃	1	4	yes	—
512	C₂×C₈	—	2	2	no	—
513	C₂×C₈	—	2	4	no	—
514	C₂×C₈	—	6	2	no	—
515	C₂×C₈	—	6	4	no	—
516	C₃×C₅	C₂×#413	1	1	yes	characteristic, complemented, Hall
517	C₂²×C₃	—	2	2	no	—
518	C₂²×C₃	—	2	2	no	—
519	C₂²×C₃	—	2	2	no	—
520	C₂²×C₃	—	4	2	no	—
521	C₂²×C₃	—	4	2	no	—
522	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
523	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
524	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
525	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
526	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
527	C₂×D₃	—	2	4	no	—
528	C₂×D₃	—	4	4	no	—
529	C₂×D₃	—	4	4	no	—
530	C₂×D₃	—	4	4	no	—
531	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
532	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
533	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
534	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
535	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
536	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
537	Dic₃	—	2	4	no	—
538	C₂×C₅	—	2	1	no	—
539	C₂×C₅	—	2	1	no	—
540	C₂×C₅	—	2	2	no	—
541	C₂×C₅	—	2	2	no	—
542	C₂×C₅	—	12	4	no	—
543	C₂×C₅	#5132	1	2	yes	direct product factor
544	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
545	C₂³	—	3	4	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	6	2	no	—
548	C₂³	—	6	2	no	—
549	C₂³	—	12	4	no	—
550	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
551	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
552	C₂³	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
553	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
554	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
555	Q₈	—	6	2	no	—
556	Q₈	—	6	2	no	—
557	Q₈	—	6	2	no	—
558	Q₈	—	6	2	no	—
559	D₄	—	6	8	no	—
560	D₄	—	6	8	no	—
561	D₄	—	6	2	no	—
562	D₄	—	6	2	no	—
563	D₄	—	6	2	no	—
564	D₄	—	6	2	no	—
565	C₂×C₄	—	3	4	no	—
566	C₂×C₄	—	6	2	no	—
567	C₂×C₄	—	6	2	no	—
568	C₂×C₄	—	6	8	no	—
569	C₂×C₄	—	6	8	no	—
570	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
571	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
572	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
573	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
574	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
575	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
576	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
577	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
578	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
579	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
580	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
581	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
582	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
583	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
584	C₂×C₄	C₂×C₅×#67	1	2	yes	—
585	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
586	C₂×C₄	C₂×C₅×#67	1	2	yes	—
587	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
588	C₈	—	2	4	no	—
589	C₈	—	6	4	no	—
590	C₂×C₃	—	2	1	no	—
591	C₂×C₃	—	2	1	no	—
592	C₂×C₃	—	2	2	no	—
593	C₂×C₃	—	2	2	no	—
594	C₂×C₃	C₅×#413	1	2	yes	complemented
595	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
596	D₃	—	4	4	no	—
597	C₅	C₂×#5132	1	1	yes	characteristic, direct product factor, Sylow
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	6	4	no	—
604	C₂²	—	12	4	no	—
605	C₂²	—	12	4	no	—
606	C₂²	—	12	4	no	—
607	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
608	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
609	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
610	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
611	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
612	C₄	—	6	4	no	—
613	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
614	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
615	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
616	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
617	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
618	C₄	C₂²×C₅×#67	1	1	yes	characteristic
619	C₃	C₂×C₅×#413	1	1	yes	characteristic, complemented, Sylow
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	2	no	—
623	C₂	—	2	2	no	—
624	C₂	—	12	4	no	—
625	C₂	C₅×#5132	1	2	yes	direct product factor
626	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×M₁₆	D₃
hypocenter	C₃	C₂×C₅×#413
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×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×#824	C₂	semidirect
5. C₅×#5132	C₂	direct (N × H)
6. C₂×C₅×#823	C₂	semidirect
24. C₂×C₃×C₅×M₁₆	C₂²	semidirect
29. C₂×C₅×#208	C₂²	semidirect
31. C₅×#824	C₂²	semidirect
32. C₅×#823	C₂²	semidirect
33. C₂×#5132	C₅	direct (N × H)
36. C₂²×C₅×M₁₆	D₃	semidirect
92. C₂²×C₃×M₁₆	C₂×C₅	semidirect
93. C₂²×#208	C₂×C₅	semidirect
94. C₂×#824	C₂×C₅	semidirect
95. #5132	C₂×C₅	direct (N × H)
96. C₂×#823	C₂×C₅	semidirect
117. C₂×C₅×M₁₆	C₂×D₃	semidirect
184. C₂×C₃×M₁₆	C₂²×C₅	semidirect
189. C₂×#208	C₂²×C₅	semidirect
191. #824	C₂²×C₅	semidirect
192. #823	C₂²×C₅	semidirect
246. C₂²×M₁₆	C₅×D₃	semidirect
387. C₂×M₁₆	C₂×C₅×D₃	semidirect
396. C₂×C₃×C₅	#413	semidirect
516. C₃×C₅	C₂×#413	semidirect
543. C₂×C₅	#5132	direct (N × H)
594. C₂×C₃	C₅×#413	semidirect
597. C₅	C₂×#5132	direct (N × H)
619. C₃	C₂×C₅×#413	semidirect
625. C₂	C₅×#5132	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×C₅×#235	2
C₂²×C₃×C₅×M₁₆	2
C₂²×C₅×#208	2
C₂×C₅×#824	2
C₅×#5132	2
C₂×C₅×#823	2
C₂×C₅×#413	3
C₂×#5132	5

Subgroups — C2×C5×#5132 #14412100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5132 #14412100