Subgroups — C₃×#10601147 #14295637

Order 1920.

640 conjugacy classes of subgroups.

The subgroup lattice has 428 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	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3969	C₂	1	1	yes	maximal, characteristic
4	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65221	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64775	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64743	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601147	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₃×Q₈×Dic₅	C₄	1	2	yes	complemented
13	C₃×D₄×Dic₅	—	2	2	no	—
14	C₃×D₄×Dic₅	C₄	1	2	yes	complemented
15	C₃×#4072	—	2	1	no	—
16	C₃×#4072	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×Dic₅	—	2	1	no	—
18	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×#681	C₂²	1	1	yes	characteristic
21	C₃×C₅×#104	C₄	1	4	yes	complemented
22	C₃×#3969	C₄	1	4	yes	complemented
23	C₃×#3963	—	2	2	no	—
24	C₃×#3947	—	2	1	no	—
25	C₃×C₈×Dic₅	—	2	1	no	—
26	C₃×#1759	—	5	1	no	maximal, Hall
27	#41×Dic₅	C₂×C₃	1	1	yes	characteristic
28	C₂×C₅×#104	C₂×C₃	1	1	yes	characteristic
29	C₂×#3969	C₂×C₃	1	1	yes	characteristic
30	M₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
31	#65221	C₂×C₃	1	1	yes	characteristic, complemented
32	#64775	C₂×C₃	1	1	yes	characteristic, complemented
33	#64743	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	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	—	2	1	no	—
45	C₂²×C₃×Dic₅	—	2	2	no	—
46	C₂²×C₃×Dic₅	D₄	1	2	yes	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
52	C₃×C₂²⋊Dic₅	—	2	1	no	—
53	C₃×C₂²⋊Dic₅	—	2	2	no	—
54	C₃×C₄⋊Dic₅	—	2	2	no	—
55	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
56	C₃×C₄×Dic₅	—	2	1	no	—
57	C₃×C₄×Dic₅	—	2	1	no	—
58	C₃×C₄×Dic₅	—	2	2	no	—
59	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
60	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
61	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
62	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
63	C₃×#681	—	2	1	no	—
64	C₃×#681	C₂×C₄	1	2	yes	complemented
65	C₂×C₃×#168	—	2	1	no	—
66	C₃×C₄×#41	—	5	1	no	—
67	C₂×C₃×#104	—	5	1	no	—
68	C₂×C₃×#104	D₅	1	1	yes	characteristic
69	C₃×C₄×M₁₆	—	5	1	no	—
70	C₃×#376	—	5	1	no	—
71	C₃×#339	—	5	1	no	—
72	C₃×#339	—	5	1	no	—
73	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
76	Q₈×Dic₅	C₃×C₄	1	2	yes	complemented
77	D₄×Dic₅	—	2	2	no	—
78	D₄×Dic₅	C₃×C₄	1	2	yes	complemented
79	#4072	—	2	1	no	—
80	#4072	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₄×Dic₅	—	2	1	no	—
82	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
84	C₂×#681	C₂²×C₃	1	1	yes	characteristic
85	C₅×#104	C₃×C₄	1	4	yes	complemented
86	#3969	C₃×C₄	1	4	yes	complemented
87	#3963	—	2	2	no	—
88	#3947	—	2	1	no	—
89	C₈×Dic₅	—	2	1	no	—
90	#1759	—	5	1	no	Sylow
91	C₂³×C₃×C₅	—	2	1	no	—
92	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
93	C₃×C₅×Q₈	—	2	1	no	—
94	C₃×C₅×Q₈	C₄²	1	2	yes	—
95	C₃×C₅×D₄	—	2	2	no	—
96	C₃×C₅×D₄	—	2	2	no	—
97	C₃×C₅×D₄	—	2	1	no	—
98	C₃×C₅×D₄	C₄²	1	2	yes	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
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	—	4	2	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×Dic₅	—	2	2	no	—
111	C₂×C₃×Dic₅	—	2	2	no	—
112	C₂×C₃×Dic₅	—	4	2	no	—
113	C₂×C₃×Dic₅	—	4	4	no	—
114	C₂×C₃×Dic₅	—	4	2	no	—
115	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
