Subgroups — C₃×#10617229 #14415466

Order 1920.

1004 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#700	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65940	C₂	1	1	yes	maximal, characteristic
4	C₃×#65776	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65773	C₂	1	2	yes	maximal, complemented
6	C₃×D₄×#170	C₂	1	2	yes	maximal, complemented
7	C₃×D₅⋊(C₂²⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65708	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65701	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65695	C₂	1	2	yes	maximal, complemented
11	C₃×#65693	C₂	1	2	yes	maximal, complemented
12	#10617229	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#711	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#704	C₂²	1	2	yes	complemented
16	C₂²×C₃×#170	C₂²	1	2	yes	—
17	C₂²×C₃×#170	C₂²	1	2	yes	complemented
18	C₃×#4131	—	2	4	no	—
19	C₂×C₃×#700	—	2	4	no	—
20	C₂×C₃×#700	C₂²	1	2	yes	—
21	C₂×C₃×#700	C₂²	1	1	yes	characteristic
22	C₂×C₃×#700	C₂²	1	1	yes	characteristic
23	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×#121	C₄	1	1	yes	characteristic
26	C₃×#4084	C₄	1	1	yes	characteristic
27	C₃×#4083	C₄	1	2	yes	—
28	C₃×D₄×Dic₅	C₂²	1	2	yes	—
29	C₃×#4070	C₄	1	1	yes	characteristic
30	C₃×#4043	C₄	1	1	yes	characteristic
31	C₃×#4038	C₂²	1	1	yes	characteristic
32	C₃×#4029	C₄	1	2	yes	—
33	C₃×#4027	C₂²	1	2	yes	—
34	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
35	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
36	C₃×C₂²⋊#170	C₂²	1	2	yes	complemented
37	C₃×C₂²⋊#170	C₂²	1	2	yes	complemented
38	C₃×#4004	C₂²	1	2	yes	complemented
39	C₃×#4003	C₂²	1	1	yes	characteristic
40	C₃×#4003	C₂²	1	1	yes	characteristic
41	C₃×#4002	C₂²	1	2	yes	complemented
42	C₃×C₄⋊#170	C₂²	1	2	yes	complemented
43	C₃×C₄×#170	C₂²	1	2	yes	complemented
44	C₃×#2933	—	5	1	no	maximal, Hall
45	C₂×#4131	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂²×#700	C₂×C₃	1	1	yes	characteristic, complemented
47	#65940	C₂×C₃	1	1	yes	characteristic
48	#65776	C₂×C₃	1	1	yes	characteristic, complemented
49	#65773	C₂×C₃	1	2	yes	complemented
50	D₄×#170	C₂×C₃	1	2	yes	complemented
51	D₅⋊(C₂²⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
52	#65708	C₂×C₃	1	1	yes	characteristic, complemented
53	#65701	C₂×C₃	1	1	yes	characteristic, complemented
54	#65695	C₂×C₃	1	2	yes	complemented
55	#65693	C₂×C₃	1	2	yes	complemented
56	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
58	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
61	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
62	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
64	C₃×#711	—	2	2	no	—
65	C₃×#711	—	2	2	no	—
66	C₂×C₃×C₄×D₅	—	2	2	no	—
67	C₂×C₃×C₄×D₅	—	2	2	no	—
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	1	yes	characteristic
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	—	2	4	no	—
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	1	yes	characteristic
