Subgroups — C₃×#10617311 #14415853

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4133	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66002	C₂	1	1	yes	maximal, characteristic
4	C₃×#65787	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65776	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65695	C₂	1	2	yes	maximal, complemented
7	C₃×#65694	C₂	1	2	yes	maximal, complemented
8	C₃×#65693	C₂	1	2	yes	maximal, complemented
9	C₃×#65692	C₂	1	2	yes	maximal, complemented
10	C₃×D₅⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#700	C₂	1	1	yes	maximal, characteristic, complemented
12	#10617311	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	1	yes	characteristic
14	C₂×C₃×#711	C₂²	1	1	yes	characteristic
15	C₂×C₃×#704	C₂²	1	2	yes	—
16	C₂²×C₃×#170	C₂²	1	2	yes	—
17	C₃×#4133	—	2	4	no	—
18	C₃×#4131	—	2	4	no	—
19	C₂×C₃×#700	C₂²	1	1	yes	characteristic
20	C₂×C₃×#700	C₂²	1	2	yes	—
21	C₂×C₃×#700	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
25	C₃×C₅×#124	C₄	1	1	yes	characteristic
26	C₃×#4090	C₄	1	1	yes	characteristic
27	C₃×#4086	C₄	1	1	yes	characteristic
28	C₃×#4030	C₄	1	2	yes	—
29	C₃×#4030	C₄	1	2	yes	—
30	C₃×#4027	C₂²	1	2	yes	—
31	C₃×#4027	C₂²	1	2	yes	—
32	C₃×#4021	C₄	1	1	yes	characteristic
33	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
34	C₃×C₂²⋊#170	C₂²	1	2	yes	—
35	C₃×C₂²⋊#170	C₂²	1	2	yes	—
36	C₃×#4004	C₂²	1	1	yes	characteristic
37	C₃×#4004	C₂²	1	1	yes	characteristic
38	C₃×#4003	C₂²	1	2	yes	—
39	C₃×#4003	C₂²	1	2	yes	—
40	C₃×#4002	C₂²	1	2	yes	—
41	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
42	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
43	C₃×C₄×#170	C₂²	1	2	yes	—
44	C₃×#2935	—	5	1	no	maximal, Hall
45	C₂×#4133	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#4131	C₂×C₃	1	1	yes	characteristic, complemented
47	#66002	C₂×C₃	1	1	yes	characteristic
48	#65787	C₂×C₃	1	1	yes	characteristic, complemented
49	#65776	C₂×C₃	1	1	yes	characteristic, complemented
50	#65695	C₂×C₃	1	2	yes	complemented
51	#65694	C₂×C₃	1	2	yes	complemented
52	#65693	C₂×C₃	1	2	yes	complemented
53	#65692	C₂×C₃	1	2	yes	complemented
54	D₅⋊(C₄⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
55	C₄×#700	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
59	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
61	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
62	C₃×#713	—	2	2	no	—
63	C₃×#713	—	2	2	no	—
64	C₃×#711	—	2	2	no	—
65	C₃×#711	—	2	2	no	—
66	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
68	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
70	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
71	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
73	C₃×#704	—	2	4	no	—
