Subgroups — C₃×#10617292 #14419155

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65983	C₂	1	1	yes	maximal, characteristic
2	C₃×#65773	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65757	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65707	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65706	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65703	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65701	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65697	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65695	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65693	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65692	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65692	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65691	C₂	1	1	yes	maximal, characteristic, complemented
16	#10617292	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×#704	C₂²	1	1	yes	characteristic
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
21	C₂×C₃×#700	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#123	C₄	1	1	yes	characteristic
24	C₃×#4085	C₄	1	1	yes	characteristic
25	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₃×#4075	C₄	1	1	yes	characteristic
27	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₃×#4044	C₄	1	1	yes	characteristic
29	C₃×#4038	C₂²	1	1	yes	characteristic
30	C₃×#4035	C₄	1	1	yes	characteristic
31	C₃×#4033	C₂²	1	1	yes	characteristic
32	C₃×#4031	C₄	1	1	yes	characteristic
33	C₃×#4027	C₂²	1	1	yes	characteristic
34	C₃×#4027	C₂²	1	1	yes	characteristic
35	C₃×#4025	C₄	1	1	yes	characteristic
36	C₃×#4024	C₄	1	1	yes	characteristic
37	C₃×#4023	C₂²	1	1	yes	characteristic
38	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
39	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
40	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
41	C₃×C₂²⋊#170	C₂²	1	1	yes	characteristic
42	C₃×#4004	C₂²	1	1	yes	characteristic
43	C₃×#4004	C₂²	1	1	yes	characteristic
44	C₃×#4004	C₂²	1	1	yes	characteristic
45	C₃×#4004	C₂²	1	1	yes	characteristic
46	C₃×#4003	C₂²	1	1	yes	characteristic
47	C₃×#4003	C₂²	1	1	yes	characteristic
48	C₃×#4002	C₂²	1	1	yes	characteristic
49	C₃×#4002	C₂²	1	1	yes	characteristic
50	C₃×#4002	C₂²	1	1	yes	characteristic
51	C₃×#4002	C₂²	1	1	yes	characteristic
52	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
53	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
54	C₃×C₄×#170	C₂²	1	1	yes	characteristic
55	C₃×C₄×#170	C₂²	1	1	yes	characteristic
56	C₃×C₄×#170	C₂²	1	1	yes	characteristic
57	C₃×C₄×#170	C₂²	1	1	yes	characteristic
58	C₃×C₄×#170	C₂²	1	1	yes	characteristic
59	C₃×C₄×#170	C₂²	1	1	yes	characteristic
60	C₃×#2966	—	5	1	no	maximal, Hall
61	#65983	C₂×C₃	1	1	yes	characteristic
62	#65773	C₂×C₃	1	1	yes	characteristic, complemented
63	D₄×#170	C₂×C₃	1	1	yes	characteristic, complemented
64	#65757	C₂×C₃	1	1	yes	characteristic, complemented
65	C₂×C₄×#170	C₂×C₃	1	1	yes	characteristic, complemented
