Subgroups — C₃×#10617227 #14415238

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 552 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	2	yes	maximal, complemented
2	C₃×#65930	C₂	1	1	yes	maximal, characteristic
3	C₃×#65775	C₂	1	2	yes	maximal, complemented
4	C₃×#65774	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65758	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×C₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65705	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65702	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65695	C₂	1	2	yes	maximal, complemented
11	C₃×#65692	C₂	1	2	yes	maximal, complemented
12	#10617227	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#711	C₂²	1	2	yes	—
14	C₂×C₃×#704	C₂²	1	2	yes	—
15	C₂×C₃×#704	C₂²	1	2	yes	—
16	C₂²×C₃×#170	C₂²	1	2	yes	—
17	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
18	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
19	C₃×#4131	—	2	8	no	—
20	C₂×C₃×#700	C₂²	1	2	yes	—
21	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
22	C₃×C₅×#121	C₄	1	1	yes	characteristic
23	C₃×#4086	C₄	1	1	yes	characteristic
24	C₃×#4085	C₄	1	2	yes	—
25	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₃×#4076	C₄	1	1	yes	characteristic
27	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₃×#4039	C₂²	1	1	yes	characteristic
29	C₃×#4034	C₄	1	1	yes	characteristic
30	C₃×#4031	C₄	1	2	yes	—
31	C₃×#4027	C₂²	1	2	yes	—
32	C₃×C₂²⋊#170	C₂²	1	2	yes	—
33	C₃×C₂²⋊#170	C₂²	1	2	yes	—
34	C₃×#4004	C₂²	1	2	yes	—
35	C₃×#4003	C₂²	1	2	yes	—
36	C₃×#4003	C₂²	1	2	yes	—
37	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
38	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
39	C₃×C₄×#170	C₂²	1	1	yes	characteristic
40	C₃×C₄×#170	C₂²	1	1	yes	characteristic
41	C₃×C₄×#170	C₂²	1	1	yes	characteristic
42	C₃×C₄×#170	C₂²	1	1	yes	characteristic
43	C₃×#2931	—	5	1	no	maximal, Hall
44	C₂×#4131	C₂×C₃	1	2	yes	complemented
45	#65930	C₂×C₃	1	1	yes	characteristic
46	#65775	C₂×C₃	1	2	yes	complemented
47	#65774	C₂×C₃	1	1	yes	characteristic, complemented
48	D₄×#170	C₂×C₃	1	1	yes	characteristic, complemented
49	#65758	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×C₄×#170	C₂×C₃	1	1	yes	characteristic, complemented
51	#65705	C₂×C₃	1	1	yes	characteristic, complemented
52	#65702	C₂×C₃	1	1	yes	characteristic, complemented
53	#65695	C₂×C₃	1	2	yes	complemented
54	#65692	C₂×C₃	1	2	yes	complemented
55	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
57	C₂²×C₃×C₄×C₅	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	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
63	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
64	C₃×#711	—	2	4	no	—
65	C₃×#711	—	2	4	no	—
66	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
68	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
69	C₃×#704	—	2	4	no	—
70	C₃×#704	—	2	4	no	—
71	C₂×C₃×#170	—	2	2	no	—
72	C₂×C₃×#170	—	2	4	no	—
73	C₂×C₃×#170	D₄	1	4	yes	complemented
74	C₂×C₃×#170	C₂³	1	2	yes	—
75	C₂×C₃×#170	C₂³	1	1	yes	characteristic
76	C₂×C₃×#170	C₂³	1	1	yes	characteristic
77	C₂×C₃×#170	C₂³	1	2	yes	—
