Subgroups — C₃×#10617137 #14413176

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 448 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
2	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic
3	C₃×#65758	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₄⋊#170	C₂	1	2	yes	maximal, complemented
5	C₃×#65708	C₂	1	2	yes	maximal, complemented
6	C₃×#65696	C₂	1	4	yes	maximal, complemented
7	C₃×#65681	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₅⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	#10617137	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#711	C₂²	1	1	yes	characteristic
11	C₂×C₃×#704	C₂²	1	4	yes	—
12	C₂²×C₃×#170	C₂²	1	4	yes	—
13	C₃×#4131	—	2	8	no	—
14	C₂×C₃×#700	C₂²	1	2	yes	—
15	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
16	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
17	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic
18	C₃×C₄×C₂²⋊D₅	C₄	1	2	yes	—
19	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
20	C₃×#4038	C₂²	1	1	yes	characteristic
21	C₃×#4033	C₄	1	1	yes	characteristic
22	C₃×#4027	C₄	1	2	yes	—
23	C₃×#4023	C₂²	1	2	yes	—
24	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
25	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
26	C₃×#4004	C₂²	1	2	yes	—
27	C₃×#4004	C₂²	1	4	yes	—
28	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
29	C₃×C₄⋊#170	C₂²	1	1	yes	characteristic
30	C₃×C₄⋊#170	C₂²	1	2	yes	—
31	C₃×C₄⋊#170	C₂²	1	2	yes	—
32	C₃×C₄⋊#170	C₂²	1	4	yes	—
33	C₃×#2906	—	5	1	no	maximal, Hall
34	C₂×#4131	C₂×C₃	1	2	yes	—
35	C₄×#711	C₂×C₃	1	1	yes	characteristic
36	#65758	C₂×C₃	1	2	yes	complemented
37	C₂×C₄⋊#170	C₂×C₃	1	2	yes	complemented
38	#65708	C₂×C₃	1	2	yes	complemented
39	#65696	C₂×C₃	1	4	yes	complemented
40	#65681	C₂×C₃	1	1	yes	characteristic, complemented
41	D₅⋊(C₄⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
45	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
46	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
47	C₃×#711	D₄	1	4	yes	—
48	C₃×#711	Q₈	1	4	yes	—
49	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
53	C₃×#704	—	2	8	no	—
54	C₂×C₃×#170	—	2	8	no	—
55	C₂×C₃×#170	C₂³	1	2	yes	—
56	C₂×C₃×#170	C₂³	1	2	yes	—
57	C₂×C₃×#170	C₂³	1	4	yes	—
58	C₃×#700	—	2	4	no	—
59	C₃×D₅⋊C₈	—	2	4	no	—
60	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
63	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
64	C₃×#685	C₂×C₄	1	2	yes	—
65	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
66	C₃×#683	C₂×C₄	1	2	yes	—
67	C₃×#683	C₂×C₄	1	2	yes	—
68	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
69	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
70	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
71	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
72	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
73	C₃×C₄×Dic₅	C₂³	1	2	yes	—
74	C₂×C₃×#131	—	5	2	no	—
75	C₃×C₄×#41	—	5	1	no	—
76	C₃×#424	—	5	4	no	—
77	C₃×#424	—	5	2	no	—
78	C₃×#423	—	5	1	no	—
79	C₃×#423	—	5	2	no	—
80	C₂×C₃×C₄⋊C₈	—	5	1	no	—
81	C₂×C₃×C₄⋊C₈	—	5	2	no	—
82	C₂×#711	C₂²×C₃	1	1	yes	characteristic
83	C₂×#704	C₂²×C₃	1	4	yes	—
84	C₂²×#170	C₂²×C₃	1	4	yes	—
85	#4131	—	2	8	no	—
86	C₂×#700	C₂²×C₃	1	2	yes	—
