Subgroups — C₅×D₃×#461 #14425860

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×SD₁₆	C₂	1	2	yes	maximal
2	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5162	C₂	1	2	yes	maximal, complemented
6	C₅×#5083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5019	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4841	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4818	C₂	1	2	yes	maximal, complemented
11	C₅×D₃×#103	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#461	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	—
14	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	—	2	1	no	—
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₅×#944	C₂²	1	2	yes	complemented
20	C₂×C₅×#215	C₂²	1	2	yes	—
21	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₅×#214	C₂²	1	2	yes	—
23	C₄×C₅×#67	—	2	1	no	—
24	C₅×D₃×SD₁₆	—	2	8	no	—
25	C₂×C₅×#204	C₂²	1	2	yes	—
26	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
27	C₅×#893	C₂²	1	1	yes	characteristic
28	C₅×D₃×C₄⋊C₄	—	2	1	no	—
29	C₅×D₃×C₄⋊C₄	—	2	1	no	—
30	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₅×#888	—	2	1	no	—
32	C₅×#888	—	2	1	no	—
33	C₅×#67⋊C₄	—	2	1	no	—
34	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
35	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
36	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
37	C₅×#869	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₅×#103	C₂²	1	2	yes	complemented
40	C₅×#835	C₂²	1	2	yes	complemented
41	C₅×#816	C₂²	1	2	yes	complemented
42	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
43	C₅×#810	C₂²	1	2	yes	complemented
44	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
45	D₃×#461	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂²×C₅×SD₁₆	—	3	2	no	—
47	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
48	C₂×C₄×C₅×D₄	—	3	1	no	—
49	C₅×#461	—	3	1	no	—
50	C₅×#461	—	3	2	no	—
51	C₅×#461	—	3	2	no	—
52	C₅×#461	—	3	1	no	—
53	C₅×#461	—	3	1	no	—
54	C₅×#461	D₃	1	1	yes	characteristic, direct product factor
55	C₂×C₅×C₄⋊C₈	—	3	1	no	—
56	C₂×C₅×#103	—	3	2	no	—
57	C₂³×C₅×D₃	—	2	1	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
59	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂×C₅×#67	—	2	1	no	—
62	C₂²×C₅×Dic₃	—	2	1	no	—
63	C₅×D₃×Q₈	—	2	4	no	—
64	C₅×D₃×Q₈	—	2	4	no	—
65	C₅×D₃×D₄	—	2	2	no	—
66	C₅×D₃×D₄	D₄	1	4	yes	—
67	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	—	2	1	no	—
69	C₂×C₄×C₅×D₃	—	2	2	no	—
70	C₂×C₄×C₅×D₃	—	2	1	no	—
71	C₂×C₄×C₅×D₃	—	2	1	no	—
72	C₂×C₄×C₅×D₃	—	4	4	no	—
73	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
74	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
75	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
76	C₂×C₅×Dic₆	—	2	2	no	—
