Subgroups — C₅×#83768 #14412549

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 540 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	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5133	C₂	1	4	yes	maximal, complemented
5	C₅×#5131	C₂	1	2	yes	maximal, complemented
6	C₅×#5120	C₂	1	2	yes	maximal, complemented
7	C₅×#5113	C₂	1	4	yes	maximal, complemented
8	C₅×#2896	—	3	1	no	maximal, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₅×#67	—	2	1	no	—
11	C₂×C₅×#235	—	2	1	no	—
12	C₂×C₅×#235	—	2	1	no	—
13	C₂×C₅×#235	—	2	4	no	—
14	C₂×C₅×#235	C₄	1	8	yes	complemented
15	C₂×C₅×#235	C₂²	1	2	yes	—
16	C₂×C₅×#235	C₂²	1	2	yes	—
17	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	—	2	1	no	—
19	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×M₁₆	—	2	4	no	—
21	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
22	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
23	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
24	C₂×C₅×#217	—	2	1	no	—
25	C₅×#926	—	2	1	no	—
26	C₅×#926	—	2	1	no	—
27	C₅×#926	C₂²	1	2	yes	—
28	C₅×#926	C₂²	1	2	yes	complemented
29	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
30	C₂×C₄×C₅×Dic₃	—	2	1	no	—
31	C₅×#821	C₂²	1	8	yes	complemented
32	C₅×#816	C₂²	1	8	yes	complemented
33	#83768	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂²×C₅×#41	—	3	1	no	—
35	C₂²×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
36	C₂×C₅×#117	—	3	1	no	—
37	C₅×#419	—	3	2	no	—
38	C₅×#418	—	3	2	no	—
39	C₅×#417	—	3	4	no	—
40	C₅×#416	—	3	4	no	—
41	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
42	C₂³×C₅×D₃	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	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	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×#67	—	2	8	no	—
52	C₂×C₅×#67	—	2	2	no	—
53	C₂×C₅×#67	—	2	2	no	—
54	C₂²×C₅×Dic₃	—	2	1	no	—
55	C₂²×C₅×Dic₃	—	2	2	no	—
56	C₅×#235	—	2	8	no	—
57	C₅×#235	—	2	8	no	—
58	C₅×#235	—	2	4	no	—
59	C₅×#235	—	2	4	no	—
60	C₅×#235	C₂×C₄	1	8	yes	—
61	C₅×#235	C₂×C₄	1	8	yes	complemented
62	C₂×C₅×D₁₂	—	2	1	no	—
63	C₂×C₅×D₁₂	—	2	2	no	—
64	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
65	C₂×C₅×D₁₂	C₂³	1	2	yes	—
66	C₂×C₄×C₅×D₃	—	2	8	no	—
67	C₂×C₄×C₅×D₃	—	2	2	no	—
68	C₂×C₄×C₅×D₃	—	2	2	no	—
69	C₂×C₅×Dic₆	—	2	1	no	—
70	C₂×C₅×Dic₆	—	2	2	no	—
71	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
72	C₂×C₅×Dic₆	C₂³	1	2	yes	—
73	C₃×C₅×M₁₆	—	2	4	no	—
74	C₃×C₅×M₁₆	—	2	4	no	—
75	C₂×C₃×C₅×C₈	—	2	4	no	—
76	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
77	C₅×#217	—	2	2	no	—
78	C₅×#217	—	2	2	no	—
79	C₅×C₄⋊Dic₃	—	2	2	no	—
80	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
81	C₄×C₅×Dic₃	—	2	2	no	—
82	C₄×C₅×Dic₃	—	2	2	no	—
83	C₂²×#235	C₂×C₅	1	1	yes	characteristic
84	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
86	#5133	C₂×C₅	1	4	yes	complemented
87	#5131	C₂×C₅	1	2	yes	complemented
88	#5120	C₂×C₅	1	2	yes	complemented
89	#5113	C₂×C₅	1	4	yes	complemented
90	C₂×C₅×#41	—	3	8	no	—
91	C₂×C₅×#41	—	3	2	no	—
92	C₂×C₅×#41	—	3	2	no	—
93	C₂×C₅×#41	—	6	1	no	—
94	C₂×C₅×#41	—	6	1	no	—
95	C₂×C₅×#41	—	6	4	no	—