74	C₂×C₃×#170	—	2	4	no	—
75	C₂×C₃×#170	C₂³	1	1	yes	characteristic
76	C₂×C₃×#170	C₂³	1	1	yes	characteristic
77	C₂×C₃×#170	C₂³	1	1	yes	characteristic
78	C₂×C₃×#170	C₂³	1	1	yes	characteristic
79	C₂×C₃×#170	C₂³	1	2	yes	—
80	C₂×C₃×#170	C₂³	1	2	yes	—
81	C₃×#700	—	2	2	no	—
82	C₃×#700	—	2	4	no	—
83	C₃×#700	D₄	1	4	yes	complemented
84	C₃×D₅⋊C₈	—	2	2	no	—
85	C₃×D₅⋊C₈	—	2	2	no	—
86	C₃×D₅⋊C₈	—	2	4	no	—
87	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
88	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
89	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
90	C₃×#685	C₂×C₄	1	2	yes	—
91	C₃×#685	C₂×C₄	1	2	yes	—
92	C₃×#683	C₂×C₄	1	2	yes	—
93	C₃×#683	C₂×C₄	1	2	yes	—
94	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
95	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
96	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
97	C₂×C₃×#131	—	5	1	no	—
98	C₂×C₃×#131	—	5	1	no	—
99	C₃×#532	—	5	1	no	—
100	C₃×#436	—	5	2	no	—
101	C₃×#435	—	5	2	no	—
102	C₃×#435	—	5	2	no	—
103	C₃×C₈×D₄	—	5	2	no	—
104	C₂×C₃×C₄⋊C₈	—	5	1	no	—
105	C₃×#408	—	5	1	no	—
106	C₃×#408	—	5	1	no	—
107	C₃×C₄×M₁₆	—	5	1	no	—
108	C₂×#713	C₂²×C₃	1	1	yes	characteristic
109	C₂×#711	C₂²×C₃	1	1	yes	characteristic
110	C₂×#704	C₂²×C₃	1	2	yes	—
111	C₂²×#170	C₂²×C₃	1	2	yes	—
112	#4133	—	2	4	no	—
113	#4131	—	2	4	no	—
114	C₂×#700	C₂²×C₃	1	1	yes	characteristic
115	C₂×#700	C₂²×C₃	1	2	yes	—
116	C₂×#700	C₂²×C₃	1	1	yes	characteristic
117	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
118	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
119	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
120	C₅×#124	C₃×C₄	1	1	yes	characteristic
121	#4090	C₃×C₄	1	1	yes	characteristic
122	#4086	C₃×C₄	1	1	yes	characteristic
123	#4030	C₃×C₄	1	2	yes	—
124	#4030	C₃×C₄	1	2	yes	—
125	#4027	C₂²×C₃	1	2	yes	—
126	#4027	C₂²×C₃	1	2	yes	—
127	#4021	C₃×C₄	1	1	yes	characteristic
128	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
129	C₂²⋊#170	C₂²×C₃	1	2	yes	—
130	C₂²⋊#170	C₂²×C₃	1	2	yes	—
131	#4004	C₂²×C₃	1	1	yes	characteristic
132	#4004	C₂²×C₃	1	1	yes	characteristic
133	#4003	C₂²×C₃	1	2	yes	—
134	#4003	C₂²×C₃	1	2	yes	—
135	#4002	C₂²×C₃	1	2	yes	—
136	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
137	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
138	C₄×#170	C₂²×C₃	1	2	yes	—
139	#2935	—	5	1	no	Sylow
140	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
141	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
142	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
143	C₃×C₅×Q₈	—	2	2	no	—
144	C₃×C₅×D₄	—	2	2	no	—
145	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
149	C₃×C₂²⋊D₅	—	2	4	no	—
150	C₃×C₂²⋊D₅	—	2	4	no	—
151	C₃×C₂²⋊D₅	—	4	2	no	—
