Subgroups — C₃×#10605000 #14281569

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×#41×Dic₅	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×Q₈⋊#170	C₂	1	2	yes	maximal, complemented
5	C₃×D₄⋊#170	C₂	1	2	yes	maximal, complemented
6	#10605000	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₄	1	1	yes	characteristic
8	C₂²×C₃×#170	—	2	1	no	—
9	C₃×Q₈×Dic₅	C₄	1	1	yes	characteristic
10	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic
11	C₃×D₄×Dic₅	—	2	1	no	—
12	C₃×D₄×Dic₅	—	2	1	no	—
13	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic
14	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₃×#4072	—	2	1	no	—
16	C₃×#4072	C₄	1	1	yes	characteristic
17	C₂×C₃×C₄×Dic₅	—	2	1	no	—
18	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
19	C₃×C₂²⋊#170	—	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	#41×Dic₅	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	Q₈⋊#170	C₂×C₃	1	2	yes	complemented
29	D₄⋊#170	C₂×C₃	1	2	yes	complemented
30	C₃×C₅×#41	—	2	2	no	—
31	C₃×C₅×#41	C₈	1	4	yes	complemented
32	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₅×D₄	—	2	1	no	—
34	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×Dic₅	—	2	1	no	—
38	C₂²×C₃×Dic₅	—	2	1	no	—
39	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
41	C₂×C₃×#170	—	2	4	no	—
42	C₂×C₃×#170	—	2	2	no	—
43	C₂×C₃×#170	—	2	2	no	—
44	C₃×C₂²⋊Dic₅	—	2	1	no	—
45	C₃×C₂²⋊Dic₅	—	2	1	no	—
46	C₃×C₂²⋊Dic₅	—	2	1	no	—
47	C₃×C₄⋊Dic₅	—	2	1	no	—
48	C₃×C₄⋊Dic₅	—	2	1	no	—
49	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
50	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄×Dic₅	—	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×C₅×#41	C₃×C₄	1	1	yes	characteristic
64	C₂²×#170	—	2	1	no	—
65	Q₈×Dic₅	C₃×C₄	1	1	yes	characteristic
66	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
67	D₄×Dic₅	—	2	1	no	—
68	D₄×Dic₅	—	2	1	no	—
69	D₄×Dic₅	C₃×C₄	1	1	yes	characteristic
70	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
71	#4072	—	2	1	no	—
72	#4072	C₃×C₄	1	1	yes	characteristic
73	C₂×C₄×Dic₅	—	2	1	no	—
74	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
75	C₂²⋊#170	—	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	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₃×C₅×Q₈	—	2	1	no	—
84	C₃×C₅×Q₈	C₂×C₈	1	2	yes	complemented
85	C₃×C₅×D₄	—	2	4	no	—
86	C₃×C₅×D₄	—	2	1	no	—
87	C₃×C₅×D₄	C₂×C₈	1	2	yes	complemented
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
92	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×Dic₅	—	2	2	no	—
95	C₂×C₃×Dic₅	—	2	2	no	—
96	C₂×C₃×Dic₅	—	2	1	no	—
97	C₂×C₃×Dic₅	—	2	1	no	—
98	C₂×C₃×Dic₅	—	4	2	no	—
99	C₂×C₃×Dic₅	—	4	2	no	—
100	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
104	C₃×#170	—	2	4	no	—
105	C₃×#170	—	4	2	no	—
106	C₂×C₃×#41	AGL(1,𝔽₅)	1	1	yes	characteristic
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	—	5	1	no	—
112	C₃×C₄×D₄	—	10	1	no	—
113	C₃×C₄×D₄	—	10	1	no	—
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	C₅×#41	—	2	2	no	—
124	C₅×#41	C₃×C₈	1	4	yes	complemented
125	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
126	C₂×C₅×D₄	—	2	1	no	—
127	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
130	C₂²×Dic₅	—	2	1	no	—
131	C₂²×Dic₅	—	2	1	no	—
132	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
133	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
134	C₂×#170	—	2	4	no	—
135	C₂×#170	—	2	2	no	—
136	C₂×#170	—	2	2	no	—
137	C₂²⋊Dic₅	—	2	1	no	—
138	C₂²⋊Dic₅	—	2	1	no	—
139	C₂²⋊Dic₅	—	2	1	no	—
140	C₄⋊Dic₅	—	2	1	no	—
141	C₄⋊Dic₅	—	2	1	no	—
142	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
