Subgroups — C₃×#10617261 #14418481

Order 1920.

728 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65956	C₂	1	1	yes	maximal, characteristic
2	C₃×#65788	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Q₈×#170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65758	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×C₄×#170	C₂	1	1	yes	maximal, characteristic
6	C₃×#65709	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65707	C₂	1	2	yes	maximal, complemented
8	C₃×#65703	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65703	C₂	1	2	yes	maximal, complemented
10	C₃×#65696	C₂	1	2	yes	maximal
11	C₃×#65691	C₂	1	2	yes	maximal
12	#10617261	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#704	C₂²	1	2	yes	—
14	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#170	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
17	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
18	C₃×#4090	C₄	1	1	yes	characteristic
19	C₃×#4070	C₄	1	1	yes	characteristic
20	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
21	C₃×#4035	C₄	1	2	yes	—
22	C₃×#4034	C₄	1	1	yes	characteristic
23	C₃×#4033	C₂²	1	2	yes	—
24	C₃×#4033	C₂²	1	1	yes	characteristic
25	C₃×#4024	C₄	1	2	yes	—
26	C₃×#4023	C₂²	1	2	yes	—
27	C₃×#4004	C₂²	1	2	yes	—
28	C₃×#4004	C₂²	1	2	yes	—
29	C₃×#4004	C₂²	1	2	yes	—
30	C₃×#4002	C₂²	1	2	yes	—
31	C₃×#4002	C₂²	1	2	yes	—
32	C₃×C₄⋊#170	C₂²	1	2	yes	—
33	C₃×C₄⋊#170	C₂²	1	2	yes	—
34	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
35	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
36	C₃×C₄×#170	C₂²	1	2	yes	—
37	C₃×C₄×#170	C₂²	1	2	yes	—
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×#2960	—	5	1	no	maximal, Hall
43	#65956	C₂×C₃	1	1	yes	characteristic
44	#65788	C₂×C₃	1	1	yes	characteristic, complemented
45	Q₈×#170	C₂×C₃	1	1	yes	characteristic, complemented
46	#65758	C₂×C₃	1	1	yes	characteristic
47	C₂×C₄×#170	C₂×C₃	1	1	yes	characteristic
48	#65709	C₂×C₃	1	1	yes	characteristic, complemented
49	#65707	C₂×C₃	1	2	yes	complemented
50	#65703	C₂×C₃	1	1	yes	characteristic, complemented
51	#65703	C₂×C₃	1	2	yes	complemented
52	#65696	C₂×C₃	1	2	yes	—
53	#65691	C₂×C₃	1	2	yes	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
60	C₃×#704	—	2	4	no	—
61	C₂×C₃×#170	—	2	2	no	—
62	C₂×C₃×#170	Q₈	1	4	yes	complemented
63	C₂×C₃×#170	C₂³	1	1	yes	characteristic
64	C₂×C₃×#170	C₂³	1	1	yes	characteristic
65	C₂×C₃×#170	C₂³	1	2	yes	—
66	C₂×C₃×#170	C₂³	1	2	yes	—
67	C₂×C₃×#170	C₂³	1	1	yes	characteristic
68	C₂×C₃×#170	C₂³	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
71	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
73	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
74	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₃×#683	C₂×C₄	1	2	yes	—
76	C₃×#683	C₂×C₄	1	2	yes	—
77	C₃×#683	C₂×C₄	1	2	yes	—
78	C₃×#683	C₂×C₄	1	2	yes	—
79	C₃×#683	C₂×C₄	1	2	yes	—
80	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	C₃×C₄×Dic₅	C₂³	1	2	yes	—
84	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
85	C₃×C₄×Dic₅	C₂³	1	2	yes	—
86	C₃×#533	—	5	1	no	—
87	C₃×#446	—	5	2	no	—
88	C₃×#446	—	5	1	no	—
89	C₃×#446	—	5	1	no	—
