Subgroups — C₃×#10617225 #14414932

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 608 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×D₅⋊C₈	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×#65756	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×#65694	C₂	1	2	yes	maximal, complemented
11	C₃×#65692	C₂	1	2	yes	maximal, complemented
12	#10617225	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	1	yes	characteristic
17	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
18	C₂²×C₃×#170	C₂²	1	2	yes	complemented
19	C₃×#4131	—	2	4	no	—
20	C₂×C₃×#700	C₂²	1	1	yes	characteristic
21	C₂×C₃×#700	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₅⋊C₈	—	2	4	no	—
23	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
27	C₃×C₅×#121	C₄	1	1	yes	characteristic
28	C₃×#4084	C₄	1	1	yes	characteristic
29	C₃×#4083	C₄	1	2	yes	—
30	C₃×D₄×Dic₅	C₂²	1	2	yes	—
31	C₃×#4070	C₄	1	1	yes	characteristic
32	C₃×#4043	C₄	1	1	yes	characteristic
33	C₃×#4038	C₂²	1	1	yes	characteristic
34	C₃×#4029	C₄	1	2	yes	—
35	C₃×#4027	C₂²	1	2	yes	—
36	C₃×C₂²⋊#170	C₂²	1	2	yes	—
37	C₃×C₂²⋊#170	C₂²	1	2	yes	complemented
38	C₃×C₂²⋊#170	C₂²	1	2	yes	complemented
39	C₃×#4004	C₂²	1	2	yes	complemented
40	C₃×#4003	C₂²	1	2	yes	—
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×#2929	—	5	1	no	maximal, Hall
45	C₂×#4131	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂²×D₅⋊C₈	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	#65756	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	#65694	C₂×C₃	1	2	yes	complemented
55	#65692	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	2	no	—
75	C₂×C₃×#170	—	2	2	no	—
76	C₂×C₃×#170	—	2	4	no	—
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	C₂×C₃×#170	C₂³	1	1	yes	characteristic
82	C₂×C₃×#170	C₂³	1	1	yes	characteristic
83	C₃×#700	—	2	2	no	—
84	C₃×#700	—	2	2	no	—
85	C₃×D₅⋊C₈	—	2	2	no	—
86	C₃×D₅⋊C₈	—	2	2	no	—
87	C₃×D₅⋊C₈	—	2	2	no	—
88	C₃×D₅⋊C₈	D₄	1	4	yes	complemented
89	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
91	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
92	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
93	C₃×#685	C₂×C₄	1	2	yes	—
94	C₃×#685	C₂×C₄	1	2	yes	—
95	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
96	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
97	C₃×#683	C₂×C₄	1	2	yes	—
98	C₃×C₄×Dic₅	C₂³	1	2	yes	—
99	C₂×C₃×#131	—	5	1	no	—
100	C₂³×C₃×C₈	—	5	1	no	—
101	C₃×#525	—	5	1	no	—
102	C₃×#435	—	5	2	no	—
103	C₃×#435	—	5	2	no	—
104	C₃×C₈×D₄	—	5	2	no	—
105	C₃×C₈×D₄	—	5	2	no	—
106	C₃×#424	—	5	1	no	—
107	C₃×#408	—	5	1	no	—
108	C₃×#407	—	5	1	no	—
109	C₃×#405	—	5	1	no	—
110	C₂×#711	C₂²×C₃	1	1	yes	characteristic
111	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
112	C₂×#704	C₂²×C₃	1	2	yes	complemented