66	#65707	C₂×C₃	1	1	yes	characteristic, complemented
67	#65706	C₂×C₃	1	1	yes	characteristic, complemented
68	#65703	C₂×C₃	1	1	yes	characteristic, complemented
69	#65701	C₂×C₃	1	1	yes	characteristic, complemented
70	#65697	C₂×C₃	1	1	yes	characteristic, complemented
71	#65695	C₂×C₃	1	1	yes	characteristic, complemented
72	#65693	C₂×C₃	1	1	yes	characteristic, complemented
73	#65692	C₂×C₃	1	1	yes	characteristic, complemented
74	#65692	C₂×C₃	1	1	yes	characteristic, complemented
75	#65691	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
85	C₃×#704	—	2	2	no	—
86	C₂×C₃×#170	—	2	2	no	—
87	C₂×C₃×#170	—	2	2	no	—
88	C₂×C₃×#170	—	2	2	no	—
89	C₂×C₃×#170	C₂³	1	1	yes	characteristic
90	C₂×C₃×#170	C₂³	1	1	yes	characteristic
91	C₂×C₃×#170	C₂³	1	1	yes	characteristic
92	C₂×C₃×#170	C₂³	1	1	yes	characteristic
93	C₂×C₃×#170	C₂³	1	1	yes	characteristic
94	C₂×C₃×#170	C₂³	1	1	yes	characteristic
95	C₂×C₃×#170	C₂³	1	1	yes	characteristic
96	C₂×C₃×#170	C₂³	1	1	yes	characteristic
97	C₃×#700	—	2	2	no	—
98	C₃×D₅⋊C₈	—	2	2	no	—
99	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
105	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
106	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
107	C₃×#685	C₂×C₄	1	1	yes	characteristic
108	C₃×#685	C₂×C₄	1	1	yes	characteristic
109	C₃×#685	C₂×C₄	1	1	yes	characteristic
110	C₃×#685	C₂×C₄	1	1	yes	characteristic
111	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
112	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
113	C₃×#683	C₂×C₄	1	1	yes	characteristic
114	C₃×#683	C₂×C₄	1	1	yes	characteristic
115	C₃×#683	C₂×C₄	1	1	yes	characteristic
116	C₃×#683	C₂×C₄	1	1	yes	characteristic
117	C₃×#683	C₂×C₄	1	1	yes	characteristic
118	C₃×#683	C₂×C₄	1	1	yes	characteristic
119	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
120	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
121	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
122	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
123	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
124	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
125	C₃×#529	—	5	1	no	—
126	C₃×#446	—	5	1	no	—
127	C₃×C₈×Q₈	—	5	1	no	—
128	C₃×#436	—	5	1	no	—
129	C₃×#435	—	5	1	no	—
130	C₃×#435	—	5	1	no	—
131	C₃×C₈×D₄	—	5	1	no	—
132	C₃×C₈×D₄	—	5	1	no	—
133	C₃×C₈×D₄	—	5	1	no	—
134	C₃×#433	—	5	1	no	—
135	C₃×#433	—	5	1	no	—
136	C₃×#432	—	5	1	no	—
137	C₃×#405	—	5	1	no	—
138	C₃×#405	—	5	1	no	—
139	C₂×C₃×C₄×C₈	—	5	1	no	—
140	C₂×#704	C₂²×C₃	1	1	yes	characteristic
141	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
142	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
143	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
144	C₂×#700	C₂²×C₃	1	1	yes	characteristic
145	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
146	C₅×#123	C₃×C₄	1	1	yes	characteristic
147	#4085	C₃×C₄	1	1	yes	characteristic
148	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
149	#4075	C₃×C₄	1	1	yes	characteristic
