Subgroups — C₃×#10617289 #14414928

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 588 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×#65990	C₂	1	1	yes	maximal, characteristic
4	C₃×#65775	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65755	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65704	C₂	1	2	yes	maximal, complemented
7	C₃×#65702	C₂	1	2	yes	maximal, complemented
8	C₃×#65696	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65694	C₂	1	2	yes	maximal, complemented
10	C₃×#65692	C₂	1	2	yes	maximal, complemented
11	C₃×#65691	C₂	1	1	yes	maximal, characteristic, complemented
12	#10617289	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	1	yes	characteristic
16	C₂×C₃×#704	C₂²	1	1	yes	characteristic
17	C₂×C₃×#704	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#170	C₂²	1	1	yes	characteristic, complemented
21	C₃×#4131	—	2	4	no	—
22	C₂×C₃×#700	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×D₅⋊C₈	—	2	4	no	—
24	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
25	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
26	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×#123	C₄	1	1	yes	characteristic
28	C₃×#4083	C₄	1	1	yes	characteristic
29	C₃×#4075	C₄	1	1	yes	characteristic
30	C₃×#4042	C₄	1	2	yes	—
31	C₃×#4039	C₂²	1	2	yes	—
32	C₃×#4030	C₄	1	2	yes	—
33	C₃×#4028	C₄	1	1	yes	characteristic
34	C₃×#4027	C₂²	1	2	yes	—
35	C₃×#4023	C₂²	1	1	yes	characteristic
36	C₃×C₂²⋊#170	C₂²	1	2	yes	complemented
37	C₃×#4004	C₂²	1	2	yes	complemented
38	C₃×#4003	C₂²	1	2	yes	—
39	C₃×#4003	C₂²	1	2	yes	—
40	C₃×#4003	C₂²	1	2	yes	complemented
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	#65990	C₂×C₃	1	1	yes	characteristic
48	#65775	C₂×C₃	1	1	yes	characteristic, complemented
49	#65755	C₂×C₃	1	1	yes	characteristic, complemented
50	#65704	C₂×C₃	1	2	yes	complemented
51	#65702	C₂×C₃	1	2	yes	complemented
52	#65696	C₂×C₃	1	1	yes	characteristic, complemented
53	#65694	C₂×C₃	1	2	yes	complemented
54	#65692	C₂×C₃	1	2	yes	complemented
55	#65691	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
64	C₃×#711	—	2	2	no	—
65	C₃×#711	—	2	2	no	—
66	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
67	C₂×C₃×C₄×D₅	—	2	2	no	—
68	C₂×C₃×C₄×D₅	—	2	2	no	—
69	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
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	2	no	—
74	C₃×#704	—	2	2	no	—
75	C₃×#704	—	2	2	no	—
76	C₂×C₃×#170	—	2	2	no	—
77	C₂×C₃×#170	—	2	2	no	—
78	C₂×C₃×#170	D₄	1	4	yes	complemented
79	C₂×C₃×#170	C₂³	1	2	yes	—
80	C₂×C₃×#170	C₂³	1	1	yes	characteristic
81	C₂×C₃×#170	C₂³	1	2	yes	—
82	C₂×C₃×#170	C₂³	1	1	yes	characteristic
83	C₂×C₃×#170	C₂³	1	1	yes	characteristic
84	C₂×C₃×#170	C₂³	1	1	yes	characteristic
85	C₃×#700	—	2	2	no	—
86	C₃×D₅⋊C₈	—	2	4	no	—
87	C₃×D₅⋊C₈	—	2	4	no	—
88	C₃×D₅⋊C₈	—	2	2	no	—
89	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
90	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
92	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
93	C₃×#685	C₂×C₄	1	2	yes	—
94	C₃×#685	C₂×C₄	1	2	yes	—