80	C₂×C₃×#170	C₂³	1	2	yes	—
81	C₂×C₃×#170	C₂³	1	2	yes	—
82	C₃×#700	—	2	2	no	—
83	C₃×#700	—	2	4	no	—
84	C₃×#700	D₄	1	4	yes	complemented
85	C₃×D₅⋊C₈	—	2	2	no	—
86	C₃×D₅⋊C₈	—	2	2	no	—
87	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
89	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
90	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
91	C₃×#685	C₂×C₄	1	2	yes	—
92	C₃×#685	C₂×C₄	1	2	yes	—
93	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
94	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
95	C₃×#683	C₂×C₄	1	2	yes	—
96	C₃×C₄×Dic₅	C₂³	1	2	yes	—
97	C₂×C₃×#131	—	5	1	no	—
98	C₂²×C₃×M₁₆	—	5	1	no	—
99	C₃×#525	—	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	C₃×#424	—	5	1	no	—
105	C₃×#408	—	5	1	no	—
106	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
107	C₃×#405	—	5	1	no	—
108	C₂×#711	C₂²×C₃	1	1	yes	characteristic
109	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
110	C₂×#704	C₂²×C₃	1	2	yes	complemented
111	C₂²×#170	C₂²×C₃	1	2	yes	—
112	C₂²×#170	C₂²×C₃	1	2	yes	complemented
113	#4131	—	2	4	no	—
114	C₂×#700	—	2	4	no	—
115	C₂×#700	C₂²×C₃	1	2	yes	—
116	C₂×#700	C₂²×C₃	1	1	yes	characteristic
117	C₂×#700	C₂²×C₃	1	1	yes	characteristic
118	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
119	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
120	C₅×#121	C₃×C₄	1	1	yes	characteristic
121	#4084	C₃×C₄	1	1	yes	characteristic
122	#4083	C₃×C₄	1	2	yes	—
123	D₄×Dic₅	C₂²×C₃	1	2	yes	—
124	#4070	C₃×C₄	1	1	yes	characteristic
125	#4043	C₃×C₄	1	1	yes	characteristic
126	#4038	C₂²×C₃	1	1	yes	characteristic
127	#4029	C₃×C₄	1	2	yes	—
128	#4027	C₂²×C₃	1	2	yes	—
129	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
130	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
131	C₂²⋊#170	C₂²×C₃	1	2	yes	complemented
132	C₂²⋊#170	C₂²×C₃	1	2	yes	complemented
133	#4004	C₂²×C₃	1	2	yes	complemented
134	#4003	C₂²×C₃	1	1	yes	characteristic
135	#4003	C₂²×C₃	1	1	yes	characteristic
136	#4002	C₂²×C₃	1	2	yes	complemented
137	C₄⋊#170	C₂²×C₃	1	2	yes	complemented
138	C₄×#170	C₂²×C₃	1	2	yes	complemented
139	#2933	—	5	1	no	Sylow
140	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
141	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₃×D₅	—	2	2	no	—
143	C₂²×C₃×D₅	—	2	2	no	—
144	C₂²×C₃×D₅	—	4	1	no	—
145	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
147	C₃×C₅×D₄	—	2	4	no	—
148	C₃×C₅×D₄	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₃×C₂²⋊D₅	—	2	4	no	—
154	C₃×C₂²⋊D₅	—	4	2	no	—
155	C₂×C₃×Dic₅	—	2	1	no	—
156	C₂×C₃×Dic₅	—	2	2	no	—
157	C₂×C₃×Dic₅	—	2	1	no	—
158	C₂×C₃×Dic₅	—	2	2	no	—
159	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
160	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
161	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
163	C₃×C₄×D₅	—	2	2	no	—
164	C₃×C₄×D₅	—	2	2	no	—
165	C₃×C₄×D₅	—	2	1	no	—
166	C₃×C₄×D₅	—	2	1	no	—