152	C₂×C₃×Dic₅	—	2	2	no	—
153	C₂×C₃×Dic₅	—	2	2	no	—
154	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
156	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
158	C₃×D₂₀	—	2	4	no	—
159	C₃×D₂₀	—	2	2	no	—
160	C₃×C₄×D₅	—	2	2	no	—
161	C₃×C₄×D₅	—	2	2	no	—
162	C₃×C₄×D₅	—	2	2	no	—
163	C₃×C₄×D₅	—	4	1	no	—
164	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
165	C₃×C₄×D₅	#41	1	2	yes	—
166	C₃×Dic₁₀	—	2	2	no	—
167	C₃×#170	—	2	1	no	—
168	C₃×#170	—	2	1	no	—
169	C₃×#170	—	2	1	no	—
170	C₃×#170	—	2	1	no	—
171	C₃×#170	—	2	2	no	—
172	C₃×#170	C₂×D₄	1	4	yes	—
173	C₂×C₃×#41	—	5	1	no	—
174	C₂×C₃×#41	—	5	1	no	—
175	C₃×#131	—	10	4	no	—
176	C₃×#131	—	10	4	no	—
177	C₂×C₃×M₁₆	—	5	1	no	—
178	C₂×C₃×M₁₆	—	5	2	no	—
179	C₂×C₃×M₁₆	—	5	2	no	—
180	C₂×C₃×M₁₆	—	5	1	no	—
181	C₂²×C₃×C₈	—	5	1	no	—
182	C₂²×C₃×C₈	—	5	1	no	—
183	C₂²×C₃×C₈	—	5	2	no	—
184	C₂²×C₃×C₈	—	5	2	no	—
185	C₃×C₄⋊Q₈	—	5	1	no	—
186	C₃×#127	—	5	1	no	—
187	C₃×#124	—	5	1	no	—
188	C₃×#124	AGL(1,𝔽₅)	1	1	yes	characteristic
189	C₃×#121	—	5	2	no	—
190	C₃×#121	—	5	2	no	—
191	C₃×C₄×D₄	—	5	2	no	—
192	C₃×C₄×D₄	—	5	2	no	—
193	C₂×C₃×C₄²	—	5	1	no	—
194	C₃×C₄⋊C₈	—	5	1	no	—
195	C₃×C₄⋊C₈	—	5	1	no	—
196	C₃×C₄⋊C₈	—	5	1	no	—
197	C₃×C₄⋊C₈	—	5	1	no	—
198	C₃×C₂²⋊C₈	—	5	2	no	—
199	C₃×C₂²⋊C₈	—	5	2	no	—
200	C₃×C₂²⋊C₈	—	5	2	no	—
201	C₃×C₂²⋊C₈	—	5	2	no	—
202	C₃×#97	—	5	2	no	—
203	C₃×C₄×C₈	—	5	2	no	—
204	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
205	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
206	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
207	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
208	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
209	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
210	#713	—	2	2	no	—
211	#713	—	2	2	no	—
212	#711	—	2	2	no	—
213	#711	—	2	2	no	—
214	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
215	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
216	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
217	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
218	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
219	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
220	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
221	#704	—	2	4	no	—
222	C₂×#170	—	2	4	no	—
223	C₂×#170	C₂³×C₃	1	1	yes	characteristic
224	C₂×#170	C₂³×C₃	1	1	yes	characteristic
225	C₂×#170	C₂³×C₃	1	1	yes	characteristic
226	C₂×#170	C₂³×C₃	1	1	yes	characteristic
227	C₂×#170	C₂³×C₃	1	2	yes	—
228	C₂×#170	C₂³×C₃	1	2	yes	—
229	#700	—	2	2	no	—
230	#700	—	2	4	no	—
231	#700	C₃×D₄	1	4	yes	complemented
232	D₅⋊C₈	—	2	2	no	—
233	D₅⋊C₈	—	2	2	no	—
234	D₅⋊C₈	—	2	4	no	—
235	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
236	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
