Subgroups — C₃×#10604401 #14281573

Order 1920.

552 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic
2	C₃×#65680	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₄⋊#170	C₂	1	2	yes	maximal, complemented
5	C₃×#64872	C₂	1	2	yes	maximal, complemented
6	#10604401	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×#711	C₄	1	1	yes	characteristic
8	C₂×C₃×D₅⋊C₈	—	2	1	no	—
9	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
10	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
12	C₂×C₃×C₄×Dic₅	—	2	1	no	—
13	C₃×#4038	C₄	1	1	yes	characteristic
14	C₃×#4033	C₂²	1	1	yes	characteristic
15	C₃×#4027	—	2	1	no	—
16	C₃×#4023	—	2	1	no	—
17	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
18	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
19	C₃×#4003	—	2	1	no	—
20	C₃×C₄⋊#170	C₂²	1	2	yes	—
21	C₃×C₄×#170	—	2	1	no	—
22	C₃×C₄×#170	—	2	1	no	—
23	C₃×C₄×#170	C₂²	1	2	yes	—
24	C₃×#1476	—	5	1	no	maximal, Hall
25	C₄×#711	C₂×C₃	1	1	yes	characteristic
26	#65680	C₂×C₃	1	1	yes	characteristic, complemented
27	C₄×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
28	D₄⋊#170	C₂×C₃	1	2	yes	complemented
29	#64872	C₂×C₃	1	2	yes	complemented
30	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	—	2	1	no	—
32	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
33	C₂²×C₃×Dic₅	—	2	1	no	—
34	C₂²×C₃×Dic₅	—	2	1	no	—
35	C₃×#711	—	2	2	no	—
36	C₃×#711	C₈	1	4	yes	complemented
37	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
39	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
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	C₃×D₅⋊C₈	—	2	4	no	—
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
47	C₃×C₂²⋊Dic₅	—	2	1	no	—
48	C₃×#685	—	2	1	no	—
49	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
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×#711	C₃×C₄	1	1	yes	characteristic
64	C₂×D₅⋊C₈	—	2	1	no	—
65	C₄×C₅×D₄	C₃×C₄	1	1	yes	characteristic
66	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
67	C₄×C₂²⋊D₅	—	2	1	no	—
68	C₂×C₄×Dic₅	—	2	1	no	—
69	#4038	C₃×C₄	1	1	yes	characteristic
70	#4033	C₂²×C₃	1	1	yes	characteristic
71	#4027	—	2	1	no	—
72	#4023	—	2	1	no	—
73	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
74	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic
75	#4003	—	2	1	no	—
76	C₄⋊#170	C₂²×C₃	1	2	yes	—
77	C₄×#170	—	2	1	no	—
78	C₄×#170	—	2	1	no	—
79	C₄×#170	C₂²×C₃	1	2	yes	—
80	#1476	—	5	1	no	Sylow
81	C₂³×C₃×C₅	—	2	1	no	—
82	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₃×C₅×D₄	—	2	1	no	—
84	C₃×C₅×D₄	C₂×C₈	1	2	yes	complemented
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	4	2	no	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₃×C₂²⋊D₅	—	2	4	no	—
91	C₂×C₃×Dic₅	—	2	1	no	—
92	C₂×C₃×Dic₅	—	2	4	no	—
93	C₂×C₃×Dic₅	—	2	1	no	—
94	C₂×C₃×Dic₅	—	4	2	no	—
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×C₄×D₅	—	2	2	no	—
99	C₃×C₄×D₅	—	2	2	no	—
100	C₃×C₄×D₅	C₂×C₈	1	2	yes	—
101	C₃×C₄×D₅	M₁₆	1	2	yes	—
102	C₃×Dic₁₀	—	2	1	no	—
103	C₃×Dic₁₀	C₂×C₈	1	2	yes	complemented
104	C₃×#170	—	2	4	no	—
105	C₃×#170	—	4	2	no	—
106	C₂×C₃×#41	—	5	1	no	—