150	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
151	#4044	C₃×C₄	1	1	yes	characteristic
152	#4038	C₂²×C₃	1	1	yes	characteristic
153	#4035	C₃×C₄	1	1	yes	characteristic
154	#4033	C₂²×C₃	1	1	yes	characteristic
155	#4031	C₃×C₄	1	1	yes	characteristic
156	#4027	C₂²×C₃	1	1	yes	characteristic
157	#4027	C₂²×C₃	1	1	yes	characteristic
158	#4025	C₃×C₄	1	1	yes	characteristic
159	#4024	C₃×C₄	1	1	yes	characteristic
160	#4023	C₂²×C₃	1	1	yes	characteristic
161	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
162	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
163	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
164	C₂²⋊#170	C₂²×C₃	1	1	yes	characteristic
165	#4004	C₂²×C₃	1	1	yes	characteristic
166	#4004	C₂²×C₃	1	1	yes	characteristic
167	#4004	C₂²×C₃	1	1	yes	characteristic
168	#4004	C₂²×C₃	1	1	yes	characteristic
169	#4003	C₂²×C₃	1	1	yes	characteristic
170	#4003	C₂²×C₃	1	1	yes	characteristic
171	#4002	C₂²×C₃	1	1	yes	characteristic
172	#4002	C₂²×C₃	1	1	yes	characteristic
173	#4002	C₂²×C₃	1	1	yes	characteristic
174	#4002	C₂²×C₃	1	1	yes	characteristic
175	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
176	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
177	C₄×#170	C₂²×C₃	1	1	yes	characteristic
178	C₄×#170	C₂²×C₃	1	1	yes	characteristic
179	C₄×#170	C₂²×C₃	1	1	yes	characteristic
180	C₄×#170	C₂²×C₃	1	1	yes	characteristic
181	C₄×#170	C₂²×C₃	1	1	yes	characteristic
182	C₄×#170	C₂²×C₃	1	1	yes	characteristic
183	#2966	—	5	1	no	Sylow
184	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
185	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
187	C₃×C₅×D₄	—	2	2	no	—
188	C₂×C₃×C₄×C₅	—	2	2	no	—
189	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
194	C₃×C₂²⋊D₅	—	2	2	no	—
195	C₃×C₂²⋊D₅	—	2	2	no	—
196	C₂×C₃×Dic₅	—	2	2	no	—
197	C₂×C₃×Dic₅	—	2	1	no	—
198	C₂×C₃×Dic₅	—	2	1	no	—
199	C₂×C₃×Dic₅	—	2	1	no	—
200	C₂×C₃×Dic₅	—	2	1	no	—
201	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
208	C₃×C₄×D₅	—	2	1	no	—
209	C₃×C₄×D₅	—	2	1	no	—
210	C₃×Dic₁₀	—	2	2	no	—
211	C₃×#170	—	2	1	no	—
212	C₃×#170	—	2	1	no	—
213	C₃×#170	—	2	1	no	—
214	C₃×#170	—	2	1	no	—
215	C₃×#170	—	2	1	no	—
216	C₃×#170	—	2	1	no	—
217	C₃×#170	#41	1	2	yes	—
218	C₃×#170	#41	1	2	yes	—
219	C₂×C₃×M₁₆	—	5	1	no	—
220	C₂×C₃×M₁₆	—	5	1	no	—
221	C₂²×C₃×C₈	—	5	1	no	—
222	C₂²×C₃×C₈	—	5	1	no	—
223	C₂²×C₃×C₈	—	5	1	no	—
224	C₂²×C₃×C₈	—	5	1	no	—
225	C₃×#126	—	5	1	no	—
226	C₃×#126	—	5	1	no	—
227	C₃×#125	—	5	1	no	—
228	C₃×#124	—	5	1	no	—
229	C₃×#123	—	5	1	no	—
230	C₃×#123	AGL(1,𝔽₅)	1	1	yes	characteristic
231	C₃×C₂²⋊Q₈	—	5	1	no	—
232	C₃×#121	—	5	1	no	—
233	C₃×C₄×Q₈	—	5	1	no	—
234	C₃×C₄×D₄	—	5	1	no	—
235	C₃×C₄×D₄	—	5	1	no	—
236	C₃×C₄×D₄	—	5	1	no	—
237	C₃×#117	—	5	1	no	—
238	C₃×#117	—	5	1	no	—
239	C₂×C₃×C₄²	—	5	1	no	—
240	C₃×C₄⋊C₈	—	5	1	no	—
241	C₃×C₄⋊C₈	—	5	1	no	—
242	C₃×C₄⋊C₈	—	5	1	no	—
243	C₃×C₄⋊C₈	—	5	1	no	—
244	C₃×C₄⋊C₈	—	5	1	no	—
245	C₃×C₄⋊C₈	—	5	1	no	—
246	C₃×C₂²⋊C₈	—	5	1	no	—
