Subgroups — C₃×#10601083 #14296012

Order 1920.

584 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	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3969	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65286	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64772	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64752	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601083	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×#117	C₂²	1	1	yes	characteristic
12	C₃×#4094	—	2	2	no	—
13	C₃×#4094	C₄	1	4	yes	complemented
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	—	2	1	no	—
16	C₂×C₃×#681	C₂²	1	1	yes	characteristic
17	C₂×C₃×#681	C₂²	1	1	yes	characteristic
18	C₂²×C₃×#168	—	2	1	no	—
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₃×C₅×#103	C₄	1	2	yes	complemented
21	C₃×C₅×#102	C₄	1	2	yes	complemented
22	C₃×#3969	C₄	1	4	yes	complemented
23	C₃×#3947	—	2	2	no	—
24	C₃×#3935	—	2	1	no	—
25	C₃×C₄×#168	—	2	1	no	—
26	C₃×#1765	—	5	1	no	maximal, Hall
27	C₂×#4094	C₂×C₃	1	1	yes	characteristic
28	C₅×#416	C₂×C₃	1	1	yes	characteristic
29	C₂×#3969	C₂×C₃	1	1	yes	characteristic
30	C₂×#3947	C₂×C₃	1	1	yes	characteristic, complemented
31	#65286	C₂×C₃	1	1	yes	characteristic, complemented
32	#64772	C₂×C₃	1	1	yes	characteristic, complemented
33	#64752	C₂×C₃	1	1	yes	characteristic, complemented
34	C₃×C₅×#41	—	2	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	C₂×C₄	1	2	yes	—
37	C₃×C₅×#41	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×Dic₅	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
47	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄×Dic₅	—	2	1	no	—
51	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
52	C₃×#681	—	2	1	no	—
53	C₃×#681	—	2	1	no	—
54	C₃×#681	—	2	4	no	—
55	C₃×#681	C₂×C₄	1	2	yes	—
56	C₃×#681	C₂×C₄	1	2	yes	—
57	C₂×C₃×#168	—	2	1	no	—
58	C₂×C₃×#168	—	2	1	no	—
59	C₂×C₃×#168	—	2	4	no	—
60	C₂×C₃×#168	C₂×C₄	1	2	yes	—
61	C₂×C₃×#168	D₄	1	2	yes	—
62	C₂×C₃×#168	D₄	1	1	yes	characteristic
63	C₂×C₃×#168	D₄	1	1	yes	characteristic
64	C₂×C₃×#131	—	5	1	no	—
65	C₂×C₃×#104	—	5	1	no	—
66	C₃×#416	D₅	1	1	yes	characteristic
67	C₃×#405	—	5	1	no	—
68	C₂×C₃×#97	—	5	1	no	—
69	C₃×#341	—	5	1	no	—
70	C₃×#339	—	5	1	no	—
71	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₅×#117	C₂²×C₃	1	1	yes	characteristic
74	#4094	—	2	2	no	—
75	#4094	C₃×C₄	1	4	yes	complemented
76	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
77	C₂×#681	—	2	1	no	—
78	C₂×#681	C₂²×C₃	1	1	yes	characteristic
79	C₂×#681	C₂²×C₃	1	1	yes	characteristic
80	C₂²×#168	—	2	1	no	—
81	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
82	C₅×#103	C₃×C₄	1	2	yes	complemented
83	C₅×#102	C₃×C₄	1	2	yes	complemented
84	#3969	C₃×C₄	1	4	yes	complemented
85	#3947	—	2	2	no	—
86	#3935	—	2	1	no	—
87	C₄×#168	—	2	1	no	—
88	#1765	—	5	1	no	Sylow
89	C₂³×C₃×C₅	—	2	1	no	—
90	C₂³×C₃×C₅	#41	1	1	yes	characteristic
91	C₃×C₅×Q₈	—	2	1	no	—
92	C₃×C₅×Q₈	C₄²	1	2	yes	—
93	C₃×C₅×D₄	—	2	2	no	—
94	C₃×C₅×D₄	—	2	2	no	—
95	C₃×C₅×D₄	—	2	1	no	—
96	C₃×C₅×D₄	C₄²	1	2	yes	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₂×C₃×Dic₅	—	2	2	no	—