77	C₂×C₅×Dic₆	C₂³	1	2	yes	—
78	C₃×C₅×SD₁₆	—	2	4	no	—
79	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
80	C₃×C₅×C₄⋊C₄	—	2	1	no	—
81	C₃×C₅×C₄⋊C₄	—	2	1	no	—
82	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₅×#217	—	2	1	no	—
86	C₅×#215	—	2	4	no	—
87	C₅×#214	—	2	4	no	—
88	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
89	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
90	C₅×C₄⋊Dic₃	—	2	1	no	—
91	C₅×C₄⋊Dic₃	—	2	1	no	—
92	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
93	C₅×Dic₃⋊C₄	—	2	1	no	—
94	C₅×Dic₃⋊C₄	—	2	2	no	—
95	C₅×Dic₃⋊C₄	—	2	2	no	—
96	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
97	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
98	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
100	C₅×#204	—	2	4	no	—
101	C₅×D₃×C₈	—	2	4	no	—
102	C₂×D₃×SD₁₆	C₂×C₅	1	2	yes	—
103	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
104	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
105	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
106	#5162	C₂×C₅	1	2	yes	complemented
107	#5083	C₂×C₅	1	1	yes	characteristic, complemented
108	#5019	C₂×C₅	1	1	yes	characteristic, complemented
109	#4841	C₂×C₅	1	1	yes	characteristic, complemented
110	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
111	#4818	C₂×C₅	1	2	yes	complemented
112	D₃×#103	C₂×C₅	1	2	yes	complemented
113	C₂²×C₅×Q₈	—	3	2	no	—
114	C₂²×C₅×D₄	—	3	1	no	—
115	C₂³×C₄×C₅	—	6	1	no	—
116	C₂×C₅×SD₁₆	—	3	2	no	—
117	C₂×C₅×SD₁₆	—	3	2	no	—
118	C₂×C₅×SD₁₆	—	3	2	no	—
119	C₂×C₅×SD₁₆	—	6	8	no	—
120	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
121	C₂²×C₅×C₈	—	3	2	no	—
122	C₅×C₄⋊Q₈	—	3	2	no	—
123	C₅×C₄⋊Q₈	—	3	1	no	—
124	C₅×C₄⋊Q₈	—	6	1	no	—
125	C₅×C₄⋊Q₈	—	6	1	no	—
126	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
127	C₄×C₅×D₄	—	3	1	no	—
128	C₄×C₅×D₄	—	3	1	no	—
129	C₄×C₅×D₄	—	3	1	no	—
130	C₄×C₅×D₄	—	6	1	no	—
131	C₄×C₅×D₄	—	6	1	no	—
132	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
133	C₂×C₅×C₄⋊C₄	—	3	1	no	—
134	C₂×C₅×C₄⋊C₄	—	6	1	no	—
135	C₂×C₅×C₄⋊C₄	—	6	1	no	—
136	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
137	C₂×C₄²×C₅	—	3	1	no	—
138	C₅×C₄⋊C₈	—	3	2	no	—
139	C₅×C₄⋊C₈	—	3	1	no	—
140	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
141	C₅×#103	—	3	2	no	—
142	C₅×#103	—	3	2	no	—
143	C₅×#103	—	3	2	no	—
144	C₅×#103	C₂×D₃	1	2	yes	complemented
145	C₂×#461	—	3	1	no	Sylow
146	C₂³×C₃×C₅	—	2	1	no	—
147	C₂²×C₅×D₃	—	2	1	no	—
148	C₂²×C₅×D₃	—	2	4	no	—
149	C₂²×C₅×D₃	—	4	2	no	—
150	C₂²×C₅×D₃	—	4	2	no	—
151	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
152	C₃×C₅×Q₈	—	2	2	no	—
153	C₃×C₅×Q₈	—	2	2	no	—
154	C₃×C₅×D₄	—	2	1	no	—
155	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	1	no	—
158	C₂×C₃×C₄×C₅	—	4	2	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