247	C₃×C₂²⋊C₈	—	5	1	no	—
248	C₃×C₂²⋊C₈	—	5	1	no	—
249	C₃×C₂²⋊C₈	—	5	1	no	—
250	C₃×C₂²⋊C₈	—	5	1	no	—
251	C₃×C₂²⋊C₈	—	5	1	no	—
252	C₃×#97	—	5	1	no	—
253	C₃×#97	—	5	1	no	—
254	C₃×#97	—	5	1	no	—
255	C₃×#97	—	5	1	no	—
256	C₃×C₄×C₈	—	5	1	no	—
257	C₃×C₄×C₈	—	5	1	no	—
258	C₃×C₄×C₈	—	5	1	no	—
259	C₃×C₄×C₈	—	5	1	no	—
260	C₃×C₄×C₈	—	5	1	no	—
261	C₃×C₄×C₈	—	5	1	no	—
262	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
263	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
264	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
265	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
266	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
267	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
268	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
270	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
271	#704	—	2	2	no	—
272	C₂×#170	—	2	2	no	—
273	C₂×#170	—	2	2	no	—
274	C₂×#170	—	2	2	no	—
275	C₂×#170	C₂³×C₃	1	1	yes	characteristic
276	C₂×#170	C₂³×C₃	1	1	yes	characteristic
277	C₂×#170	C₂³×C₃	1	1	yes	characteristic
278	C₂×#170	C₂³×C₃	1	1	yes	characteristic
279	C₂×#170	C₂³×C₃	1	1	yes	characteristic
280	C₂×#170	C₂³×C₃	1	1	yes	characteristic
281	C₂×#170	C₂³×C₃	1	1	yes	characteristic
282	C₂×#170	C₂³×C₃	1	1	yes	characteristic
283	#700	—	2	2	no	—
284	D₅⋊C₈	—	2	2	no	—
285	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
286	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
287	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
288	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
289	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
290	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
291	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
292	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
293	#685	C₂×C₃×C₄	1	1	yes	characteristic
294	#685	C₂×C₃×C₄	1	1	yes	characteristic
295	#685	C₂×C₃×C₄	1	1	yes	characteristic
296	#685	C₂×C₃×C₄	1	1	yes	characteristic
297	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
298	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
299	#683	C₂×C₃×C₄	1	1	yes	characteristic
300	#683	C₂×C₃×C₄	1	1	yes	characteristic
301	#683	C₂×C₃×C₄	1	1	yes	characteristic
302	#683	C₂×C₃×C₄	1	1	yes	characteristic
303	#683	C₂×C₃×C₄	1	1	yes	characteristic
304	#683	C₂×C₃×C₄	1	1	yes	characteristic
305	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
306	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
307	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
308	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
309	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
310	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
311	#529	—	5	1	no	—
312	#446	—	5	1	no	—
313	C₈×Q₈	—	5	1	no	—
314	#436	—	5	1	no	—
315	#435	—	5	1	no	—
316	#435	—	5	1	no	—
317	C₈×D₄	—	5	1	no	—
318	C₈×D₄	—	5	1	no	—
319	C₈×D₄	—	5	1	no	—
320	#433	—	5	1	no	—
321	#433	—	5	1	no	—
322	#432	—	5	1	no	—
323	#405	—	5	1	no	—
324	#405	—	5	1	no	—