113	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
114	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
115	C₂²×#170	C₂²×C₃	1	2	yes	complemented
116	#4131	—	2	4	no	—
117	C₂×#700	C₂²×C₃	1	1	yes	characteristic
118	C₂×#700	C₂²×C₃	1	1	yes	characteristic
119	C₂×D₅⋊C₈	—	2	4	no	—
120	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
121	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
122	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
123	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
124	C₅×#121	C₃×C₄	1	1	yes	characteristic
125	#4084	C₃×C₄	1	1	yes	characteristic
126	#4083	C₃×C₄	1	2	yes	—
127	D₄×Dic₅	C₂²×C₃	1	2	yes	—
128	#4070	C₃×C₄	1	1	yes	characteristic
129	#4043	C₃×C₄	1	1	yes	characteristic
130	#4038	C₂²×C₃	1	1	yes	characteristic
131	#4029	C₃×C₄	1	2	yes	—
132	#4027	C₂²×C₃	1	2	yes	—
133	C₂²⋊#170	C₂²×C₃	1	2	yes	—
134	C₂²⋊#170	C₂²×C₃	1	2	yes	complemented
135	C₂²⋊#170	C₂²×C₃	1	2	yes	complemented
136	#4004	C₂²×C₃	1	2	yes	complemented
137	#4003	C₂²×C₃	1	2	yes	—
138	#4002	C₂²×C₃	1	2	yes	complemented
139	C₄⋊#170	C₂²×C₃	1	2	yes	complemented
140	C₄×#170	C₂²×C₃	1	2	yes	complemented
141	#2929	—	5	1	no	Sylow
142	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
143	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₃×D₅	—	2	2	no	—
145	C₂²×C₃×D₅	—	2	2	no	—
146	C₂²×C₃×D₅	—	2	2	no	—
147	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
149	C₃×C₅×D₄	—	2	4	no	—
150	C₃×C₅×D₄	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₃×C₂²⋊D₅	—	2	4	no	—
156	C₃×C₂²⋊D₅	—	2	4	no	—
157	C₂×C₃×Dic₅	—	2	1	no	—
158	C₂×C₃×Dic₅	—	2	2	no	—
159	C₂×C₃×Dic₅	—	2	1	no	—
160	C₂×C₃×Dic₅	—	2	2	no	—
161	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
162	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
163	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
165	C₃×C₄×D₅	—	2	2	no	—
166	C₃×C₄×D₅	—	2	2	no	—
167	C₃×C₄×D₅	—	2	1	no	—
168	C₃×C₄×D₅	—	2	1	no	—
169	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
170	C₃×C₄×D₅	#41	1	2	yes	—
171	C₃×Dic₁₀	—	2	2	no	—
172	C₃×#170	—	2	1	no	—
173	C₃×#170	—	2	1	no	—
174	C₃×#170	—	2	2	no	—
175	C₃×#170	—	2	2	no	—
176	C₃×#170	C₂×D₄	1	2	yes	—
177	C₃×#170	C₂×D₄	1	2	yes	—
178	C₂×C₃×#41	—	5	1	no	—
179	C₂³×C₃×C₄	—	5	1	no	—
180	C₃×#131	—	10	4	no	—
181	C₂×C₃×M₁₆	—	5	1	no	—
182	C₂×C₃×M₁₆	—	5	2	no	—
183	C₂×C₃×M₁₆	—	5	1	no	—
184	C₂²×C₃×C₈	—	5	1	no	—
185	C₂²×C₃×C₈	—	5	1	no	—
186	C₂²×C₃×C₈	—	5	1	no	—
187	C₂²×C₃×C₈	—	5	1	no	—
188	C₂²×C₃×C₈	—	5	1	no	—
189	C₂²×C₃×C₈	—	5	1	no	—
190	C₂²×C₃×C₈	—	5	2	no	—
191	C₂²×C₃×C₈	—	10	4	no	—
192	C₃×#123	—	5	2	no	—
193	C₃×C₂²⋊Q₈	—	5	1	no	—
194	C₃×C₂²⋊Q₈	—	5	1	no	—
195	C₃×#121	—	5	1	no	—
196	C₃×#121	AGL(1,𝔽₅)	1	1	yes	characteristic
197	C₃×#120	—	5	2	no	—
198	C₃×C₄×D₄	—	5	2	no	—
199	C₃×C₄×D₄	—	5	2	no	—