116	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
117	C₃×C₅×C₈	—	2	2	no	—
118	C₃×#168	—	2	2	no	—
119	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
120	C₂×C₃×M₁₆	—	5	1	no	—
121	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
122	C₃×C₄×Q₈	—	5	2	no	—
123	C₃×C₄×D₄	—	5	2	no	—
124	C₃×C₄×D₄	—	10	2	no	—
125	C₃×#117	—	5	1	no	—
126	C₃×#117	—	10	1	no	—
127	C₂×C₃×C₄²	—	5	1	no	—
128	C₂×C₃×C₄²	—	5	1	no	—
129	C₂×C₃×C₄²	—	10	1	no	—
130	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
131	C₃×#104	—	5	4	no	—
132	C₃×#104	Dic₅	1	4	yes	complemented
133	C₃×#97	—	10	1	no	—
134	C₃×C₄×C₈	—	10	1	no	—
135	C₃×#95	—	10	2	no	—
136	C₅×#41	—	2	1	no	—
137	C₅×#41	—	2	1	no	—
138	C₅×#41	C₂×C₃×C₄	1	2	yes	—
139	C₅×#41	C₂×C₃×C₄	1	2	yes	—
140	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
141	C₂×C₅×D₄	—	2	1	no	—
142	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
146	C₂²×Dic₅	—	2	1	no	—
147	C₂²×Dic₅	—	2	2	no	—
148	C₂²×Dic₅	C₃×D₄	1	2	yes	—
149	C₅×M₁₆	—	2	1	no	—
150	C₅×M₁₆	C₂×C₃×C₄	1	2	yes	complemented
151	C₂×C₅×C₈	—	2	1	no	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	C₂×C₃×C₄	1	2	yes	complemented
154	C₂²⋊Dic₅	—	2	1	no	—
155	C₂²⋊Dic₅	—	2	2	no	—
156	C₄⋊Dic₅	—	2	2	no	—
157	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
158	C₄×Dic₅	—	2	1	no	—
159	C₄×Dic₅	—	2	1	no	—
160	C₄×Dic₅	—	2	2	no	—
161	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
162	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	complemented
163	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
164	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
165	#681	—	2	1	no	—
166	#681	C₂×C₃×C₄	1	2	yes	complemented
167	C₂×#168	—	2	1	no	—
168	C₄×#41	—	5	1	no	—
169	C₂×#104	—	5	1	no	—
170	C₂×#104	C₃×D₅	1	1	yes	characteristic
171	C₄×M₁₆	—	5	1	no	—
172	#376	—	5	1	no	—
173	#339	—	5	1	no	—
174	#339	—	5	1	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	2	2	no	—
177	C₂²×C₃×C₅	—	4	2	no	—
178	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
180	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
181	C₃×C₄×C₅	—	2	2	no	—
182	C₃×C₄×C₅	—	4	2	no	—
183	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
184	C₃×C₄×C₅	#117	1	1	yes	characteristic
185	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
186	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
187	C₃×Dic₅	—	2	2	no	—
188	C₃×Dic₅	—	2	2	no	—
189	C₃×Dic₅	—	4	2	no	—
190	C₃×Dic₅	—	4	2	no	—
191	C₃×#41	—	2	1	no	—
192	C₃×#41	—	2	1	no	—
193	C₃×#41	C₄×D₅	1	2	yes	—
194	C₃×#41	C₂×Dic₅	1	2	yes	—
195	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
196	C₂×C₃×D₄	—	2	1	no	—
197	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	5	2	no	—
201	C₂²×C₃×C₄	—	10	2	no	—
202	C₂²×C₃×C₄	—	10	1	no	—
203	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
204	C₃×M₁₆	—	2	1	no	—
205	C₃×M₁₆	—	5	2	no	—
206	C₃×M₁₆	—	10	1	no	—
207	C₃×M₁₆	C₂×Dic₅	1	2	yes	complemented
208	C₂×C₃×C₈	—	2	1	no	—
209	C₂×C₃×C₈	—	10	1	no	—
210	C₃×C₄⋊C₄	—	5	2	no	—
211	C₃×C₄⋊C₄	—	10	2	no	—
212	C₃×C₂²⋊C₄	—	10	2	no	—
213	C₃×C₂²⋊C₄	—	10	1	no	—
214	C₃×C₄²	—	2	1	no	—
215	C₃×C₄²	—	5	2	no	—
216	C₃×C₄²	—	5	1	no	—
217	C₃×C₄²	—	5	1	no	—
218	C₃×C₄²	—	5	2	no	—
219	C₃×C₄²	—	10	2	no	—
220	C₃×C₄²	—	10	1	no	—
221	C₃×C₄²	—	10	1	no	—
222	C₃×C₄²	C₂×Dic₅	1	2	yes	complemented
223	C₂³×C₅	—	2	1	no	—
224	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
225	C₅×Q₈	—	2	1	no	—
