Subgroups — C₃×#10605400 #14332543

Order 1920.

1008 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×Dic₁₀	C₂	1	2	yes	maximal
2	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#65273	C₂	1	2	yes	maximal
4	C₃×#65268	C₂	1	2	yes	maximal
5	C₃×C₄×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
6	C₃×#65221	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×#683	C₂	1	2	yes	maximal
8	C₃×#64946	C₂	1	2	yes	maximal
9	C₃×#64945	C₂	1	2	yes	maximal
10	#10605400	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×#683	C₂²	1	2	yes	—
18	C₂×C₃×#683	C₂²	1	2	yes	—
19	C₂×C₃×#683	C₂²	1	2	yes	—
20	C₂×C₃×#683	C₂²	1	2	yes	—
21	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
24	C₃×C₄×Dic₁₀	—	2	8	no	—
25	C₃×C₅×#95	C₂²	1	1	yes	characteristic
26	C₃×C₅×#95	C₂²	1	1	yes	characteristic
27	C₃×#3963	C₂²	1	2	yes	—
28	C₃×#3963	C₂²	1	2	yes	—
29	C₃×#3963	C₂²	1	2	yes	—
30	C₃×#3963	C₂²	1	2	yes	—
31	C₃×#3963	C₂²	1	1	yes	characteristic
32	C₃×#3963	C₂²	1	1	yes	characteristic
33	C₃×#2399	—	5	1	no	maximal, Hall
34	C₂×C₄×Dic₁₀	C₂×C₃	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
36	#65273	C₂×C₃	1	2	yes	—
37	#65268	C₂×C₃	1	2	yes	—
38	C₄×C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic
39	#65221	C₂×C₃	1	1	yes	characteristic
40	C₄×#683	C₂×C₃	1	2	yes	—
41	#64946	C₂×C₃	1	2	yes	—
42	#64945	C₂×C₃	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
49	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
50	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
51	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
52	C₂×C₃×Dic₁₀	—	2	4	no	—
53	C₂×C₃×Dic₁₀	—	2	4	no	—
54	C₂×C₃×Dic₁₀	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₄²×C₅	—	2	4	no	—
57	C₃×C₄²×C₅	Q₈	1	4	yes	complemented
58	C₃×C₄⋊Dic₅	—	2	4	no	—
59	C₃×C₄⋊Dic₅	—	2	4	no	—
60	C₃×#683	—	2	4	no	—
61	C₃×#683	—	2	4	no	—
62	C₃×#683	—	2	4	no	—
63	C₃×#683	—	2	4	no	—
64	C₃×C₄×Dic₅	—	2	4	no	—
65	C₃×C₄×Dic₅	D₄	1	4	yes	—
66	C₃×C₄×Dic₅	Q₈	1	4	yes	complemented
67	C₂×C₃×C₄×Q₈	—	5	2	no	—
68	C₃×#398	—	5	2	no	—
69	C₃×#398	—	5	2	no	—
70	C₃×#395	—	5	2	no	—
71	C₃×#395	—	5	2	no	—
72	C₃×C₄×C₄⋊C₄	—	5	2	no	—
73	C₃×C₄×C₄⋊C₄	—	5	1	no	—
74	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic
75	C₃×#376	—	5	1	no	—
76	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
79	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
81	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
82	C₂×#683	C₂²×C₃	1	2	yes	—
83	C₂×#683	C₂²×C₃	1	2	yes	—
84	C₂×#683	C₂²×C₃	1	2	yes	—
85	C₂×#683	C₂²×C₃	1	2	yes	—
86	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
87	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
89	C₄×Dic₁₀	—	2	8	no	—
90	C₅×#95	C₂²×C₃	1	1	yes	characteristic
91	C₅×#95	C₂²×C₃	1	1	yes	characteristic
92	#3963	C₂²×C₃	1	2	yes	—
93	#3963	C₂²×C₃	1	2	yes	—
94	#3963	C₂²×C₃	1	2	yes	—
95	#3963	C₂²×C₃	1	2	yes	—
96	#3963	C₂²×C₃	1	1	yes	characteristic
97	#3963	C₂²×C₃	1	1	yes	characteristic
98	#2399	—	5	1	no	Sylow
99	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
112	C₂×C₃×C₄×C₅	#41	1	4	yes	—
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	—	2	2	no	—
115	C₂×C₃×Dic₅	—	2	2	no	—
116	C₂×C₃×Dic₅	—	2	2	no	—
117	C₂×C₃×Dic₅	—	2	2	no	—