167	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
168	C₃×C₄×D₅	#41	1	2	yes	—
169	C₃×Dic₁₀	—	2	2	no	—
170	C₃×#170	—	2	1	no	—
171	C₃×#170	—	2	1	no	—
172	C₃×#170	—	2	2	no	—
173	C₃×#170	—	2	1	no	—
174	C₃×#170	—	2	1	no	—
175	C₃×#170	C₂×D₄	1	4	yes	—
176	C₂×C₃×#41	—	5	1	no	—
177	C₂³×C₃×C₄	—	5	1	no	—
178	C₃×#131	—	10	4	no	—
179	C₂×C₃×M₁₆	—	5	1	no	—
180	C₂×C₃×M₁₆	—	5	1	no	—
181	C₂×C₃×M₁₆	—	5	2	no	—
182	C₂×C₃×M₁₆	—	5	2	no	—
183	C₂×C₃×M₁₆	—	10	4	no	—
184	C₂²×C₃×C₈	—	5	2	no	—
185	C₂²×C₃×C₈	—	5	1	no	—
186	C₂²×C₃×C₈	—	5	2	no	—
187	C₂²×C₃×C₈	—	5	1	no	—
188	C₃×#123	—	5	2	no	—
189	C₃×C₂²⋊Q₈	—	5	1	no	—
190	C₃×C₂²⋊Q₈	—	5	1	no	—
191	C₃×#121	—	5	1	no	—
192	C₃×#121	AGL(1,𝔽₅)	1	1	yes	characteristic
193	C₃×#120	—	5	2	no	—
194	C₃×C₄×D₄	—	5	2	no	—
195	C₃×C₄×D₄	—	5	2	no	—
196	C₃×#117	—	5	1	no	—
197	C₃×C₄⋊C₈	—	5	2	no	—
198	C₃×C₄⋊C₈	—	5	2	no	—
199	C₃×C₂²⋊C₈	—	5	1	no	—
200	C₃×C₂²⋊C₈	—	5	1	no	—
201	C₃×C₂²⋊C₈	—	5	1	no	—
202	C₃×C₂²⋊C₈	—	5	1	no	—
203	C₃×C₂²⋊C₈	—	5	2	no	—
204	C₃×C₂²⋊C₈	—	5	2	no	—
205	C₃×#97	—	5	2	no	—
206	C₃×C₄×C₈	—	5	2	no	—
207	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
208	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
209	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
210	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
211	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
212	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
213	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
214	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
215	#711	—	2	2	no	—
216	#711	—	2	2	no	—
217	C₂×C₄×D₅	—	2	2	no	—
218	C₂×C₄×D₅	—	2	2	no	—
219	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
220	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
221	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
223	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
224	#704	—	2	4	no	—
225	C₂×#170	—	2	4	no	—
226	C₂×#170	—	2	4	no	—
227	C₂×#170	C₂³×C₃	1	1	yes	characteristic
228	C₂×#170	C₂³×C₃	1	1	yes	characteristic
229	C₂×#170	C₂³×C₃	1	1	yes	characteristic
230	C₂×#170	C₂³×C₃	1	1	yes	characteristic
231	C₂×#170	C₂³×C₃	1	2	yes	—
232	C₂×#170	C₂³×C₃	1	2	yes	—
233	#700	—	2	2	no	—
234	#700	—	2	4	no	—
235	#700	C₃×D₄	1	4	yes	complemented
236	D₅⋊C₈	—	2	2	no	—
237	D₅⋊C₈	—	2	2	no	—
238	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
239	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
240	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
241	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
242	#685	C₂×C₃×C₄	1	2	yes	—
243	#685	C₂×C₃×C₄	1	2	yes	—
244	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
245	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
246	#683	C₂×C₃×C₄	1	2	yes	—
247	C₄×Dic₅	C₂³×C₃	1	2	yes	—
248	C₂×#131	—	5	1	no	—
249	C₂²×M₁₆	—	5	1	no	—
250	#525	—	5	1	no	—
251	#436	—	5	2	no	—
252	#435	—	5	2	no	—
253	#435	—	5	2	no	—
254	C₈×D₄	—	5	2	no	—