78	C₂×C₃×#170	C₂³	1	1	yes	characteristic
79	C₂×C₃×#170	C₂³	1	1	yes	characteristic
80	C₃×#700	—	2	4	no	—
81	C₃×D₅⋊C₈	—	2	4	no	—
82	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
84	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
85	C₃×#685	C₂×C₄	1	2	yes	—
86	C₃×#685	C₂×C₄	1	2	yes	—
87	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
88	C₃×#683	C₂×C₄	1	2	yes	—
89	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
90	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
91	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
92	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
93	C₂×C₃×#131	—	5	2	no	—
94	C₃×#532	—	5	1	no	—
95	C₃×#436	—	5	2	no	—
96	C₃×#436	—	5	1	no	—
97	C₃×#436	—	5	1	no	—
98	C₃×C₈×D₄	—	5	2	no	—
99	C₃×C₈×D₄	—	5	1	no	—
100	C₃×C₈×D₄	—	5	1	no	—
101	C₃×#423	—	5	1	no	—
102	C₃×#408	—	5	2	no	—
103	C₂×C₃×C₄×C₈	—	5	1	no	—
104	C₂×#711	C₂²×C₃	1	2	yes	—
105	C₂×#704	C₂²×C₃	1	2	yes	—
106	C₂×#704	C₂²×C₃	1	2	yes	—
107	C₂²×#170	C₂²×C₃	1	2	yes	—
108	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
109	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
110	#4131	—	2	8	no	—
111	C₂×#700	C₂²×C₃	1	2	yes	—
112	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
113	C₅×#121	C₃×C₄	1	1	yes	characteristic
114	#4086	C₃×C₄	1	1	yes	characteristic
115	#4085	C₃×C₄	1	2	yes	—
116	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
117	#4076	C₃×C₄	1	1	yes	characteristic
118	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
119	#4039	C₂²×C₃	1	1	yes	characteristic
120	#4034	C₃×C₄	1	1	yes	characteristic
121	#4031	C₃×C₄	1	2	yes	—
122	#4027	C₂²×C₃	1	2	yes	—
123	C₂²⋊#170	C₂²×C₃	1	2	yes	—
124	C₂²⋊#170	C₂²×C₃	1	2	yes	—
125	#4004	C₂²×C₃	1	2	yes	—
126	#4003	C₂²×C₃	1	2	yes	—
127	#4003	C₂²×C₃	1	2	yes	—
128	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
129	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
130	C₄×#170	C₂²×C₃	1	1	yes	characteristic
131	C₄×#170	C₂²×C₃	1	1	yes	characteristic
132	C₄×#170	C₂²×C₃	1	1	yes	characteristic
133	C₄×#170	C₂²×C₃	1	1	yes	characteristic
134	#2931	—	5	1	no	Sylow
135	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
136	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
138	C₃×C₅×D₄	—	2	4	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
144	C₃×C₂²⋊D₅	—	2	4	no	—
145	C₃×C₂²⋊D₅	—	2	4	no	—
146	C₃×C₂²⋊D₅	—	2	4	no	—
147	C₂×C₃×Dic₅	—	2	2	no	—
148	C₂×C₃×Dic₅	—	2	2	no	—
149	C₂×C₃×Dic₅	—	2	2	no	—
150	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
152	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
155	C₂×C₃×Dic₅	#41	1	2	yes	—
156	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
157	C₃×D₂₀	—	2	2	no	—
158	C₃×C₄×D₅	—	2	2	no	—
159	C₃×C₄×D₅	—	2	2	no	—
160	C₃×Dic₁₀	—	2	4	no	—
161	C₃×#170	—	2	2	no	—
162	C₃×#170	—	2	2	no	—
163	C₃×#170	—	2	1	no	—
164	C₃×#170	—	2	1	no	—
165	C₃×#170	C₂×D₄	1	2	yes	—
166	C₃×#170	C₂×D₄	1	2	yes	—
167	C₂×C₃×#41	—	5	2	no	—
168	C₃×#131	—	10	8	no	—
169	C₂×C₃×M₁₆	—	5	2	no	—
170	C₂×C₃×M₁₆	—	5	2	no	—
171	C₂×C₃×M₁₆	—	5	2	no	—
172	C₂²×C₃×C₈	—	5	1	no	—
173	C₂²×C₃×C₈	—	5	2	no	—
174	C₂²×C₃×C₈	—	5	2	no	—
175	C₂²×C₃×C₈	—	5	1	no	—