200	C₃×#117	—	5	1	no	—
201	C₃×C₄⋊C₈	—	5	2	no	—
202	C₃×C₄⋊C₈	—	5	2	no	—
203	C₃×C₂²⋊C₈	—	5	2	no	—
204	C₃×C₂²⋊C₈	—	5	2	no	—
205	C₃×C₂²⋊C₈	—	5	2	no	—
206	C₃×C₂²⋊C₈	—	5	2	no	—
207	C₃×#97	—	5	2	no	—
208	C₃×C₄×C₈	—	5	2	no	—
209	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
210	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
211	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
212	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
213	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
214	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
215	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
216	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
217	#711	—	2	2	no	—
218	#711	—	2	2	no	—
219	C₂×C₄×D₅	—	2	2	no	—
220	C₂×C₄×D₅	—	2	2	no	—
221	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
222	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
223	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
225	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
226	#704	—	2	4	no	—
227	C₂×#170	—	2	2	no	—
228	C₂×#170	—	2	2	no	—
229	C₂×#170	—	2	4	no	—
230	C₂×#170	C₂³×C₃	1	1	yes	characteristic
231	C₂×#170	C₂³×C₃	1	1	yes	characteristic
232	C₂×#170	C₂³×C₃	1	2	yes	—
233	C₂×#170	C₂³×C₃	1	2	yes	—
234	C₂×#170	C₂³×C₃	1	1	yes	characteristic
235	C₂×#170	C₂³×C₃	1	1	yes	characteristic
236	#700	—	2	2	no	—
237	#700	—	2	2	no	—
238	D₅⋊C₈	—	2	2	no	—
239	D₅⋊C₈	—	2	2	no	—
240	D₅⋊C₈	—	2	2	no	—
241	D₅⋊C₈	C₃×D₄	1	4	yes	complemented
242	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
243	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
244	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
245	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
246	#685	C₂×C₃×C₄	1	2	yes	—
247	#685	C₂×C₃×C₄	1	2	yes	—
248	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
249	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
250	#683	C₂×C₃×C₄	1	2	yes	—
251	C₄×Dic₅	C₂³×C₃	1	2	yes	—
252	C₂×#131	—	5	1	no	—
253	C₂³×C₈	—	5	1	no	—
254	#525	—	5	1	no	—
255	#435	—	5	2	no	—
256	#435	—	5	2	no	—
257	C₈×D₄	—	5	2	no	—
258	C₈×D₄	—	5	2	no	—
259	#424	—	5	1	no	—
260	#408	—	5	1	no	—
261	#407	—	5	1	no	—
262	#405	—	5	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	—	2	1	no	—
265	C₂²×C₃×C₅	—	2	2	no	—
266	C₂²×C₃×C₅	—	2	2	no	—
267	C₂²×C₃×C₅	—	2	2	no	—
268	C₂²×C₃×C₅	#131	1	2	yes	complemented
269	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₃×D₅	—	2	8	no	—
271	C₂×C₃×D₅	—	2	1	no	—
272	C₂×C₃×D₅	—	2	1	no	—
273	C₂×C₃×D₅	—	2	1	no	—
274	C₂×C₃×D₅	—	2	1	no	—
275	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
276	C₂×C₃×D₅	#131	1	2	yes	complemented
277	C₃×C₄×C₅	—	2	1	no	—
278	C₃×C₄×C₅	—	2	2	no	—
279	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
280	C₃×Dic₅	—	2	2	no	—