95	C₃×#685	C₂×C₄	1	2	yes	—
96	C₃×#683	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
113	C₂×#704	C₂²×C₃	1	1	yes	characteristic
114	C₂×#704	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
116	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
117	C₂²×#170	C₂²×C₃	1	1	yes	characteristic, complemented
118	#4131	—	2	4	no	—
119	C₂×#700	C₂²×C₃	1	1	yes	characteristic, complemented
120	C₂×D₅⋊C₈	—	2	4	no	—
121	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
122	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
123	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₅×#123	C₃×C₄	1	1	yes	characteristic
125	#4083	C₃×C₄	1	1	yes	characteristic
126	#4075	C₃×C₄	1	1	yes	characteristic
127	#4042	C₃×C₄	1	2	yes	—
128	#4039	C₂²×C₃	1	2	yes	—
129	#4030	C₃×C₄	1	2	yes	—
130	#4028	C₃×C₄	1	1	yes	characteristic
131	#4027	C₂²×C₃	1	2	yes	—
132	#4023	C₂²×C₃	1	1	yes	characteristic
133	C₂²⋊#170	C₂²×C₃	1	2	yes	complemented
134	#4004	C₂²×C₃	1	2	yes	complemented
135	#4003	C₂²×C₃	1	2	yes	—
136	#4003	C₂²×C₃	1	2	yes	—
137	#4003	C₂²×C₃	1	2	yes	complemented
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	1	yes	characteristic
143	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₃×D₅	—	2	2	no	—
145	C₂²×C₃×D₅	—	2	4	no	—
146	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
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	2	yes	—
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
153	C₃×C₂²⋊D₅	—	2	2	no	—
154	C₃×C₂²⋊D₅	—	2	4	no	—
155	C₃×C₂²⋊D₅	—	2	2	no	—
156	C₂×C₃×Dic₅	—	2	1	no	—
157	C₂×C₃×Dic₅	—	2	1	no	—
158	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
159	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×Dic₅	#41	1	2	yes	—
163	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
164	C₃×D₂₀	—	2	4	no	—
165	C₃×C₄×D₅	—	2	4	no	—
166	C₃×C₄×D₅	—	2	2	no	—
167	C₃×C₄×D₅	—	2	1	no	—
168	C₃×C₄×D₅	—	2	2	no	—
169	C₃×C₄×D₅	—	2	1	no	—
170	C₃×Dic₁₀	—	2	2	no	—
171	C₃×#170	—	2	2	no	—
172	C₃×#170	—	2	1	no	—
173	C₃×#170	—	2	1	no	—
174	C₃×#170	—	2	2	no	—
175	C₃×#170	C₂×D₄	1	2	yes	—
176	C₃×#170	C₂×D₄	1	2	yes	—
177	C₂×C₃×#41	—	5	1	no	—
178	C₂³×C₃×C₄	—	5	1	no	—
179	C₃×#131	—	10	4	no	—
180	C₂×C₃×M₁₆	—	5	1	no	—
181	C₂×C₃×M₁₆	—	5	1	no	—
182	C₂×C₃×M₁₆	—	5	1	no	—
183	C₂×C₃×M₁₆	—	5	1	no	—
184	C₂²×C₃×C₈	—	5	1	no	—
185	C₂²×C₃×C₈	—	5	2	no	—
186	C₂²×C₃×C₈	—	5	2	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	—	10	4	no	—
191	C₃×#123	—	5	1	no	—
192	C₃×#123	AGL(1,𝔽₅)	1	1	yes	characteristic
193	C₃×C₂²⋊Q₈	—	5	2	no	—
194	C₃×#121	—	5	2	no	—
195	C₃×#120	—	5	1	no	—
196	C₃×#120	—	5	1	no	—
197	C₃×C₄×D₄	—	5	2	no	—
198	C₃×C₄×D₄	—	5	2	no	—
199	C₃×#117	—	5	1	no	—
200	C₃×C₄⋊C₈	—	5	2	no	—
201	C₃×C₄⋊C₈	—	5	2	no	—
202	C₃×C₂²⋊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×#97	—	5	2	no	—
207	C₃×C₄×C₈	—	5	2	no	—
208	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
209	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
211	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
212	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
213	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