87	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
88	C₄×C₅×D₄	C₃×C₄	1	1	yes	characteristic
89	D₄×Dic₅	C₃×C₄	1	1	yes	characteristic
90	C₄×C₂²⋊D₅	C₃×C₄	1	2	yes	—
91	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
92	#4038	C₂²×C₃	1	1	yes	characteristic
93	#4033	C₃×C₄	1	1	yes	characteristic
94	#4027	C₃×C₄	1	2	yes	—
95	#4023	C₂²×C₃	1	2	yes	—
96	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
97	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic
98	#4004	C₂²×C₃	1	2	yes	—
99	#4004	C₂²×C₃	1	4	yes	—
100	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
101	C₄⋊#170	C₂²×C₃	1	1	yes	characteristic
102	C₄⋊#170	C₂²×C₃	1	2	yes	—
103	C₄⋊#170	C₂²×C₃	1	2	yes	—
104	C₄⋊#170	C₂²×C₃	1	4	yes	—
105	#2906	—	5	1	no	Sylow
106	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
107	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
108	C₃×C₅×D₄	C₄⋊C₄	1	4	yes	—
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₃×C₂²⋊D₅	C₄⋊C₄	1	8	yes	—
115	C₂×C₃×Dic₅	—	4	2	no	—
116	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
119	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
120	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
121	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	—
122	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
123	C₃×C₄×D₅	—	2	2	no	—
124	C₃×C₄×D₅	—	4	1	no	—
125	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
126	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
127	C₃×Dic₁₀	C₄⋊C₄	1	4	yes	—
128	C₃×#170	—	2	2	no	—
129	C₃×#170	—	2	2	no	—
130	C₃×#170	—	2	4	no	—
131	C₂×C₃×#41	—	5	1	no	—
132	C₃×#131	—	10	8	no	—
133	C₂×C₃×M₁₆	—	5	2	no	—
134	C₂×C₃×M₁₆	—	5	4	no	—
135	C₂²×C₃×C₈	—	5	2	no	—
136	C₂²×C₃×C₈	—	5	4	no	—
137	C₃×C₄×Q₈	—	5	1	no	—
138	C₃×C₄×Q₈	—	5	1	no	—
139	C₃×C₄×D₄	—	5	1	no	—
140	C₃×C₄×D₄	—	5	2	no	—
141	C₃×C₄×D₄	—	5	2	no	—
142	C₃×C₄×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
143	C₃×#117	—	5	1	no	—
144	C₃×#117	—	5	2	no	—
145	C₂×C₃×C₄²	—	5	2	no	—
146	C₂×C₃×C₄²	—	5	1	no	—
147	C₃×C₄⋊C₈	—	5	1	no	—
148	C₃×C₄⋊C₈	—	5	1	no	—
149	C₃×C₄⋊C₈	—	5	2	no	—
150	C₃×C₄⋊C₈	—	5	4	no	—
151	C₃×C₄⋊C₈	—	5	2	no	—
152	C₃×C₄⋊C₈	—	5	2	no	—
153	C₃×C₄⋊C₈	—	5	4	no	—
154	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
156	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
157	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
158	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
159	#711	C₃×D₄	1	4	yes	—
160	#711	C₃×Q₈	1	4	yes	—
161	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
162	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
163	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
164	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
165	#704	—	2	8	no	—
166	C₂×#170	—	2	8	no	—
167	C₂×#170	C₂³×C₃	1	2	yes	—
168	C₂×#170	C₂³×C₃	1	2	yes	—
169	C₂×#170	C₂³×C₃	1	4	yes	—
170	#700	—	2	4	no	—
171	D₅⋊C₈	—	2	4	no	—
172	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
173	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
174	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
175	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
176	#685	C₂×C₃×C₄	1	2	yes	—
177	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