143	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
144	C₄×Dic₅	—	2	1	no	—
145	C₄×Dic₅	—	2	1	no	—
146	C₄×Dic₅	—	2	1	no	—
147	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
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	1	no	—
157	C₂²×C₃×C₅	—	2	1	no	—
158	C₂²×C₃×C₅	—	2	2	no	—
159	C₂²×C₃×C₅	—	4	1	no	—
160	C₂²×C₃×C₅	—	4	1	no	—
161	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
162	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₃×C₄×C₅	—	2	2	no	—
164	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
165	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
166	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
167	C₃×Dic₅	—	2	1	no	—
168	C₃×Dic₅	—	2	1	no	—
169	C₃×Dic₅	—	4	1	no	—
170	C₃×Dic₅	—	4	1	no	—
171	C₃×Dic₅	#104	1	2	yes	—
172	C₃×Dic₅	#135	1	2	yes	—
173	C₃×#41	—	2	2	no	—
174	C₃×#41	#170	1	4	yes	complemented
175	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
176	C₂×C₃×D₄	—	2	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	—	10	1	no	—
182	C₂²×C₃×C₄	—	10	1	no	—
183	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
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	—	5	1	no	—
189	C₃×C₄⋊C₄	—	10	1	no	—
190	C₃×C₄⋊C₄	—	10	1	no	—
191	C₃×C₂²⋊C₄	—	10	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	—	5	1	no	—
198	C₃×C₄²	—	10	1	no	—
199	C₃×C₄²	—	10	1	no	—
200	C₃×C₄²	—	10	1	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
203	C₅×Q₈	—	2	1	no	—
204	C₅×Q₈	C₂×C₃×C₈	1	2	yes	complemented
205	C₅×D₄	—	2	4	no	—
206	C₅×D₄	—	2	1	no	—
207	C₅×D₄	C₂×C₃×C₈	1	2	yes	complemented
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×C₃×C₈	1	2	yes	—
212	C₂×C₄×C₅	C₃×M₁₆	1	2	yes	—
213	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
214	C₂×Dic₅	—	2	2	no	—
215	C₂×Dic₅	—	2	2	no	—
216	C₂×Dic₅	—	2	1	no	—
217	C₂×Dic₅	—	2	1	no	—
218	C₂×Dic₅	—	4	2	no	—
219	C₂×Dic₅	—	4	2	no	—
220	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
223	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
224	#170	—	2	4	no	—
225	#170	—	4	2	no	—
226	C₂×#41	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
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	—	5	1	no	—
232	C₄×D₄	—	10	1	no	—
233	C₄×D₄	—	10	1	no	—
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	—	2	2	no	—
244	C₂×C₃×C₅	—	4	2	no	—
245	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
246	C₂×C₃×C₅	#416	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
250	C₃×Q₈	—	2	1	no	—
251	C₃×Q₈	C₂×#170	1	2	yes	complemented
252	C₃×D₄	—	2	4	no	—
253	C₃×D₄	—	2	1	no	—
254	C₃×D₄	C₂×#170	1	2	yes	complemented
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	5	1	no	—
258	C₂×C₃×C₄	—	5	1	no	—
259	C₂×C₃×C₄	—	5	1	no	—
260	C₂×C₃×C₄	—	5	1	no	—
261	C₂×C₃×C₄	—	10	2	no	—
262	C₂×C₃×C₄	—	10	2	no	—
263	C₂×C₃×C₄	—	10	1	no	—
264	C₂×C₃×C₄	—	10	1	no	—
265	C₂×C₃×C₄	—	20	2	no	—
266	C₂×C₃×C₄	—	20	2	no	—
267	C₂×C₃×C₄	C₂×#170	1	2	yes	—
268	C₂×C₃×C₄	#704	1	2	yes	—
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	1	no	—
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	4	1	no	—
277	C₂²×C₅	—	4	1	no	—
278	C₂²×C₅	C₃×C₂²⋊C₈	1	2	yes	—
279	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	C₃×C₂²⋊C₈	1	2	yes	—
282	C₄×C₅	C₂²×C₃×C₈	1	1	yes	characteristic
283	C₄×C₅	C₂×C₃×M₁₆	1	1	yes	characteristic
284	Dic₅	—	2	1	no	—
285	Dic₅	—	2	1	no	—
286	Dic₅	—	4	1	no	—
287	Dic₅	—	4	1	no	—
288	Dic₅	C₃×#104	1	2	yes	—
289	Dic₅	C₃×#135	1	2	yes	—
290	#41	—	2	2	no	—
291	#41	C₃×#170	1	4	yes	complemented
292	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
293	C₂×D₄	—	2	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	—	10	1	no	—
299	C₂²×C₄	—	10	1	no	—