107	C₂²×C₃×C₈	—	10	1	no	—
108	C₃×C₄×Q₈	—	5	1	no	—
109	C₃×C₄×Q₈	—	5	1	no	—
110	C₃×C₄×D₄	—	5	1	no	—
111	C₃×C₄×D₄	—	10	1	no	—
112	C₃×C₄×D₄	—	10	1	no	—
113	C₃×C₄×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
114	C₃×#117	—	5	1	no	—
115	C₃×#117	—	10	1	no	—
116	C₂×C₃×C₄²	—	5	1	no	—
117	C₂×C₃×C₄²	—	10	1	no	—
118	C₃×C₄⋊C₈	—	5	2	no	—
119	C₃×C₂²⋊C₈	—	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	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂×C₂²⋊D₅	—	2	1	no	—
126	C₂²×Dic₅	—	2	1	no	—
127	C₂²×Dic₅	—	2	1	no	—
128	#711	—	2	2	no	—
129	#711	C₃×C₈	1	4	yes	complemented
130	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
131	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
132	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
133	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂×#170	—	2	2	no	—
135	C₂×#170	—	2	2	no	—
136	D₅⋊C₈	—	2	4	no	—
137	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
138	C₅×C₂²⋊C₄	—	2	1	no	—
139	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
140	C₂²⋊Dic₅	—	2	1	no	—
141	#685	—	2	1	no	—
142	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
143	#683	—	2	1	no	—
144	#683	—	2	1	no	—
145	C₄×Dic₅	—	2	1	no	—
146	C₄×Dic₅	—	2	1	no	—
147	C₄×Dic₅	—	2	1	no	—
148	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
149	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
150	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
151	C₄×#41	—	5	1	no	—
152	#431	—	5	1	no	—
153	C₂×C₄×C₈	—	5	1	no	—
154	Q₈⋊C₈	—	5	2	no	—
155	D₄⋊C₈	—	5	2	no	—
156	C₂²×C₃×C₅	—	2	2	no	—
157	C₂²×C₃×C₅	—	4	1	no	—
158	C₂²×C₃×C₅	—	4	1	no	—
159	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₃×D₅	—	2	1	no	—
161	C₂×C₃×D₅	—	2	1	no	—
162	C₂×C₃×D₅	C₂²⋊C₈	1	2	yes	—
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	4	1	no	—
165	C₃×C₄×C₅	#104	1	2	yes	—
166	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
167	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
168	C₃×Dic₅	—	2	2	no	—
169	C₃×Dic₅	—	2	1	no	—
170	C₃×Dic₅	—	4	1	no	—
171	C₃×Dic₅	C₂²⋊C₈	1	2	yes	—
172	C₃×Dic₅	#135	1	2	yes	—
173	C₃×#41	—	5	4	no	—
174	C₃×#41	—	10	2	no	—
175	C₂×C₃×Q₈	—	5	1	no	—
176	C₂×C₃×D₄	—	10	1	no	—
177	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	5	1	no	—
180	C₂²×C₃×C₄	—	5	1	no	—
181	C₂²×C₃×C₄	—	5	1	no	—
182	C₂²×C₃×C₄	—	10	1	no	—
183	C₂²×C₃×C₄	—	10	1	no	—
184	C₂×C₃×C₈	—	10	2	no	—
185	C₂×C₃×C₈	—	10	4	no	—
186	C₂×C₃×C₈	—	10	2	no	—
187	C₃×C₄⋊C₄	—	5	1	no	—
188	C₃×C₄⋊C₄	—	10	1	no	—
189	C₃×C₄⋊C₄	—	10	1	no	—
190	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
191	C₃×C₂²⋊C₄	—	2	1	no	—
192	C₃×C₂²⋊C₄	—	10	1	no	—
193	C₃×C₂²⋊C₄	—	10	1	no	—
194	C₃×C₄²	—	5	1	no	—
195	C₃×C₄²	—	5	1	no	—
196	C₃×C₄²	—	5	1	no	—
197	C₃×C₄²	—	10	1	no	—
198	C₃×C₄²	—	10	1	no	—
199	C₃×C₄²	—	10	1	no	—
200	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
201	C₂³×C₅	—	2	1	no	—
202	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
203	C₅×D₄	—	2	1	no	—
204	C₅×D₄	C₂×C₃×C₈	1	2	yes	complemented
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
210	C₂²⋊D₅	—	2	4	no	—
211	C₂×Dic₅	—	2	1	no	—