162	C₅×#67	—	2	4	no	—
163	C₂×C₅×Dic₃	—	2	2	no	—
164	C₂×C₅×Dic₃	—	2	1	no	—
165	C₂×C₅×Dic₃	—	4	2	no	—
166	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
167	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
168	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
169	C₅×D₁₂	—	2	1	no	—
170	C₅×D₁₂	C₂×D₄	1	2	yes	—
171	C₄×C₅×D₃	—	2	2	no	—
172	C₄×C₅×D₃	—	4	4	no	—
173	C₄×C₅×D₃	—	4	2	no	—
174	C₄×C₅×D₃	—	4	2	no	—
175	C₄×C₅×D₃	—	4	2	no	—
176	C₄×C₅×D₃	SD₁₆	1	4	yes	complemented
177	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
178	C₄×C₅×D₃	#41	1	2	yes	—
179	C₅×Dic₆	—	2	2	no	—
180	C₅×Dic₆	—	2	2	no	—
181	C₅×Dic₆	—	4	4	no	—
182	C₃×C₅×C₈	—	2	2	no	—
183	C₅×C₃⋊C₈	—	2	2	no	—
184	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	—
185	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
186	C₂²×C₄×D₃	—	2	1	no	—
187	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
188	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
189	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
190	#944	C₂²×C₅	1	2	yes	complemented
191	C₂×#215	C₂²×C₅	1	2	yes	—
192	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
193	C₂×#214	C₂²×C₅	1	2	yes	—
194	C₄×#67	—	2	1	no	—
195	D₃×SD₁₆	—	2	8	no	—
196	C₂×#204	C₂²×C₅	1	2	yes	—
197	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
198	#893	C₂²×C₅	1	1	yes	characteristic
199	D₃×C₄⋊C₄	—	2	1	no	—
200	D₃×C₄⋊C₄	—	2	1	no	—
201	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
202	#888	—	2	1	no	—
203	#888	—	2	1	no	—
204	#67⋊C₄	—	2	1	no	—
205	D₃×C₂²⋊C₄	—	2	1	no	—
206	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
207	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
208	#869	C₂²×C₅	1	1	yes	characteristic, complemented
209	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
210	C₃×#103	C₂²×C₅	1	2	yes	complemented
211	#835	C₂²×C₅	1	2	yes	complemented
212	#816	C₂²×C₅	1	2	yes	complemented
213	Dic₃⋊C₈	C₂²×C₅	1	2	yes	complemented
214	#810	C₂²×C₅	1	2	yes	complemented
215	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
216	C₂⁴×C₅	—	6	1	no	—
217	C₂×C₅×Q₈	—	3	2	no	—
218	C₂×C₅×Q₈	—	6	2	no	—
219	C₂×C₅×Q₈	—	6	4	no	—
220	C₂×C₅×Q₈	—	6	4	no	—
221	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
222	C₂×C₅×D₄	—	3	4	no	—
223	C₂×C₅×D₄	—	3	1	no	—
224	C₂×C₅×D₄	—	6	2	no	—
225	C₂×C₅×D₄	—	6	1	no	—
226	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
227	C₂²×C₄×C₅	—	2	1	no	—
228	C₂²×C₄×C₅	—	3	1	no	—
229	C₂²×C₄×C₅	—	3	1	no	—
230	C₂²×C₄×C₅	—	3	1	no	—
231	C₂²×C₄×C₅	—	6	1	no	—
232	C₂²×C₄×C₅	—	6	1	no	—
233	C₂²×C₄×C₅	—	6	2	no	—
234	C₂²×C₄×C₅	—	6	1	no	—
235	C₂²×C₄×C₅	—	6	1	no	—
236	C₂²×C₄×C₅	—	12	4	no	—
237	C₅×SD₁₆	—	2	4	no	—
238	C₅×SD₁₆	—	6	4	no	—
239	C₅×SD₁₆	—	6	4	no	—
