Subgroups — C₃×#10605350 #14320983

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 460 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	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#65267	C₂	1	2	yes	maximal
4	C₃×#65261	C₂	1	2	yes	maximal
5	C₃×#65221	C₂	1	1	yes	maximal, characteristic
6	C₃×#65221	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×#683	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×#683	C₂	1	1	yes	maximal, characteristic
9	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
10	C₃×#64942	C₂	1	2	yes	maximal
11	C₃×#64935	C₂	1	2	yes	maximal
12	#10605350	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×#683	C₂²	1	2	yes	—
20	C₂×C₃×#683	C₂²	1	2	yes	—
21	C₂×C₃×#683	C₂²	1	1	yes	characteristic
22	C₂×C₃×#683	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₁₀	C₄	1	8	yes	complemented
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×#3963	C₂²	1	2	yes	—
32	C₃×#3963	C₂²	1	2	yes	—
33	C₃×#3963	C₂²	1	2	yes	—
34	C₃×#3963	C₂²	1	2	yes	—
35	C₃×#3963	C₂²	1	2	yes	—
36	C₃×#3963	C₂²	1	2	yes	—
37	C₃×#2295	—	5	1	no	maximal, Hall
38	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic
39	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
40	#65267	C₂×C₃	1	2	yes	—
41	#65261	C₂×C₃	1	2	yes	—
42	#65221	C₂×C₃	1	1	yes	characteristic
43	#65221	C₂×C₃	1	1	yes	characteristic
44	C₄×#683	C₂×C₃	1	1	yes	characteristic
45	C₄×#683	C₂×C₃	1	1	yes	characteristic
46	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic
47	#64942	C₂×C₃	1	2	yes	—
48	#64935	C₂×C₃	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
55	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
59	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×Dic₁₀	—	2	4	no	—
61	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	—
62	C₃×C₅×C₄⋊C₄	—	2	4	no	—
63	C₃×C₄²×C₅	—	2	2	no	—
64	C₃×C₄²×C₅	—	2	2	no	—
65	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
66	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
67	C₃×#683	—	2	4	no	—
68	C₃×#683	—	2	4	no	—
69	C₃×#683	C₂×C₄	1	4	yes	—
70	C₃×#683	C₂×C₄	1	4	yes	—
71	C₃×C₄×Dic₅	—	2	4	no	—
72	C₃×C₄×Dic₅	—	2	2	no	—
73	C₃×C₄×Dic₅	—	2	4	no	—
74	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
75	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
76	C₃×C₄×Dic₅	Q₈	1	4	yes	complemented
77	C₂×C₃×C₄×Q₈	—	5	1	no	—
78	C₃×#391	—	5	2	no	—
79	C₃×#389	—	5	2	no	—
80	C₃×#387	—	5	2	no	—
81	C₃×#387	—	5	2	no	—
82	C₃×C₄×C₄⋊C₄	—	5	1	no	—
83	C₃×C₄×C₄⋊C₄	—	5	1	no	—
84	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic
85	C₃×#376	—	5	1	no	—
86	C₃×#376	—	5	1	no	—
87	C₃×C₄³	—	5	1	no	—
88	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
94	C₂×#683	C₂²×C₃	1	2	yes	—
95	C₂×#683	C₂²×C₃	1	2	yes	—
96	C₂×#683	C₂²×C₃	1	1	yes	characteristic
97	C₂×#683	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
99	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
100	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
104	C₄×Dic₁₀	C₃×C₄	1	8	yes	complemented
105	C₅×#95	C₂²×C₃	1	2	yes	—
106	#3963	C₂²×C₃	1	2	yes	—
107	#3963	C₂²×C₃	1	2	yes	—
108	#3963	C₂²×C₃	1	2	yes	—
109	#3963	C₂²×C₃	1	2	yes	—
110	#3963	C₂²×C₃	1	2	yes	—
111	#3963	C₂²×C₃	1	2	yes	—
112	#2295	—	5	1	no	Sylow
113	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
125	C₂×C₃×C₄×C₅	#41	1	4	yes	—
126	C₂×C₃×C₄×C₅	#41	1	2	yes	—
127	C₂×C₃×Dic₅	—	2	2	no	—
128	C₂×C₃×Dic₅	—	2	2	no	—
129	C₂×C₃×Dic₅	—	2	2	no	—
130	C₂×C₃×Dic₅	—	2	2	no	—
131	C₂×C₃×Dic₅	—	2	2	no	—
132	C₂×C₃×Dic₅	—	2	2	no	—