118	C₂×C₃×Dic₅	—	2	2	no	—
119	C₂×C₃×Dic₅	—	2	2	no	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
123	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	—
124	C₂×C₃×Dic₅	#41	1	4	yes	—
125	C₃×Dic₁₀	—	2	16	no	—
126	C₂²×C₃×Q₈	—	5	2	no	—
127	C₃×C₄×Q₈	—	10	8	no	—
128	C₂×C₃×C₄⋊C₄	—	5	2	no	—
129	C₂×C₃×C₄⋊C₄	—	5	2	no	—
130	C₂×C₃×C₄⋊C₄	—	5	2	no	—
131	C₂×C₃×C₄⋊C₄	—	5	2	no	—
132	C₂×C₃×C₄⋊C₄	—	5	2	no	—
133	C₂×C₃×C₄⋊C₄	—	5	2	no	—
134	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
135	C₂×C₃×C₄²	—	5	1	no	—
136	C₂×C₃×C₄²	—	5	1	no	—
137	C₂×C₃×C₄²	—	5	2	no	—
138	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
139	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
140	C₃×#95	—	5	2	no	—
141	C₃×#95	—	5	2	no	—
142	C₃×#95	—	5	2	no	—
143	C₃×#95	—	5	1	no	—
144	C₃×#95	—	5	2	no	—
145	C₃×#95	—	5	1	no	—
146	C₃×#95	C₂×D₅	1	1	yes	characteristic
147	C₃×#95	C₂×D₅	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
149	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
154	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
155	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
156	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
157	C₂×Dic₁₀	—	2	4	no	—
158	C₂×Dic₁₀	—	2	4	no	—
159	C₂×Dic₁₀	—	2	4	no	—
160	C₅×C₄⋊C₄	—	2	4	no	—
161	C₄²×C₅	—	2	4	no	—
162	C₄²×C₅	C₃×Q₈	1	4	yes	complemented
163	C₄⋊Dic₅	—	2	4	no	—
164	C₄⋊Dic₅	—	2	4	no	—
165	#683	—	2	4	no	—
166	#683	—	2	4	no	—
167	#683	—	2	4	no	—
168	#683	—	2	4	no	—
169	C₄×Dic₅	—	2	4	no	—
170	C₄×Dic₅	C₃×D₄	1	4	yes	—
171	C₄×Dic₅	C₃×Q₈	1	4	yes	complemented
172	C₂×C₄×Q₈	—	5	2	no	—
173	#398	—	5	2	no	—
174	#398	—	5	2	no	—
175	#395	—	5	2	no	—
176	#395	—	5	2	no	—
177	C₄×C₄⋊C₄	—	5	2	no	—
178	C₄×C₄⋊C₄	—	5	1	no	—
179	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic
180	#376	—	5	1	no	—
181	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
183	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
185	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
186	C₃×C₄×C₅	—	2	4	no	—
187	C₃×C₄×C₅	—	2	2	no	—
188	C₃×C₄×C₅	—	2	2	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	C₄⋊Q₈	1	4	yes	—
191	C₃×Dic₅	—	2	4	no	—
192	C₃×Dic₅	—	2	4	no	—
193	C₃×Dic₅	—	2	4	no	—
194	C₃×Dic₅	—	4	2	no	—
195	C₂×C₃×Q₈	—	10	4	no	—
196	C₂×C₃×Q₈	—	10	4	no	—
197	C₂×C₃×Q₈	—	10	4	no	—
198	C₂²×C₃×C₄	—	5	2	no	—
199	C₂²×C₃×C₄	—	5	2	no	—
200	C₂²×C₃×C₄	—	5	2	no	—
201	C₂²×C₃×C₄	—	5	2	no	—
202	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
203	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
207	C₃×C₄⋊C₄	—	2	4	no	—
208	C₃×C₄⋊C₄	—	10	4	no	—
209	C₃×C₄⋊C₄	—	10	4	no	—
210	C₃×C₄⋊C₄	—	10	4	no	—
211	C₃×C₄⋊C₄	—	10	4	no	—
212	C₃×C₄⋊C₄	—	10	4	no	—
213	C₃×C₄⋊C₄	—	10	4	no	—
214	C₃×C₄²	—	2	4	no	—
215	C₃×C₄²	—	5	4	no	—
216	C₃×C₄²	—	5	4	no	—
217	C₃×C₄²	—	10	4	no	—
218	C₃×C₄²	Dic₁₀	1	4	yes	complemented
219	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
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	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
228	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
229	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
230	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