108	C₂×C₃×Dic₅	—	4	2	no	—
109	C₃×C₅×C₈	—	2	2	no	—
110	C₃×#168	—	2	2	no	—
111	C₃×#168	—	2	2	no	—
112	C₃×#168	C₂²⋊C₄	1	2	yes	—
113	C₃×#168	C₂²⋊C₄	1	2	yes	—
114	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
115	C₃×#131	—	5	4	no	—
116	C₃×#131	—	10	2	no	—
117	C₂×C₃×M₁₆	—	5	1	no	—
118	C₂×C₃×M₁₆	—	5	1	no	—
119	C₂×C₃×M₁₆	—	10	1	no	—
120	C₂²×C₃×C₈	—	5	1	no	—
121	C₂²×C₃×C₈	—	10	1	no	—
122	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
123	C₃×#117	C₂×D₅	1	1	yes	characteristic
124	C₂×C₃×C₄²	—	5	1	no	—
125	C₃×#104	—	5	4	no	—
126	C₃×#103	Dic₅	1	2	yes	complemented
127	C₃×#102	Dic₅	1	2	yes	complemented
128	C₃×#97	—	10	1	no	—
129	C₃×#97	—	10	2	no	—
130	C₃×C₄×C₈	—	10	1	no	—
131	C₅×#41	—	2	1	no	—
132	C₅×#41	—	2	1	no	—
133	C₅×#41	C₂×C₃×C₄	1	2	yes	—
134	C₅×#41	C₂×C₃×C₄	1	2	yes	—
135	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₂²×Dic₅	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
144	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
145	C₅×C₂²⋊C₄	—	2	1	no	—
146	C₄²×C₅	—	2	1	no	—
147	C₄×Dic₅	—	2	1	no	—
148	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
149	#681	—	2	1	no	—
150	#681	—	2	1	no	—
151	#681	—	2	4	no	—
152	#681	C₂×C₃×C₄	1	2	yes	—
153	#681	C₂×C₃×C₄	1	2	yes	—
154	C₂×#168	—	2	1	no	—
155	C₂×#168	—	2	1	no	—
156	C₂×#168	—	2	4	no	—
157	C₂×#168	C₂×C₃×C₄	1	2	yes	—
158	C₂×#168	C₃×D₄	1	1	yes	characteristic
159	C₂×#168	C₃×D₄	1	1	yes	characteristic
160	C₂×#168	C₃×D₄	1	2	yes	—
161	C₂×#131	—	5	1	no	—
162	C₂×#104	—	5	1	no	—
163	#416	C₃×D₅	1	1	yes	characteristic
164	#405	—	5	1	no	—
165	C₂×#97	—	5	1	no	—
166	#341	—	5	1	no	—
167	#339	—	5	1	no	—
168	C₂²×C₃×C₅	—	2	2	no	—
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	—	4	2	no	—
171	C₂²×C₃×C₅	#117	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
173	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
174	C₃×C₄×C₅	—	2	2	no	—
175	C₃×C₄×C₅	—	4	2	no	—
176	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
177	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
179	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
180	C₃×Dic₅	—	4	2	no	—
181	C₃×#41	—	2	1	no	—
182	C₃×#41	—	2	1	no	—
183	C₃×#41	C₄×D₅	1	2	yes	—
184	C₃×#41	C₄×D₅	1	2	yes	—
185	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
186	C₂×C₃×D₄	—	2	1	no	—
187	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₂²×C₃×C₄	—	10	1	no	—
190	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
191	C₃×M₁₆	—	5	2	no	—
192	C₃×M₁₆	—	5	2	no	—
193	C₃×M₁₆	—	10	4	no	—
194	C₃×M₁₆	—	10	1	no	—
195	C₃×M₁₆	—	10	1	no	—
196	C₂×C₃×C₈	—	2	1	no	—
197	C₂×C₃×C₈	—	2	1	no	—
198	C₂×C₃×C₈	—	5	2	no	—
199	C₂×C₃×C₈	—	5	2	no	—
200	C₂×C₃×C₈	—	5	1	no	—
201	C₂×C₃×C₈	—	5	1	no	—
202	C₂×C₃×C₈	—	10	4	no	—
203	C₂×C₃×C₈	—	10	1	no	—
204	C₂×C₃×C₈	—	10	1	no	—
205	C₂×C₃×C₈	C₂×Dic₅	1	2	yes	—
206	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
207	C₃×C₂²⋊C₄	—	2	1	no	—
208	C₃×C₄²	—	2	1	no	—
209	C₃×C₄²	—	5	2	no	—
210	C₃×C₄²	—	10	1	no	—
211	C₂³×C₅	—	2	1	no	—
212	C₂³×C₅	C₃×#41	1	1	yes	characteristic
213	C₅×Q₈	—	2	1	no	—
214	C₅×Q₈	C₃×C₄²	1	2	yes	—
215	C₅×D₄	—	2	2	no	—
216	C₅×D₄	—	2	2	no	—