237	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
238	#685	C₂×C₃×C₄	1	2	yes	—
239	#685	C₂×C₃×C₄	1	2	yes	—
240	#683	C₂×C₃×C₄	1	2	yes	—
241	#683	C₂×C₃×C₄	1	2	yes	—
242	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
243	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
244	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
245	C₂×#131	—	5	1	no	—
246	C₂×#131	—	5	1	no	—
247	#532	—	5	1	no	—
248	#436	—	5	2	no	—
249	#435	—	5	2	no	—
250	#435	—	5	2	no	—
251	C₈×D₄	—	5	2	no	—
252	C₂×C₄⋊C₈	—	5	1	no	—
253	#408	—	5	1	no	—
254	#408	—	5	1	no	—
255	C₄×M₁₆	—	5	1	no	—
256	C₂²×C₃×C₅	—	2	2	no	—
257	C₂²×C₃×C₅	—	2	2	no	—
258	C₂²×C₃×C₅	—	2	2	no	—
259	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₃×D₅	—	2	1	no	—
261	C₂×C₃×D₅	—	2	1	no	—
262	C₂×C₃×D₅	—	2	2	no	—
263	C₂×C₃×D₅	—	2	2	no	—
264	C₂×C₃×D₅	—	2	2	no	—
265	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
266	C₃×C₄×C₅	—	2	2	no	—
267	C₃×C₄×C₅	—	2	1	no	—
268	C₃×C₄×C₅	—	2	1	no	—
269	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
270	C₃×Dic₅	—	2	2	no	—
271	C₃×Dic₅	—	2	1	no	—
272	C₃×Dic₅	#131	1	2	yes	complemented
273	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
274	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
275	C₃×#41	—	10	2	no	—
276	C₃×#41	—	10	2	no	—
277	C₃×#41	—	10	2	no	—
278	C₃×#41	—	10	2	no	—
279	C₂×C₃×Q₈	—	5	1	no	—
280	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
281	C₂×C₃×D₄	—	5	2	no	—
282	C₂×C₃×D₄	—	5	2	no	—
283	C₂×C₃×D₄	—	5	2	no	—
284	C₂×C₃×D₄	—	5	2	no	—
285	C₂×C₃×D₄	—	5	1	no	—
286	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
287	C₂²×C₃×C₄	—	5	1	no	—
288	C₂²×C₃×C₄	—	5	2	no	—
289	C₂²×C₃×C₄	—	5	2	no	—
290	C₂²×C₃×C₄	—	5	1	no	—
291	C₂²×C₃×C₄	—	5	1	no	—
292	C₃×M₁₆	—	5	4	no	—
293	C₃×M₁₆	—	10	4	no	—
294	C₃×M₁₆	—	10	4	no	—
295	C₃×M₁₆	—	10	2	no	—
296	C₂×C₃×C₈	—	5	2	no	—
297	C₂×C₃×C₈	—	5	2	no	—
298	C₂×C₃×C₈	—	5	1	no	—
299	C₂×C₃×C₈	—	5	1	no	—
300	C₂×C₃×C₈	—	5	1	no	—
301	C₂×C₃×C₈	—	5	1	no	—
302	C₂×C₃×C₈	—	10	4	no	—
303	C₂×C₃×C₈	—	10	4	no	—
304	C₂×C₃×C₈	—	10	2	no	—
305	C₂×C₃×C₈	—	10	2	no	—
306	C₃×C₄⋊C₄	—	5	2	no	—
307	C₃×C₄⋊C₄	—	5	2	no	—
308	C₃×C₂²⋊C₄	—	5	2	no	—
309	C₃×C₂²⋊C₄	—	5	2	no	—
310	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
311	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
312	C₃×C₄²	—	5	1	no	—
313	C₃×C₄²	—	5	1	no	—
314	C₃×C₄²	—	5	1	no	—
315	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
316	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
317	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
318	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
319	C₅×Q₈	—	2	2	no	—
320	C₅×D₄	—	2	2	no	—
321	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