214	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
215	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
216	#711	—	2	2	no	—
217	#711	—	2	2	no	—
218	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
219	C₂×C₄×D₅	—	2	2	no	—
220	C₂×C₄×D₅	—	2	2	no	—
221	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
222	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
223	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
224	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
225	#704	—	2	2	no	—
226	#704	—	2	2	no	—
227	#704	—	2	2	no	—
228	C₂×#170	—	2	2	no	—
229	C₂×#170	—	2	2	no	—
230	C₂×#170	C₃×D₄	1	4	yes	complemented
231	C₂×#170	C₂³×C₃	1	2	yes	—
232	C₂×#170	C₂³×C₃	1	1	yes	characteristic
233	C₂×#170	C₂³×C₃	1	1	yes	characteristic
234	C₂×#170	C₂³×C₃	1	2	yes	—
235	C₂×#170	C₂³×C₃	1	1	yes	characteristic
236	C₂×#170	C₂³×C₃	1	1	yes	characteristic
237	#700	—	2	2	no	—
238	D₅⋊C₈	—	2	4	no	—
239	D₅⋊C₈	—	2	4	no	—
240	D₅⋊C₈	—	2	2	no	—
241	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
242	C₅×C₂²⋊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	1	yes	characteristic
245	#685	C₂×C₃×C₄	1	2	yes	—
246	#685	C₂×C₃×C₄	1	2	yes	—
247	#685	C₂×C₃×C₄	1	2	yes	—
248	#683	C₂×C₃×C₄	1	2	yes	—
249	#683	C₂×C₃×C₄	1	2	yes	—
250	C₄×Dic₅	C₂³×C₃	1	2	yes	—
251	C₂×#131	—	5	1	no	—
252	C₂³×C₈	—	5	1	no	—
253	#525	—	5	1	no	—
254	#435	—	5	2	no	—
255	#435	—	5	2	no	—
256	C₈×D₄	—	5	2	no	—
257	C₈×D₄	—	5	2	no	—
258	#424	—	5	1	no	—
259	#408	—	5	1	no	—
260	#407	—	5	1	no	—
261	#405	—	5	1	no	—
262	C₂²×C₃×C₅	—	2	2	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
266	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
267	C₂×C₃×D₅	—	2	8	no	—
268	C₂×C₃×D₅	—	2	2	no	—
269	C₂×C₃×D₅	—	2	2	no	—
270	C₂×C₃×D₅	—	2	1	no	—
271	C₂×C₃×D₅	—	2	2	no	—
272	C₂×C₃×D₅	#131	1	4	yes	complemented
273	C₃×C₄×C₅	—	2	1	no	—
274	C₃×C₄×C₅	—	2	2	no	—
275	C₃×C₄×C₅	—	2	2	no	—
276	C₃×Dic₅	—	2	1	no	—
277	C₃×Dic₅	—	2	2	no	—
278	C₃×Dic₅	C₄×D₄	1	2	yes	—
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	1	no	—
287	C₂×C₃×D₄	—	5	1	no	—
288	C₂×C₃×D₄	—	5	2	no	—
289	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
290	C₂²×C₃×C₄	—	5	1	no	—
291	C₂²×C₃×C₄	—	5	1	no	—
292	C₂²×C₃×C₄	—	5	2	no	—
293	C₂²×C₃×C₄	—	5	1	no	—
294	C₂²×C₃×C₄	—	5	2	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	—	10	2	no	—
299	C₃×M₁₆	—	10	2	no	—
300	C₃×M₁₆	—	10	2	no	—
301	C₃×M₁₆	—	10	2	no	—
302	C₂×C₃×C₈	—	5	1	no	—
303	C₂×C₃×C₈	—	5	1	no	—
304	C₂×C₃×C₈	—	5	4	no	—
305	C₂×C₃×C₈	—	5	2	no	—
306	C₂×C₃×C₈	—	5	2	no	—
307	C₂×C₃×C₈	—	5	1	no	—
308	C₂×C₃×C₈	—	5	1	no	—
309	C₂×C₃×C₈	—	10	4	no	—
310	C₂×C₃×C₈	—	10	4	no	—
311	C₂×C₃×C₈	—	10	2	no	—
312	C₂×C₃×C₈	—	10	2	no	—
313	C₂×C₃×C₈	—	10	2	no	—
314	C₃×C₄⋊C₄	—	5	2	no	—
315	C₃×C₄⋊C₄	—	5	2	no	—
316	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
317	C₃×C₂²⋊C₄	—	5	1	no	—
318	C₃×C₂²⋊C₄	—	5	2	no	—
319	C₃×C₂²⋊C₄	—	5	2	no	—
320	C₃×C₂²⋊C₄	—	5	2	no	—
321	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
322	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
323	C₃×C₄²	—	5	2	no	—