178	#683	C₂×C₃×C₄	1	2	yes	—
179	#683	C₂×C₃×C₄	1	2	yes	—
180	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
181	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
182	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
183	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
184	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
185	C₄×Dic₅	C₂³×C₃	1	2	yes	—
186	C₂×#131	—	5	2	no	—
187	C₄×#41	—	5	1	no	—
188	#424	—	5	4	no	—
189	#424	—	5	2	no	—
190	#423	—	5	1	no	—
191	#423	—	5	2	no	—
192	C₂×C₄⋊C₈	—	5	1	no	—
193	C₂×C₄⋊C₈	—	5	2	no	—
194	C₂²×C₃×C₅	—	2	2	no	—
195	C₂²×C₃×C₅	—	2	2	no	—
196	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	4	yes	—
197	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₃×D₅	—	2	1	no	—
199	C₂×C₃×D₅	—	2	1	no	—
200	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
201	C₃×C₄×C₅	—	2	2	no	—
202	C₃×C₄×C₅	—	2	1	no	—
203	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
204	C₃×C₄×C₅	#131	1	2	yes	complemented
205	C₃×Dic₅	—	2	1	no	—
206	C₃×Dic₅	—	2	1	no	—
207	C₃×Dic₅	—	2	2	no	—
208	C₃×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
209	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
210	C₃×Dic₅	C₂²×Q₈	1	1	yes	characteristic
211	C₃×#41	—	5	4	no	—
212	C₃×#41	—	5	4	no	—
213	C₂×C₃×Q₈	—	5	1	no	—
214	C₂×C₃×D₄	—	5	2	no	—
215	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
216	C₂²×C₃×C₄	—	5	2	no	—
217	C₂²×C₃×C₄	—	5	1	no	—
218	C₂²×C₃×C₄	—	5	2	no	—
219	C₂²×C₃×C₄	—	5	1	no	—
220	C₂²×C₃×C₄	—	5	1	no	—
221	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
222	C₃×M₁₆	—	10	4	no	—
223	C₃×M₁₆	—	10	8	no	—
224	C₂×C₃×C₈	—	5	2	no	—
225	C₂×C₃×C₈	—	5	4	no	—
226	C₂×C₃×C₈	—	5	2	no	—
227	C₂×C₃×C₈	—	10	4	no	—
228	C₂×C₃×C₈	—	10	8	no	—
229	C₃×C₄⋊C₄	—	5	2	no	—
230	C₃×C₄⋊C₄	—	5	2	no	—
231	C₃×C₄⋊C₄	—	5	1	no	—
232	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
233	C₃×C₂²⋊C₄	—	5	2	no	—
234	C₃×C₂²⋊C₄	—	5	2	no	—
235	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
236	C₃×C₄²	—	5	2	no	—
237	C₃×C₄²	—	5	2	no	—
238	C₃×C₄²	—	5	1	no	—
239	C₃×C₄²	—	5	1	no	—
240	C₃×C₄²	—	5	2	no	—
241	C₃×C₄²	—	5	1	no	—
242	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
243	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
244	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
245	C₅×D₄	C₃×C₄⋊C₄	1	4	yes	—
246	C₂×C₄×C₅	—	2	4	no	—
247	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
248	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
251	C₂²⋊D₅	C₃×C₄⋊C₄	1	8	yes	—
252	C₂×Dic₅	—	4	2	no	—
253	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
254	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
255	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
256	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
257	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
258	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	—
259	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
260	C₄×D₅	—	2	2	no	—
261	C₄×D₅	—	4	1	no	—
262	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
263	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
264	Dic₁₀	C₃×C₄⋊C₄	1	4	yes	—
265	#170	—	2	2	no	—
266	#170	—	2	2	no	—
267	#170	—	2	4	no	—
