Subgroups — C₃×#10604360 #14281634

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65856	C₂	1	1	yes	maximal, characteristic
2	C₃×#65748	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄⋊#170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64872	C₂	1	2	yes	maximal, complemented
5	C₃×#64871	C₂	1	2	yes	maximal, complemented
6	#10604360	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×#709	C₄	1	1	yes	characteristic
8	C₂²×C₃×#170	—	2	1	no	—
9	C₃×C₅×#117	C₄	1	1	yes	characteristic
10	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
11	C₃×#4039	C₄	1	1	yes	characteristic
12	C₃×#4039	C₂²	1	1	yes	characteristic
13	C₃×#4033	C₄	1	1	yes	characteristic
14	C₃×#4033	C₂²	1	1	yes	characteristic
15	C₃×#4027	—	2	1	no	—
16	C₃×#4027	—	2	1	no	—
17	C₃×#4018	—	2	1	no	—
18	C₃×C₄²×D₅	—	2	1	no	—
19	C₃×C₂²⋊#170	—	2	1	no	—
20	C₃×C₄⋊#170	—	2	1	no	—
21	C₃×C₄⋊#170	—	2	1	no	—
22	C₃×C₄⋊#170	C₂²	1	2	yes	—
23	C₃×C₄×#170	C₂²	1	2	yes	—
24	C₃×#1477	—	5	1	no	maximal, Hall
25	#65856	C₂×C₃	1	1	yes	characteristic
26	#65748	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₄⋊#170	C₂×C₃	1	1	yes	characteristic, complemented
28	#64872	C₂×C₃	1	2	yes	complemented
29	#64871	C₂×C₃	1	2	yes	complemented
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
32	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
34	C₃×#709	—	2	2	no	—
35	C₃×#709	C₈	1	4	yes	complemented
36	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	—	2	1	no	—
38	C₂×C₃×C₄×D₅	—	2	1	no	—
39	C₂×C₃×C₄×D₅	—	2	1	no	—
40	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×#170	—	2	2	no	—
42	C₂×C₃×#170	—	2	2	no	—
43	C₂×C₃×#170	—	4	2	no	—
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₄²×C₅	—	2	1	no	—
48	C₃×#685	—	2	1	no	—
49	C₃×#685	—	2	1	no	—
50	C₃×#683	—	2	1	no	—
51	C₃×#683	—	2	1	no	—
52	C₃×C₄×Dic₅	—	2	1	no	—
53	C₃×C₄×Dic₅	—	2	1	no	—
54	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
56	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
57	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
58	C₃×C₄×#41	—	5	1	no	—
59	C₃×#431	—	5	1	no	—
60	C₂×C₃×C₄⋊C₈	—	5	1	no	—
61	C₃×Q₈⋊C₈	—	5	2	no	—
62	C₃×D₄⋊C₈	—	5	2	no	—
63	C₂×#709	C₃×C₄	1	1	yes	characteristic
64	C₂²×#170	—	2	1	no	—
65	C₅×#117	C₃×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
67	#4039	C₃×C₄	1	1	yes	characteristic
68	#4039	C₂²×C₃	1	1	yes	characteristic
69	#4033	C₃×C₄	1	1	yes	characteristic
70	#4033	C₂²×C₃	1	1	yes	characteristic
71	#4027	—	2	1	no	—
72	#4027	—	2	1	no	—
73	#4018	—	2	1	no	—
74	C₄²×D₅	—	2	1	no	—
75	C₂²⋊#170	—	2	1	no	—
76	C₄⋊#170	—	2	1	no	—
77	C₄⋊#170	—	2	1	no	—
78	C₄⋊#170	C₂²×C₃	1	2	yes	—
79	C₄×#170	C₂²×C₃	1	2	yes	—
80	#1477	—	5	1	no	Sylow
81	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₃×D₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
87	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₃×C₂²⋊D₅	—	2	4	no	—
90	C₂×C₃×Dic₅	—	2	1	no	—
91	C₂×C₃×Dic₅	—	2	1	no	—
92	C₂×C₃×Dic₅	—	2	1	no	—
93	C₂×C₃×Dic₅	—	4	1	no	—
94	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
98	C₃×D₂₀	—	2	1	no	—
99	C₃×D₂₀	C₂×C₈	1	2	yes	complemented
100	C₃×C₄×D₅	—	2	4	no	—
101	C₃×C₄×D₅	—	4	2	no	—
102	C₃×C₄×D₅	—	4	1	no	—
103	C₃×C₄×D₅	—	4	1	no	—