255	#424	—	5	1	no	—
256	#408	—	5	1	no	—
257	C₂×C₂²⋊C₈	—	5	1	no	—
258	#405	—	5	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	—	2	2	no	—
262	C₂²×C₃×C₅	—	2	2	no	—
263	C₂²×C₃×C₅	—	2	2	no	—
264	C₂²×C₃×C₅	#131	1	2	yes	complemented
265	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₃×D₅	—	2	1	no	—
267	C₂×C₃×D₅	—	2	1	no	—
268	C₂×C₃×D₅	—	2	1	no	—
269	C₂×C₃×D₅	—	2	1	no	—
270	C₂×C₃×D₅	—	2	1	no	—
271	C₂×C₃×D₅	—	4	4	no	—
272	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
273	C₃×C₄×C₅	—	2	1	no	—
274	C₃×C₄×C₅	—	2	2	no	—
275	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
276	C₃×Dic₅	—	2	2	no	—
277	C₃×Dic₅	—	2	1	no	—
278	C₃×Dic₅	—	2	2	no	—
279	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
280	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
281	C₂⁴×C₃	—	5	1	no	—
282	C₃×#41	—	10	2	no	—
283	C₃×#41	—	10	2	no	—
284	C₂×C₃×Q₈	—	5	1	no	—
285	C₂×C₃×D₄	—	5	2	no	—
286	C₂×C₃×D₄	—	5	2	no	—
287	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
288	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
289	C₂²×C₃×C₄	—	5	1	no	—
290	C₂²×C₃×C₄	—	5	1	no	—
291	C₂²×C₃×C₄	—	5	2	no	—
292	C₂²×C₃×C₄	—	5	1	no	—
293	C₂²×C₃×C₄	—	5	1	no	—
294	C₂²×C₃×C₄	—	5	1	no	—
295	C₂²×C₃×C₄	—	10	2	no	—
296	C₂²×C₃×C₄	—	10	2	no	—
297	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
298	C₃×M₁₆	—	5	4	no	—
299	C₃×M₁₆	—	10	4	no	—
300	C₃×M₁₆	—	10	4	no	—
301	C₃×M₁₆	—	10	2	no	—
302	C₂×C₃×C₈	—	5	2	no	—
303	C₂×C₃×C₈	—	5	1	no	—
304	C₂×C₃×C₈	—	5	1	no	—
305	C₂×C₃×C₈	—	5	1	no	—
306	C₂×C₃×C₈	—	5	1	no	—
307	C₂×C₃×C₈	—	5	2	no	—
308	C₂×C₃×C₈	—	10	4	no	—
309	C₂×C₃×C₈	—	10	4	no	—
310	C₂×C₃×C₈	—	10	2	no	—
311	C₂×C₃×C₈	—	10	2	no	—
312	C₃×C₄⋊C₄	—	5	2	no	—
313	C₃×C₄⋊C₄	—	5	1	no	—
314	C₃×C₄⋊C₄	—	5	2	no	—
315	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
316	C₃×C₂²⋊C₄	—	5	2	no	—
317	C₃×C₂²⋊C₄	—	5	2	no	—
318	C₃×C₂²⋊C₄	—	5	2	no	—
319	C₃×C₂²⋊C₄	—	5	2	no	—
320	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
321	C₃×C₄²	—	5	2	no	—
322	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
323	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
324	C₂²×D₅	—	2	2	no	—
325	C₂²×D₅	—	2	2	no	—
326	C₂²×D₅	—	4	1	no	—
327	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
328	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
329	C₅×D₄	—	2	4	no	—
330	C₅×D₄	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
333	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
335	C₂²⋊D₅	—	2	4	no	—
336	C₂²⋊D₅	—	4	2	no	—
337	C₂×Dic₅	—	2	1	no	—
338	C₂×Dic₅	—	2	2	no	—
339	C₂×Dic₅	—	2	1	no	—
340	C₂×Dic₅	—	2	2	no	—
341	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
342	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
343	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
344	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
345	C₄×D₅	—	2	2	no	—
346	C₄×D₅	—	2	2	no	—
347	C₄×D₅	—	2	1	no	—
348	C₄×D₅	—	2	1	no	—