217	C₅×D₄	—	2	1	no	—
218	C₅×D₄	C₃×C₄²	1	2	yes	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
229	C₂×Dic₅	—	2	2	no	—
230	C₂×Dic₅	—	4	2	no	—
231	C₅×C₈	—	2	2	no	—
232	#168	—	2	2	no	—
233	#168	—	2	2	no	—
234	#168	C₃×C₂²⋊C₄	1	2	yes	—
235	#168	C₃×C₂²⋊C₄	1	2	yes	—
236	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
237	#131	—	5	4	no	—
238	#131	—	10	2	no	—
239	C₂×M₁₆	—	5	1	no	—
240	C₂×M₁₆	—	5	1	no	—
241	C₂×M₁₆	—	10	1	no	—
242	C₂²×C₈	—	5	1	no	—
243	C₂²×C₈	—	10	1	no	—
244	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
245	#117	C₂×C₃×D₅	1	1	yes	characteristic
246	C₂×C₄²	—	5	1	no	—
247	#104	—	5	4	no	—
248	#103	C₃×Dic₅	1	2	yes	complemented
249	#102	C₃×Dic₅	1	2	yes	complemented
250	#97	—	10	1	no	—
251	#97	—	10	2	no	—
252	C₄×C₈	—	10	1	no	—
253	C₂×C₃×C₅	—	2	1	no	—
254	C₂×C₃×C₅	—	2	1	no	—
255	C₂×C₃×C₅	—	4	2	no	—
256	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₃×C₅	#444	1	2	yes	—
258	C₂³×C₃	—	2	1	no	—
259	C₂³×C₃	#711	1	1	yes	characteristic
260	C₃×Q₈	—	2	1	no	—
261	C₃×Q₈	C₄×Dic₅	1	2	yes	—
262	C₃×D₄	—	2	2	no	—
263	C₃×D₄	—	2	2	no	—
264	C₃×D₄	—	2	1	no	—
265	C₃×D₄	C₄×Dic₅	1	2	yes	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	10	2	no	—
271	C₂×C₃×C₄	—	20	2	no	—
272	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
274	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
275	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
276	C₂×C₃×C₄	#711	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
278	C₃×C₈	—	2	2	no	—
279	C₃×C₈	—	5	2	no	—
280	C₃×C₈	—	5	2	no	—
281	C₃×C₈	—	10	2	no	—
282	C₃×C₈	—	10	2	no	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	—	4	2	no	—
286	C₂²×C₅	C₃×#117	1	1	yes	characteristic
287	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
288	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	4	2	no	—
291	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
292	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
293	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
294	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
295	Dic₅	—	4	2	no	—
296	#41	—	2	1	no	—
297	#41	—	2	1	no	—
298	#41	C₃×C₄×D₅	1	2	yes	—
299	#41	C₃×C₄×D₅	1	2	yes	—
300	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	10	1	no	—
305	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
306	M₁₆	—	5	2	no	—
307	M₁₆	—	5	2	no	—
308	M₁₆	—	10	4	no	—
309	M₁₆	—	10	1	no	—
310	M₁₆	—	10	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	5	2	no	—
314	C₂×C₈	—	5	1	no	—
315	C₂×C₈	—	5	1	no	—
316	C₂×C₈	—	5	2	no	—
317	C₂×C₈	—	10	4	no	—
318	C₂×C₈	—	10	1	no	—
319	C₂×C₈	—	10	1	no	—
320	C₂×C₈	C₂×C₃×Dic₅	1	2	yes	—
321	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
322	C₂²⋊C₄	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	5	2	no	—
325	C₄²	—	10	1	no	—
326	C₃×C₅	#1765	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	4	2	no	—
330	C₂²×C₃	#4023	1	1	yes	characteristic
331	C₂²×C₃	#4027	1	1	yes	characteristic
332	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
333	C₃×C₄	—	2	2	no	—
334	C₃×C₄	—	4	2	no	—
335	C₃×C₄	—	20	2	no	—
336	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