325	C₂×C₄×C₈	—	5	1	no	—
326	C₂²×C₃×C₅	—	2	1	no	—
327	C₂²×C₃×C₅	—	2	1	no	—
328	C₂²×C₃×C₅	—	2	1	no	—
329	C₂²×C₃×C₅	—	2	1	no	—
330	C₂²×C₃×C₅	—	2	1	no	—
331	C₂²×C₃×C₅	#131	1	2	yes	—
332	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
333	C₂×C₃×D₅	—	2	1	no	—
334	C₂×C₃×D₅	—	2	1	no	—
335	C₂×C₃×D₅	—	2	1	no	—
336	C₃×C₄×C₅	—	2	1	no	—
337	C₃×C₄×C₅	—	2	1	no	—
338	C₃×C₄×C₅	—	2	1	no	—
339	C₃×C₄×C₅	—	2	1	no	—
340	C₃×C₄×C₅	—	2	1	no	—
341	C₃×Dic₅	—	2	1	no	—
342	C₃×Dic₅	—	2	1	no	—
343	C₃×Dic₅	—	2	1	no	—
344	C₃×Dic₅	—	2	1	no	—
345	C₃×Dic₅	—	2	1	no	—
346	C₃×Dic₅	#131	1	2	yes	—
347	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
348	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
349	C₂×C₃×Q₈	—	5	1	no	—
350	C₂×C₃×D₄	—	5	1	no	—
351	C₂×C₃×D₄	—	5	1	no	—
352	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
353	C₂²×C₃×C₄	—	5	1	no	—
354	C₂²×C₃×C₄	—	5	1	no	—
355	C₂²×C₃×C₄	—	5	1	no	—
356	C₂²×C₃×C₄	—	5	1	no	—
357	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
358	C₃×M₁₆	—	10	2	no	—
359	C₃×M₁₆	—	10	2	no	—
360	C₂×C₃×C₈	—	5	1	no	—
361	C₂×C₃×C₈	—	5	1	no	—
362	C₂×C₃×C₈	—	5	1	no	—
363	C₂×C₃×C₈	—	5	1	no	—
364	C₂×C₃×C₈	—	5	1	no	—
365	C₂×C₃×C₈	—	5	1	no	—
366	C₂×C₃×C₈	—	5	1	no	—
367	C₂×C₃×C₈	—	5	1	no	—
368	C₂×C₃×C₈	—	10	2	no	—
369	C₂×C₃×C₈	—	10	2	no	—
370	C₂×C₃×C₈	—	10	2	no	—
371	C₂×C₃×C₈	—	10	2	no	—
372	C₃×C₄⋊C₄	—	5	1	no	—
373	C₃×C₄⋊C₄	—	5	1	no	—
374	C₃×C₄⋊C₄	—	5	1	no	—
375	C₃×C₄⋊C₄	—	5	1	no	—
376	C₃×C₄⋊C₄	—	5	1	no	—
377	C₃×C₄⋊C₄	—	5	1	no	—
378	C₃×C₄⋊C₄	—	5	1	no	—
379	C₃×C₄⋊C₄	—	5	1	no	—
380	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
381	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
382	C₃×C₂²⋊C₄	—	5	1	no	—
383	C₃×C₂²⋊C₄	—	5	1	no	—
384	C₃×C₂²⋊C₄	—	5	1	no	—
385	C₃×C₂²⋊C₄	—	5	1	no	—
386	C₃×C₂²⋊C₄	—	5	1	no	—
387	C₃×C₂²⋊C₄	—	5	1	no	—
388	C₃×C₂²⋊C₄	—	5	1	no	—
389	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
390	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
391	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
392	C₃×C₄²	—	5	1	no	—
393	C₃×C₄²	—	5	1	no	—
394	C₃×C₄²	—	5	1	no	—
395	C₃×C₄²	—	5	1	no	—
396	C₃×C₄²	—	5	1	no	—
397	C₃×C₄²	—	5	1	no	—
398	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
399	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
400	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
401	C₅×D₄	—	2	2	no	—
402	C₂×C₄×C₅	—	2	2	no	—
403	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
404	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
405	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
406	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
407	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
408	C₂²⋊D₅	—	2	2	no	—
409	C₂²⋊D₅	—	2	2	no	—
410	C₂×Dic₅	—	2	2	no	—
411	C₂×Dic₅	—	2	1	no	—
412	C₂×Dic₅	—	2	1	no	—
413	C₂×Dic₅	—	2	1	no	—
414	C₂×Dic₅	—	2	1	no	—
415	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
416	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