240	C₅×SD₁₆	—	6	4	no	—
241	C₂×C₅×C₈	—	3	2	no	—
242	C₂×C₅×C₈	—	6	4	no	—
243	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
244	C₅×C₄⋊C₄	—	2	1	no	—
245	C₅×C₄⋊C₄	—	2	1	no	—
246	C₅×C₄⋊C₄	—	3	1	no	—
247	C₅×C₄⋊C₄	—	6	1	no	—
248	C₅×C₄⋊C₄	—	6	2	no	—
249	C₅×C₄⋊C₄	—	6	2	no	—
250	C₅×C₄⋊C₄	—	6	1	no	—
251	C₅×C₄⋊C₄	—	6	1	no	—
252	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
253	C₅×C₂²⋊C₄	—	2	1	no	—
254	C₅×C₂²⋊C₄	—	6	1	no	—
255	C₅×C₂²⋊C₄	—	6	1	no	—
256	C₅×C₂²⋊C₄	—	6	1	no	—
257	C₄²×C₅	—	3	1	no	—
258	C₄²×C₅	—	3	1	no	—
259	C₄²×C₅	—	3	1	no	—
260	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
261	C₂²×SD₁₆	—	3	2	no	—
262	C₂×C₄⋊Q₈	—	3	1	no	—
263	C₂×C₄×D₄	—	3	1	no	—
264	#461	—	3	2	no	—
265	#461	—	3	1	no	—
266	#461	—	3	1	no	—
267	#461	—	3	1	no	—
268	#461	—	3	2	no	—
269	#461	C₅×D₃	1	1	yes	characteristic, direct product factor
270	C₂×C₄⋊C₈	—	3	1	no	—
271	C₂×#103	—	3	2	no	—
272	C₂²×C₃×C₅	—	2	2	no	—
273	C₂²×C₃×C₅	—	4	1	no	—
274	C₂²×C₃×C₅	—	4	1	no	—
275	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₅×D₃	—	2	2	no	—
277	C₂×C₅×D₃	—	4	1	no	—
278	C₂×C₅×D₃	—	4	1	no	—
279	C₂×C₅×D₃	—	4	8	no	—
280	C₂×C₅×D₃	#121	1	2	yes	—
281	C₂×C₅×D₃	C₂×SD₁₆	1	2	yes	—
282	C₂×C₅×D₃	#137	1	2	yes	—
283	C₃×C₄×C₅	—	2	1	no	—
284	C₃×C₄×C₅	—	4	2	no	—
285	C₃×C₄×C₅	—	4	1	no	—
286	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	complemented
287	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
288	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
289	C₅×Dic₃	—	2	1	no	—
290	C₅×Dic₃	—	4	2	no	—
291	C₅×Dic₃	—	4	1	no	—
292	C₅×Dic₃	#121	1	2	yes	—
293	C₅×Dic₃	C₂×SD₁₆	1	2	yes	complemented
294	C₂³×D₃	—	2	1	no	—
295	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
296	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
297	C₂²×C₃×C₄	—	2	1	no	—
298	C₂×#67	—	2	1	no	—
299	C₂²×Dic₃	—	2	1	no	—
300	D₃×Q₈	—	2	4	no	—
301	D₃×Q₈	—	2	4	no	—
302	D₃×D₄	—	2	2	no	—
303	D₃×D₄	C₅×D₄	1	4	yes	—
304	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
305	C₂×C₄×D₃	—	2	1	no	—
306	C₂×C₄×D₃	—	2	2	no	—
307	C₂×C₄×D₃	—	2	1	no	—
308	C₂×C₄×D₃	—	2	1	no	—
309	C₂×C₄×D₃	—	4	4	no	—
310	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
311	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
312	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
313	C₂×Dic₆	—	2	2	no	—
314	C₂×Dic₆	C₂³×C₅	1	2	yes	—
315	C₃×SD₁₆	—	2	4	no	—
316	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
317	C₃×C₄⋊C₄	—	2	1	no	—
318	C₃×C₄⋊C₄	—	2	1	no	—
319	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
320	C₃×C₂²⋊C₄	—	2	1	no	—
321	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
322	#217	—	2	1	no	—
323	#215	—	2	4	no	—
324	#214	—	2	4	no	—
325	(C₂×D₃)⋊C₄	—	2	1	no	—
326	(C₂×D₃)⋊C₄	—	2	1	no	—
327	C₄⋊Dic₃	—	2	1	no	—