231	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
232	C₂×C₄×C₅	C₃×#41	1	4	yes	—
233	C₂×Dic₅	—	2	2	no	—
234	C₂×Dic₅	—	2	2	no	—
235	C₂×Dic₅	—	2	2	no	—
236	C₂×Dic₅	—	2	2	no	—
237	C₂×Dic₅	—	2	2	no	—
238	C₂×Dic₅	—	2	2	no	—
239	C₂×Dic₅	—	2	2	no	—
240	C₂×Dic₅	—	2	2	no	—
241	C₂×Dic₅	—	2	2	no	—
242	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
243	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	—
244	C₂×Dic₅	C₃×#41	1	4	yes	—
245	Dic₁₀	—	2	16	no	—
246	C₂²×Q₈	—	5	2	no	—
247	C₄×Q₈	—	10	8	no	—
248	C₂×C₄⋊C₄	—	5	2	no	—
249	C₂×C₄⋊C₄	—	5	2	no	—
250	C₂×C₄⋊C₄	—	5	2	no	—
251	C₂×C₄⋊C₄	—	5	2	no	—
252	C₂×C₄⋊C₄	—	5	2	no	—
253	C₂×C₄⋊C₄	—	5	2	no	—
254	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
255	C₂×C₄²	—	5	1	no	—
256	C₂×C₄²	—	5	1	no	—
257	C₂×C₄²	—	5	2	no	—
258	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
259	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
260	#95	—	5	2	no	—
261	#95	—	5	2	no	—
262	#95	—	5	2	no	—
263	#95	—	5	1	no	—
264	#95	—	5	2	no	—
265	#95	—	5	1	no	—
266	#95	C₂×C₃×D₅	1	1	yes	characteristic
267	#95	C₂×C₃×D₅	1	1	yes	characteristic
268	C₂×C₃×C₅	#525	1	2	yes	—
269	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
270	C₂×C₃×C₅	#533	1	1	yes	characteristic
271	C₂×C₃×C₅	#533	1	1	yes	characteristic
272	C₂×C₃×C₅	#533	1	2	yes	—
273	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
274	C₃×Q₈	—	10	16	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	5	4	no	—
283	C₂×C₃×C₄	—	5	4	no	—
284	C₂×C₃×C₄	—	5	4	no	—
285	C₂×C₃×C₄	—	10	2	no	—
286	C₂×C₃×C₄	—	10	2	no	—
287	C₂×C₃×C₄	—	10	2	no	—
288	C₂×C₃×C₄	—	10	2	no	—
289	C₂×C₃×C₄	—	10	2	no	—
290	C₂×C₃×C₄	—	10	2	no	—
291	C₂×C₃×C₄	—	10	2	no	—
292	C₂×C₃×C₄	—	10	2	no	—
293	C₂×C₃×C₄	—	10	2	no	—
294	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
295	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
296	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
297	C₂×C₃×C₄	#709	1	4	yes	—
298	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
299	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
300	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
301	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
302	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
303	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
304	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
305	C₄×C₅	—	2	4	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	2	2	no	—
308	C₄×C₅	—	4	2	no	—
309	C₄×C₅	C₃×C₄⋊Q₈	1	4	yes	—
310	Dic₅	—	2	4	no	—
311	Dic₅	—	2	4	no	—
312	Dic₅	—	2	4	no	—
313	Dic₅	—	4	2	no	—
314	C₂×Q₈	—	10	4	no	—
315	C₂×Q₈	—	10	4	no	—
316	C₂×Q₈	—	10	4	no	—
317	C₂²×C₄	—	5	2	no	—
318	C₂²×C₄	—	5	2	no	—
319	C₂²×C₄	—	5	2	no	—
320	C₂²×C₄	—	5	2	no	—
321	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
322	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
325	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	10	4	no	—
328	C₄⋊C₄	—	10	4	no	—
329	C₄⋊C₄	—	10	4	no	—
330	C₄⋊C₄	—	10	4	no	—
331	C₄⋊C₄	—	10	4	no	—
332	C₄⋊C₄	—	10	4	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	5	4	no	—
335	C₄²	—	5	4	no	—
336	C₄²	—	10	4	no	—
337	C₄²	C₃×Dic₁₀	1	4	yes	complemented
338	C₃×C₅	#2399	1	1	yes	characteristic, complemented, Hall