281	C₃×Dic₅	—	2	1	no	—
282	C₃×Dic₅	—	2	2	no	—
283	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
284	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
285	C₂⁴×C₃	—	5	1	no	—
286	C₃×#41	—	10	2	no	—
287	C₃×#41	—	10	2	no	—
288	C₂×C₃×Q₈	—	5	1	no	—
289	C₂×C₃×D₄	—	5	2	no	—
290	C₂×C₃×D₄	—	5	2	no	—
291	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
292	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
293	C₂²×C₃×C₄	—	5	1	no	—
294	C₂²×C₃×C₄	—	5	1	no	—
295	C₂²×C₃×C₄	—	5	2	no	—
296	C₂²×C₃×C₄	—	5	1	no	—
297	C₂²×C₃×C₄	—	5	1	no	—
298	C₂²×C₃×C₄	—	5	1	no	—
299	C₂²×C₃×C₄	—	10	2	no	—
300	C₂²×C₃×C₄	—	10	2	no	—
301	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
302	C₃×M₁₆	—	10	4	no	—
303	C₃×M₁₆	—	10	2	no	—
304	C₃×M₁₆	—	10	2	no	—
305	C₂×C₃×C₈	—	5	1	no	—
306	C₂×C₃×C₈	—	5	1	no	—
307	C₂×C₃×C₈	—	5	4	no	—
308	C₂×C₃×C₈	—	5	2	no	—
309	C₂×C₃×C₈	—	5	1	no	—
310	C₂×C₃×C₈	—	5	1	no	—
311	C₂×C₃×C₈	—	5	2	no	—
312	C₂×C₃×C₈	—	10	2	no	—
313	C₂×C₃×C₈	—	10	2	no	—
314	C₂×C₃×C₈	—	10	2	no	—
315	C₂×C₃×C₈	—	10	2	no	—
316	C₂×C₃×C₈	—	10	4	no	—
317	C₂×C₃×C₈	—	10	2	no	—
318	C₃×C₄⋊C₄	—	5	2	no	—
319	C₃×C₄⋊C₄	—	5	1	no	—
320	C₃×C₄⋊C₄	—	5	2	no	—
321	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₃×C₂²⋊C₄	—	5	2	no	—
323	C₃×C₂²⋊C₄	—	5	2	no	—
324	C₃×C₂²⋊C₄	—	5	2	no	—
325	C₃×C₂²⋊C₄	—	5	2	no	—
326	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
327	C₃×C₄²	—	5	2	no	—
328	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
329	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
330	C₂²×D₅	—	2	2	no	—
331	C₂²×D₅	—	2	2	no	—
332	C₂²×D₅	—	2	2	no	—
333	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
334	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
335	C₅×D₄	—	2	4	no	—
336	C₅×D₄	—	2	2	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
339	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
341	C₂²⋊D₅	—	2	4	no	—
342	C₂²⋊D₅	—	2	4	no	—
343	C₂×Dic₅	—	2	1	no	—
344	C₂×Dic₅	—	2	2	no	—
345	C₂×Dic₅	—	2	1	no	—
346	C₂×Dic₅	—	2	2	no	—
347	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
348	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
349	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
350	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
351	C₄×D₅	—	2	2	no	—
352	C₄×D₅	—	2	2	no	—
353	C₄×D₅	—	2	1	no	—
354	C₄×D₅	—	2	1	no	—
355	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
356	C₄×D₅	C₃×#41	1	2	yes	—
357	Dic₁₀	—	2	2	no	—
358	#170	—	2	1	no	—
359	#170	—	2	1	no	—
360	#170	—	2	2	no	—
361	#170	—	2	2	no	—
362	#170	C₂×C₃×D₄	1	2	yes	—
363	#170	C₂×C₃×D₄	1	2	yes	—
364	C₂×#41	—	5	1	no	—
365	C₂³×C₄	—	5	1	no	—
366	#131	—	10	4	no	—
367	C₂×M₁₆	—	5	1	no	—
368	C₂×M₁₆	—	5	1	no	—
369	C₂×M₁₆	—	5	2	no	—
370	C₂²×C₈	—	5	1	no	—
371	C₂²×C₈	—	5	1	no	—
372	C₂²×C₈	—	5	1	no	—