90	C₃×C₈×Q₈	—	5	1	no	—
91	C₃×C₈×Q₈	—	5	2	no	—
92	C₃×C₈×Q₈	—	5	1	no	—
93	C₃×#424	—	5	2	no	—
94	C₃×#423	—	5	1	no	—
95	C₃×#405	—	5	2	no	—
96	C₂×C₃×C₄×C₈	—	5	1	no	—
97	C₂×#704	C₂²×C₃	1	2	yes	—
98	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
99	C₂²×#170	C₂²×C₃	1	1	yes	characteristic
100	C₅×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
101	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
102	#4090	C₃×C₄	1	1	yes	characteristic
103	#4070	C₃×C₄	1	1	yes	characteristic
104	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
105	#4035	C₃×C₄	1	2	yes	—
106	#4034	C₃×C₄	1	1	yes	characteristic
107	#4033	C₂²×C₃	1	2	yes	—
108	#4033	C₂²×C₃	1	1	yes	characteristic
109	#4024	C₃×C₄	1	2	yes	—
110	#4023	C₂²×C₃	1	2	yes	—
111	#4004	C₂²×C₃	1	2	yes	—
112	#4004	C₂²×C₃	1	2	yes	—
113	#4004	C₂²×C₃	1	2	yes	—
114	#4002	C₂²×C₃	1	2	yes	—
115	#4002	C₂²×C₃	1	2	yes	—
116	C₄⋊#170	C₂²×C₃	1	2	yes	—
117	C₄⋊#170	C₂²×C₃	1	2	yes	—
118	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
119	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
120	C₄×#170	C₂²×C₃	1	2	yes	—
121	C₄×#170	C₂²×C₃	1	2	yes	—
122	C₄×#170	C₂²×C₃	1	1	yes	characteristic
123	C₄×#170	C₂²×C₃	1	1	yes	characteristic
124	C₄×#170	C₂²×C₃	1	1	yes	characteristic
125	C₄×#170	C₂²×C₃	1	1	yes	characteristic
126	#2960	—	5	1	no	Sylow
127	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₃×C₅×Q₈	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×Dic₅	—	2	2	no	—
135	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
137	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₃×Dic₅	C₂×Q₈	1	2	yes	—
141	C₂×C₃×Dic₅	#41	1	2	yes	—
142	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
143	C₃×Dic₁₀	—	2	2	no	—
144	C₃×Dic₁₀	—	2	4	no	—
145	C₃×#170	—	2	1	no	—
146	C₃×#170	—	2	1	no	—
147	C₃×#170	—	2	2	no	—
148	C₃×#170	—	2	2	no	—
149	C₃×#170	C₂×Q₈	1	2	yes	—
150	C₃×#170	C₂×Q₈	1	2	yes	—
151	C₂×C₃×M₁₆	—	5	2	no	—
152	C₂²×C₃×C₈	—	5	1	no	—
153	C₂²×C₃×C₈	—	5	1	no	—
154	C₃×C₄⋊Q₈	—	5	1	no	—
155	C₃×C₄⋊Q₈	—	5	1	no	—
156	C₃×#125	—	5	2	no	—
157	C₃×C₂²⋊Q₈	—	5	1	no	—
158	C₃×C₂²⋊Q₈	—	5	2	no	—
159	C₃×C₂²⋊Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic
160	C₃×C₄×Q₈	—	5	1	no	—
161	C₃×C₄×Q₈	—	5	1	no	—
162	C₃×C₄×Q₈	—	5	2	no	—
163	C₃×#117	—	5	2	no	—
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₃×C₄⋊C₈	—	5	1	no	—
166	C₃×C₄⋊C₈	—	5	1	no	—
167	C₃×C₄⋊C₈	—	5	2	no	—
168	C₃×C₄⋊C₈	—	5	2	no	—
169	C₃×C₄⋊C₈	—	5	2	no	—
170	C₃×C₄⋊C₈	—	5	2	no	—
171	C₃×C₄⋊C₈	—	5	2	no	—
172	C₃×#97	—	5	2	no	—
173	C₃×#97	—	5	2	no	—
174	C₃×C₄×C₈	—	5	1	no	—
175	C₃×C₄×C₈	—	5	1	no	—
176	C₃×C₄×C₈	—	5	1	no	—
177	C₃×C₄×C₈	—	5	1	no	—
178	C₃×C₄×C₈	—	5	2	no	—
179	C₃×C₄×C₈	—	5	2	no	—
180	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
182	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
183	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
184	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
185	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
186	#704	—	2	4	no	—
187	C₂×#170	—	2	2	no	—
188	C₂×#170	C₃×Q₈	1	4	yes	complemented
189	C₂×#170	C₂³×C₃	1	1	yes	characteristic
190	C₂×#170	C₂³×C₃	1	1	yes	characteristic