133	C₂×C₃×Dic₅	—	2	2	no	—
134	C₂×C₃×Dic₅	—	2	2	no	—
135	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
136	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
137	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
139	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	—
140	C₂×C₃×Dic₅	#41	1	4	yes	—
141	C₃×Dic₁₀	—	2	8	no	—
142	C₂²×C₃×Q₈	—	5	1	no	—
143	C₃×C₄×Q₈	—	5	8	no	—
144	C₂×C₃×C₄⋊C₄	—	5	1	no	—
145	C₂×C₃×C₄⋊C₄	—	5	1	no	—
146	C₂×C₃×C₄⋊C₄	—	5	1	no	—
147	C₂×C₃×C₄⋊C₄	—	5	2	no	—
148	C₂×C₃×C₄⋊C₄	—	5	2	no	—
149	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
150	C₂×C₃×C₄²	—	5	1	no	—
151	C₂×C₃×C₄²	—	5	1	no	—
152	C₂×C₃×C₄²	—	5	1	no	—
153	C₂×C₃×C₄²	—	5	2	no	—
154	C₂×C₃×C₄²	—	5	2	no	—
155	C₂×C₃×C₄²	—	5	1	no	—
156	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
157	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
158	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
159	C₃×#95	—	5	2	no	—
160	C₃×#95	—	5	2	no	—
161	C₃×#95	—	5	2	no	—
162	C₃×#95	—	5	2	no	—
163	C₃×#95	—	5	2	no	—
164	C₃×#95	—	5	2	no	—
165	C₃×#95	C₂×D₅	1	2	yes	—
166	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
167	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
170	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
172	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
173	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
174	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
175	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
176	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
177	C₂×Dic₁₀	—	2	4	no	—
178	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	—
179	C₅×C₄⋊C₄	—	2	4	no	—
180	C₄²×C₅	—	2	2	no	—
181	C₄²×C₅	—	2	2	no	—
182	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
183	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
184	#683	—	2	4	no	—
185	#683	—	2	4	no	—
186	#683	C₂×C₃×C₄	1	4	yes	—
187	#683	C₂×C₃×C₄	1	4	yes	—
188	C₄×Dic₅	—	2	4	no	—
189	C₄×Dic₅	—	2	2	no	—
190	C₄×Dic₅	—	2	4	no	—
191	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
192	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
193	C₄×Dic₅	C₃×Q₈	1	4	yes	complemented
194	C₂×C₄×Q₈	—	5	1	no	—
195	#391	—	5	2	no	—
196	#389	—	5	2	no	—
197	#387	—	5	2	no	—
198	#387	—	5	2	no	—
199	C₄×C₄⋊C₄	—	5	1	no	—
200	C₄×C₄⋊C₄	—	5	1	no	—
201	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic
202	#376	—	5	1	no	—
203	#376	—	5	1	no	—
204	C₄³	—	5	1	no	—
205	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
206	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
207	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
208	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
209	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
210	C₃×C₄×C₅	—	2	2	no	—
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	—	2	4	no	—
213	C₃×C₄×C₅	—	4	2	no	—
214	C₃×C₄×C₅	C₄×Q₈	1	4	yes	—
215	C₃×Dic₅	—	2	2	no	—
216	C₃×Dic₅	—	2	2	no	—
217	C₃×Dic₅	—	2	2	no	—
218	C₃×Dic₅	—	2	4	no	—
219	C₃×Dic₅	—	4	2	no	—
220	C₃×Dic₅	#117	1	4	yes	—
221	C₂×C₃×Q₈	—	5	4	no	—
222	C₂×C₃×Q₈	—	10	4	no	—
223	C₂²×C₃×C₄	—	5	1	no	—
224	C₂²×C₃×C₄	—	5	2	no	—
225	C₂²×C₃×C₄	—	5	1	no	—
226	C₂²×C₃×C₄	—	5	1	no	—
227	C₂²×C₃×C₄	—	5	1	no	—
228	C₂²×C₃×C₄	—	5	2	no	—
229	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
230	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
233	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
234	C₃×C₄⋊C₄	—	2	4	no	—
235	C₃×C₄⋊C₄	—	5	4	no	—
236	C₃×C₄⋊C₄	—	5	4	no	—