96	C₂²×C₅×Q₈	—	3	1	no	—
97	C₂²×C₅×D₄	—	3	1	no	—
98	C₂²×C₅×D₄	—	6	1	no	—
99	C₂³×C₄×C₅	—	6	1	no	—
100	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
101	C₂×C₅×M₁₆	—	2	4	no	—
102	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
103	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	complemented
104	C₂²×C₅×C₈	C₂×D₃	1	2	yes	complemented
105	C₅×#117	—	3	2	no	—
106	C₅×#117	—	3	2	no	—
107	C₅×#117	—	6	1	no	—
108	C₅×#117	—	6	1	no	—
109	C₂×C₅×C₄⋊C₄	—	3	2	no	—
110	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
111	C₂×C₄²×C₅	—	6	1	no	—
112	C₅×#103	—	3	8	no	—
113	C₅×#102	—	3	8	no	—
114	#2896	—	3	1	no	Sylow
115	C₂³×C₃×C₅	—	4	2	no	—
116	C₂³×C₃×C₅	C₂²⋊C₄	1	4	yes	—
117	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₅×D₃	—	2	4	no	—
121	C₂²×C₅×D₃	—	2	2	no	—
122	C₂²×C₅×D₃	—	4	4	no	—
123	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
124	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
125	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₅×#67	—	2	8	no	—
137	C₅×#67	—	2	8	no	—
138	C₂×C₅×Dic₃	—	2	4	no	—
139	C₂×C₅×Dic₃	—	2	2	no	—
140	C₂×C₅×Dic₃	—	2	4	no	—
141	C₂×C₅×Dic₃	—	4	4	no	—
142	C₅×D₁₂	—	2	4	no	—
143	C₅×D₁₂	—	2	2	no	—
144	C₅×D₁₂	C₂²×C₄	1	4	yes	—
145	C₄×C₅×D₃	—	2	8	no	—
146	C₄×C₅×D₃	—	2	8	no	—
147	C₅×Dic₆	—	2	4	no	—
148	C₅×Dic₆	—	2	2	no	—
149	C₅×Dic₆	C₂²×C₄	1	4	yes	—
150	C₃×C₅×C₈	—	2	4	no	—
151	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
152	C₂²×#67	—	2	1	no	—
153	C₂×#235	—	2	1	no	—
154	C₂×#235	—	2	1	no	—
155	C₂×#235	—	2	4	no	—
156	C₂×#235	C₄×C₅	1	8	yes	complemented
157	C₂×#235	C₂²×C₅	1	2	yes	—
158	C₂×#235	C₂²×C₅	1	2	yes	—
159	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
160	C₂²×C₄×D₃	—	2	1	no	—
161	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₃×M₁₆	—	2	4	no	—
163	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
164	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
165	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
166	C₂×#217	—	2	1	no	—
167	#926	—	2	1	no	—
168	#926	—	2	1	no	—
169	#926	C₂²×C₅	1	2	yes	—
170	#926	C₂²×C₅	1	2	yes	complemented
171	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
172	C₂×C₄×Dic₃	—	2	1	no	—
173	#821	C₂²×C₅	1	8	yes	complemented
174	#816	C₂²×C₅	1	8	yes	complemented
175	C₂⁴×C₅	—	6	1	no	—
176	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
177	C₅×#41	—	3	8	no	—
178	C₅×#41	—	3	8	no	—
179	C₅×#41	—	6	8	no	—
180	C₅×#41	—	6	8	no	—
181	C₅×#41	—	6	4	no	—
182	C₅×#41	—	6	4	no	—
183	C₂×C₅×Q₈	—	3	4	no	—
184	C₂×C₅×Q₈	—	3	2	no	—
185	C₂×C₅×Q₈	—	6	1	no	—
186	C₂×C₅×Q₈	—	6	2	no	—
187	C₂×C₅×D₄	—	3	4	no	—
188	C₂×C₅×D₄	—	3	2	no	—
189	C₂×C₅×D₄	—	6	8	no	—
190	C₂×C₅×D₄	—	6	2	no	—
191	C₂×C₅×D₄	—	6	2	no	—
192	C₂×C₅×D₄	—	6	1	no	—
193	C₂×C₅×D₄	—	6	2	no	—
194	C₂²×C₄×C₅	—	6	1	no	—
195	C₂²×C₄×C₅	—	6	8	no	—
196	C₂²×C₄×C₅	—	6	2	no	—
197	C₂²×C₄×C₅	—	6	2	no	—
198	C₂²×C₄×C₅	—	6	2	no	—
199	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
200	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
201	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
202	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