324	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
325	C₂²⋊D₅	—	2	4	no	—
326	C₂²⋊D₅	—	2	4	no	—
327	C₂²⋊D₅	—	4	2	no	—
328	C₂×Dic₅	—	2	2	no	—
329	C₂×Dic₅	—	2	2	no	—
330	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
331	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
332	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
333	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
334	D₂₀	—	2	4	no	—
335	D₂₀	—	2	2	no	—
336	C₄×D₅	—	2	2	no	—
337	C₄×D₅	—	2	2	no	—
338	C₄×D₅	—	2	2	no	—
339	C₄×D₅	—	4	1	no	—
340	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
341	C₄×D₅	C₃×#41	1	2	yes	—
342	Dic₁₀	—	2	2	no	—
343	#170	—	2	1	no	—
344	#170	—	2	1	no	—
345	#170	—	2	1	no	—
346	#170	—	2	1	no	—
347	#170	—	2	2	no	—
348	#170	C₂×C₃×D₄	1	4	yes	—
349	C₂×#41	—	5	1	no	—
350	C₂×#41	—	5	1	no	—
351	#131	—	10	4	no	—
352	#131	—	10	4	no	—
353	C₂×M₁₆	—	5	1	no	—
354	C₂×M₁₆	—	5	2	no	—
355	C₂×M₁₆	—	5	1	no	—
356	C₂×M₁₆	—	5	2	no	—
357	C₂²×C₈	—	5	1	no	—
358	C₂²×C₈	—	5	1	no	—
359	C₂²×C₈	—	5	2	no	—
360	C₂²×C₈	—	5	2	no	—
361	C₄⋊Q₈	—	5	1	no	—
362	#127	—	5	1	no	—
363	#124	—	5	1	no	—
364	#124	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
365	#121	—	5	2	no	—
366	#121	—	5	2	no	—
367	C₄×D₄	—	5	2	no	—
368	C₄×D₄	—	5	2	no	—
369	C₂×C₄²	—	5	1	no	—
370	C₄⋊C₈	—	5	1	no	—
371	C₄⋊C₈	—	5	1	no	—
372	C₄⋊C₈	—	5	1	no	—
373	C₄⋊C₈	—	5	1	no	—
374	C₂²⋊C₈	—	5	2	no	—
375	C₂²⋊C₈	—	5	2	no	—
376	C₂²⋊C₈	—	5	2	no	—
377	C₂²⋊C₈	—	5	2	no	—
378	#97	—	5	2	no	—
379	C₄×C₈	—	5	2	no	—
380	C₂×C₃×C₅	—	4	2	no	—
381	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
382	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
383	C₂×C₃×C₅	#568	1	1	yes	characteristic
384	C₃×D₅	—	2	2	no	—
385	C₃×D₅	—	4	2	no	—
386	C₂³×C₃	—	5	1	no	—
387	C₂³×C₃	—	5	2	no	—
388	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
389	C₃×Q₈	—	2	2	no	—
390	C₃×Q₈	—	10	2	no	—
391	C₃×D₄	—	2	2	no	—
392	C₃×D₄	—	10	4	no	—
393	C₃×D₄	—	10	4	no	—
394	C₃×D₄	—	10	4	no	—
395	C₃×D₄	—	10	2	no	—
396	C₃×D₄	—	20	2	no	—
397	C₂×C₃×C₄	—	5	1	no	—
398	C₂×C₃×C₄	—	5	1	no	—
399	C₂×C₃×C₄	—	5	2	no	—
400	C₂×C₃×C₄	—	5	2	no	—
401	C₂×C₃×C₄	—	5	1	no	—
402	C₂×C₃×C₄	—	5	2	no	—
403	C₂×C₃×C₄	—	10	2	no	—
404	C₂×C₃×C₄	—	10	2	no	—
405	C₂×C₃×C₄	—	10	2	no	—
406	C₂×C₃×C₄	—	10	2	no	—
407	C₂×C₃×C₄	—	10	2	no	—
408	C₂×C₃×C₄	—	20	1	no	—
409	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
412	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₃×C₈	—	5	4	no	—
414	C₃×C₈	—	10	1	no	—
415	C₃×C₈	—	10	1	no	—
416	C₃×C₈	—	10	1	no	—
417	C₃×C₈	—	10	1	no	—
418	C₃×C₈	—	10	2	no	—
419	C₂²×C₅	—	2	2	no	—
420	C₂²×C₅	—	2	2	no	—
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
423	C₂×D₅	—	2	1	no	—
424	C₂×D₅	—	2	1	no	—
425	C₂×D₅	—	2	2	no	—
426	C₂×D₅	—	2	2	no	—