324	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
325	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
326	C₂²×D₅	—	2	2	no	—
327	C₂²×D₅	—	2	4	no	—
328	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
329	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
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	2	yes	—
334	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
335	C₂²⋊D₅	—	2	2	no	—
336	C₂²⋊D₅	—	2	4	no	—
337	C₂²⋊D₅	—	2	2	no	—
338	C₂×Dic₅	—	2	1	no	—
339	C₂×Dic₅	—	2	1	no	—
340	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
341	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
342	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
343	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
344	C₂×Dic₅	C₃×#41	1	2	yes	—
345	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
346	D₂₀	—	2	4	no	—
347	C₄×D₅	—	2	4	no	—
348	C₄×D₅	—	2	2	no	—
349	C₄×D₅	—	2	1	no	—
350	C₄×D₅	—	2	2	no	—
351	C₄×D₅	—	2	1	no	—
352	Dic₁₀	—	2	2	no	—
353	#170	—	2	2	no	—
354	#170	—	2	1	no	—
355	#170	—	2	1	no	—
356	#170	—	2	2	no	—
357	#170	C₂×C₃×D₄	1	2	yes	—
358	#170	C₂×C₃×D₄	1	2	yes	—
359	C₂×#41	—	5	1	no	—
360	C₂³×C₄	—	5	1	no	—
361	#131	—	10	4	no	—
362	C₂×M₁₆	—	5	1	no	—
363	C₂×M₁₆	—	5	1	no	—
364	C₂×M₁₆	—	5	1	no	—
365	C₂×M₁₆	—	5	1	no	—
366	C₂²×C₈	—	5	1	no	—
367	C₂²×C₈	—	5	2	no	—
368	C₂²×C₈	—	5	2	no	—
369	C₂²×C₈	—	5	1	no	—
370	C₂²×C₈	—	5	1	no	—
371	C₂²×C₈	—	5	1	no	—
372	C₂²×C₈	—	10	4	no	—
373	#123	—	5	1	no	—
374	#123	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
375	C₂²⋊Q₈	—	5	2	no	—
376	#121	—	5	2	no	—
377	#120	—	5	1	no	—
378	#120	—	5	1	no	—
379	C₄×D₄	—	5	2	no	—
380	C₄×D₄	—	5	2	no	—
381	#117	—	5	1	no	—
382	C₄⋊C₈	—	5	2	no	—
383	C₄⋊C₈	—	5	2	no	—
384	C₂²⋊C₈	—	5	2	no	—
385	C₂²⋊C₈	—	5	2	no	—
386	C₂²⋊C₈	—	5	2	no	—
387	C₂²⋊C₈	—	5	2	no	—
388	#97	—	5	2	no	—
389	C₄×C₈	—	5	2	no	—
390	C₂×C₃×C₅	—	2	2	no	—
391	C₂×C₃×C₅	—	4	1	no	—
392	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
393	C₂×C₃×C₅	C₂×#131	1	2	yes	—
394	C₃×D₅	—	2	4	no	—
395	C₃×D₅	—	4	1	no	—
396	C₂³×C₃	—	5	2	no	—
397	C₂³×C₃	—	5	1	no	—
398	C₂³×C₃	—	10	4	no	—
399	C₂³×C₃	—	10	2	no	—
400	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
401	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
402	C₃×Q₈	—	10	2	no	—
403	C₃×D₄	—	2	2	no	—
404	C₃×D₄	—	10	4	no	—
405	C₃×D₄	—	10	2	no	—
406	C₃×D₄	—	10	4	no	—
407	C₃×D₄	—	10	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	5	2	no	—
410	C₂×C₃×C₄	—	5	2	no	—
411	C₂×C₃×C₄	—	5	1	no	—
412	C₂×C₃×C₄	—	5	1	no	—
413	C₂×C₃×C₄	—	5	2	no	—
414	C₂×C₃×C₄	—	5	1	no	—
415	C₂×C₃×C₄	—	10	2	no	—
416	C₂×C₃×C₄	—	10	1	no	—
417	C₂×C₃×C₄	—	10	4	no	—
418	C₂×C₃×C₄	—	10	2	no	—
419	C₂×C₃×C₄	—	10	1	no	—
420	C₂×C₃×C₄	—	10	1	no	—
421	C₂×C₃×C₄	—	10	1	no	—
422	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
423	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
425	C₃×C₈	—	5	2	no	—
426	C₃×C₈	—	5	2	no	—
427	C₃×C₈	—	10	2	no	—
428	C₃×C₈	—	10	1	no	—
429	C₃×C₈	—	10	1	no	—
430	C₃×C₈	—	10	2	no	—
431	C₂²×C₅	—	2	2	no	—
432	C₂²×C₅	—	2	2	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