203	C₂²×C₄×C₅	#67	1	4	yes	—
204	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₅×M₁₆	—	2	4	no	—
208	C₅×M₁₆	—	2	4	no	—
209	C₂×C₅×C₈	—	2	4	no	—
210	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
211	C₅×C₄⋊C₄	—	3	4	no	—
212	C₅×C₄⋊C₄	—	6	2	no	—
213	C₅×C₂²⋊C₄	—	6	2	no	—
214	C₅×C₂²⋊C₄	—	6	2	no	—
215	C₄²×C₅	—	6	2	no	—
216	C₄²×C₅	—	6	2	no	—
217	C₂²×#41	—	3	1	no	—
218	C₂²×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
219	C₂×#117	—	3	1	no	—
220	#419	—	3	2	no	—
221	#418	—	3	2	no	—
222	#417	—	3	4	no	—
223	#416	—	3	4	no	—
224	C₂²×C₃×C₅	—	2	2	no	—
225	C₂²×C₃×C₅	—	2	2	no	—
226	C₂²×C₃×C₅	—	2	2	no	—
227	C₂²×C₃×C₅	—	4	4	no	—
228	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
231	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₅×D₃	—	2	4	no	—
233	C₂×C₅×D₃	—	4	8	no	—
234	C₂×C₅×D₃	—	4	4	no	—
235	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
236	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
237	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
238	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
240	C₅×Dic₃	—	2	4	no	—
241	C₅×Dic₃	—	4	4	no	—
242	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
243	C₂³×D₃	—	2	1	no	—
244	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
245	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
249	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂×#67	—	2	8	no	—
253	C₂×#67	—	2	2	no	—
254	C₂×#67	—	2	2	no	—
255	C₂²×Dic₃	—	2	1	no	—
256	C₂²×Dic₃	—	2	2	no	—
257	#235	—	2	8	no	—
258	#235	—	2	8	no	—
259	#235	—	2	4	no	—
260	#235	—	2	4	no	—
261	#235	C₂×C₄×C₅	1	8	yes	—
262	#235	C₂×C₄×C₅	1	8	yes	complemented
263	C₂×D₁₂	—	2	1	no	—
264	C₂×D₁₂	—	2	2	no	—
265	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
266	C₂×D₁₂	C₂³×C₅	1	2	yes	—
267	C₂×C₄×D₃	—	2	8	no	—
268	C₂×C₄×D₃	—	2	2	no	—
269	C₂×C₄×D₃	—	2	2	no	—
270	C₂×Dic₆	—	2	1	no	—
271	C₂×Dic₆	—	2	2	no	—
272	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
273	C₂×Dic₆	C₂³×C₅	1	2	yes	—
274	C₃×M₁₆	—	2	4	no	—
275	C₃×M₁₆	—	2	4	no	—
276	C₂×C₃×C₈	—	2	4	no	—
277	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
278	#217	—	2	2	no	—
279	#217	—	2	2	no	—
280	C₄⋊Dic₃	—	2	2	no	—
281	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
282	C₄×Dic₃	—	2	2	no	—
283	C₄×Dic₃	—	2	2	no	—
284	C₂³×C₅	—	4	2	no	—
285	C₂³×C₅	—	6	4	no	—
286	C₂³×C₅	—	6	2	no	—
287	C₂³×C₅	—	12	4	no	—
288	C₂³×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
289	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
290	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
291	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
292	C₅×Q₈	—	3	4	no	—
293	C₅×Q₈	—	6	4	no	—
294	C₅×Q₈	—	6	2	no	—
295	C₅×D₄	—	3	4	no	—
296	C₅×D₄	—	6	8	no	—
297	C₅×D₄	—	6	8	no	—
298	C₅×D₄	—	6	4	no	—
299	C₅×D₄	—	6	2	no	—
300	C₂×C₄×C₅	—	6	4	no	—
301	C₂×C₄×C₅	—	6	2	no	—
302	C₂×C₄×C₅	—	6	8	no	—
303	C₂×C₄×C₅	—	6	8	no	—
304	C₂×C₄×C₅	—	6	4	no	—
305	C₂×C₄×C₅	—	12	4	no	—
306	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
307	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