337	C₃×C₄	#4027	1	1	yes	characteristic
338	C₃×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
339	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
340	C₂×C₅	—	2	1	no	—
341	C₂×C₅	—	2	1	no	—
342	C₂×C₅	—	4	2	no	—
343	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
344	C₂×C₅	C₃×#444	1	2	yes	—
345	C₂³	—	2	1	no	—
346	C₂³	C₃×#711	1	1	yes	characteristic
347	Q₈	—	2	1	no	—
348	Q₈	C₃×C₄×Dic₅	1	2	yes	—
349	D₄	—	2	2	no	—
350	D₄	—	2	2	no	—
351	D₄	—	2	1	no	—
352	D₄	C₃×C₄×Dic₅	1	2	yes	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	10	2	no	—
358	C₂×C₄	—	20	2	no	—
359	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
360	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
361	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
362	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
363	C₂×C₄	C₃×#711	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	5	2	no	—
367	C₈	—	5	2	no	—
368	C₈	—	10	2	no	—
369	C₈	—	10	2	no	—
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	4	2	no	—
373	C₂×C₃	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
374	C₂×C₃	#65486	1	2	yes	—
375	C₅	C₃×#1765	1	1	yes	characteristic, complemented, Sylow
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	C₃×#4023	1	1	yes	characteristic
380	C₂²	C₃×#4027	1	1	yes	characteristic
381	C₂²	C₃×D₄×Dic₅	1	1	yes	characteristic
382	C₄	—	2	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	20	2	no	—
385	C₄	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
386	C₄	C₃×#4027	1	1	yes	characteristic
387	C₄	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
388	C₄	C₃×D₄×Dic₅	1	1	yes	characteristic
389	C₃	#10601083	1	1	yes	characteristic, direct product factor, Sylow
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	4	2	no	—
393	C₂	C₃×C₂²⋊C₄×Dic₅	1	1	yes	characteristic
394	C₂	C₃×#65486	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator	C₄×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#416	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#416	D₅
hypocenter	C₅	C₃×#1765
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#416

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×#3947	C₂	semidirect
5. C₃×#65286	C₂	semidirect
6. C₃×#64772	C₂	semidirect
7. C₃×#64752	C₂	semidirect
8. #10601083	C₃	direct (N × H)
13. C₃×#4094	C₄	semidirect
20. C₃×C₅×#103	C₄	semidirect
21. C₃×C₅×#102	C₄	semidirect
22. C₃×#3969	C₄	semidirect
30. C₂×#3947	C₂×C₃	semidirect
31. #65286	C₂×C₃	semidirect
32. #64772	C₂×C₃	semidirect
33. #64752	C₂×C₃	semidirect
75. #4094	C₃×C₄	semidirect
82. C₅×#103	C₃×C₄	semidirect
83. C₅×#102	C₃×C₄	semidirect
84. #3969	C₃×C₄	semidirect
126. C₃×#103	Dic₅	semidirect
127. C₃×#102	Dic₅	semidirect
248. #103	C₃×Dic₅	semidirect
249. #102	C₃×Dic₅	semidirect
326. C₃×C₅	#1765	semidirect
375. C₅	C₃×#1765	semidirect
389. C₃	#10601083	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×#4094	2
C₃×C₅×#416	2
C₂×C₃×#3969	2
C₂×C₃×#3947	2
C₃×#65286	2
C₃×#64772	2
C₃×#64752	2
#10601083	3
C₃×#1765	5

Subgroups — C3×#10601083 #14296012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601083 #14296012