349	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
350	C₄×D₅	C₃×#41	1	2	yes	—
351	Dic₁₀	—	2	2	no	—
352	#170	—	2	1	no	—
353	#170	—	2	1	no	—
354	#170	—	2	2	no	—
355	#170	—	2	1	no	—
356	#170	—	2	1	no	—
357	#170	C₂×C₃×D₄	1	4	yes	—
358	C₂×#41	—	5	1	no	—
359	C₂³×C₄	—	5	1	no	—
360	#131	—	10	4	no	—
361	C₂×M₁₆	—	5	1	no	—
362	C₂×M₁₆	—	5	1	no	—
363	C₂×M₁₆	—	5	2	no	—
364	C₂×M₁₆	—	5	2	no	—
365	C₂×M₁₆	—	10	4	no	—
366	C₂²×C₈	—	5	1	no	—
367	C₂²×C₈	—	5	1	no	—
368	C₂²×C₈	—	5	2	no	—
369	C₂²×C₈	—	5	2	no	—
370	#123	—	5	2	no	—
371	C₂²⋊Q₈	—	5	1	no	—
372	C₂²⋊Q₈	—	5	1	no	—
373	#121	—	5	1	no	—
374	#121	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
375	#120	—	5	2	no	—
376	C₄×D₄	—	5	2	no	—
377	C₄×D₄	—	5	2	no	—
378	#117	—	5	1	no	—
379	C₄⋊C₈	—	5	2	no	—
380	C₄⋊C₈	—	5	2	no	—
381	C₂²⋊C₈	—	5	1	no	—
382	C₂²⋊C₈	—	5	1	no	—
383	C₂²⋊C₈	—	5	1	no	—
384	C₂²⋊C₈	—	5	1	no	—
385	C₂²⋊C₈	—	5	2	no	—
386	C₂²⋊C₈	—	5	2	no	—
387	#97	—	5	2	no	—
388	C₄×C₈	—	5	2	no	—
389	C₂×C₃×C₅	—	2	2	no	—
390	C₂×C₃×C₅	—	4	2	no	—
391	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
392	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
393	C₂×C₃×C₅	#568	1	1	yes	characteristic
394	C₃×D₅	—	2	2	no	—
395	C₃×D₅	—	4	1	no	—
396	C₂³×C₃	—	5	1	no	—
397	C₂³×C₃	—	5	1	no	—
398	C₂³×C₃	—	10	2	no	—
399	C₂³×C₃	—	10	2	no	—
400	C₂³×C₃	—	20	1	no	—
401	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
402	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₃×Q₈	—	10	2	no	—
404	C₃×D₄	—	2	4	no	—
405	C₃×D₄	—	2	2	no	—
406	C₃×D₄	—	10	4	no	—
407	C₃×D₄	—	20	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	5	1	no	—
410	C₂×C₃×C₄	—	5	2	no	—
411	C₂×C₃×C₄	—	5	2	no	—
412	C₂×C₃×C₄	—	5	2	no	—
413	C₂×C₃×C₄	—	5	1	no	—
414	C₂×C₃×C₄	—	5	2	no	—
415	C₂×C₃×C₄	—	10	1	no	—
416	C₂×C₃×C₄	—	10	1	no	—
417	C₂×C₃×C₄	—	10	2	no	—
418	C₂×C₃×C₄	—	10	1	no	—
419	C₂×C₃×C₄	—	10	2	no	—
420	C₂×C₃×C₄	—	10	1	no	—
421	C₂×C₃×C₄	—	10	2	no	—
422	C₂×C₃×C₄	—	10	2	no	—
423	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
424	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
426	C₃×C₈	—	5	4	no	—
427	C₃×C₈	—	10	1	no	—
428	C₃×C₈	—	10	1	no	—
429	C₃×C₈	—	10	1	no	—
430	C₃×C₈	—	10	1	no	—
431	C₃×C₈	—	10	2	no	—
432	C₂²×C₅	—	2	1	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	2	2	no	—
435	C₂²×C₅	—	2	2	no	—
436	C₂²×C₅	—	2	2	no	—
437	C₂²×C₅	C₃×#131	1	2	yes	complemented
438	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
439	C₂×D₅	—	2	1	no	—
440	C₂×D₅	—	2	1	no	—
441	C₂×D₅	—	2	1	no	—
442	C₂×D₅	—	2	1	no	—
443	C₂×D₅	—	2	1	no	—
444	C₂×D₅	—	4	4	no	—
445	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
446	C₄×C₅	—	2	2	no	—
447	C₄×C₅	—	2	1	no	—
448	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
449	Dic₅	—	2	2	no	—
450	Dic₅	—	2	2	no	—
451	Dic₅	—	2	1	no	—
452	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
453	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
454	C₂⁴	—	5	1	no	—
455	#41	—	10	2	no	—