176	C₃×C₄⋊Q₈	—	5	1	no	—
177	C₃×#127	—	5	1	no	—
178	C₃×#124	—	5	2	no	—
179	C₃×#121	—	5	2	no	—
180	C₃×#121	—	5	1	no	—
181	C₃×#121	AGL(1,𝔽₅)	1	1	yes	characteristic
182	C₃×C₄×D₄	—	5	1	no	—
183	C₃×C₄×D₄	—	5	1	no	—
184	C₃×C₄×D₄	—	5	2	no	—
185	C₂×C₃×C₄²	—	5	1	no	—
186	C₃×C₄⋊C₈	—	5	1	no	—
187	C₃×C₄⋊C₈	—	5	1	no	—
188	C₃×C₄⋊C₈	—	5	2	no	—
189	C₃×C₂²⋊C₈	—	5	2	no	—
190	C₃×C₂²⋊C₈	—	5	2	no	—
191	C₃×C₂²⋊C₈	—	5	2	no	—
192	C₃×C₂²⋊C₈	—	5	2	no	—
193	C₃×C₄×C₈	—	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	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
198	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
200	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
201	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
202	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
203	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
204	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
205	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
206	#711	—	2	4	no	—
207	#711	—	2	4	no	—
208	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
209	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
210	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
211	#704	—	2	4	no	—
212	#704	—	2	4	no	—
213	C₂×#170	—	2	2	no	—
214	C₂×#170	—	2	4	no	—
215	C₂×#170	C₃×D₄	1	4	yes	complemented
216	C₂×#170	C₂³×C₃	1	2	yes	—
217	C₂×#170	C₂³×C₃	1	2	yes	—
218	C₂×#170	C₂³×C₃	1	1	yes	characteristic
219	C₂×#170	C₂³×C₃	1	1	yes	characteristic
220	C₂×#170	C₂³×C₃	1	1	yes	characteristic
221	C₂×#170	C₂³×C₃	1	1	yes	characteristic
222	#700	—	2	4	no	—
223	D₅⋊C₈	—	2	4	no	—
224	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
225	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
226	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
227	#685	C₂×C₃×C₄	1	2	yes	—
228	#685	C₂×C₃×C₄	1	2	yes	—
229	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
230	#683	C₂×C₃×C₄	1	2	yes	—
231	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
232	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
233	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
234	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
235	C₂×#131	—	5	2	no	—
236	#532	—	5	1	no	—
237	#436	—	5	2	no	—
238	#436	—	5	1	no	—
239	#436	—	5	1	no	—
240	C₈×D₄	—	5	2	no	—
241	C₈×D₄	—	5	1	no	—
242	C₈×D₄	—	5	1	no	—
243	#423	—	5	1	no	—
244	#408	—	5	2	no	—
245	C₂×C₄×C₈	—	5	1	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	—	2	2	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
252	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₃×D₅	—	2	2	no	—
254	C₂×C₃×D₅	—	2	2	no	—
255	C₂×C₃×D₅	—	2	2	no	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	—	2	1	no	—
258	C₃×C₄×C₅	#131	1	2	yes	complemented
259	C₃×Dic₅	—	2	2	no	—
260	C₃×Dic₅	—	2	1	no	—
261	C₃×Dic₅	C₄×D₄	1	2	yes	—
262	C₃×Dic₅	#131	1	2	yes	complemented
263	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
264	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
265	C₃×#41	—	10	4	no	—
266	C₃×#41	—	10	4	no	—
267	C₂×C₃×Q₈	—	5	2	no	—
268	C₂×C₃×D₄	—	5	2	no	—
269	C₂×C₃×D₄	—	5	2	no	—
270	C₂×C₃×D₄	—	5	2	no	—
271	C₂×C₃×D₄	—	5	1	no	—