373	C₂²×C₈	—	5	1	no	—
374	C₂²×C₈	—	5	1	no	—
375	C₂²×C₈	—	5	1	no	—
376	C₂²×C₈	—	5	2	no	—
377	C₂²×C₈	—	10	4	no	—
378	#123	—	5	2	no	—
379	C₂²⋊Q₈	—	5	1	no	—
380	C₂²⋊Q₈	—	5	1	no	—
381	#121	—	5	1	no	—
382	#121	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
383	#120	—	5	2	no	—
384	C₄×D₄	—	5	2	no	—
385	C₄×D₄	—	5	2	no	—
386	#117	—	5	1	no	—
387	C₄⋊C₈	—	5	2	no	—
388	C₄⋊C₈	—	5	2	no	—
389	C₂²⋊C₈	—	5	2	no	—
390	C₂²⋊C₈	—	5	2	no	—
391	C₂²⋊C₈	—	5	2	no	—
392	C₂²⋊C₈	—	5	2	no	—
393	#97	—	5	2	no	—
394	C₄×C₈	—	5	2	no	—
395	C₂×C₃×C₅	—	2	2	no	—
396	C₂×C₃×C₅	—	4	2	no	—
397	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
398	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
399	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
400	C₃×D₅	—	2	2	no	—
401	C₃×D₅	—	2	2	no	—
402	C₂³×C₃	—	5	1	no	—
403	C₂³×C₃	—	5	1	no	—
404	C₂³×C₃	—	10	2	no	—
405	C₂³×C₃	—	10	2	no	—
406	C₂³×C₃	—	10	2	no	—
407	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
408	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
409	C₃×Q₈	—	10	2	no	—
410	C₃×D₄	—	2	4	no	—
411	C₃×D₄	—	2	2	no	—
412	C₃×D₄	—	10	4	no	—
413	C₃×D₄	—	10	4	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	5	1	no	—
416	C₂×C₃×C₄	—	5	2	no	—
417	C₂×C₃×C₄	—	5	2	no	—
418	C₂×C₃×C₄	—	5	2	no	—
419	C₂×C₃×C₄	—	5	1	no	—
420	C₂×C₃×C₄	—	5	2	no	—
421	C₂×C₃×C₄	—	10	1	no	—
422	C₂×C₃×C₄	—	10	1	no	—
423	C₂×C₃×C₄	—	10	2	no	—
424	C₂×C₃×C₄	—	10	1	no	—
425	C₂×C₃×C₄	—	10	2	no	—
426	C₂×C₃×C₄	—	10	1	no	—
427	C₂×C₃×C₄	—	10	2	no	—
428	C₂×C₃×C₄	—	10	2	no	—
429	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
430	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
431	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
432	C₃×C₈	—	5	2	no	—
433	C₃×C₈	—	5	2	no	—
434	C₃×C₈	—	10	1	no	—
435	C₃×C₈	—	10	1	no	—
436	C₃×C₈	—	10	2	no	—
437	C₃×C₈	—	10	2	no	—
438	C₂²×C₅	—	2	1	no	—
439	C₂²×C₅	—	2	1	no	—
440	C₂²×C₅	—	2	2	no	—
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	2	2	no	—
443	C₂²×C₅	C₃×#131	1	2	yes	complemented
444	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
445	C₂×D₅	—	2	8	no	—
446	C₂×D₅	—	2	1	no	—
447	C₂×D₅	—	2	1	no	—
448	C₂×D₅	—	2	1	no	—
449	C₂×D₅	—	2	1	no	—
450	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
451	C₂×D₅	C₃×#131	1	2	yes	complemented
452	C₄×C₅	—	2	2	no	—
453	C₄×C₅	—	2	1	no	—
454	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
455	Dic₅	—	2	2	no	—
456	Dic₅	—	2	2	no	—
457	Dic₅	—	2	1	no	—
458	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
459	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
460	C₂⁴	—	5	1	no	—
461	#41	—	10	2	no	—
462	#41	—	10	2	no	—
463	C₂×Q₈	—	5	1	no	—
464	C₂×D₄	—	5	2	no	—
465	C₂×D₄	—	5	2	no	—
466	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