417	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
418	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
419	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
420	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
421	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
422	C₄×D₅	—	2	1	no	—
423	C₄×D₅	—	2	1	no	—
424	Dic₁₀	—	2	2	no	—
425	#170	—	2	1	no	—
426	#170	—	2	1	no	—
427	#170	—	2	1	no	—
428	#170	—	2	1	no	—
429	#170	—	2	1	no	—
430	#170	—	2	1	no	—
431	#170	C₃×#41	1	2	yes	—
432	#170	C₃×#41	1	2	yes	—
433	C₂×M₁₆	—	5	1	no	—
434	C₂×M₁₆	—	5	1	no	—
435	C₂²×C₈	—	5	1	no	—
436	C₂²×C₈	—	5	1	no	—
437	C₂²×C₈	—	5	1	no	—
438	C₂²×C₈	—	5	1	no	—
439	#126	—	5	1	no	—
440	#126	—	5	1	no	—
441	#125	—	5	1	no	—
442	#124	—	5	1	no	—
443	#123	—	5	1	no	—
444	#123	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
445	C₂²⋊Q₈	—	5	1	no	—
446	#121	—	5	1	no	—
447	C₄×Q₈	—	5	1	no	—
448	C₄×D₄	—	5	1	no	—
449	C₄×D₄	—	5	1	no	—
450	C₄×D₄	—	5	1	no	—
451	#117	—	5	1	no	—
452	#117	—	5	1	no	—
453	C₂×C₄²	—	5	1	no	—
454	C₄⋊C₈	—	5	1	no	—
455	C₄⋊C₈	—	5	1	no	—
456	C₄⋊C₈	—	5	1	no	—
457	C₄⋊C₈	—	5	1	no	—
458	C₄⋊C₈	—	5	1	no	—
459	C₄⋊C₈	—	5	1	no	—
460	C₂²⋊C₈	—	5	1	no	—
461	C₂²⋊C₈	—	5	1	no	—
462	C₂²⋊C₈	—	5	1	no	—
463	C₂²⋊C₈	—	5	1	no	—
464	C₂²⋊C₈	—	5	1	no	—
465	C₂²⋊C₈	—	5	1	no	—
466	#97	—	5	1	no	—
467	#97	—	5	1	no	—
468	#97	—	5	1	no	—
469	#97	—	5	1	no	—
470	C₄×C₈	—	5	1	no	—
471	C₄×C₈	—	5	1	no	—
472	C₄×C₈	—	5	1	no	—
473	C₄×C₈	—	5	1	no	—
474	C₄×C₈	—	5	1	no	—
475	C₄×C₈	—	5	1	no	—
476	C₂×C₃×C₅	—	2	2	no	—
477	C₂×C₃×C₅	—	4	1	no	—
478	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
479	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
480	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
481	C₃×D₅	—	4	1	no	—
482	C₂³×C₃	—	5	1	no	—
483	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
484	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
485	C₃×Q₈	—	10	2	no	—
486	C₃×D₄	—	2	2	no	—
487	C₃×D₄	—	10	2	no	—
488	C₃×D₄	—	10	2	no	—
489	C₂×C₃×C₄	—	2	2	no	—
490	C₂×C₃×C₄	—	5	1	no	—
491	C₂×C₃×C₄	—	5	1	no	—
492	C₂×C₃×C₄	—	5	1	no	—
493	C₂×C₃×C₄	—	5	1	no	—
494	C₂×C₃×C₄	—	5	1	no	—
495	C₂×C₃×C₄	—	5	1	no	—
496	C₂×C₃×C₄	—	5	1	no	—
497	C₂×C₃×C₄	—	10	1	no	—
498	C₂×C₃×C₄	—	10	1	no	—
499	C₂×C₃×C₄	—	10	1	no	—
500	C₂×C₃×C₄	—	10	1	no	—
501	C₂×C₃×C₄	—	10	1	no	—
502	C₂×C₃×C₄	—	10	1	no	—
503	C₂×C₃×C₄	—	10	2	no	—
504	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
507	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
508	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
509	C₃×C₈	—	5	2	no	—
510	C₃×C₈	—	5	2	no	—
511	C₃×C₈	—	10	1	no	—
512	C₃×C₈	—	10	1	no	—
513	C₃×C₈	—	10	1	no	—
514	C₃×C₈	—	10	1	no	—
515	C₃×C₈	—	10	1	no	—
516	C₃×C₈	—	10	1	no	—
517	C₂²×C₅	—	2	1	no	—
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	—	2	1	no	—
521	C₂²×C₅	—	2	1	no	—
522	C₂²×C₅	C₃×#131	1	2	yes	—
523	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
524	C₂×D₅	—	2	1	no	—
525	C₂×D₅	—	2	1	no	—
526	C₂×D₅	—	2	1	no	—