191	C₂×#170	C₂³×C₃	1	2	yes	—
192	C₂×#170	C₂³×C₃	1	2	yes	—
193	C₂×#170	C₂³×C₃	1	1	yes	characteristic
194	C₂×#170	C₂³×C₃	1	1	yes	characteristic
195	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
196	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
197	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
198	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
199	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
200	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
201	#683	C₂×C₃×C₄	1	2	yes	—
202	#683	C₂×C₃×C₄	1	2	yes	—
203	#683	C₂×C₃×C₄	1	2	yes	—
204	#683	C₂×C₃×C₄	1	2	yes	—
205	#683	C₂×C₃×C₄	1	2	yes	—
206	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
207	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
208	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
209	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
210	C₄×Dic₅	C₂³×C₃	1	2	yes	—
211	C₄×Dic₅	C₂³×C₃	1	2	yes	—
212	#533	—	5	1	no	—
213	#446	—	5	2	no	—
214	#446	—	5	1	no	—
215	#446	—	5	1	no	—
216	C₈×Q₈	—	5	1	no	—
217	C₈×Q₈	—	5	2	no	—
218	C₈×Q₈	—	5	1	no	—
219	#424	—	5	2	no	—
220	#423	—	5	1	no	—
221	#405	—	5	2	no	—
222	C₂×C₄×C₈	—	5	1	no	—
223	C₂²×C₃×C₅	—	2	1	no	—
224	C₂²×C₃×C₅	—	2	1	no	—
225	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
226	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	2	1	no	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	#131	1	2	yes	—
231	C₃×Dic₅	—	2	2	no	—
232	C₃×Dic₅	—	2	2	no	—
233	C₃×Dic₅	—	2	1	no	—
234	C₃×Dic₅	C₄×Q₈	1	2	yes	—
235	C₃×Dic₅	#131	1	2	yes	—
236	C₃×Dic₅	C₂²×Q₈	1	1	yes	characteristic
237	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
238	C₂×C₃×Q₈	—	5	2	no	—
239	C₂×C₃×Q₈	—	5	1	no	—
240	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
241	C₂²×C₃×C₄	—	5	1	no	—
242	C₂²×C₃×C₄	—	5	1	no	—
243	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
244	C₃×M₁₆	—	10	4	no	—
245	C₂×C₃×C₈	—	5	1	no	—
246	C₂×C₃×C₈	—	5	1	no	—
247	C₂×C₃×C₈	—	5	4	no	—
248	C₂×C₃×C₈	—	5	1	no	—
249	C₂×C₃×C₈	—	5	1	no	—
250	C₂×C₃×C₈	—	5	2	no	—
251	C₂×C₃×C₈	—	5	2	no	—
252	C₂×C₃×C₈	—	10	2	no	—
253	C₃×C₄⋊C₄	—	5	2	no	—
254	C₃×C₄⋊C₄	—	5	2	no	—
255	C₃×C₄⋊C₄	—	5	2	no	—
256	C₃×C₄⋊C₄	—	5	2	no	—
257	C₃×C₄⋊C₄	—	5	2	no	—
258	C₃×C₄⋊C₄	—	5	2	no	—
259	C₃×C₄⋊C₄	—	5	1	no	—
260	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
261	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
262	C₃×C₂²⋊C₄	—	5	2	no	—
263	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
264	C₃×C₄²	—	5	1	no	—
265	C₃×C₄²	—	5	1	no	—
266	C₃×C₄²	—	5	1	no	—
267	C₃×C₄²	—	5	1	no	—
268	C₃×C₄²	—	5	2	no	—
269	C₃×C₄²	—	5	2	no	—
270	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
271	C₅×Q₈	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
275	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
276	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
277	C₂×Dic₅	—	2	2	no	—
278	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
279	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
280	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
281	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