456	#41	—	10	2	no	—
457	C₂×Q₈	—	5	1	no	—
458	C₂×D₄	—	5	2	no	—
459	C₂×D₄	—	5	2	no	—
460	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
461	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
462	C₂²×C₄	—	5	1	no	—
463	C₂²×C₄	—	5	1	no	—
464	C₂²×C₄	—	5	2	no	—
465	C₂²×C₄	—	5	1	no	—
466	C₂²×C₄	—	5	1	no	—
467	C₂²×C₄	—	5	1	no	—
468	C₂²×C₄	—	10	2	no	—
469	C₂²×C₄	—	10	2	no	—
470	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
471	M₁₆	—	5	4	no	—
472	M₁₆	—	10	4	no	—
473	M₁₆	—	10	4	no	—
474	M₁₆	—	10	2	no	—
475	C₂×C₈	—	5	2	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	5	1	no	—
478	C₂×C₈	—	5	1	no	—
479	C₂×C₈	—	5	1	no	—
480	C₂×C₈	—	5	2	no	—
481	C₂×C₈	—	10	4	no	—
482	C₂×C₈	—	10	4	no	—
483	C₂×C₈	—	10	2	no	—
484	C₂×C₈	—	10	2	no	—
485	C₄⋊C₄	—	5	1	no	—
486	C₄⋊C₄	—	5	2	no	—
487	C₄⋊C₄	—	5	2	no	—
488	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
489	C₂²⋊C₄	—	5	2	no	—
490	C₂²⋊C₄	—	5	2	no	—
491	C₂²⋊C₄	—	5	2	no	—
492	C₂²⋊C₄	—	5	2	no	—
493	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
494	C₄²	—	5	2	no	—
495	C₃×C₅	#2933	1	1	yes	characteristic, complemented, Hall
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	2	no	—
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	—	2	2	no	—
501	C₂²×C₃	—	5	2	no	—
502	C₂²×C₃	—	10	1	no	—
503	C₂²×C₃	—	10	1	no	—
504	C₂²×C₃	—	10	1	no	—
505	C₂²×C₃	—	10	1	no	—
506	C₂²×C₃	—	10	1	no	—
507	C₂²×C₃	—	20	4	no	—
508	C₂²×C₃	#4131	1	2	yes	complemented
509	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
510	C₃×C₄	—	2	2	no	—
511	C₃×C₄	—	2	1	no	—
512	C₃×C₄	—	5	1	no	—
513	C₃×C₄	—	5	1	no	—
514	C₃×C₄	—	10	1	no	—
515	C₃×C₄	—	10	2	no	—
516	C₃×C₄	—	10	2	no	—
517	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
518	C₂×C₅	—	2	2	no	—
519	C₂×C₅	—	4	2	no	—
520	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
521	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
522	C₂×C₅	C₃×#568	1	1	yes	characteristic
523	D₅	—	2	2	no	—
524	D₅	—	4	1	no	—
525	C₂³	—	5	1	no	—
526	C₂³	—	5	1	no	—
527	C₂³	—	10	2	no	—
528	C₂³	—	10	2	no	—
529	C₂³	—	20	1	no	—
530	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
531	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
532	Q₈	—	10	2	no	—
533	D₄	—	2	4	no	—
534	D₄	—	2	2	no	—
535	D₄	—	10	4	no	—
536	D₄	—	20	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	5	1	no	—
539	C₂×C₄	—	5	2	no	—
540	C₂×C₄	—	5	2	no	—
541	C₂×C₄	—	5	2	no	—
542	C₂×C₄	—	5	1	no	—
543	C₂×C₄	—	5	2	no	—
544	C₂×C₄	—	10	1	no	—
545	C₂×C₄	—	10	1	no	—
546	C₂×C₄	—	10	2	no	—
547	C₂×C₄	—	10	1	no	—
548	C₂×C₄	—	10	2	no	—
549	C₂×C₄	—	10	1	no	—
550	C₂×C₄	—	10	2	no	—
551	C₂×C₄	—	10	2	no	—
552	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
553	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
554	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
555	C₈	—	5	4	no	—
556	C₈	—	10	1	no	—
557	C₈	—	10	2	no	—
558	C₈	—	10	1	no	—
559	C₈	—	10	1	no	—
560	C₈	—	10	1	no	—