527	C₄×C₅	—	2	1	no	—
528	C₄×C₅	—	2	1	no	—
529	C₄×C₅	—	2	1	no	—
530	C₄×C₅	—	2	1	no	—
531	C₄×C₅	—	2	1	no	—
532	Dic₅	—	2	1	no	—
533	Dic₅	—	2	1	no	—
534	Dic₅	—	2	1	no	—
535	Dic₅	—	2	1	no	—
536	Dic₅	—	2	1	no	—
537	Dic₅	C₃×#131	1	2	yes	—
538	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
539	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
540	C₂×Q₈	—	5	1	no	—
541	C₂×D₄	—	5	1	no	—
542	C₂×D₄	—	5	1	no	—
543	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
544	C₂²×C₄	—	5	1	no	—
545	C₂²×C₄	—	5	1	no	—
546	C₂²×C₄	—	5	1	no	—
547	C₂²×C₄	—	5	1	no	—
548	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
549	M₁₆	—	10	2	no	—
550	M₁₆	—	10	2	no	—
551	C₂×C₈	—	5	1	no	—
552	C₂×C₈	—	5	1	no	—
553	C₂×C₈	—	5	1	no	—
554	C₂×C₈	—	5	1	no	—
555	C₂×C₈	—	5	1	no	—
556	C₂×C₈	—	5	1	no	—
557	C₂×C₈	—	5	1	no	—
558	C₂×C₈	—	5	1	no	—
559	C₂×C₈	—	10	2	no	—
560	C₂×C₈	—	10	2	no	—
561	C₂×C₈	—	10	2	no	—
562	C₂×C₈	—	10	2	no	—
563	C₄⋊C₄	—	5	1	no	—
564	C₄⋊C₄	—	5	1	no	—
565	C₄⋊C₄	—	5	1	no	—
566	C₄⋊C₄	—	5	1	no	—
567	C₄⋊C₄	—	5	1	no	—
568	C₄⋊C₄	—	5	1	no	—
569	C₄⋊C₄	—	5	1	no	—
570	C₄⋊C₄	—	5	1	no	—
571	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
572	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
573	C₂²⋊C₄	—	5	1	no	—
574	C₂²⋊C₄	—	5	1	no	—
575	C₂²⋊C₄	—	5	1	no	—
576	C₂²⋊C₄	—	5	1	no	—
577	C₂²⋊C₄	—	5	1	no	—
578	C₂²⋊C₄	—	5	1	no	—
579	C₂²⋊C₄	—	5	1	no	—
580	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
581	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
582	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
583	C₄²	—	5	1	no	—
584	C₄²	—	5	1	no	—
585	C₄²	—	5	1	no	—
586	C₄²	—	5	1	no	—
587	C₄²	—	5	1	no	—
588	C₄²	—	5	1	no	—
589	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
590	C₂²×C₃	—	2	1	no	—
591	C₂²×C₃	—	2	1	no	—
592	C₂²×C₃	—	2	1	no	—
593	C₂²×C₃	—	2	1	no	—
594	C₂²×C₃	—	2	1	no	—
595	C₂²×C₃	—	10	1	no	—
596	C₂²×C₃	—	10	1	no	—
597	C₂²×C₃	—	10	1	no	—
598	C₂²×C₃	#4131	1	2	yes	—
599	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	2	1	no	—
602	C₃×C₄	—	2	1	no	—
603	C₃×C₄	—	2	1	no	—
604	C₃×C₄	—	2	1	no	—
605	C₃×C₄	—	5	2	no	—
606	C₃×C₄	—	5	1	no	—
607	C₃×C₄	—	5	1	no	—
608	C₃×C₄	—	10	1	no	—
609	C₃×C₄	—	10	1	no	—
610	C₃×C₄	—	10	1	no	—
611	C₃×C₄	—	10	1	no	—
612	C₃×C₄	—	10	1	no	—
613	C₂×C₅	—	2	2	no	—
614	C₂×C₅	—	4	1	no	—
615	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
616	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
617	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
618	D₅	—	4	1	no	—
619	C₂³	—	5	1	no	—
620	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
621	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
622	Q₈	—	10	2	no	—
623	D₄	—	2	2	no	—
624	D₄	—	10	2	no	—
625	D₄	—	10	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	5	1	no	—
628	C₂×C₄	—	5	1	no	—
629	C₂×C₄	—	5	1	no	—
630	C₂×C₄	—	5	1	no	—
631	C₂×C₄	—	5	1	no	—
632	C₂×C₄	—	5	1	no	—
633	C₂×C₄	—	5	1	no	—
634	C₂×C₄	—	10	1	no	—
635	C₂×C₄	—	10	1	no	—
636	C₂×C₄	—	10	1	no	—