328	C₄⋊Dic₃	—	2	1	no	—
329	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
330	Dic₃⋊C₄	—	2	1	no	—
331	Dic₃⋊C₄	—	2	2	no	—
332	Dic₃⋊C₄	—	2	2	no	—
333	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
334	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
335	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
336	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
337	#204	—	2	4	no	—
338	D₃×C₈	—	2	4	no	—
339	C₂³×C₅	—	2	1	no	—
340	C₂³×C₅	—	3	1	no	—
341	C₂³×C₅	—	6	4	no	—
342	C₂³×C₅	—	6	1	no	—
343	C₂³×C₅	—	12	2	no	—
344	C₂³×C₅	—	12	2	no	—
345	C₅×Q₈	—	2	2	no	—
346	C₅×Q₈	—	2	2	no	—
347	C₅×Q₈	—	6	2	no	—
348	C₅×Q₈	—	6	2	no	—
349	C₅×Q₈	—	12	4	no	—
350	C₅×D₄	—	2	1	no	—
351	C₅×D₄	—	3	2	no	—
352	C₅×D₄	—	6	4	no	—
353	C₅×D₄	—	6	1	no	—
354	C₅×D₄	D₃×D₄	1	2	yes	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	2	2	no	—
357	C₂×C₄×C₅	—	3	1	no	—
358	C₂×C₄×C₅	—	3	1	no	—
359	C₂×C₄×C₅	—	3	4	no	—
360	C₂×C₄×C₅	—	3	2	no	—
361	C₂×C₄×C₅	—	3	2	no	—
362	C₂×C₄×C₅	—	3	1	no	—
363	C₂×C₄×C₅	—	4	2	no	—
364	C₂×C₄×C₅	—	6	2	no	—
365	C₂×C₄×C₅	—	6	1	no	—
366	C₂×C₄×C₅	—	6	2	no	—
367	C₂×C₄×C₅	—	12	2	no	—
368	C₂×C₄×C₅	—	12	2	no	—
369	C₂×C₄×C₅	—	12	2	no	—
370	C₂×C₄×C₅	—	12	4	no	—
371	C₂×C₄×C₅	—	12	2	no	—
372	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
373	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
374	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
375	C₅×C₈	—	2	2	no	—
376	C₅×C₈	—	6	2	no	—
377	C₂²×Q₈	—	3	2	no	—
378	C₂²×D₄	—	3	1	no	—
379	C₂³×C₄	—	6	1	no	—
380	C₂×SD₁₆	—	3	2	no	—
381	C₂×SD₁₆	—	3	2	no	—
382	C₂×SD₁₆	—	3	2	no	—
383	C₂×SD₁₆	—	6	8	no	—
384	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
385	C₂²×C₈	—	3	2	no	—
386	C₄⋊Q₈	—	3	2	no	—
387	C₄⋊Q₈	—	3	1	no	—
388	C₄⋊Q₈	—	6	1	no	—
389	C₄⋊Q₈	—	6	1	no	—
390	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
391	C₄×D₄	—	3	1	no	—
392	C₄×D₄	—	3	1	no	—
393	C₄×D₄	—	3	1	no	—
394	C₄×D₄	—	6	1	no	—
395	C₄×D₄	—	6	1	no	—
396	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	—	3	1	no	—
398	C₂×C₄⋊C₄	—	6	1	no	—
399	C₂×C₄⋊C₄	—	6	1	no	—
400	C₂×C₂²⋊C₄	—	6	1	no	—
401	C₂×C₄²	—	3	1	no	—
402	C₄⋊C₈	—	3	2	no	—
403	C₄⋊C₈	—	3	1	no	—
404	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
405	#103	—	3	2	no	—
406	#103	—	3	2	no	—
407	#103	—	3	2	no	—
408	#103	C₂×C₅×D₃	1	2	yes	complemented
409	C₂×C₃×C₅	—	4	2	no	—
410	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
411	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
412	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
413	C₅×D₃	—	4	2	no	—
414	C₅×D₃	#461	1	4	yes	direct product factor
415	C₂³×C₃	—	2	1	no	—
416	C₂²×D₃	—	2	1	no	—
417	C₂²×D₃	—	2	4	no	—
418	C₂²×D₃	—	4	2	no	—
419	C₂²×D₃	—	4	2	no	—
420	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