435	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
436	C₂×D₅	—	2	8	no	—
437	C₂×D₅	—	2	2	no	—
438	C₂×D₅	—	2	2	no	—
439	C₂×D₅	—	2	2	no	—
440	C₂×D₅	—	2	1	no	—
441	C₂×D₅	C₃×#131	1	4	yes	complemented
442	C₄×C₅	—	2	2	no	—
443	C₄×C₅	—	2	1	no	—
444	C₄×C₅	—	2	2	no	—
445	Dic₅	—	2	2	no	—
446	Dic₅	—	2	1	no	—
447	Dic₅	C₃×C₄×D₄	1	2	yes	—
448	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
449	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
450	C₂⁴	—	5	1	no	—
451	#41	—	10	2	no	—
452	#41	—	10	2	no	—
453	C₂×Q₈	—	5	1	no	—
454	C₂×D₄	—	5	2	no	—
455	C₂×D₄	—	5	1	no	—
456	C₂×D₄	—	5	1	no	—
457	C₂×D₄	—	5	2	no	—
458	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
459	C₂²×C₄	—	5	1	no	—
460	C₂²×C₄	—	5	1	no	—
461	C₂²×C₄	—	5	2	no	—
462	C₂²×C₄	—	5	1	no	—
463	C₂²×C₄	—	5	2	no	—
464	C₂²×C₄	—	10	2	no	—
465	C₂²×C₄	—	10	2	no	—
466	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
467	M₁₆	—	10	2	no	—
468	M₁₆	—	10	2	no	—
469	M₁₆	—	10	2	no	—
470	M₁₆	—	10	2	no	—
471	C₂×C₈	—	5	1	no	—
472	C₂×C₈	—	5	1	no	—
473	C₂×C₈	—	5	4	no	—
474	C₂×C₈	—	5	2	no	—
475	C₂×C₈	—	5	2	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	5	1	no	—
478	C₂×C₈	—	10	4	no	—
479	C₂×C₈	—	10	4	no	—
480	C₂×C₈	—	10	2	no	—
481	C₂×C₈	—	10	2	no	—
482	C₂×C₈	—	10	2	no	—
483	C₄⋊C₄	—	5	2	no	—
484	C₄⋊C₄	—	5	2	no	—
485	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
486	C₂²⋊C₄	—	5	1	no	—
487	C₂²⋊C₄	—	5	2	no	—
488	C₂²⋊C₄	—	5	2	no	—
489	C₂²⋊C₄	—	5	2	no	—
490	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
491	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
492	C₄²	—	5	2	no	—
493	C₃×C₅	#2929	1	1	yes	characteristic, complemented, Hall
494	C₂²×C₃	—	2	2	no	—
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	2	2	no	—
497	C₂²×C₃	—	5	4	no	—
498	C₂²×C₃	—	10	8	no	—
499	C₂²×C₃	—	10	2	no	—
500	C₂²×C₃	—	10	2	no	—
501	C₂²×C₃	—	10	1	no	—
502	C₂²×C₃	—	10	2	no	—
503	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	2	yes	—
504	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
505	C₃×C₄	—	2	2	no	—
506	C₃×C₄	—	2	1	no	—
507	C₃×C₄	—	2	2	no	—
508	C₃×C₄	—	5	2	no	—
509	C₃×C₄	—	5	1	no	—
510	C₃×C₄	—	5	1	no	—
511	C₃×C₄	—	10	1	no	—
512	C₃×C₄	—	10	2	no	—
513	C₂×C₅	—	2	2	no	—
514	C₂×C₅	—	4	1	no	—
515	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
516	C₂×C₅	C₂×C₃×#131	1	2	yes	—
517	D₅	—	2	4	no	—
518	D₅	—	4	1	no	—
519	C₂³	—	5	2	no	—
520	C₂³	—	5	1	no	—
521	C₂³	—	10	4	no	—
522	C₂³	—	10	2	no	—
523	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
524	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
525	Q₈	—	10	2	no	—
526	D₄	—	2	2	no	—
527	D₄	—	10	4	no	—
528	D₄	—	10	2	no	—
529	D₄	—	10	4	no	—
530	D₄	—	10	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	5	2	no	—
533	C₂×C₄	—	5	2	no	—
534	C₂×C₄	—	5	1	no	—
535	C₂×C₄	—	5	1	no	—
536	C₂×C₄	—	5	2	no	—
537	C₂×C₄	—	5	1	no	—
538	C₂×C₄	—	10	2	no	—
539	C₂×C₄	—	10	1	no	—
540	C₂×C₄	—	10	2	no	—
541	C₂×C₄	—	10	4	no	—
542	C₂×C₄	—	10	1	no	—
543	C₂×C₄	—	10	1	no	—
544	C₂×C₄	—	10	1	no	—
545	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