272	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
273	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
274	C₂²×C₃×C₄	—	5	1	no	—
275	C₂²×C₃×C₄	—	5	2	no	—
276	C₂²×C₃×C₄	—	5	1	no	—
277	C₂²×C₃×C₄	—	5	2	no	—
278	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
279	C₃×M₁₆	—	10	4	no	—
280	C₃×M₁₆	—	10	4	no	—
281	C₃×M₁₆	—	10	4	no	—
282	C₂×C₃×C₈	—	5	1	no	—
283	C₂×C₃×C₈	—	5	1	no	—
284	C₂×C₃×C₈	—	5	4	no	—
285	C₂×C₃×C₈	—	5	1	no	—
286	C₂×C₃×C₈	—	5	1	no	—
287	C₂×C₃×C₈	—	5	2	no	—
288	C₂×C₃×C₈	—	5	2	no	—
289	C₂×C₃×C₈	—	10	4	no	—
290	C₂×C₃×C₈	—	10	4	no	—
291	C₂×C₃×C₈	—	10	2	no	—
292	C₃×C₄⋊C₄	—	5	2	no	—
293	C₃×C₄⋊C₄	—	5	1	no	—
294	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
295	C₃×C₂²⋊C₄	—	5	2	no	—
296	C₃×C₂²⋊C₄	—	5	2	no	—
297	C₃×C₂²⋊C₄	—	5	2	no	—
298	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
299	C₃×C₄²	—	5	1	no	—
300	C₃×C₄²	—	5	1	no	—
301	C₃×C₄²	—	5	1	no	—
302	C₃×C₄²	—	5	1	no	—
303	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
304	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
305	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
306	C₅×D₄	—	2	4	no	—
307	C₅×D₄	—	2	2	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
311	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
312	C₂²⋊D₅	—	2	4	no	—
313	C₂²⋊D₅	—	2	4	no	—
314	C₂²⋊D₅	—	2	4	no	—
315	C₂×Dic₅	—	2	2	no	—
316	C₂×Dic₅	—	2	2	no	—
317	C₂×Dic₅	—	2	2	no	—
318	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
319	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
320	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
321	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
322	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
323	C₂×Dic₅	C₃×#41	1	2	yes	—
324	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
325	D₂₀	—	2	2	no	—
326	C₄×D₅	—	2	2	no	—
327	C₄×D₅	—	2	2	no	—
328	Dic₁₀	—	2	4	no	—
329	#170	—	2	2	no	—
330	#170	—	2	2	no	—
331	#170	—	2	1	no	—
332	#170	—	2	1	no	—
333	#170	C₂×C₃×D₄	1	2	yes	—
334	#170	C₂×C₃×D₄	1	2	yes	—
335	C₂×#41	—	5	2	no	—
336	#131	—	10	8	no	—
337	C₂×M₁₆	—	5	2	no	—
338	C₂×M₁₆	—	5	2	no	—
339	C₂×M₁₆	—	5	2	no	—
340	C₂²×C₈	—	5	1	no	—
341	C₂²×C₈	—	5	2	no	—
342	C₂²×C₈	—	5	2	no	—
343	C₂²×C₈	—	5	1	no	—
344	C₄⋊Q₈	—	5	1	no	—
345	#127	—	5	1	no	—
346	#124	—	5	2	no	—
347	#121	—	5	2	no	—
348	#121	—	5	1	no	—
349	#121	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
350	C₄×D₄	—	5	1	no	—
351	C₄×D₄	—	5	1	no	—
352	C₄×D₄	—	5	2	no	—
353	C₂×C₄²	—	5	1	no	—
354	C₄⋊C₈	—	5	1	no	—
355	C₄⋊C₈	—	5	1	no	—
356	C₄⋊C₈	—	5	2	no	—
357	C₂²⋊C₈	—	5	2	no	—
358	C₂²⋊C₈	—	5	2	no	—
359	C₂²⋊C₈	—	5	2	no	—
360	C₂²⋊C₈	—	5	2	no	—
361	C₄×C₈	—	5	1	no	—
362	C₄×C₈	—	5	1	no	—
363	C₄×C₈	—	5	1	no	—
364	C₄×C₈	—	5	1	no	—
365	C₂×C₃×C₅	—	2	2	no	—
366	C₂×C₃×C₅	—	4	2	no	—
367	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
368	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
369	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
370	C₃×D₅	—	4	2	no	—
371	C₂³×C₃	—	5	2	no	—
372	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
373	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₃×Q₈	—	10	4	no	—
375	C₃×D₄	—	2	4	no	—