421	C₃×Q₈	—	2	2	no	—
422	C₃×Q₈	—	2	2	no	—
423	C₃×D₄	—	2	1	no	—
424	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
425	C₂×C₃×C₄	—	2	2	no	—
426	C₂×C₃×C₄	—	2	1	no	—
427	C₂×C₃×C₄	—	4	2	no	—
428	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
429	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
430	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
431	#67	—	2	4	no	—
432	C₂×Dic₃	—	2	2	no	—
433	C₂×Dic₃	—	2	1	no	—
434	C₂×Dic₃	—	4	2	no	—
435	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
436	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
437	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
438	D₁₂	—	2	1	no	—
439	D₁₂	C₂×C₅×D₄	1	2	yes	—
440	C₄×D₃	—	2	2	no	—
441	C₄×D₃	—	4	4	no	—
442	C₄×D₃	—	4	2	no	—
443	C₄×D₃	—	4	2	no	—
444	C₄×D₃	—	4	2	no	—
445	C₄×D₃	C₅×SD₁₆	1	4	yes	complemented
446	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
447	C₄×D₃	C₅×#41	1	2	yes	—
448	Dic₆	—	2	2	no	—
449	Dic₆	—	2	2	no	—
450	Dic₆	—	4	4	no	—
451	C₃×C₈	—	2	2	no	—
452	C₃⋊C₈	—	2	2	no	—
453	C₂²×C₅	—	2	2	no	—
454	C₂²×C₅	—	3	2	no	—
455	C₂²×C₅	—	3	2	no	—
456	C₂²×C₅	—	3	2	no	—
457	C₂²×C₅	—	4	1	no	—
458	C₂²×C₅	—	4	1	no	—
459	C₂²×C₅	—	6	2	no	—
460	C₂²×C₅	—	12	8	no	—
461	C₂²×C₅	—	12	1	no	—
462	C₂²×C₅	—	12	1	no	—
463	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
464	C₄×C₅	—	2	1	no	—
465	C₄×C₅	—	3	2	no	—
466	C₄×C₅	—	3	2	no	—
467	C₄×C₅	—	4	1	no	—
468	C₄×C₅	—	4	2	no	—
469	C₄×C₅	—	6	1	no	—
470	C₄×C₅	—	12	1	no	—
471	C₄×C₅	—	12	2	no	—
472	C₄×C₅	D₃×SD₁₆	1	2	yes	complemented
473	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
474	C₄×C₅	D₃×#41	1	1	yes	characteristic
475	C₂⁴	—	6	1	no	—
476	C₂×Q₈	—	3	2	no	—
477	C₂×Q₈	—	6	2	no	—
478	C₂×Q₈	—	6	4	no	—
479	C₂×Q₈	—	6	4	no	—
480	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
481	C₂×D₄	—	3	4	no	—
482	C₂×D₄	—	3	1	no	—
483	C₂×D₄	—	6	2	no	—
484	C₂×D₄	—	6	1	no	—
485	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	3	1	no	—
488	C₂²×C₄	—	3	1	no	—
489	C₂²×C₄	—	3	1	no	—
490	C₂²×C₄	—	6	1	no	—
491	C₂²×C₄	—	6	1	no	—
492	C₂²×C₄	—	6	2	no	—
493	C₂²×C₄	—	6	1	no	—
494	C₂²×C₄	—	6	1	no	—
495	C₂²×C₄	—	12	4	no	—
496	SD₁₆	—	2	4	no	—
497	SD₁₆	—	6	4	no	—
498	SD₁₆	—	6	4	no	—
499	SD₁₆	—	6	4	no	—
500	C₂×C₈	—	3	2	no	—
501	C₂×C₈	—	6	4	no	—
502	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	3	1	no	—
506	C₄⋊C₄	—	6	1	no	—
507	C₄⋊C₄	—	6	2	no	—
508	C₄⋊C₄	—	6	2	no	—
509	C₄⋊C₄	—	6	1	no	—
510	C₄⋊C₄	—	6	1	no	—
511	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	6	1	no	—
514	C₂²⋊C₄	—	6	1	no	—
515	C₂²⋊C₄	—	6	1	no	—
516	C₄²	—	3	1	no	—
517	C₄²	—	3	1	no	—
518	C₄²	—	3	1	no	—
519	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
520	C₃×C₅	C₂×#461	1	1	yes	characteristic, complemented, Hall