237	C₃×C₄⋊C₄	—	5	4	no	—
238	C₃×C₄⋊C₄	—	10	4	no	—
239	C₃×C₄⋊C₄	—	10	4	no	—
240	C₃×C₄²	—	2	2	no	—
241	C₃×C₄²	—	2	2	no	—
242	C₃×C₄²	—	5	4	no	—
243	C₃×C₄²	—	5	4	no	—
244	C₃×C₄²	—	5	4	no	—
245	C₃×C₄²	—	10	4	no	—
246	C₃×C₄²	—	10	4	no	—
247	C₃×C₄²	—	10	2	no	—
248	C₃×C₄²	C₄×D₅	1	4	yes	—
249	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
258	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
259	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
260	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
261	C₂×C₄×C₅	C₃×#41	1	4	yes	—
262	C₂×C₄×C₅	C₃×#41	1	2	yes	—
263	C₂×Dic₅	—	2	2	no	—
264	C₂×Dic₅	—	2	2	no	—
265	C₂×Dic₅	—	2	2	no	—
266	C₂×Dic₅	—	2	2	no	—
267	C₂×Dic₅	—	2	2	no	—
268	C₂×Dic₅	—	2	2	no	—
269	C₂×Dic₅	—	2	2	no	—
270	C₂×Dic₅	—	2	2	no	—
271	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
272	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
273	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
274	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
275	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	—
276	C₂×Dic₅	C₃×#41	1	4	yes	—
277	Dic₁₀	—	2	8	no	—
278	C₂²×Q₈	—	5	1	no	—
279	C₄×Q₈	—	5	8	no	—
280	C₂×C₄⋊C₄	—	5	1	no	—
281	C₂×C₄⋊C₄	—	5	1	no	—
282	C₂×C₄⋊C₄	—	5	1	no	—
283	C₂×C₄⋊C₄	—	5	2	no	—
284	C₂×C₄⋊C₄	—	5	2	no	—
285	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
286	C₂×C₄²	—	5	1	no	—
287	C₂×C₄²	—	5	1	no	—
288	C₂×C₄²	—	5	1	no	—
289	C₂×C₄²	—	5	2	no	—
290	C₂×C₄²	—	5	2	no	—
291	C₂×C₄²	—	5	1	no	—
292	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
293	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
294	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
295	#95	—	5	2	no	—
296	#95	—	5	2	no	—
297	#95	—	5	2	no	—
298	#95	—	5	2	no	—
299	#95	—	5	2	no	—
300	#95	—	5	2	no	—
301	#95	C₂×C₃×D₅	1	2	yes	—
302	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
304	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
305	C₂×C₃×C₅	#529	1	2	yes	—
306	C₂×C₃×C₅	#533	1	2	yes	—
307	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
308	C₃×Q₈	—	10	8	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	5	2	no	—
317	C₂×C₃×C₄	—	5	4	no	—
318	C₂×C₃×C₄	—	5	2	no	—
319	C₂×C₃×C₄	—	5	2	no	—
320	C₂×C₃×C₄	—	5	2	no	—
321	C₂×C₃×C₄	—	5	4	no	—
322	C₂×C₃×C₄	—	10	2	no	—
323	C₂×C₃×C₄	—	10	2	no	—
324	C₂×C₃×C₄	—	10	2	no	—
325	C₂×C₃×C₄	—	10	2	no	—
326	C₂×C₃×C₄	—	10	2	no	—
327	C₂×C₃×C₄	—	10	2	no	—
328	C₂×C₃×C₄	—	10	2	no	—
329	C₂×C₃×C₄	—	10	2	no	—
330	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
331	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
332	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
333	C₂×C₃×C₄	#709	1	4	yes	—
334	C₂×C₃×C₄	#711	1	2	yes	—
335	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
336	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
337	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
338	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
339	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
340	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	2	4	no	—
344	C₄×C₅	—	4	2	no	—
345	C₄×C₅	C₃×C₄×Q₈	1	4	yes	—
346	Dic₅	—	2	2	no	—
347	Dic₅	—	2	2	no	—
348	Dic₅	—	2	2	no	—
349	Dic₅	—	2	4	no	—
350	Dic₅	—	4	2	no	—
351	Dic₅	C₃×#117	1	4	yes	—
352	C₂×Q₈	—	5	4	no	—
353	C₂×Q₈	—	10	4	no	—
354	C₂²×C₄	—	5	1	no	—
355	C₂²×C₄	—	5	2	no	—
356	C₂²×C₄	—	5	1	no	—
357	C₂²×C₄	—	5	1	no	—
358	C₂²×C₄	—	5	1	no	—
359	C₂²×C₄	—	5	2	no	—
360	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