104	C₃×Dic₁₀	—	2	1	no	—
105	C₃×Dic₁₀	C₂×C₈	1	2	yes	complemented
106	C₃×#170	—	4	2	no	—
107	C₃×#170	—	4	2	no	—
108	C₂×C₃×#41	—	5	1	no	—
109	C₂²×C₃×C₈	—	10	1	no	—
110	C₃×C₄×Q₈	—	5	1	no	—
111	C₃×C₄×Q₈	—	5	1	no	—
112	C₃×C₄×D₄	—	5	1	no	—
113	C₃×C₄×D₄	—	5	1	no	—
114	C₃×C₄×D₄	—	10	1	no	—
115	C₃×C₄×D₄	—	10	1	no	—
116	C₃×#117	—	10	1	no	—
117	C₃×#117	AGL(1,𝔽₅)	1	1	yes	characteristic
118	C₂×C₃×C₄²	—	5	1	no	—
119	C₂×C₃×C₄²	—	10	1	no	—
120	C₃×C₄⋊C₈	—	5	2	no	—
121	C₃×C₄⋊C₈	—	10	1	no	—
122	C₃×C₄⋊C₈	—	10	1	no	—
123	C₃×C₂²⋊C₈	—	10	1	no	—
124	C₃×C₄×C₈	—	5	2	no	—
125	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
126	C₂×C₂²⋊D₅	—	2	1	no	—
127	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
128	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
129	#709	—	2	2	no	—
130	#709	C₃×C₈	1	4	yes	complemented
131	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂×C₄×D₅	—	2	1	no	—
133	C₂×C₄×D₅	—	2	1	no	—
134	C₂×C₄×D₅	—	2	1	no	—
135	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂×#170	—	2	2	no	—
137	C₂×#170	—	2	2	no	—
138	C₂×#170	—	4	2	no	—
139	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
140	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
141	C₅×C₂²⋊C₄	—	2	1	no	—
142	C₄²×C₅	—	2	1	no	—
143	#685	—	2	1	no	—
144	#685	—	2	1	no	—
145	#683	—	2	1	no	—
146	#683	—	2	1	no	—
147	C₄×Dic₅	—	2	1	no	—
148	C₄×Dic₅	—	2	1	no	—
149	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
150	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
151	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
152	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
153	C₄×#41	—	5	1	no	—
154	#431	—	5	1	no	—
155	C₂×C₄⋊C₈	—	5	1	no	—
156	Q₈⋊C₈	—	5	2	no	—
157	D₄⋊C₈	—	5	2	no	—
158	C₂²×C₃×C₅	—	2	1	no	—
159	C₂²×C₃×C₅	—	2	1	no	—
160	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
161	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₃×D₅	—	2	2	no	—
163	C₂×C₃×D₅	—	4	1	no	—
164	C₂×C₃×D₅	—	4	1	no	—
165	C₃×C₄×C₅	—	4	1	no	—
166	C₃×C₄×C₅	—	4	1	no	—
167	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
168	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
170	C₃×Dic₅	—	2	2	no	—
171	C₃×Dic₅	—	2	1	no	—
172	C₃×Dic₅	—	2	1	no	—
173	C₃×Dic₅	—	2	1	no	—
174	C₃×Dic₅	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₃×Dic₅	#137	1	1	yes	characteristic
176	C₃×#41	—	5	4	no	—
177	C₃×#41	—	10	2	no	—
178	C₂×C₃×Q₈	—	5	1	no	—
179	C₂×C₃×D₄	—	5	1	no	—
180	C₂×C₃×D₄	—	10	1	no	—
181	C₂²×C₃×C₄	—	5	1	no	—
182	C₂²×C₃×C₄	—	5	1	no	—
183	C₂²×C₃×C₄	—	10	1	no	—
184	C₂²×C₃×C₄	—	10	1	no	—
185	C₂²×C₃×C₄	—	10	1	no	—
186	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
187	C₂×C₃×C₈	—	10	2	no	—
188	C₂×C₃×C₈	—	10	2	no	—
189	C₂×C₃×C₈	—	20	2	no	—
190	C₃×C₄⋊C₄	—	10	1	no	—
191	C₃×C₄⋊C₄	—	10	1	no	—
192	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
194	C₃×C₂²⋊C₄	—	2	1	no	—
195	C₃×C₂²⋊C₄	—	10	1	no	—
196	C₃×C₂²⋊C₄	—	10	1	no	—
197	C₃×C₄²	—	2	1	no	—
198	C₃×C₄²	—	5	1	no	—
199	C₃×C₄²	—	5	1	no	—
200	C₃×C₄²	—	5	1	no	—
201	C₃×C₄²	—	5	1	no	—
202	C₃×C₄²	—	10	1	no	—
203	C₃×C₄²	—	10	1	no	—
204	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×D₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