561	C₂×C₃	—	2	2	no	—
562	C₂×C₃	—	4	2	no	—
563	C₂×C₃	—	10	2	no	—
564	C₂×C₃	—	20	1	no	—
565	C₂×C₃	C₂×#4131	1	1	yes	characteristic
566	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
567	C₂×C₃	#66264	1	1	yes	characteristic
568	C₅	C₃×#2933	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	5	2	no	—
575	C₂²	—	10	1	no	—
576	C₂²	—	10	1	no	—
577	C₂²	—	10	1	no	—
578	C₂²	—	10	1	no	—
579	C₂²	—	10	1	no	—
580	C₂²	—	20	4	no	—
581	C₂²	C₃×#4131	1	2	yes	complemented
582	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	5	1	no	—
586	C₄	—	5	1	no	—
587	C₄	—	10	1	no	—
588	C₄	—	10	2	no	—
589	C₄	—	10	2	no	—
590	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
591	C₃	#10617229	1	1	yes	characteristic, direct product factor, Sylow
592	C₂	—	2	2	no	—
593	C₂	—	4	2	no	—
594	C₂	—	10	2	no	—
595	C₂	—	20	1	no	—
596	C₂	C₂×C₃×#4131	1	1	yes	characteristic
597	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
598	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×#121	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#65940	C₂
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#121	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2933
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4131	C₂	semidirect
2. C₂²×C₃×#700	C₂	semidirect
4. C₃×#65776	C₂	semidirect
5. C₃×#65773	C₂	semidirect
6. C₃×D₄×#170	C₂	semidirect
7. C₃×D₅⋊(C₂²⋊C₈)	C₂	semidirect
8. C₃×#65708	C₂	semidirect
9. C₃×#65701	C₂	semidirect
10. C₃×#65695	C₂	semidirect
11. C₃×#65693	C₂	semidirect
12. #10617229	C₃	direct (N × H)
15. C₂×C₃×#704	C₂²	semidirect
17. C₂²×C₃×#170	C₂²	semidirect
36. C₃×C₂²⋊#170	C₂²	semidirect
37. C₃×C₂²⋊#170	C₂²	semidirect
38. C₃×#4004	C₂²	semidirect
41. C₃×#4002	C₂²	semidirect
42. C₃×C₄⋊#170	C₂²	semidirect
43. C₃×C₄×#170	C₂²	semidirect
45. C₂×#4131	C₂×C₃	semidirect
46. C₂²×#700	C₂×C₃	semidirect
48. #65776	C₂×C₃	semidirect
49. #65773	C₂×C₃	semidirect
50. D₄×#170	C₂×C₃	semidirect
51. D₅⋊(C₂²⋊C₈)	C₂×C₃	semidirect
52. #65708	C₂×C₃	semidirect
53. #65701	C₂×C₃	semidirect
54. #65695	C₂×C₃	semidirect
55. #65693	C₂×C₃	semidirect
84. C₃×#700	D₄	semidirect
110. C₂×#704	C₂²×C₃	semidirect
112. C₂²×#170	C₂²×C₃	semidirect
131. C₂²⋊#170	C₂²×C₃	semidirect
132. C₂²⋊#170	C₂²×C₃	semidirect
133. #4004	C₂²×C₃	semidirect
136. #4002	C₂²×C₃	semidirect
137. C₄⋊#170	C₂²×C₃	semidirect
138. C₄×#170	C₂²×C₃	semidirect
235. #700	C₃×D₄	semidirect
264. C₂²×C₃×C₅	#131	semidirect
437. C₂²×C₅	C₃×#131	semidirect
495. C₃×C₅	#2933	semidirect
508. C₂²×C₃	#4131	semidirect
568. C₅	C₃×#2933	semidirect
581. C₂²	C₃×#4131	semidirect
591. C₃	#10617229	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×#4131	2
C₂²×C₃×#700	2
C₃×#65940	2
C₃×#65776	2
C₃×#65773	2
C₃×D₄×#170	2
C₃×D₅⋊(C₂²⋊C₈)	2
C₃×#65708	2
C₃×#65701	2
C₃×#65695	2
C₃×#65693	2
#10617229	3
C₃×#2933	5

Subgroups — C3×#10617229 #14415466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617229 #14415466