361	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
364	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	5	4	no	—
367	C₄⋊C₄	—	5	4	no	—
368	C₄⋊C₄	—	5	4	no	—
369	C₄⋊C₄	—	10	4	no	—
370	C₄⋊C₄	—	10	4	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	5	4	no	—
374	C₄²	—	5	4	no	—
375	C₄²	—	5	4	no	—
376	C₄²	—	10	4	no	—
377	C₄²	—	10	4	no	—
378	C₄²	—	10	2	no	—
379	C₄²	C₃×C₄×D₅	1	4	yes	—
380	C₃×C₅	#2295	1	1	yes	characteristic, complemented, Hall
381	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
382	C₂²×C₃	C₂×#709	1	2	yes	—
383	C₂²×C₃	C₂×#711	1	1	yes	characteristic
384	C₂²×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
385	C₂²×C₃	D₅×#41	1	2	yes	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	2	no	—
388	C₃×C₄	—	2	4	no	—
389	C₃×C₄	—	4	2	no	—
390	C₃×C₄	—	5	4	no	—
391	C₃×C₄	—	10	2	no	—
392	C₃×C₄	—	10	2	no	—
393	C₃×C₄	—	10	2	no	—
394	C₃×C₄	—	10	4	no	—
395	C₃×C₄	—	20	2	no	—
396	C₃×C₄	#4033	1	4	yes	—
397	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
398	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
399	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
400	C₂×C₅	C₃×#529	1	2	yes	—
401	C₂×C₅	C₃×#533	1	2	yes	—
402	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
403	Q₈	—	10	8	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	5	2	no	—
412	C₂×C₄	—	5	4	no	—
413	C₂×C₄	—	5	2	no	—
414	C₂×C₄	—	5	2	no	—
415	C₂×C₄	—	5	2	no	—
416	C₂×C₄	—	5	4	no	—
417	C₂×C₄	—	10	2	no	—
418	C₂×C₄	—	10	2	no	—
419	C₂×C₄	—	10	2	no	—
420	C₂×C₄	—	10	2	no	—
421	C₂×C₄	—	10	2	no	—
422	C₂×C₄	—	10	2	no	—
423	C₂×C₄	—	10	2	no	—
424	C₂×C₄	—	10	2	no	—
425	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
426	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
427	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
428	C₂×C₄	C₃×#709	1	4	yes	—
429	C₂×C₄	C₃×#711	1	2	yes	—
430	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
431	C₂×C₃	C₄×#709	1	1	yes	characteristic
432	C₂×C₃	C₂×#4033	1	1	yes	characteristic
433	C₂×C₃	D₅×#117	1	1	yes	characteristic
434	C₂×C₃	#65872	1	2	yes	—
435	C₂×C₃	#65912	1	2	yes	—
436	C₅	C₃×#2295	1	1	yes	characteristic, complemented, Sylow
437	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
438	C₂²	C₂×C₃×#709	1	2	yes	—
439	C₂²	C₂×C₃×#711	1	1	yes	characteristic
440	C₂²	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
441	C₂²	C₃×D₅×#41	1	2	yes	—
442	C₄	—	2	2	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	5	4	no	—
447	C₄	—	10	2	no	—
448	C₄	—	10	4	no	—
449	C₄	—	10	2	no	—
450	C₄	—	10	2	no	—
451	C₄	—	20	2	no	—
452	C₄	C₃×#4033	1	4	yes	—
453	C₃	#10605350	1	1	yes	characteristic, direct product factor, Sylow
454	C₂	C₃×C₄×#709	1	1	yes	characteristic
455	C₂	C₂×C₃×#4033	1	1	yes	characteristic
456	C₂	C₃×D₅×#117	1	1	yes	characteristic
457	C₂	C₃×#65872	1	2	yes	—
458	C₂	C₃×#65912	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃×C₅	C₂⁴
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#2295
LCS	G ▷ C₂²×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
12. #10605350	C₃	direct (N × H)
29. C₃×C₄×Dic₁₀	C₄	semidirect
76. C₃×C₄×Dic₅	Q₈	semidirect
104. C₄×Dic₁₀	C₃×C₄	semidirect
193. C₄×Dic₅	C₃×Q₈	semidirect
380. C₃×C₅	#2295	semidirect
436. C₅	C₃×#2295	semidirect
453. C₃	#10605350	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×#65267	2
C₃×#65261	2
C₃×#65221	2
C₃×C₄×#683	2
C₃×C₄²×Dic₅	2
C₃×#64942	2
C₃×#64935	2
#10605350	3
C₃×#2295	5

Subgroups — C3×#10605350 #14320983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605350 #14320983