308	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
309	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
310	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
311	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
312	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂×#67	1	2	yes	—
316	C₂×C₄×C₅	C₂×#67	1	2	yes	—
317	C₂×C₄×C₅	C₂×#67	1	2	yes	—
318	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
319	C₅×C₈	—	2	4	no	—
320	C₂×#41	—	3	8	no	—
321	C₂×#41	—	3	2	no	—
322	C₂×#41	—	3	2	no	—
323	C₂×#41	—	6	1	no	—
324	C₂×#41	—	6	1	no	—
325	C₂×#41	—	6	4	no	—
326	C₂²×Q₈	—	3	1	no	—
327	C₂²×D₄	—	3	1	no	—
328	C₂²×D₄	—	6	1	no	—
329	C₂³×C₄	—	6	1	no	—
330	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
331	C₂×M₁₆	—	2	4	no	—
332	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
333	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	complemented
334	C₂²×C₈	C₂×C₅×D₃	1	2	yes	complemented
335	#117	—	3	2	no	—
336	#117	—	3	2	no	—
337	#117	—	6	1	no	—
338	#117	—	6	1	no	—
339	C₂×C₄⋊C₄	—	3	2	no	—
340	C₂×C₂²⋊C₄	—	6	1	no	—
341	C₂×C₄²	—	6	1	no	—
342	#103	—	3	8	no	—
343	#102	—	3	8	no	—
344	C₂×C₃×C₅	—	2	2	no	—
345	C₂×C₃×C₅	—	2	2	no	—
346	C₂×C₃×C₅	—	2	2	no	—
347	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×C₃×C₅	#575	1	2	yes	—
349	C₅×D₃	—	4	4	no	—
350	C₂³×C₃	—	4	2	no	—
351	C₂³×C₃	C₅×C₂²⋊C₄	1	4	yes	—
352	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂²×D₃	—	2	4	no	—
356	C₂²×D₃	—	2	2	no	—
357	C₂²×D₃	—	4	4	no	—
358	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
359	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
360	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
361	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
362	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
363	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
364	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
365	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
368	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
369	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
370	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
371	#67	—	2	8	no	—
372	#67	—	2	8	no	—
373	C₂×Dic₃	—	2	4	no	—
374	C₂×Dic₃	—	2	2	no	—
375	C₂×Dic₃	—	2	4	no	—
376	C₂×Dic₃	—	4	4	no	—
377	D₁₂	—	2	4	no	—
378	D₁₂	—	2	2	no	—
379	D₁₂	C₂²×C₄×C₅	1	4	yes	—
380	C₄×D₃	—	2	8	no	—
381	C₄×D₃	—	2	8	no	—
382	Dic₆	—	2	4	no	—
383	Dic₆	—	2	2	no	—
384	Dic₆	C₂²×C₄×C₅	1	4	yes	—
385	C₃×C₈	—	2	4	no	—
386	C₂²×C₅	—	2	2	no	—
387	C₂²×C₅	—	2	2	no	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	4	4	no	—
390	C₂²×C₅	—	6	4	no	—
391	C₂²×C₅	—	12	8	no	—
392	C₂²×C₅	—	12	4	no	—
393	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
394	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
395	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
396	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
397	C₄×C₅	—	6	4	no	—
398	C₄×C₅	—	12	4	no	—
399	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
400	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
401	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