226	C₅×Q₈	C₃×C₄²	1	2	yes	—
227	C₅×D₄	—	2	2	no	—
228	C₅×D₄	—	2	2	no	—
229	C₅×D₄	—	2	1	no	—
230	C₅×D₄	C₃×C₄²	1	2	yes	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
241	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
242	C₂×Dic₅	—	2	2	no	—
243	C₂×Dic₅	—	2	2	no	—
244	C₂×Dic₅	—	4	2	no	—
245	C₂×Dic₅	—	4	4	no	—
246	C₂×Dic₅	—	4	2	no	—
247	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
248	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
249	C₅×C₈	—	2	2	no	—
250	#168	—	2	2	no	—
251	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
252	C₂×M₁₆	—	5	1	no	—
253	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
254	C₄×Q₈	—	5	2	no	—
255	C₄×D₄	—	5	2	no	—
256	C₄×D₄	—	10	2	no	—
257	#117	—	5	1	no	—
258	#117	—	10	1	no	—
259	C₂×C₄²	—	5	1	no	—
260	C₂×C₄²	—	5	1	no	—
261	C₂×C₄²	—	10	1	no	—
262	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
263	#104	—	5	4	no	—
264	#104	C₃×Dic₅	1	4	yes	complemented
265	#97	—	10	1	no	—
266	C₄×C₈	—	10	1	no	—
267	#95	—	10	2	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	—	4	2	no	—
271	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₃×C₅	#421	1	2	yes	—
273	C₂³×C₃	—	2	1	no	—
274	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
275	C₃×Q₈	—	2	1	no	—
276	C₃×Q₈	C₄×Dic₅	1	2	yes	—
277	C₃×D₄	—	2	2	no	—
278	C₃×D₄	—	2	2	no	—
279	C₃×D₄	—	2	1	no	—
280	C₃×D₄	C₄×Dic₅	1	2	yes	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	4	2	no	—
286	C₂×C₃×C₄	—	5	2	no	—
287	C₂×C₃×C₄	—	5	2	no	—
288	C₂×C₃×C₄	—	10	2	no	—
289	C₂×C₃×C₄	—	10	2	no	—
290	C₂×C₃×C₄	—	20	2	no	—
291	C₂×C₃×C₄	—	20	4	no	—
292	C₂×C₃×C₄	—	20	2	no	—
293	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
295	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
296	C₂×C₃×C₄	#711	1	1	yes	characteristic
297	C₂×C₃×C₄	#711	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
299	C₃×C₈	—	2	2	no	—
300	C₃×C₈	—	10	2	no	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
305	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
306	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
307	C₄×C₅	—	2	2	no	—
308	C₄×C₅	—	4	2	no	—
309	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
310	C₄×C₅	C₃×#117	1	1	yes	characteristic
311	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
312	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
313	Dic₅	—	2	2	no	—
314	Dic₅	—	2	2	no	—
315	Dic₅	—	4	2	no	—
316	Dic₅	—	4	2	no	—
317	#41	—	2	1	no	—
318	#41	—	2	1	no	—
319	#41	C₃×C₄×D₅	1	2	yes	—
320	#41	C₂×C₃×Dic₅	1	2	yes	—
321	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	5	2	no	—
327	C₂²×C₄	—	10	2	no	—
328	C₂²×C₄	—	10	1	no	—
329	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
330	M₁₆	—	2	1	no	—
331	M₁₆	—	5	2	no	—
332	M₁₆	—	10	1	no	—
333	M₁₆	C₂×C₃×Dic₅	1	2	yes	complemented
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	10	1	no	—
336	C₄⋊C₄	—	5	2	no	—
337	C₄⋊C₄	—	10	2	no	—
338	C₂²⋊C₄	—	10	2	no	—
339	C₂²⋊C₄	—	10	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	5	2	no	—
342	C₄²	—	5	1	no	—
343	C₄²	—	5	1	no	—
344	C₄²	—	5	2	no	—
345	C₄²	—	10	2	no	—
346	C₄²	—	10	1	no	—
347	C₄²	—	10	1	no	—
348	C₄²	C₂×C₃×Dic₅	1	2	yes	complemented
349	C₃×C₅	#1759	1	1	yes	characteristic, complemented, Hall
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²×C₃	#4027	1	1	yes	characteristic
355	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
356	C₃×C₄	—	2	2	no	—
357	C₃×C₄	—	4	2	no	—