210	C₂×C₄×C₅	C₃×M₁₆	1	2	yes	—
211	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
212	C₂²⋊D₅	—	2	4	no	—
213	C₂×Dic₅	—	2	1	no	—
214	C₂×Dic₅	—	2	1	no	—
215	C₂×Dic₅	—	2	1	no	—
216	C₂×Dic₅	—	4	1	no	—
217	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
221	D₂₀	—	2	1	no	—
222	D₂₀	C₂×C₃×C₈	1	2	yes	complemented
223	C₄×D₅	—	2	4	no	—
224	C₄×D₅	—	4	2	no	—
225	C₄×D₅	—	4	1	no	—
226	C₄×D₅	—	4	1	no	—
227	Dic₁₀	—	2	1	no	—
228	Dic₁₀	C₂×C₃×C₈	1	2	yes	complemented
229	#170	—	4	2	no	—
230	#170	—	4	2	no	—
231	C₂×#41	—	5	1	no	—
232	C₂²×C₈	—	10	1	no	—
233	C₄×Q₈	—	5	1	no	—
234	C₄×Q₈	—	5	1	no	—
235	C₄×D₄	—	5	1	no	—
236	C₄×D₄	—	5	1	no	—
237	C₄×D₄	—	10	1	no	—
238	C₄×D₄	—	10	1	no	—
239	#117	—	10	1	no	—
240	#117	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
241	C₂×C₄²	—	5	1	no	—
242	C₂×C₄²	—	10	1	no	—
243	C₄⋊C₈	—	5	2	no	—
244	C₄⋊C₈	—	10	1	no	—
245	C₄⋊C₈	—	10	1	no	—
246	C₂²⋊C₈	—	10	1	no	—
247	C₄×C₈	—	5	2	no	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
250	C₂×C₃×C₅	#417	1	1	yes	characteristic
251	C₂×C₃×C₅	#421	1	1	yes	characteristic
252	C₃×D₅	—	4	2	no	—
253	C₂³×C₃	—	10	1	no	—
254	C₂³×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
255	C₃×Q₈	—	5	2	no	—
256	C₃×Q₈	—	10	1	no	—
257	C₃×D₄	—	5	2	no	—
258	C₃×D₄	—	10	4	no	—
259	C₃×D₄	—	10	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	5	1	no	—
263	C₂×C₃×C₄	—	5	1	no	—
264	C₂×C₃×C₄	—	5	1	no	—
265	C₂×C₃×C₄	—	5	1	no	—
266	C₂×C₃×C₄	—	10	1	no	—
267	C₂×C₃×C₄	—	10	1	no	—
268	C₂×C₃×C₄	—	10	1	no	—
269	C₂×C₃×C₄	—	10	4	no	—
270	C₂×C₃×C₄	—	20	1	no	—
271	C₂×C₃×C₄	—	20	1	no	—
272	C₂×C₃×C₄	—	20	2	no	—
273	C₂×C₃×C₄	—	20	1	no	—
274	C₂×C₃×C₄	D₅⋊C₈	1	2	yes	—
275	C₂×C₃×C₄	#700	1	2	yes	—
276	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
278	C₃×C₈	—	20	2	no	—
279	C₃×C₈	—	20	2	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	C₃×C₂²⋊C₈	1	2	yes	—
283	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×D₅	—	2	2	no	—
285	C₂×D₅	—	4	1	no	—
286	C₂×D₅	—	4	1	no	—
287	C₄×C₅	—	4	1	no	—
288	C₄×C₅	—	4	1	no	—
289	C₄×C₅	C₃×C₂²⋊C₈	1	2	yes	—
290	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
291	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
292	Dic₅	—	2	2	no	—
293	Dic₅	—	2	1	no	—
294	Dic₅	—	2	1	no	—
295	Dic₅	—	2	1	no	—
296	Dic₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
297	Dic₅	C₃×#137	1	1	yes	characteristic
298	#41	—	5	4	no	—
299	#41	—	10	2	no	—
300	C₂×Q₈	—	5	1	no	—
301	C₂×D₄	—	5	1	no	—
302	C₂×D₄	—	10	1	no	—
303	C₂²×C₄	—	5	1	no	—
304	C₂²×C₄	—	5	1	no	—
305	C₂²×C₄	—	10	1	no	—
306	C₂²×C₄	—	10	1	no	—
307	C₂²×C₄	—	10	1	no	—
308	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
309	C₂×C₈	—	10	2	no	—
310	C₂×C₈	—	10	2	no	—
311	C₂×C₈	—	20	2	no	—
312	C₄⋊C₄	—	10	1	no	—
313	C₄⋊C₄	—	10	1	no	—
314	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
315	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	10	1	no	—
318	C₂²⋊C₄	—	10	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	5	1	no	—
321	C₄²	—	5	1	no	—
322	C₄²	—	5	1	no	—
323	C₄²	—	5	1	no	—
324	C₄²	—	10	1	no	—
325	C₄²	—	10	1	no	—
326	C₃×C₅	#1477	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	10	2	no	—
330	C₂²×C₃	—	20	1	no	—
331	C₂²×C₃	—	20	1	no	—