402	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
403	C₄×C₅	C₂²×#67	1	1	yes	characteristic
404	C₂⁴	—	6	1	no	—
405	C₂⁴	C₅×D₁₂	1	1	yes	characteristic
406	#41	—	3	8	no	—
407	#41	—	3	8	no	—
408	#41	—	6	8	no	—
409	#41	—	6	8	no	—
410	#41	—	6	4	no	—
411	#41	—	6	4	no	—
412	C₂×Q₈	—	3	4	no	—
413	C₂×Q₈	—	3	2	no	—
414	C₂×Q₈	—	6	1	no	—
415	C₂×Q₈	—	6	2	no	—
416	C₂×D₄	—	3	4	no	—
417	C₂×D₄	—	3	2	no	—
418	C₂×D₄	—	6	8	no	—
419	C₂×D₄	—	6	2	no	—
420	C₂×D₄	—	6	2	no	—
421	C₂×D₄	—	6	1	no	—
422	C₂×D₄	—	6	2	no	—
423	C₂²×C₄	—	6	1	no	—
424	C₂²×C₄	—	6	8	no	—
425	C₂²×C₄	—	6	2	no	—
426	C₂²×C₄	—	6	2	no	—
427	C₂²×C₄	—	6	2	no	—
428	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
429	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
430	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
431	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
432	C₂²×C₄	C₅×#67	1	4	yes	—
433	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
436	M₁₆	—	2	4	no	—
437	M₁₆	—	2	4	no	—
438	C₂×C₈	—	2	4	no	—
439	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
440	C₄⋊C₄	—	3	4	no	—
441	C₄⋊C₄	—	6	2	no	—
442	C₂²⋊C₄	—	6	2	no	—
443	C₂²⋊C₄	—	6	2	no	—
444	C₄²	—	6	2	no	—
445	C₄²	—	6	2	no	—
446	C₃×C₅	#2896	1	1	yes	characteristic, complemented, Hall
447	C₂²×C₃	—	2	2	no	—
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	2	no	—
450	C₂²×C₃	—	4	4	no	—
451	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
452	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
453	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
454	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
455	C₂×D₃	—	2	4	no	—
456	C₂×D₃	—	4	8	no	—
457	C₂×D₃	—	4	4	no	—
458	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
459	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
460	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
461	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
462	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
463	Dic₃	—	2	4	no	—
464	Dic₃	—	4	4	no	—
465	C₂×C₅	—	2	2	no	—
466	C₂×C₅	—	2	2	no	—
467	C₂×C₅	—	2	2	no	—
468	C₂×C₅	—	12	4	no	—
469	C₂×C₅	#5748	1	2	yes	—
470	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
471	C₂³	—	4	2	no	—
472	C₂³	—	6	4	no	—
473	C₂³	—	6	2	no	—
474	C₂³	—	12	4	no	—
475	C₂³	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
476	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
477	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
478	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
479	Q₈	—	3	4	no	—
480	Q₈	—	6	4	no	—
481	Q₈	—	6	2	no	—
482	D₄	—	3	4	no	—
483	D₄	—	6	8	no	—
484	D₄	—	6	8	no	—
485	D₄	—	6	4	no	—
486	D₄	—	6	2	no	—
487	C₂×C₄	—	6	4	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	—	6	8	no	—
490	C₂×C₄	—	6	8	no	—
491	C₂×C₄	—	6	4	no	—
492	C₂×C₄	—	12	4	no	—
493	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
494	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
495	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
496	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
497	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