376	C₃×D₄	—	2	2	no	—
377	C₃×D₄	—	10	4	no	—
378	C₃×D₄	—	10	4	no	—
379	C₃×D₄	—	10	4	no	—
380	C₃×D₄	—	10	2	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	5	2	no	—
383	C₂×C₃×C₄	—	5	2	no	—
384	C₂×C₃×C₄	—	5	1	no	—
385	C₂×C₃×C₄	—	5	1	no	—
386	C₂×C₃×C₄	—	5	1	no	—
387	C₂×C₃×C₄	—	5	1	no	—
388	C₂×C₃×C₄	—	5	2	no	—
389	C₂×C₃×C₄	—	10	2	no	—
390	C₂×C₃×C₄	—	10	2	no	—
391	C₂×C₃×C₄	—	10	2	no	—
392	C₂×C₃×C₄	—	10	2	no	—
393	C₂×C₃×C₄	—	10	2	no	—
394	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
396	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
397	C₃×C₈	—	5	2	no	—
398	C₃×C₈	—	5	2	no	—
399	C₃×C₈	—	10	1	no	—
400	C₃×C₈	—	10	1	no	—
401	C₃×C₈	—	10	2	no	—
402	C₃×C₈	—	10	2	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	2	2	no	—
408	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
409	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
410	C₂×D₅	—	2	2	no	—
411	C₂×D₅	—	2	2	no	—
412	C₂×D₅	—	2	2	no	—
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	2	no	—
415	C₄×C₅	C₃×#131	1	2	yes	complemented
416	Dic₅	—	2	1	no	—
417	Dic₅	—	2	2	no	—
418	Dic₅	C₃×C₄×D₄	1	2	yes	—
419	Dic₅	C₃×#131	1	2	yes	complemented
420	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
421	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
422	#41	—	10	4	no	—
423	#41	—	10	4	no	—
424	C₂×Q₈	—	5	2	no	—
425	C₂×D₄	—	5	2	no	—
426	C₂×D₄	—	5	2	no	—
427	C₂×D₄	—	5	2	no	—
428	C₂×D₄	—	5	1	no	—
429	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
430	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
431	C₂²×C₄	—	5	1	no	—
432	C₂²×C₄	—	5	2	no	—
433	C₂²×C₄	—	5	1	no	—
434	C₂²×C₄	—	5	2	no	—
435	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
436	M₁₆	—	10	4	no	—
437	M₁₆	—	10	4	no	—
438	M₁₆	—	10	4	no	—
439	C₂×C₈	—	5	1	no	—
440	C₂×C₈	—	5	1	no	—
441	C₂×C₈	—	5	4	no	—
442	C₂×C₈	—	5	1	no	—
443	C₂×C₈	—	5	1	no	—
444	C₂×C₈	—	5	2	no	—
445	C₂×C₈	—	5	2	no	—
446	C₂×C₈	—	10	4	no	—
447	C₂×C₈	—	10	4	no	—
448	C₂×C₈	—	10	2	no	—
449	C₄⋊C₄	—	5	2	no	—
450	C₄⋊C₄	—	5	1	no	—
451	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
452	C₂²⋊C₄	—	5	2	no	—
453	C₂²⋊C₄	—	5	2	no	—
454	C₂²⋊C₄	—	5	2	no	—
455	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
456	C₄²	—	5	1	no	—
457	C₄²	—	5	1	no	—
458	C₄²	—	5	1	no	—
459	C₄²	—	5	1	no	—
460	C₃×C₅	#2931	1	1	yes	characteristic, complemented, Hall
461	C₂²×C₃	—	2	1	no	—
462	C₂²×C₃	—	2	1	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	10	2	no	—
467	C₂²×C₃	—	10	2	no	—
468	C₂²×C₃	—	10	2	no	—
469	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	2	yes	—
470	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	2	2	no	—
473	C₃×C₄	—	5	2	no	—
474	C₃×C₄	—	5	1	no	—
475	C₃×C₄	—	5	1	no	—
476	C₃×C₄	—	5	2	no	—
477	C₃×C₄	—	10	2	no	—
478	C₃×C₄	—	10	1	no	—
479	C₃×C₄	#4131	1	2	yes	complemented
480	C₂×C₅	—	2	2	no	—
481	C₂×C₅	—	4	2	no	—
482	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
483	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
484	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
485	D₅	—	4	2	no	—
486	C₂³	—	5	2	no	—
487	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