332	C₂²×C₃	#4003	1	2	yes	—
333	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
334	C₃×C₄	—	4	1	no	—
335	C₃×C₄	—	4	1	no	—
336	C₃×C₄	—	5	1	no	—
337	C₃×C₄	—	5	1	no	—
338	C₃×C₄	—	10	1	no	—
339	C₃×C₄	—	10	1	no	—
340	C₃×C₄	—	10	1	no	—
341	C₃×C₄	—	10	2	no	—
342	C₃×C₄	#4003	1	2	yes	—
343	C₃×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
344	C₃×C₄	C₂×#700	1	1	yes	characteristic
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
347	C₂×C₅	C₃×#417	1	1	yes	characteristic
348	C₂×C₅	C₃×#421	1	1	yes	characteristic
349	D₅	—	4	2	no	—
350	C₂³	—	10	1	no	—
351	C₂³	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
352	Q₈	—	5	2	no	—
353	Q₈	—	10	1	no	—
354	D₄	—	5	2	no	—
355	D₄	—	10	4	no	—
356	D₄	—	10	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	5	1	no	—
360	C₂×C₄	—	5	1	no	—
361	C₂×C₄	—	5	1	no	—
362	C₂×C₄	—	5	1	no	—
363	C₂×C₄	—	10	1	no	—
364	C₂×C₄	—	10	1	no	—
365	C₂×C₄	—	10	1	no	—
366	C₂×C₄	—	10	4	no	—
367	C₂×C₄	—	20	1	no	—
368	C₂×C₄	—	20	1	no	—
369	C₂×C₄	—	20	2	no	—
370	C₂×C₄	—	20	1	no	—
371	C₂×C₄	C₃×D₅⋊C₈	1	2	yes	—
372	C₂×C₄	C₃×#700	1	2	yes	—
373	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
375	C₈	—	20	2	no	—
376	C₈	—	20	2	no	—
377	C₂×C₃	—	2	2	no	—
378	C₂×C₃	—	20	2	no	—
379	C₂×C₃	C₂×#4003	1	1	yes	characteristic
380	C₂×C₃	#65793	1	1	yes	characteristic
381	C₂×C₃	#65795	1	1	yes	characteristic
382	C₅	C₃×#1477	1	1	yes	characteristic, complemented, Sylow
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	10	2	no	—
386	C₂²	—	20	1	no	—
387	C₂²	—	20	1	no	—
388	C₂²	C₃×#4003	1	2	yes	—
389	C₂²	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	5	1	no	—
393	C₄	—	5	1	no	—
394	C₄	—	10	2	no	—
395	C₄	—	10	1	no	—
396	C₄	—	10	1	no	—
397	C₄	—	10	1	no	—
398	C₄	C₃×#4003	1	2	yes	—
399	C₄	C₂×C₃×D₅⋊C₈	1	1	yes	characteristic
400	C₄	C₂×C₃×#700	1	1	yes	characteristic
401	C₃	#10604360	1	1	yes	characteristic, direct product factor, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	20	2	no	—
404	C₂	C₂×C₃×#4003	1	1	yes	characteristic
405	C₂	C₃×#65793	1	1	yes	characteristic
406	C₂	C₃×#65795	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₃×C₈
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#117	C₄
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#709	C₄
cosocle	C₄×Dic₅	C₂³×C₃
hypercenter	C₃×#117	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1477
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
2. C₃×#65748	C₂	semidirect
3. C₂×C₃×C₄⋊#170	C₂	semidirect
4. C₃×#64872	C₂	semidirect
5. C₃×#64871	C₂	semidirect
6. #10604360	C₃	direct (N × H)
26. #65748	C₂×C₃	semidirect
27. C₂×C₄⋊#170	C₂×C₃	semidirect
28. #64872	C₂×C₃	semidirect
29. #64871	C₂×C₃	semidirect
35. C₃×#709	C₈	semidirect
99. C₃×D₂₀	C₂×C₈	semidirect
105. C₃×Dic₁₀	C₂×C₈	semidirect
130. #709	C₃×C₈	semidirect
222. D₂₀	C₂×C₃×C₈	semidirect
228. Dic₁₀	C₂×C₃×C₈	semidirect
326. C₃×C₅	#1477	semidirect
382. C₅	C₃×#1477	semidirect
401. C₃	#10604360	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×#65856	2
C₃×#65748	2
C₂×C₃×C₄⋊#170	2
C₃×#64872	2
C₃×#64871	2
#10604360	3
C₃×#1477	5

Subgroups — C3×#10604360 #14281634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10604360 #14281634