212	C₂×Dic₅	—	2	4	no	—
213	C₂×Dic₅	—	2	1	no	—
214	C₂×Dic₅	—	4	2	no	—
215	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
217	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
218	C₄×D₅	—	2	2	no	—
219	C₄×D₅	—	2	2	no	—
220	C₄×D₅	C₂×C₃×C₈	1	2	yes	—
221	C₄×D₅	C₃×M₁₆	1	2	yes	—
222	Dic₁₀	—	2	1	no	—
223	Dic₁₀	C₂×C₃×C₈	1	2	yes	complemented
224	#170	—	2	4	no	—
225	#170	—	4	2	no	—
226	C₂×#41	—	5	1	no	—
227	C₂²×C₈	—	10	1	no	—
228	C₄×Q₈	—	5	1	no	—
229	C₄×Q₈	—	5	1	no	—
230	C₄×D₄	—	5	1	no	—
231	C₄×D₄	—	10	1	no	—
232	C₄×D₄	—	10	1	no	—
233	C₄×D₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
234	#117	—	5	1	no	—
235	#117	—	10	1	no	—
236	C₂×C₄²	—	5	1	no	—
237	C₂×C₄²	—	10	1	no	—
238	C₄⋊C₈	—	5	2	no	—
239	C₂²⋊C₈	—	10	1	no	—
240	C₄×C₈	—	5	2	no	—
241	C₄×C₈	—	10	1	no	—
242	C₄×C₈	—	10	1	no	—
243	C₂×C₃×C₅	—	4	2	no	—
244	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
245	C₂×C₃×C₅	#416	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
247	C₃×D₅	—	2	2	no	—
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	—	5	1	no	—
250	C₃×Q₈	—	5	2	no	—
251	C₃×Q₈	—	10	1	no	—
252	C₃×D₄	—	2	1	no	—
253	C₃×D₄	—	10	4	no	—
254	C₃×D₄	D₅⋊C₈	1	2	yes	complemented
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	4	2	no	—
257	C₂×C₃×C₄	—	5	1	no	—
258	C₂×C₃×C₄	—	5	1	no	—
259	C₂×C₃×C₄	—	5	2	no	—
260	C₂×C₃×C₄	—	5	2	no	—
261	C₂×C₃×C₄	—	5	1	no	—
262	C₂×C₃×C₄	—	10	2	no	—
263	C₂×C₃×C₄	—	10	4	no	—
264	C₂×C₃×C₄	—	10	1	no	—
265	C₂×C₃×C₄	—	10	2	no	—
266	C₂×C₃×C₄	—	10	1	no	—
267	C₂×C₃×C₄	—	20	2	no	—
268	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
271	C₃×C₈	—	10	4	no	—
272	C₃×C₈	—	20	2	no	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	4	1	no	—
275	C₂²×C₅	—	4	1	no	—
276	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×D₅	—	2	1	no	—
278	C₂×D₅	—	2	1	no	—
279	C₂×D₅	C₃×C₂²⋊C₈	1	2	yes	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	4	1	no	—
282	C₄×C₅	C₃×#104	1	2	yes	—
283	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
284	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
285	Dic₅	—	2	2	no	—
286	Dic₅	—	2	1	no	—
287	Dic₅	—	4	1	no	—
288	Dic₅	C₃×C₂²⋊C₈	1	2	yes	—
289	Dic₅	C₃×#135	1	2	yes	—
290	#41	—	5	4	no	—
291	#41	—	10	2	no	—
292	C₂×Q₈	—	5	1	no	—
293	C₂×D₄	—	10	1	no	—
294	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	5	1	no	—
297	C₂²×C₄	—	5	1	no	—
298	C₂²×C₄	—	5	1	no	—
299	C₂²×C₄	—	10	1	no	—
300	C₂²×C₄	—	10	1	no	—
301	C₂×C₈	—	10	2	no	—
302	C₂×C₈	—	10	4	no	—
303	C₂×C₈	—	10	2	no	—
304	C₄⋊C₄	—	5	1	no	—
305	C₄⋊C₄	—	10	1	no	—
306	C₄⋊C₄	—	10	1	no	—
307	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
308	C₂²⋊C₄	—	2	1	no	—
309	C₂²⋊C₄	—	10	1	no	—
310	C₂²⋊C₄	—	10	1	no	—
311	C₄²	—	5	1	no	—
312	C₄²	—	5	1	no	—
313	C₄²	—	5	1	no	—
314	C₄²	—	10	1	no	—
315	C₄²	—	10	1	no	—
316	C₄²	—	10	1	no	—
317	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
318	C₃×C₅	#1476	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	4	1	no	—
321	C₂²×C₃	—	4	1	no	—
322	C₂²×C₃	—	5	2	no	—
323	C₂²×C₃	—	10	1	no	—
324	C₂²×C₃	—	10	1	no	—
325	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	—	5	2	no	—