282	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
283	C₂×Dic₅	C₂×C₃×Q₈	1	2	yes	—
284	C₂×Dic₅	C₃×#41	1	2	yes	—
285	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
286	Dic₁₀	—	2	2	no	—
287	Dic₁₀	—	2	4	no	—
288	#170	—	2	1	no	—
289	#170	—	2	1	no	—
290	#170	—	2	2	no	—
291	#170	—	2	2	no	—
292	#170	C₂×C₃×Q₈	1	2	yes	—
293	#170	C₂×C₃×Q₈	1	2	yes	—
294	C₂×M₁₆	—	5	2	no	—
295	C₂²×C₈	—	5	1	no	—
296	C₂²×C₈	—	5	1	no	—
297	C₄⋊Q₈	—	5	1	no	—
298	C₄⋊Q₈	—	5	1	no	—
299	#125	—	5	2	no	—
300	C₂²⋊Q₈	—	5	1	no	—
301	C₂²⋊Q₈	—	5	2	no	—
302	C₂²⋊Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
303	C₄×Q₈	—	5	1	no	—
304	C₄×Q₈	—	5	1	no	—
305	C₄×Q₈	—	5	2	no	—
306	#117	—	5	2	no	—
307	C₂×C₄²	—	5	1	no	—
308	C₄⋊C₈	—	5	1	no	—
309	C₄⋊C₈	—	5	1	no	—
310	C₄⋊C₈	—	5	2	no	—
311	C₄⋊C₈	—	5	2	no	—
312	C₄⋊C₈	—	5	2	no	—
313	C₄⋊C₈	—	5	2	no	—
314	C₄⋊C₈	—	5	2	no	—
315	#97	—	5	2	no	—
316	#97	—	5	2	no	—
317	C₄×C₈	—	5	1	no	—
318	C₄×C₈	—	5	1	no	—
319	C₄×C₈	—	5	1	no	—
320	C₄×C₈	—	5	1	no	—
321	C₄×C₈	—	5	2	no	—
322	C₄×C₈	—	5	2	no	—
323	C₂×C₃×C₅	—	2	2	no	—
324	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
325	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
326	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
327	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
328	C₃×Q₈	—	2	2	no	—
329	C₃×Q₈	—	10	4	no	—
330	C₃×Q₈	—	10	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	5	2	no	—
333	C₂×C₃×C₄	—	5	2	no	—
334	C₂×C₃×C₄	—	5	1	no	—
335	C₂×C₃×C₄	—	5	1	no	—
336	C₂×C₃×C₄	—	5	1	no	—
337	C₂×C₃×C₄	—	5	1	no	—
338	C₂×C₃×C₄	—	5	2	no	—
339	C₂×C₃×C₄	—	5	2	no	—
340	C₂×C₃×C₄	—	10	2	no	—
341	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
343	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
344	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
345	C₃×C₈	—	5	2	no	—
346	C₃×C₈	—	5	2	no	—
347	C₃×C₈	—	10	1	no	—
348	C₃×C₈	—	10	1	no	—
349	C₃×C₈	—	10	2	no	—
350	C₃×C₈	—	10	2	no	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	1	no	—
353	C₂²×C₅	C₃×C₄×Q₈	1	2	yes	—
354	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	1	no	—
357	C₄×C₅	—	2	2	no	—
358	C₄×C₅	C₃×#131	1	2	yes	—
359	Dic₅	—	2	2	no	—
360	Dic₅	—	2	2	no	—
361	Dic₅	—	2	1	no	—
362	Dic₅	C₃×C₄×Q₈	1	2	yes	—
363	Dic₅	C₃×#131	1	2	yes	—
364	Dic₅	C₂²×C₃×Q₈	1	1	yes	characteristic
365	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
366	C₂×Q₈	—	5	2	no	—
367	C₂×Q₈	—	5	1	no	—
368	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
369	C₂²×C₄	—	5	1	no	—
370	C₂²×C₄	—	5	1	no	—
371	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
372	M₁₆	—	10	4	no	—
373	C₂×C₈	—	5	1	no	—
374	C₂×C₈	—	5	1	no	—
375	C₂×C₈	—	5	4	no	—
376	C₂×C₈	—	5	1	no	—
377	C₂×C₈	—	5	1	no	—
378	C₂×C₈	—	5	2	no	—
379	C₂×C₈	—	5	2	no	—
380	C₂×C₈	—	10	2	no	—
381	C₄⋊C₄	—	5	2	no	—
382	C₄⋊C₄	—	5	2	no	—
383	C₄⋊C₄	—	5	2	no	—
384	C₄⋊C₄	—	5	2	no	—
385	C₄⋊C₄	—	5	2	no	—
386	C₄⋊C₄	—	5	2	no	—
387	C₄⋊C₄	—	5	1	no	—
388	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
389	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
390	C₂²⋊C₄	—	5	2	no	—
391	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
392	C₄²	—	5	1	no	—
393	C₄²	—	5	1	no	—