427	C₂×D₅	—	2	2	no	—
428	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	2	1	no	—
431	C₄×C₅	—	2	2	no	—
432	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
433	Dic₅	—	2	1	no	—
434	Dic₅	—	2	2	no	—
435	Dic₅	C₃×#131	1	2	yes	complemented
436	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
437	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
438	#41	—	10	2	no	—
439	#41	—	10	2	no	—
440	#41	—	10	2	no	—
441	#41	—	10	2	no	—
442	C₂×Q₈	—	5	1	no	—
443	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
444	C₂×D₄	—	5	2	no	—
445	C₂×D₄	—	5	2	no	—
446	C₂×D₄	—	5	2	no	—
447	C₂×D₄	—	5	2	no	—
448	C₂×D₄	—	5	1	no	—
449	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
450	C₂²×C₄	—	5	1	no	—
451	C₂²×C₄	—	5	2	no	—
452	C₂²×C₄	—	5	2	no	—
453	C₂²×C₄	—	5	1	no	—
454	C₂²×C₄	—	5	1	no	—
455	M₁₆	—	5	4	no	—
456	M₁₆	—	10	4	no	—
457	M₁₆	—	10	4	no	—
458	M₁₆	—	10	2	no	—
459	C₂×C₈	—	5	2	no	—
460	C₂×C₈	—	5	2	no	—
461	C₂×C₈	—	5	1	no	—
462	C₂×C₈	—	5	1	no	—
463	C₂×C₈	—	5	1	no	—
464	C₂×C₈	—	5	1	no	—
465	C₂×C₈	—	10	4	no	—
466	C₂×C₈	—	10	4	no	—
467	C₂×C₈	—	10	2	no	—
468	C₂×C₈	—	10	2	no	—
469	C₄⋊C₄	—	5	2	no	—
470	C₄⋊C₄	—	5	2	no	—
471	C₂²⋊C₄	—	5	2	no	—
472	C₂²⋊C₄	—	5	2	no	—
473	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
474	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
475	C₄²	—	5	1	no	—
476	C₄²	—	5	1	no	—
477	C₄²	—	5	1	no	—
478	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
479	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	2	2	no	—
482	C₂²×C₃	—	2	2	no	—
483	C₂²×C₃	—	5	2	no	—
484	C₂²×C₃	—	10	1	no	—
485	C₂²×C₃	—	10	1	no	—
486	C₂²×C₃	—	10	2	no	—
487	C₂²×C₃	—	10	2	no	—
488	C₂²×C₃	—	10	2	no	—
489	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
490	C₃×C₄	—	2	2	no	—
491	C₃×C₄	—	2	1	no	—
492	C₃×C₄	—	2	1	no	—
493	C₃×C₄	—	5	1	no	—
494	C₃×C₄	—	5	1	no	—
495	C₃×C₄	—	5	2	no	—
496	C₃×C₄	—	10	2	no	—
497	C₃×C₄	—	10	1	no	—
498	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
499	C₂×C₅	—	4	2	no	—
500	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
501	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
502	C₂×C₅	C₃×#568	1	1	yes	characteristic
503	D₅	—	2	2	no	—
504	D₅	—	4	2	no	—
505	C₂³	—	5	1	no	—
506	C₂³	—	5	2	no	—
507	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
508	Q₈	—	2	2	no	—
509	Q₈	—	10	2	no	—
510	D₄	—	2	2	no	—
511	D₄	—	10	4	no	—
512	D₄	—	10	4	no	—
513	D₄	—	10	4	no	—
514	D₄	—	10	2	no	—
515	D₄	—	20	2	no	—
516	C₂×C₄	—	5	1	no	—
517	C₂×C₄	—	5	1	no	—
518	C₂×C₄	—	5	2	no	—
519	C₂×C₄	—	5	2	no	—
520	C₂×C₄	—	5	1	no	—
521	C₂×C₄	—	5	2	no	—
522	C₂×C₄	—	10	2	no	—
523	C₂×C₄	—	10	2	no	—
524	C₂×C₄	—	10	2	no	—
525	C₂×C₄	—	10	2	no	—
526	C₂×C₄	—	10	2	no	—
527	C₂×C₄	—	20	1	no	—