498	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
499	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
500	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
501	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
502	C₂×C₄	C₂×C₅×#67	1	2	yes	—
503	C₂×C₄	C₂×C₅×#67	1	2	yes	—
504	C₂×C₄	C₂×C₅×#67	1	2	yes	—
505	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
506	C₈	—	2	4	no	—
507	C₂×C₃	—	2	2	no	—
508	C₂×C₃	—	2	2	no	—
509	C₂×C₃	—	2	2	no	—
510	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
511	C₂×C₃	C₅×#575	1	2	yes	—
512	D₃	—	4	4	no	—
513	C₅	#83768	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	6	4	no	—
519	C₂²	—	12	8	no	—
520	C₂²	—	12	4	no	—
521	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
522	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
523	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
524	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
525	C₄	—	6	4	no	—
526	C₄	—	12	4	no	—
527	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
528	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
529	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
530	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
531	C₄	C₂²×C₅×#67	1	1	yes	characteristic
532	C₃	C₅×#2896	1	1	yes	characteristic, complemented, Sylow
533	C₂	—	2	2	no	—
534	C₂	—	2	2	no	—
535	C₂	—	2	2	no	—
536	C₂	—	12	4	no	—
537	C₂	C₅×#5748	1	2	yes	—
538	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#2896
LCS	G ▷ C₃×C₄ ▷ 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. C₂×C₅×#926	C₂	semidirect
4. C₅×#5133	C₂	semidirect
5. C₅×#5131	C₂	semidirect
6. C₅×#5120	C₂	semidirect
7. C₅×#5113	C₂	semidirect
14. C₂×C₅×#235	C₄	semidirect
22. C₂×C₃×C₅×M₁₆	C₂²	semidirect
23. C₂²×C₃×C₅×C₈	C₂²	semidirect
28. C₅×#926	C₂²	semidirect
29. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
31. C₅×#821	C₂²	semidirect
32. C₅×#816	C₂²	semidirect
33. #83768	C₅	direct (N × H)
35. C₂²×C₅×M₁₆	D₃	semidirect
61. C₅×#235	C₂×C₄	semidirect
64. C₂×C₅×D₁₂	C₂×C₄	semidirect
71. C₂×C₅×Dic₆	C₂×C₄	semidirect
84. C₂²×C₃×M₁₆	C₂×C₅	semidirect
85. C₂×#926	C₂×C₅	semidirect
86. #5133	C₂×C₅	semidirect
87. #5131	C₂×C₅	semidirect
88. #5120	C₂×C₅	semidirect
89. #5113	C₂×C₅	semidirect
103. C₂×C₅×M₁₆	C₂×D₃	semidirect
104. C₂²×C₅×C₈	C₂×D₃	semidirect
156. C₂×#235	C₄×C₅	semidirect
164. C₂×C₃×M₁₆	C₂²×C₅	semidirect
165. C₂²×C₃×C₈	C₂²×C₅	semidirect
170. #926	C₂²×C₅	semidirect
171. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
173. #821	C₂²×C₅	semidirect
174. #816	C₂²×C₅	semidirect
218. C₂²×M₁₆	C₅×D₃	semidirect
262. #235	C₂×C₄×C₅	semidirect
265. C₂×D₁₂	C₂×C₄×C₅	semidirect
272. C₂×Dic₆	C₂×C₄×C₅	semidirect
333. C₂×M₁₆	C₂×C₅×D₃	semidirect
334. C₂²×C₈	C₂×C₅×D₃	semidirect
446. C₃×C₅	#2896	semidirect
513. C₅	#83768	direct (N × H)
532. C₃	C₅×#2896	semidirect

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
C₂×C₅×#926	2
C₅×#5133	2
C₅×#5131	2
C₅×#5120	2
C₅×#5113	2
C₅×#2896	3
#83768	5

Subgroups — C5×#83768 #14412549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83768 #14412549