394	C₄²	—	5	2	no	—
395	C₄²	—	5	2	no	—
396	C₄²	—	5	1	no	—
397	C₄²	—	5	1	no	—
398	C₃×C₅	#2960	1	1	yes	characteristic, complemented, Hall
399	C₂²×C₃	—	2	1	no	—
400	C₂²×C₃	—	2	1	no	—
401	C₂²×C₃	Q₈×AGL(1,𝔽₅)	1	2	yes	—
402	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₃×C₄	—	2	1	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	5	2	no	—
407	C₃×C₄	—	5	1	no	—
408	C₃×C₄	—	5	1	no	—
409	C₃×C₄	—	5	2	no	—
410	C₃×C₄	—	10	2	no	—
411	C₃×C₄	—	10	1	no	—
412	C₃×C₄	—	10	2	no	—
413	C₃×C₄	#4131	1	2	yes	—
414	C₂×C₅	—	2	2	no	—
415	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
416	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
417	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
418	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
419	Q₈	—	2	2	no	—
420	Q₈	—	10	4	no	—
421	Q₈	—	10	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	5	2	no	—
424	C₂×C₄	—	5	2	no	—
425	C₂×C₄	—	5	1	no	—
426	C₂×C₄	—	5	1	no	—
427	C₂×C₄	—	5	1	no	—
428	C₂×C₄	—	5	1	no	—
429	C₂×C₄	—	5	2	no	—
430	C₂×C₄	—	5	2	no	—
431	C₂×C₄	—	10	2	no	—
432	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
434	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
435	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
436	C₈	—	5	2	no	—
437	C₈	—	5	2	no	—
438	C₈	—	10	1	no	—
439	C₈	—	10	1	no	—
440	C₈	—	10	2	no	—
441	C₈	—	10	2	no	—
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	C₂×#4131	1	1	yes	characteristic
444	C₂×C₃	C₂×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
445	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
446	C₅	C₃×#2960	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	C₃×Q₈×AGL(1,𝔽₅)	1	2	yes	—
450	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	5	1	no	—
455	C₄	—	5	1	no	—
456	C₄	—	5	2	no	—
457	C₄	—	5	2	no	—
458	C₄	—	10	2	no	—
459	C₄	—	10	1	no	—
460	C₄	—	10	2	no	—
461	C₄	C₃×#4131	1	2	yes	—
462	C₃	#10617261	1	1	yes	characteristic, direct product factor, Sylow
463	C₂	—	2	2	no	—
464	C₂	C₂×C₃×#4131	1	1	yes	characteristic
465	C₂	C₂×C₃×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
466	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×C₂²⋊Q₈	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×C₂²⋊Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2960
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₃×#65788	C₂	semidirect
3. C₃×Q₈×#170	C₂	semidirect
6. C₃×#65709	C₂	semidirect
7. C₃×#65707	C₂	semidirect
8. C₃×#65703	C₂	semidirect
9. C₃×#65703	C₂	semidirect
12. #10617261	C₃	direct (N × H)
44. #65788	C₂×C₃	semidirect
45. Q₈×#170	C₂×C₃	semidirect
48. #65709	C₂×C₃	semidirect
49. #65707	C₂×C₃	semidirect
50. #65703	C₂×C₃	semidirect
51. #65703	C₂×C₃	semidirect
62. C₂×C₃×#170	Q₈	semidirect
188. C₂×#170	C₃×Q₈	semidirect
398. C₃×C₅	#2960	semidirect
446. C₅	C₃×#2960	semidirect
462. C₃	#10617261	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×#65956	2
C₃×#65788	2
C₃×Q₈×#170	2
C₃×#65758	2
C₂×C₃×C₄×#170	2
C₃×#65709	2
C₃×#65707	2
C₃×#65703	2
C₃×#65696	2
C₃×#65691	2
#10617261	3
C₃×#2960	5

Subgroups — C3×#10617261 #14418481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617261 #14418481