521	C₂²×C₃	—	2	2	no	—
522	C₂²×C₃	—	4	1	no	—
523	C₂²×C₃	—	4	1	no	—
524	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
525	C₂×D₃	—	2	2	no	—
526	C₂×D₃	—	4	1	no	—
527	C₂×D₃	—	4	1	no	—
528	C₂×D₃	—	4	8	no	—
529	C₂×D₃	C₅×#121	1	2	yes	—
530	C₂×D₃	C₂×C₅×SD₁₆	1	2	yes	—
531	C₂×D₃	C₅×#137	1	2	yes	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	4	2	no	—
534	C₃×C₄	—	4	1	no	—
535	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	complemented
536	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
537	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
538	Dic₃	—	2	1	no	—
539	Dic₃	—	4	2	no	—
540	Dic₃	—	4	1	no	—
541	Dic₃	C₅×#121	1	2	yes	—
542	Dic₃	C₂×C₅×SD₁₆	1	2	yes	complemented
543	C₂×C₅	—	3	4	no	—
544	C₂×C₅	—	4	2	no	—
545	C₂×C₅	—	12	2	no	—
546	C₂×C₅	D₃×#121	1	1	yes	characteristic
547	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
548	C₂×C₅	D₃×#137	1	1	yes	characteristic
549	C₂³	—	2	1	no	—
550	C₂³	—	3	1	no	—
551	C₂³	—	6	4	no	—
552	C₂³	—	6	1	no	—
553	C₂³	—	12	2	no	—
554	C₂³	—	12	2	no	—
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	6	2	no	—
558	Q₈	—	6	2	no	—
559	Q₈	—	12	4	no	—
560	D₄	—	2	1	no	—
561	D₄	—	3	2	no	—
562	D₄	—	6	4	no	—
563	D₄	—	6	1	no	—
564	D₄	C₅×D₃×D₄	1	2	yes	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	3	1	no	—
568	C₂×C₄	—	3	1	no	—
569	C₂×C₄	—	3	4	no	—
570	C₂×C₄	—	3	2	no	—
571	C₂×C₄	—	3	2	no	—
572	C₂×C₄	—	3	1	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	6	2	no	—
575	C₂×C₄	—	6	1	no	—
576	C₂×C₄	—	6	2	no	—
577	C₂×C₄	—	12	2	no	—
578	C₂×C₄	—	12	2	no	—
579	C₂×C₄	—	12	2	no	—
580	C₂×C₄	—	12	4	no	—
581	C₂×C₄	—	12	2	no	—
582	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
583	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
584	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
585	C₈	—	2	2	no	—
586	C₈	—	6	2	no	—
587	C₂×C₃	—	4	2	no	—
588	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
589	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
590	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
591	D₃	—	4	2	no	—
592	D₃	C₅×#461	1	4	yes	direct product factor
593	C₅	D₃×#461	1	1	yes	characteristic, direct product factor, Sylow
594	C₂²	—	2	2	no	—
595	C₂²	—	3	2	no	—
596	C₂²	—	3	2	no	—
597	C₂²	—	3	2	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	6	2	no	—
601	C₂²	—	12	8	no	—
602	C₂²	—	12	1	no	—
603	C₂²	—	12	1	no	—
604	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	3	2	no	—
607	C₄	—	3	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	2	no	—
610	C₄	—	6	1	no	—
611	C₄	—	12	1	no	—
612	C₄	—	12	2	no	—
613	C₄	C₅×D₃×SD₁₆	1	2	yes	complemented
614	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
615	C₄	C₅×D₃×#41	1	1	yes	characteristic