488	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
489	Q₈	—	10	4	no	—
490	D₄	—	2	4	no	—
491	D₄	—	2	2	no	—
492	D₄	—	10	4	no	—
493	D₄	—	10	4	no	—
494	D₄	—	10	4	no	—
495	D₄	—	10	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	5	2	no	—
498	C₂×C₄	—	5	2	no	—
499	C₂×C₄	—	5	1	no	—
500	C₂×C₄	—	5	1	no	—
501	C₂×C₄	—	5	1	no	—
502	C₂×C₄	—	5	1	no	—
503	C₂×C₄	—	5	2	no	—
504	C₂×C₄	—	10	2	no	—
505	C₂×C₄	—	10	2	no	—
506	C₂×C₄	—	10	2	no	—
507	C₂×C₄	—	10	2	no	—
508	C₂×C₄	—	10	2	no	—
509	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
510	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
511	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
512	C₈	—	5	2	no	—
513	C₈	—	5	2	no	—
514	C₈	—	10	2	no	—
515	C₈	—	10	2	no	—
516	C₈	—	10	1	no	—
517	C₈	—	10	1	no	—
518	C₂×C₃	—	2	2	no	—
519	C₂×C₃	—	4	2	no	—
520	C₂×C₃	—	20	2	no	—
521	C₂×C₃	C₂×#4131	1	1	yes	characteristic
522	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
523	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
524	C₅	C₃×#2931	1	1	yes	characteristic, complemented, Sylow
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	10	2	no	—
531	C₂²	—	10	2	no	—
532	C₂²	—	10	2	no	—
533	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
534	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	2	2	no	—
537	C₄	—	5	1	no	—
538	C₄	—	5	1	no	—
539	C₄	—	5	2	no	—
540	C₄	—	5	2	no	—
541	C₄	—	10	2	no	—
542	C₄	—	10	1	no	—
543	C₄	C₃×#4131	1	2	yes	complemented
544	C₃	#10617227	1	1	yes	characteristic, direct product factor, Sylow
545	C₂	—	2	2	no	—
546	C₂	—	4	2	no	—
547	C₂	—	20	2	no	—
548	C₂	C₂×C₃×#4131	1	1	yes	characteristic
549	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
550	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×#65930	C₂
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#121	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2931
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
3. C₃×#65775	C₂	semidirect
4. C₃×#65774	C₂	semidirect
5. C₃×D₄×#170	C₂	semidirect
6. C₃×#65758	C₂	semidirect
7. C₂×C₃×C₄×#170	C₂	semidirect
8. C₃×#65705	C₂	semidirect
9. C₃×#65702	C₂	semidirect
10. C₃×#65695	C₂	semidirect
11. C₃×#65692	C₂	semidirect
12. #10617227	C₃	direct (N × H)
44. C₂×#4131	C₂×C₃	semidirect
46. #65775	C₂×C₃	semidirect
47. #65774	C₂×C₃	semidirect
48. D₄×#170	C₂×C₃	semidirect
49. #65758	C₂×C₃	semidirect
50. C₂×C₄×#170	C₂×C₃	semidirect
51. #65705	C₂×C₃	semidirect
52. #65702	C₂×C₃	semidirect
53. #65695	C₂×C₃	semidirect
54. #65692	C₂×C₃	semidirect
73. C₂×C₃×#170	D₄	semidirect
215. C₂×#170	C₃×D₄	semidirect
258. C₃×C₄×C₅	#131	semidirect
262. C₃×Dic₅	#131	semidirect
415. C₄×C₅	C₃×#131	semidirect
419. Dic₅	C₃×#131	semidirect
460. C₃×C₅	#2931	semidirect
479. C₃×C₄	#4131	semidirect
524. C₅	C₃×#2931	semidirect
543. C₄	C₃×#4131	semidirect
544. C₃	#10617227	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
C₃×#65930	2
C₃×#65775	2
C₃×#65774	2
C₃×D₄×#170	2
C₃×#65758	2
C₂×C₃×C₄×#170	2
C₃×#65705	2
C₃×#65702	2
C₃×#65695	2
C₃×#65692	2
#10617227	3
C₃×#2931	5

Subgroups — C3×#10617227 #14415238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617227 #14415238