467	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
468	C₂²×C₄	—	5	1	no	—
469	C₂²×C₄	—	5	1	no	—
470	C₂²×C₄	—	5	2	no	—
471	C₂²×C₄	—	5	1	no	—
472	C₂²×C₄	—	5	1	no	—
473	C₂²×C₄	—	5	1	no	—
474	C₂²×C₄	—	10	2	no	—
475	C₂²×C₄	—	10	2	no	—
476	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
477	M₁₆	—	10	4	no	—
478	M₁₆	—	10	2	no	—
479	M₁₆	—	10	2	no	—
480	C₂×C₈	—	5	1	no	—
481	C₂×C₈	—	5	1	no	—
482	C₂×C₈	—	5	4	no	—
483	C₂×C₈	—	5	2	no	—
484	C₂×C₈	—	5	1	no	—
485	C₂×C₈	—	5	1	no	—
486	C₂×C₈	—	5	2	no	—
487	C₂×C₈	—	10	2	no	—
488	C₂×C₈	—	10	2	no	—
489	C₂×C₈	—	10	2	no	—
490	C₂×C₈	—	10	2	no	—
491	C₂×C₈	—	10	4	no	—
492	C₂×C₈	—	10	2	no	—
493	C₄⋊C₄	—	5	1	no	—
494	C₄⋊C₄	—	5	2	no	—
495	C₄⋊C₄	—	5	2	no	—
496	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
497	C₂²⋊C₄	—	5	2	no	—
498	C₂²⋊C₄	—	5	2	no	—
499	C₂²⋊C₄	—	5	2	no	—
500	C₂²⋊C₄	—	5	2	no	—
501	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
502	C₄²	—	5	2	no	—
503	C₃×C₅	#2929	1	1	yes	characteristic, complemented, Hall
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	1	no	—
506	C₂²×C₃	—	2	2	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	2	2	no	—
509	C₂²×C₃	—	5	2	no	—
510	C₂²×C₃	—	5	2	no	—
511	C₂²×C₃	—	10	8	no	—
512	C₂²×C₃	—	10	1	no	—
513	C₂²×C₃	—	10	1	no	—
514	C₂²×C₃	—	10	1	no	—
515	C₂²×C₃	—	10	1	no	—
516	C₂²×C₃	#4131	1	2	yes	complemented
517	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
518	C₃×C₄	—	2	2	no	—
519	C₃×C₄	—	2	1	no	—
520	C₃×C₄	—	5	1	no	—
521	C₃×C₄	—	5	1	no	—
522	C₃×C₄	—	10	1	no	—
523	C₃×C₄	—	10	2	no	—
524	C₃×C₄	—	10	2	no	—
525	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
526	C₂×C₅	—	2	2	no	—
527	C₂×C₅	—	4	2	no	—
528	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
529	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
530	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
531	D₅	—	2	2	no	—
532	D₅	—	2	2	no	—
533	C₂³	—	5	1	no	—
534	C₂³	—	5	1	no	—
535	C₂³	—	10	2	no	—
536	C₂³	—	10	2	no	—
537	C₂³	—	10	2	no	—
538	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
539	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
540	Q₈	—	10	2	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	2	no	—
543	D₄	—	10	4	no	—
544	D₄	—	10	4	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	5	1	no	—
547	C₂×C₄	—	5	2	no	—
548	C₂×C₄	—	5	2	no	—
549	C₂×C₄	—	5	2	no	—
550	C₂×C₄	—	5	1	no	—
551	C₂×C₄	—	5	2	no	—
552	C₂×C₄	—	10	1	no	—
553	C₂×C₄	—	10	1	no	—
554	C₂×C₄	—	10	2	no	—
555	C₂×C₄	—	10	1	no	—
556	C₂×C₄	—	10	2	no	—
557	C₂×C₄	—	10	1	no	—
558	C₂×C₄	—	10	2	no	—
559	C₂×C₄	—	10	2	no	—
560	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
561	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
562	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
563	C₈	—	5	2	no	—
564	C₈	—	5	2	no	—
565	C₈	—	10	1	no	—