637	C₂×C₄	—	10	1	no	—
638	C₂×C₄	—	10	1	no	—
639	C₂×C₄	—	10	1	no	—
640	C₂×C₄	—	10	2	no	—
641	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
642	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
643	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
644	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
645	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
646	C₈	—	5	2	no	—
647	C₈	—	5	2	no	—
648	C₈	—	10	1	no	—
649	C₈	—	10	1	no	—
650	C₈	—	10	1	no	—
651	C₈	—	10	1	no	—
652	C₈	—	10	1	no	—
653	C₈	—	10	1	no	—
654	C₂×C₃	—	2	2	no	—
655	C₂×C₃	—	4	1	no	—
656	C₂×C₃	—	20	1	no	—
657	C₂×C₃	C₂×#4131	1	1	yes	characteristic
658	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
659	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
660	C₅	C₃×#2966	1	1	yes	characteristic, complemented, Sylow
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	10	1	no	—
667	C₂²	—	10	1	no	—
668	C₂²	—	10	1	no	—
669	C₂²	C₃×#4131	1	2	yes	—
670	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	5	2	no	—
677	C₄	—	5	1	no	—
678	C₄	—	5	1	no	—
679	C₄	—	10	1	no	—
680	C₄	—	10	1	no	—
681	C₄	—	10	1	no	—
682	C₄	—	10	1	no	—
683	C₄	—	10	1	no	—
684	C₃	#10617292	1	1	yes	characteristic, direct product factor, Sylow
685	C₂	—	2	2	no	—
686	C₂	—	4	1	no	—
687	C₂	—	20	1	no	—
688	C₂	C₂×C₃×#4131	1	1	yes	characteristic
689	C₂	C₃×D₅⋊#131	1	1	yes	characteristic
690	C₂	C₃×#41×AGL(1,𝔽₅)	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×#123	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#4085	C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#123	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2966
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
2. C₃×#65773	C₂	semidirect
3. C₃×D₄×#170	C₂	semidirect
4. C₃×#65757	C₂	semidirect
5. C₂×C₃×C₄×#170	C₂	semidirect
6. C₃×#65707	C₂	semidirect
7. C₃×#65706	C₂	semidirect
8. C₃×#65703	C₂	semidirect
9. C₃×#65701	C₂	semidirect
10. C₃×#65697	C₂	semidirect
11. C₃×#65695	C₂	semidirect
12. C₃×#65693	C₂	semidirect
13. C₃×#65692	C₂	semidirect
14. C₃×#65692	C₂	semidirect
15. C₃×#65691	C₂	semidirect
16. #10617292	C₃	direct (N × H)
62. #65773	C₂×C₃	semidirect
63. D₄×#170	C₂×C₃	semidirect
64. #65757	C₂×C₃	semidirect
65. C₂×C₄×#170	C₂×C₃	semidirect
66. #65707	C₂×C₃	semidirect
67. #65706	C₂×C₃	semidirect
68. #65703	C₂×C₃	semidirect
69. #65701	C₂×C₃	semidirect
70. #65697	C₂×C₃	semidirect
71. #65695	C₂×C₃	semidirect
72. #65693	C₂×C₃	semidirect
73. #65692	C₂×C₃	semidirect
74. #65692	C₂×C₃	semidirect
75. #65691	C₂×C₃	semidirect
589. C₃×C₅	#2966	semidirect
660. C₅	C₃×#2966	semidirect
684. C₃	#10617292	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#65983	2
C₃×#65773	2
C₃×D₄×#170	2
C₃×#65757	2
C₂×C₃×C₄×#170	2
C₃×#65707	2
C₃×#65706	2
C₃×#65703	2
C₃×#65701	2
C₃×#65697	2
C₃×#65695	2
C₃×#65693	2
C₃×#65692	2
C₃×#65691	2
#10617292	3
C₃×#2966	5

Subgroups — C3×#10617292 #14419155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617292 #14419155