528	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
529	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
530	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
531	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
532	C₈	—	5	4	no	—
533	C₈	—	10	1	no	—
534	C₈	—	10	1	no	—
535	C₈	—	10	1	no	—
536	C₈	—	10	1	no	—
537	C₈	—	10	2	no	—
538	C₂×C₃	—	4	2	no	—
539	C₂×C₃	—	10	2	no	—
540	C₂×C₃	—	20	2	no	—
541	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
542	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
543	C₂×C₃	#66264	1	1	yes	characteristic
544	C₅	C₃×#2935	1	1	yes	characteristic, complemented, Sylow
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	5	2	no	—
549	C₂²	—	10	1	no	—
550	C₂²	—	10	1	no	—
551	C₂²	—	10	2	no	—
552	C₂²	—	10	2	no	—
553	C₂²	—	10	2	no	—
554	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
555	C₄	—	2	2	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	5	1	no	—
559	C₄	—	5	1	no	—
560	C₄	—	5	2	no	—
561	C₄	—	10	2	no	—
562	C₄	—	10	1	no	—
563	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
564	C₃	#10617311	1	1	yes	characteristic, direct product factor, Sylow
565	C₂	—	4	2	no	—
566	C₂	—	10	2	no	—
567	C₂	—	20	2	no	—
568	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
569	C₂	C₃×D₅⋊#131	1	1	yes	characteristic
570	C₂	C₃×#66264	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#124	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#66002	C₂
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#124	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2935
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4133	C₂	semidirect
2. C₂×C₃×#4131	C₂	semidirect
4. C₃×#65787	C₂	semidirect
5. C₃×#65776	C₂	semidirect
6. C₃×#65695	C₂	semidirect
7. C₃×#65694	C₂	semidirect
8. C₃×#65693	C₂	semidirect
9. C₃×#65692	C₂	semidirect
10. C₃×D₅⋊(C₄⋊C₈)	C₂	semidirect
11. C₃×C₄×#700	C₂	semidirect
12. #10617311	C₃	direct (N × H)
45. C₂×#4133	C₂×C₃	semidirect
46. C₂×#4131	C₂×C₃	semidirect
48. #65787	C₂×C₃	semidirect
49. #65776	C₂×C₃	semidirect
50. #65695	C₂×C₃	semidirect
51. #65694	C₂×C₃	semidirect
52. #65693	C₂×C₃	semidirect
53. #65692	C₂×C₃	semidirect
54. D₅⋊(C₄⋊C₈)	C₂×C₃	semidirect
55. C₄×#700	C₂×C₃	semidirect
83. C₃×#700	D₄	semidirect
231. #700	C₃×D₄	semidirect
272. C₃×Dic₅	#131	semidirect
435. Dic₅	C₃×#131	semidirect
479. C₃×C₅	#2935	semidirect
544. C₅	C₃×#2935	semidirect
564. C₃	#10617311	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#4133	2
C₂×C₃×#4131	2
C₃×#66002	2
C₃×#65787	2
C₃×#65776	2
C₃×#65695	2
C₃×#65694	2
C₃×#65693	2
C₃×#65692	2
C₃×D₅⋊(C₄⋊C₈)	2
C₃×C₄×#700	2
#10617311	3
C₃×#2935	5

Subgroups — C3×#10617311 #14415853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617311 #14415853