616	C₃	C₂×C₅×#461	1	1	yes	characteristic, complemented, Sylow
617	C₂	—	3	4	no	—
618	C₂	—	4	2	no	—
619	C₂	—	12	2	no	—
620	C₂	C₅×D₃×#121	1	1	yes	characteristic
621	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
622	C₂	C₅×D₃×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#461	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×#461	D₃
hypocenter	C₃	C₂×C₅×#461
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#461

Complements

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

N	H ≅ G/N	type
2. C₅×D₃×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#461	C₂	semidirect
5. C₅×#5162	C₂	semidirect
6. C₅×#5083	C₂	semidirect
7. C₅×#5019	C₂	semidirect
8. C₅×#4841	C₂	semidirect
9. C₅×D₃×C₄⋊C₈	C₂	semidirect
10. C₅×#4818	C₂	semidirect
11. C₅×D₃×#103	C₂	semidirect
17. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
19. C₅×#944	C₂²	semidirect
37. C₅×#869	C₂²	semidirect
38. C₃×C₅×C₄⋊C₈	C₂²	semidirect
39. C₃×C₅×#103	C₂²	semidirect
40. C₅×#835	C₂²	semidirect
41. C₅×#816	C₂²	semidirect
42. C₅×Dic₃⋊C₈	C₂²	semidirect
43. C₅×#810	C₂²	semidirect
44. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
45. D₃×#461	C₅	direct (N × H)
54. C₅×#461	D₃	direct (N × H)
103. D₃×C₄⋊Q₈	C₂×C₅	semidirect
105. C₃×#461	C₂×C₅	semidirect
106. #5162	C₂×C₅	semidirect
107. #5083	C₂×C₅	semidirect
108. #5019	C₂×C₅	semidirect
109. #4841	C₂×C₅	semidirect
110. D₃×C₄⋊C₈	C₂×C₅	semidirect
111. #4818	C₂×C₅	semidirect
112. D₃×#103	C₂×C₅	semidirect
126. C₅×C₄⋊Q₈	C₂×D₃	semidirect
140. C₅×C₄⋊C₈	C₂×D₃	semidirect
144. C₅×#103	C₂×D₃	semidirect
176. C₄×C₅×D₃	SD₁₆	semidirect
188. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
190. #944	C₂²×C₅	semidirect
208. #869	C₂²×C₅	semidirect
209. C₃×C₄⋊C₈	C₂²×C₅	semidirect
210. C₃×#103	C₂²×C₅	semidirect
211. #835	C₂²×C₅	semidirect
212. #816	C₂²×C₅	semidirect
213. Dic₃⋊C₈	C₂²×C₅	semidirect
214. #810	C₂²×C₅	semidirect
215. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
269. #461	C₅×D₃	direct (N × H)
286. C₃×C₄×C₅	C₂×SD₁₆	semidirect
293. C₅×Dic₃	C₂×SD₁₆	semidirect
390. C₄⋊Q₈	C₂×C₅×D₃	semidirect
404. C₄⋊C₈	C₂×C₅×D₃	semidirect
408. #103	C₂×C₅×D₃	semidirect
414. C₅×D₃	#461	direct (N × H)
445. C₄×D₃	C₅×SD₁₆	semidirect
472. C₄×C₅	D₃×SD₁₆	semidirect
520. C₃×C₅	C₂×#461	semidirect
535. C₃×C₄	C₂×C₅×SD₁₆	semidirect
542. Dic₃	C₂×C₅×SD₁₆	semidirect
592. D₃	C₅×#461	direct (N × H)
593. C₅	D₃×#461	direct (N × H)
613. C₄	C₅×D₃×SD₁₆	semidirect
616. C₃	C₂×C₅×#461	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×SD₁₆	2
C₅×D₃×C₄⋊Q₈	2
C₄×C₅×D₃×D₄	2
C₃×C₅×#461	2
C₅×#5162	2
C₅×#5083	2
C₅×#5019	2
C₅×#4841	2
C₅×D₃×C₄⋊C₈	2
C₅×#4818	2
C₅×D₃×#103	2
C₂×C₅×#461	3
D₃×#461	5

Subgroups — C5×D3×#461 #14425860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#461 #14425860