339	C₂²×C₃	C₂²×Dic₁₀	1	1	yes	characteristic
340	C₂²×C₃	C₂×#709	1	2	yes	—
341	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
342	C₂²×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
343	C₂²×C₃	D₅×#41	1	2	yes	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	—	2	4	no	—
347	C₃×C₄	—	4	2	no	—
348	C₃×C₄	—	10	4	no	—
349	C₃×C₄	—	10	4	no	—
350	C₃×C₄	—	10	4	no	—
351	C₃×C₄	—	20	2	no	—
352	C₃×C₄	#4034	1	4	yes	—
353	C₂×C₅	C₃×#525	1	2	yes	—
354	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
355	C₂×C₅	C₃×#533	1	1	yes	characteristic
356	C₂×C₅	C₃×#533	1	2	yes	—
357	C₂×C₅	C₃×#533	1	1	yes	characteristic
358	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
359	Q₈	—	10	16	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	5	4	no	—
368	C₂×C₄	—	5	4	no	—
369	C₂×C₄	—	5	4	no	—
370	C₂×C₄	—	10	2	no	—
371	C₂×C₄	—	10	2	no	—
372	C₂×C₄	—	10	2	no	—
373	C₂×C₄	—	10	2	no	—
374	C₂×C₄	—	10	2	no	—
375	C₂×C₄	—	10	2	no	—
376	C₂×C₄	—	10	2	no	—
377	C₂×C₄	—	10	2	no	—
378	C₂×C₄	—	10	2	no	—
379	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
380	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
381	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
382	C₂×C₄	C₃×#709	1	4	yes	—
383	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
384	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
385	C₂×C₃	#65804	1	1	yes	characteristic
386	C₂×C₃	C₂×#4034	1	1	yes	characteristic
387	C₂×C₃	#65851	1	1	yes	characteristic
388	C₂×C₃	#65881	1	2	yes	—
389	C₂×C₃	#65912	1	2	yes	—
390	C₅	C₃×#2399	1	1	yes	characteristic, complemented, Sylow
391	C₂²	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
392	C₂²	C₂×C₃×#709	1	2	yes	—
393	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
394	C₂²	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
395	C₂²	C₃×D₅×#41	1	2	yes	—
396	C₄	—	2	2	no	—
397	C₄	—	2	4	no	—
398	C₄	—	2	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	10	4	no	—
401	C₄	—	10	4	no	—
402	C₄	—	10	4	no	—
403	C₄	—	20	2	no	—
404	C₄	C₃×#4034	1	4	yes	—
405	C₃	#10605400	1	1	yes	characteristic, direct product factor, Sylow
406	C₂	C₃×#65804	1	1	yes	characteristic
407	C₂	C₂×C₃×#4034	1	1	yes	characteristic
408	C₂	C₃×#65851	1	1	yes	characteristic
409	C₂	C₃×#65881	1	2	yes	—
410	C₂	C₃×#65912	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator, cosocle	C₂³×C₅	C₂⁴×C₃
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃×C₅	C₂⁴
hypercenter	C₃×C₄×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#2399
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
10. #10605400	C₃	direct (N × H)
57. C₃×C₄²×C₅	Q₈	semidirect
66. C₃×C₄×Dic₅	Q₈	semidirect
162. C₄²×C₅	C₃×Q₈	semidirect
171. C₄×Dic₅	C₃×Q₈	semidirect
218. C₃×C₄²	Dic₁₀	semidirect
337. C₄²	C₃×Dic₁₀	semidirect
338. C₃×C₅	#2399	semidirect
390. C₅	C₃×#2399	semidirect
405. C₃	#10605400	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×C₄×Dic₁₀	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×#65273	2
C₃×#65268	2
C₃×C₄×C₄⋊Dic₅	2
C₃×#65221	2
C₃×C₄×#683	2
C₃×#64946	2
C₃×#64945	2
#10605400	3
C₃×#2399	5

Subgroups — C3×#10605400 #14332543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605400 #14332543