329	C₃×C₄	—	5	2	no	—
330	C₃×C₄	—	10	2	no	—
331	C₃×C₄	—	10	1	no	—
332	C₃×C₄	—	20	1	no	—
333	C₃×C₄	#4008	1	2	yes	—
334	C₃×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
335	C₃×C₄	D₅⋊M₁₆	1	1	yes	characteristic
336	C₂×C₅	—	4	2	no	—
337	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
338	C₂×C₅	C₃×#416	1	1	yes	characteristic
339	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
340	D₅	—	2	2	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	5	1	no	—
343	Q₈	—	5	2	no	—
344	Q₈	—	10	1	no	—
345	D₄	—	2	1	no	—
346	D₄	—	10	4	no	—
347	D₄	C₃×D₅⋊C₈	1	2	yes	complemented
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	5	1	no	—
351	C₂×C₄	—	5	1	no	—
352	C₂×C₄	—	5	2	no	—
353	C₂×C₄	—	5	2	no	—
354	C₂×C₄	—	5	1	no	—
355	C₂×C₄	—	10	2	no	—
356	C₂×C₄	—	10	4	no	—
357	C₂×C₄	—	10	1	no	—
358	C₂×C₄	—	10	2	no	—
359	C₂×C₄	—	10	1	no	—
360	C₂×C₄	—	20	2	no	—
361	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
362	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
363	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
364	C₈	—	10	4	no	—
365	C₈	—	20	2	no	—
366	C₂×C₃	—	4	2	no	—
367	C₂×C₃	—	10	2	no	—
368	C₂×C₃	D₅⋊(C₂²⋊C₈)	1	1	yes	characteristic
369	C₂×C₃	C₂×#4008	1	1	yes	characteristic
370	C₂×C₃	#65794	1	1	yes	characteristic
371	C₅	C₃×#1476	1	1	yes	characteristic, complemented, Sylow
372	C₂²	—	2	2	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	5	2	no	—
376	C₂²	—	10	1	no	—
377	C₂²	—	10	1	no	—
378	C₂²	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	5	2	no	—
382	C₄	—	5	2	no	—
383	C₄	—	10	2	no	—
384	C₄	—	10	1	no	—
385	C₄	—	20	1	no	—
386	C₄	C₃×#4008	1	2	yes	—
387	C₄	C₂×C₃×D₅⋊C₈	1	1	yes	characteristic
388	C₄	C₃×D₅⋊M₁₆	1	1	yes	characteristic
389	C₃	#10604401	1	1	yes	characteristic, direct product factor, Sylow
390	C₂	—	4	2	no	—
391	C₂	—	10	2	no	—
392	C₂	C₃×D₅⋊(C₂²⋊C₈)	1	1	yes	characteristic
393	C₂	C₂×C₃×#4008	1	1	yes	characteristic
394	C₂	C₃×#65794	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂²×C₃×C₈
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₄×C₅×D₄	C₄
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#711	C₄
cosocle	C₄×Dic₅	C₂³×C₃
hypercenter	C₃×C₄×D₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1476
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₃×#65680	C₂	semidirect
3. C₃×C₄×D₅⋊C₈	C₂	semidirect
4. C₃×D₄⋊#170	C₂	semidirect
5. C₃×#64872	C₂	semidirect
6. #10604401	C₃	direct (N × H)
26. #65680	C₂×C₃	semidirect
27. C₄×D₅⋊C₈	C₂×C₃	semidirect
28. D₄⋊#170	C₂×C₃	semidirect
29. #64872	C₂×C₃	semidirect
36. C₃×#711	C₈	semidirect
84. C₃×C₅×D₄	C₂×C₈	semidirect
103. C₃×Dic₁₀	C₂×C₈	semidirect
129. #711	C₃×C₈	semidirect
204. C₅×D₄	C₂×C₃×C₈	semidirect
223. Dic₁₀	C₂×C₃×C₈	semidirect
254. C₃×D₄	D₅⋊C₈	semidirect
318. C₃×C₅	#1476	semidirect
347. D₄	C₃×D₅⋊C₈	semidirect
371. C₅	C₃×#1476	semidirect
389. C₃	#10604401	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×C₄×#711	2
C₃×#65680	2
C₃×C₄×D₅⋊C₈	2
C₃×D₄⋊#170	2
C₃×#64872	2
#10604401	3
C₃×#1476	5

Subgroups — C3×#10604401 #14281573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10604401 #14281573