546	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
547	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
548	C₈	—	5	2	no	—
549	C₈	—	5	2	no	—
550	C₈	—	10	2	no	—
551	C₈	—	10	1	no	—
552	C₈	—	10	1	no	—
553	C₈	—	10	2	no	—
554	C₂×C₃	—	2	2	no	—
555	C₂×C₃	—	4	1	no	—
556	C₂×C₃	—	10	4	no	—
557	C₂×C₃	—	20	1	no	—
558	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
559	C₂×C₃	D₅⋊#131	1	2	yes	—
560	C₅	C₃×#2929	1	1	yes	characteristic, complemented, Sylow
561	C₂²	—	2	2	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	5	4	no	—
565	C₂²	—	10	8	no	—
566	C₂²	—	10	2	no	—
567	C₂²	—	10	2	no	—
568	C₂²	—	10	1	no	—
569	C₂²	—	10	2	no	—
570	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
571	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
572	C₄	—	2	2	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	5	1	no	—
576	C₄	—	5	1	no	—
577	C₄	—	5	2	no	—
578	C₄	—	10	1	no	—
579	C₄	—	10	2	no	—
580	C₃	#10617289	1	1	yes	characteristic, direct product factor, Sylow
581	C₂	—	2	2	no	—
582	C₂	—	4	1	no	—
583	C₂	—	10	4	no	—
584	C₂	—	20	1	no	—
585	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
586	C₂	C₃×D₅⋊#131	1	2	yes	—

	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×#123	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#65990	C₂
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#123	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2929
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

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×#65775	C₂	semidirect
5. C₃×#65755	C₂	semidirect
6. C₃×#65704	C₂	semidirect
7. C₃×#65702	C₂	semidirect
8. C₃×#65696	C₂	semidirect
9. C₃×#65694	C₂	semidirect
10. C₃×#65692	C₂	semidirect
11. C₃×#65691	C₂	semidirect
12. #10617289	C₃	direct (N × H)
17. C₂×C₃×#704	C₂²	semidirect
20. C₂²×C₃×#170	C₂²	semidirect
22. C₂×C₃×#700	C₂²	semidirect
26. C₂×C₃×D₅⋊C₈	C₂²	semidirect
36. C₃×C₂²⋊#170	C₂²	semidirect
37. C₃×#4004	C₂²	semidirect
40. C₃×#4003	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. #65775	C₂×C₃	semidirect
49. #65755	C₂×C₃	semidirect
50. #65704	C₂×C₃	semidirect
51. #65702	C₂×C₃	semidirect
52. #65696	C₂×C₃	semidirect
53. #65694	C₂×C₃	semidirect
54. #65692	C₂×C₃	semidirect
55. #65691	C₂×C₃	semidirect
78. C₂×C₃×#170	D₄	semidirect
114. C₂×#704	C₂²×C₃	semidirect
117. C₂²×#170	C₂²×C₃	semidirect
119. C₂×#700	C₂²×C₃	semidirect
123. C₂×D₅⋊C₈	C₂²×C₃	semidirect
133. C₂²⋊#170	C₂²×C₃	semidirect
134. #4004	C₂²×C₃	semidirect
137. #4003	C₂²×C₃	semidirect
138. #4002	C₂²×C₃	semidirect
139. C₄⋊#170	C₂²×C₃	semidirect
140. C₄×#170	C₂²×C₃	semidirect
230. C₂×#170	C₃×D₄	semidirect
272. C₂×C₃×D₅	#131	semidirect
441. C₂×D₅	C₃×#131	semidirect
493. C₃×C₅	#2929	semidirect
560. C₅	C₃×#2929	semidirect
580. C₃	#10617289	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×#65990	2
C₃×#65775	2
C₃×#65755	2
C₃×#65704	2
C₃×#65702	2
C₃×#65696	2
C₃×#65694	2
C₃×#65692	2
C₃×#65691	2
#10617289	3
C₃×#2929	5

Subgroups — C3×#10617289 #14414928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617289 #14414928