268	C₂×#41	—	5	1	no	—
269	#131	—	10	8	no	—
270	C₂×M₁₆	—	5	2	no	—
271	C₂×M₁₆	—	5	4	no	—
272	C₂²×C₈	—	5	2	no	—
273	C₂²×C₈	—	5	4	no	—
274	C₄×Q₈	—	5	1	no	—
275	C₄×Q₈	—	5	1	no	—
276	C₄×D₄	—	5	1	no	—
277	C₄×D₄	—	5	2	no	—
278	C₄×D₄	—	5	2	no	—
279	C₄×D₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
280	#117	—	5	1	no	—
281	#117	—	5	2	no	—
282	C₂×C₄²	—	5	2	no	—
283	C₂×C₄²	—	5	1	no	—
284	C₄⋊C₈	—	5	1	no	—
285	C₄⋊C₈	—	5	1	no	—
286	C₄⋊C₈	—	5	2	no	—
287	C₄⋊C₈	—	5	4	no	—
288	C₄⋊C₈	—	5	2	no	—
289	C₄⋊C₈	—	5	2	no	—
290	C₄⋊C₈	—	5	4	no	—
291	C₂×C₃×C₅	—	2	4	no	—
292	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
293	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
294	C₂×C₃×C₅	#568	1	1	yes	characteristic
295	C₃×D₅	—	2	2	no	—
296	C₂³×C₃	—	5	1	no	—
297	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
298	C₃×Q₈	—	5	4	no	—
299	C₃×D₄	—	5	8	no	—
300	C₃×D₄	C₄⋊AGL(1,𝔽₅)	1	4	yes	—
301	C₂×C₃×C₄	—	2	4	no	—
302	C₂×C₃×C₄	—	5	4	no	—
303	C₂×C₃×C₄	—	5	4	no	—
304	C₂×C₃×C₄	—	5	2	no	—
305	C₂×C₃×C₄	—	5	1	no	—
306	C₂×C₃×C₄	—	5	2	no	—
307	C₂×C₃×C₄	—	5	2	no	—
308	C₂×C₃×C₄	—	5	1	no	—
309	C₂×C₃×C₄	—	5	1	no	—
310	C₂×C₃×C₄	—	5	2	no	—
311	C₂×C₃×C₄	—	10	2	no	—
312	C₂×C₃×C₄	—	20	1	no	—
313	C₂×C₃×C₄	—	20	2	no	—
314	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
315	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
318	C₃×C₈	—	10	2	no	—
319	C₃×C₈	—	10	2	no	—
320	C₃×C₈	—	10	4	no	—
321	C₂²×C₅	—	2	2	no	—
322	C₂²×C₅	—	2	2	no	—
323	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
324	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
325	C₂×D₅	—	2	1	no	—
326	C₂×D₅	—	2	1	no	—
327	C₂×D₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
328	C₄×C₅	—	2	2	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
331	C₄×C₅	C₃×#131	1	2	yes	complemented
332	Dic₅	—	2	1	no	—
333	Dic₅	—	2	1	no	—
334	Dic₅	—	2	2	no	—
335	Dic₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
336	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
337	Dic₅	C₂²×C₃×Q₈	1	1	yes	characteristic
338	#41	—	5	4	no	—
339	#41	—	5	4	no	—
340	C₂×Q₈	—	5	1	no	—
341	C₂×D₄	—	5	2	no	—
342	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
343	C₂²×C₄	—	5	2	no	—
344	C₂²×C₄	—	5	1	no	—
345	C₂²×C₄	—	5	2	no	—
346	C₂²×C₄	—	5	1	no	—
347	C₂²×C₄	—	5	1	no	—
348	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
349	M₁₆	—	10	4	no	—
350	M₁₆	—	10	8	no	—
351	C₂×C₈	—	5	2	no	—
352	C₂×C₈	—	5	4	no	—
353	C₂×C₈	—	5	2	no	—
354	C₂×C₈	—	10	4	no	—
355	C₂×C₈	—	10	8	no	—
356	C₄⋊C₄	—	5	2	no	—
357	C₄⋊C₄	—	5	2	no	—
358	C₄⋊C₄	—	5	1	no	—
359	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₂²⋊C₄	—	5	2	no	—
361	C₂²⋊C₄	—	5	2	no	—
362	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
363	C₄²	—	5	1	no	—
364	C₄²	—	5	2	no	—
365	C₄²	—	5	1	no	—
366	C₄²	—	5	2	no	—
367	C₄²	—	5	2	no	—
368	C₄²	—	5	1	no	—
369	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
370	C₃×C₅	#2906	1	1	yes	characteristic, complemented, Hall
371	C₂²×C₃	—	2	2	no	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	5	2	no	—
374	C₂²×C₃	—	10	1	no	—
375	C₂²×C₃	—	10	1	no	—
376	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	4	yes	—
377	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	—	2	1	no	—