566	C₈	—	10	1	no	—
567	C₈	—	10	2	no	—
568	C₈	—	10	2	no	—
569	C₂×C₃	—	2	2	no	—
570	C₂×C₃	—	4	2	no	—
571	C₂×C₃	—	10	2	no	—
572	C₂×C₃	—	10	2	no	—
573	C₂×C₃	C₂×#4131	1	1	yes	characteristic
574	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
575	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
576	C₅	C₃×#2929	1	1	yes	characteristic, complemented, Sylow
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	5	2	no	—
583	C₂²	—	5	2	no	—
584	C₂²	—	10	8	no	—
585	C₂²	—	10	1	no	—
586	C₂²	—	10	1	no	—
587	C₂²	—	10	1	no	—
588	C₂²	—	10	1	no	—
589	C₂²	C₃×#4131	1	2	yes	complemented
590	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	5	1	no	—
594	C₄	—	5	1	no	—
595	C₄	—	10	1	no	—
596	C₄	—	10	2	no	—
597	C₄	—	10	2	no	—
598	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
599	C₃	#10617225	1	1	yes	characteristic, direct product factor, Sylow
600	C₂	—	2	2	no	—
601	C₂	—	4	2	no	—
602	C₂	—	10	2	no	—
603	C₂	—	10	2	no	—
604	C₂	C₂×C₃×#4131	1	1	yes	characteristic
605	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
606	C₂	C₃×D₅⋊#131	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×#2929
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×D₅⋊C₈	C₂	semidirect
4. C₃×#65776	C₂	semidirect
5. C₃×#65773	C₂	semidirect
6. C₃×D₄×#170	C₂	semidirect
7. C₃×#65756	C₂	semidirect
8. C₃×#65708	C₂	semidirect
9. C₃×#65701	C₂	semidirect
10. C₃×#65694	C₂	semidirect
11. C₃×#65692	C₂	semidirect
12. #10617225	C₃	direct (N × H)
15. C₂×C₃×#704	C₂²	semidirect
18. C₂²×C₃×#170	C₂²	semidirect
37. C₃×C₂²⋊#170	C₂²	semidirect
38. C₃×C₂²⋊#170	C₂²	semidirect
39. 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×D₅⋊C₈	C₂×C₃	semidirect
48. #65776	C₂×C₃	semidirect
49. #65773	C₂×C₃	semidirect
50. D₄×#170	C₂×C₃	semidirect
51. #65756	C₂×C₃	semidirect
52. #65708	C₂×C₃	semidirect
53. #65701	C₂×C₃	semidirect
54. #65694	C₂×C₃	semidirect
55. #65692	C₂×C₃	semidirect
88. C₃×D₅⋊C₈	D₄	semidirect
112. C₂×#704	C₂²×C₃	semidirect
115. C₂²×#170	C₂²×C₃	semidirect
134. C₂²⋊#170	C₂²×C₃	semidirect
135. C₂²⋊#170	C₂²×C₃	semidirect
136. #4004	C₂²×C₃	semidirect
138. #4002	C₂²×C₃	semidirect
139. C₄⋊#170	C₂²×C₃	semidirect
140. C₄×#170	C₂²×C₃	semidirect
241. D₅⋊C₈	C₃×D₄	semidirect
268. C₂²×C₃×C₅	#131	semidirect
276. C₂×C₃×D₅	#131	semidirect
443. C₂²×C₅	C₃×#131	semidirect
451. C₂×D₅	C₃×#131	semidirect
503. C₃×C₅	#2929	semidirect
516. C₂²×C₃	#4131	semidirect
576. C₅	C₃×#2929	semidirect
589. C₂²	C₃×#4131	semidirect
599. C₃	#10617225	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×D₅⋊C₈	2
C₃×#65940	2
C₃×#65776	2
C₃×#65773	2
C₃×D₄×#170	2
C₃×#65756	2
C₃×#65708	2
C₃×#65701	2
C₃×#65694	2
C₃×#65692	2
#10617225	3
C₃×#2929	5

Subgroups — C3×#10617225 #14414932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617225 #14414932