300	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
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	—	5	1	no	—
306	C₄⋊C₄	—	10	1	no	—
307	C₄⋊C₄	—	10	1	no	—
308	C₂²⋊C₄	—	10	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	—	5	1	no	—
315	C₄²	—	10	1	no	—
316	C₄²	—	10	1	no	—
317	C₄²	—	10	1	no	—
318	C₃×C₅	#1476	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	4	1	no	—
323	C₂²×C₃	—	4	1	no	—
324	C₂²×C₃	C₂²⋊#170	1	2	yes	—
325	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	5	2	no	—
328	C₃×C₄	—	5	2	no	—
329	C₃×C₄	—	10	1	no	—
330	C₃×C₄	—	10	1	no	—
331	C₃×C₄	—	20	1	no	—
332	C₃×C₄	—	20	1	no	—
333	C₃×C₄	C₂²⋊#170	1	2	yes	—
334	C₃×C₄	C₂²×#170	1	1	yes	characteristic
335	C₃×C₄	C₂×#704	1	1	yes	characteristic
336	C₂×C₅	—	2	2	no	—
337	C₂×C₅	—	4	2	no	—
338	C₂×C₅	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
339	C₂×C₅	C₃×#416	1	1	yes	characteristic
340	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
341	C₂³	—	2	1	no	—
342	C₂³	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
343	Q₈	—	2	1	no	—
344	Q₈	C₂×C₃×#170	1	2	yes	complemented
345	D₄	—	2	4	no	—
346	D₄	—	2	1	no	—
347	D₄	C₂×C₃×#170	1	2	yes	complemented
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	5	1	no	—
351	C₂×C₄	—	5	1	no	—
352	C₂×C₄	—	5	1	no	—
353	C₂×C₄	—	5	1	no	—
354	C₂×C₄	—	10	2	no	—
355	C₂×C₄	—	10	2	no	—
356	C₂×C₄	—	10	1	no	—
357	C₂×C₄	—	10	1	no	—
358	C₂×C₄	—	20	2	no	—
359	C₂×C₄	—	20	2	no	—
360	C₂×C₄	C₂×C₃×#170	1	2	yes	—
361	C₂×C₄	C₃×#704	1	2	yes	—
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	—	2	2	no	—
367	C₂×C₃	—	4	2	no	—
368	C₂×C₃	D₅⋊#104	1	1	yes	characteristic
369	C₂×C₃	#65794	1	1	yes	characteristic
370	C₂×C₃	C₂×C₂²⋊#170	1	1	yes	characteristic
371	C₅	C₃×#1476	1	1	yes	characteristic, complemented, Sylow
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	C₃×C₂²⋊#170	1	2	yes	—
378	C₂²	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	5	2	no	—
381	C₄	—	5	2	no	—
382	C₄	—	10	1	no	—
383	C₄	—	10	1	no	—
384	C₄	—	20	1	no	—
385	C₄	—	20	1	no	—
386	C₄	C₃×C₂²⋊#170	1	2	yes	—
387	C₄	C₂²×C₃×#170	1	1	yes	characteristic
388	C₄	C₂×C₃×#704	1	1	yes	characteristic
389	C₃	#10605000	1	1	yes	characteristic, direct product factor, Sylow
390	C₂	—	2	2	no	—
391	C₂	—	4	2	no	—
392	C₂	C₃×D₅⋊#104	1	1	yes	characteristic
393	C₂	C₃×#65794	1	1	yes	characteristic
394	C₂	C₂×C₃×C₂²⋊#170	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, prime radical	C₂×C₃×C₅×#41	C₄
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
cosocle	C₄×Dic₅	C₂³×C₃
hypercenter	C₂×C₃×#41	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1476
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#41

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×Q₈⋊#170	C₂	semidirect
5. C₃×D₄⋊#170	C₂	semidirect
6. #10605000	C₃	direct (N × H)
26. #65748	C₂×C₃	semidirect
27. C₂×C₄×#170	C₂×C₃	semidirect
28. Q₈⋊#170	C₂×C₃	semidirect
29. D₄⋊#170	C₂×C₃	semidirect
31. C₃×C₅×#41	C₈	semidirect
84. C₃×C₅×Q₈	C₂×C₈	semidirect
87. C₃×C₅×D₄	C₂×C₈	semidirect
124. C₅×#41	C₃×C₈	semidirect
174. C₃×#41	#170	semidirect
204. C₅×Q₈	C₂×C₃×C₈	semidirect
207. C₅×D₄	C₂×C₃×C₈	semidirect
251. C₃×Q₈	C₂×#170	semidirect
254. C₃×D₄	C₂×#170	semidirect
291. #41	C₃×#170	semidirect
318. C₃×C₅	#1476	semidirect
344. Q₈	C₂×C₃×#170	semidirect
347. D₄	C₂×C₃×#170	semidirect
371. C₅	C₃×#1476	semidirect
389. C₃	#10605000	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×#41×Dic₅	2
C₃×#65748	2
C₂×C₃×C₄×#170	2
C₃×Q₈⋊#170	2
C₃×D₄⋊#170	2
#10605000	3
C₃×#1476	5

Subgroups — C3×#10605000 #14281569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605000 #14281569