380	C₃×C₄	—	5	4	no	—
381	C₃×C₄	—	5	1	no	—
382	C₃×C₄	—	5	1	no	—
383	C₃×C₄	—	10	1	no	—
384	C₃×C₄	—	10	2	no	—
385	C₃×C₄	—	10	1	no	—
386	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
387	C₃×C₄	#4131	1	2	yes	complemented
388	C₂×C₅	—	2	4	no	—
389	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
390	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
391	C₂×C₅	C₃×#568	1	1	yes	characteristic
392	D₅	—	2	2	no	—
393	C₂³	—	5	1	no	—
394	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
395	Q₈	—	5	4	no	—
396	D₄	—	5	8	no	—
397	D₄	C₃×C₄⋊AGL(1,𝔽₅)	1	4	yes	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	5	4	no	—
400	C₂×C₄	—	5	4	no	—
401	C₂×C₄	—	5	1	no	—
402	C₂×C₄	—	5	2	no	—
403	C₂×C₄	—	5	2	no	—
404	C₂×C₄	—	5	2	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	5	1	no	—
407	C₂×C₄	—	5	2	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	—	20	1	no	—
410	C₂×C₄	—	20	2	no	—
411	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
412	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
415	C₈	—	10	2	no	—
416	C₈	—	10	2	no	—
417	C₈	—	10	4	no	—
418	C₂×C₃	—	2	4	no	—
419	C₂×C₃	—	10	2	no	—
420	C₂×C₃	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
421	C₂×C₃	C₂×#4131	1	1	yes	characteristic
422	C₂×C₃	#66264	1	1	yes	characteristic
423	C₅	C₃×#2906	1	1	yes	characteristic, complemented, Sylow
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	5	2	no	—
427	C₂²	—	10	1	no	—
428	C₂²	—	10	1	no	—
429	C₂²	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	4	yes	—
430	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	1	no	—
433	C₄	—	5	1	no	—
434	C₄	—	5	1	no	—
435	C₄	—	5	4	no	—
436	C₄	—	10	1	no	—
437	C₄	—	10	1	no	—
438	C₄	—	10	2	no	—
439	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
440	C₄	C₃×#4131	1	2	yes	complemented
441	C₃	#10617137	1	1	yes	characteristic, direct product factor, Sylow
442	C₂	—	2	4	no	—
443	C₂	—	10	2	no	—
444	C₂	C₂²×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
445	C₂	C₂×C₃×#4131	1	1	yes	characteristic
446	C₂	C₃×#66264	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×C₄×C₅×D₄	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#711	C₂²
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×C₄×D₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2906
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
3. C₃×#65758	C₂	semidirect
4. C₂×C₃×C₄⋊#170	C₂	semidirect
5. C₃×#65708	C₂	semidirect
6. C₃×#65696	C₂	semidirect
7. C₃×#65681	C₂	semidirect
8. C₃×D₅⋊(C₄⋊C₈)	C₂	semidirect
9. #10617137	C₃	direct (N × H)
36. #65758	C₂×C₃	semidirect
37. C₂×C₄⋊#170	C₂×C₃	semidirect
38. #65708	C₂×C₃	semidirect
39. #65696	C₂×C₃	semidirect
40. #65681	C₂×C₃	semidirect
41. D₅⋊(C₄⋊C₈)	C₂×C₃	semidirect
204. C₃×C₄×C₅	#131	semidirect
331. C₄×C₅	C₃×#131	semidirect
370. C₃×C₅	#2906	semidirect
387. C₃×C₄	#4131	semidirect
423. C₅	C₃×#2906	semidirect
440. C₄	C₃×#4131	semidirect
441. C₃	#10617137	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×C₄×#711	2
C₃×#65758	2
C₂×C₃×C₄⋊#170	2
C₃×#65708	2
C₃×#65696	2
C₃×#65681	2
C₃×D₅⋊(C₄⋊C₈)	2
#10617137	3
C₃×#2906	5

Subgroups — C3×#10617137 #14413176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617137 #14413176