358	C₃×C₄	—	10	2	no	—
359	C₃×C₄	—	10	2	no	—
360	C₃×C₄	—	20	2	no	—
361	C₃×C₄	—	20	2	no	—
362	C₃×C₄	#4023	1	1	yes	characteristic
363	C₃×C₄	#4027	1	1	yes	characteristic
364	C₃×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
365	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
366	C₂×C₅	—	2	1	no	—
367	C₂×C₅	—	2	1	no	—
368	C₂×C₅	—	4	2	no	—
369	C₂×C₅	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
370	C₂×C₅	C₃×#421	1	2	yes	—
371	C₂³	—	2	1	no	—
372	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
373	Q₈	—	2	1	no	—
374	Q₈	C₃×C₄×Dic₅	1	2	yes	—
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	2	1	no	—
378	D₄	C₃×C₄×Dic₅	1	2	yes	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	5	2	no	—
385	C₂×C₄	—	5	2	no	—
386	C₂×C₄	—	10	2	no	—
387	C₂×C₄	—	10	2	no	—
388	C₂×C₄	—	20	2	no	—
389	C₂×C₄	—	20	4	no	—
390	C₂×C₄	—	20	2	no	—
391	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
392	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
393	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
394	C₂×C₄	C₃×#711	1	1	yes	characteristic
395	C₂×C₄	C₃×#711	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	10	2	no	—
399	C₂×C₃	—	2	1	no	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	—	4	2	no	—
402	C₂×C₃	#65110	1	2	yes	—
403	C₂×C₃	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
404	C₅	C₃×#1759	1	1	yes	characteristic, complemented, Sylow
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
409	C₂²	C₃×#4027	1	1	yes	characteristic
410	C₂²	C₃×D₄×Dic₅	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	10	2	no	—
414	C₄	—	10	2	no	—
415	C₄	—	20	2	no	—
416	C₄	—	20	2	no	—
417	C₄	C₃×#4023	1	1	yes	characteristic
418	C₄	C₃×#4027	1	1	yes	characteristic
419	C₄	C₂×C₃×C₄×Dic₅	1	1	yes	characteristic
420	C₄	C₃×D₄×Dic₅	1	1	yes	characteristic
421	C₃	#10601147	1	1	yes	characteristic, direct product factor, Sylow
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	C₃×#65110	1	2	yes	—
426	C₂	C₃×C₂²⋊C₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator	C₄×C₅	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×#104	D₅
hypocenter	C₅	C₃×#1759
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#104

Complements

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

N	H ≅ G/N	type
4. C₃×M₁₆×Dic₅	C₂	semidirect
5. C₃×#65221	C₂	semidirect
6. C₃×#64775	C₂	semidirect
7. C₃×#64743	C₂	semidirect
8. #10601147	C₃	direct (N × H)
12. C₃×Q₈×Dic₅	C₄	semidirect
14. C₃×D₄×Dic₅	C₄	semidirect
21. C₃×C₅×#104	C₄	semidirect
22. C₃×#3969	C₄	semidirect
30. M₁₆×Dic₅	C₂×C₃	semidirect
31. #65221	C₂×C₃	semidirect
32. #64775	C₂×C₃	semidirect
33. #64743	C₂×C₃	semidirect
48. C₃×C₅×M₁₆	C₂×C₄	semidirect
51. C₃×C₄²×C₅	C₂×C₄	semidirect
60. C₃×C₄×Dic₅	C₂×C₄	semidirect
64. C₃×#681	C₂×C₄	semidirect
76. Q₈×Dic₅	C₃×C₄	semidirect
78. D₄×Dic₅	C₃×C₄	semidirect
85. C₅×#104	C₃×C₄	semidirect
86. #3969	C₃×C₄	semidirect
132. C₃×#104	Dic₅	semidirect
150. C₅×M₁₆	C₂×C₃×C₄	semidirect
153. C₄²×C₅	C₂×C₃×C₄	semidirect
162. C₄×Dic₅	C₂×C₃×C₄	semidirect
166. #681	C₂×C₃×C₄	semidirect
207. C₃×M₁₆	C₂×Dic₅	semidirect
222. C₃×C₄²	C₂×Dic₅	semidirect
264. #104	C₃×Dic₅	semidirect
333. M₁₆	C₂×C₃×Dic₅	semidirect
348. C₄²	C₂×C₃×Dic₅	semidirect
349. C₃×C₅	#1759	semidirect
404. C₅	C₃×#1759	semidirect
421. C₃	#10601147	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
C₂×C₃×C₅×#104	2
C₂×C₃×#3969	2
C₃×M₁₆×Dic₅	2
C₃×#65221	2
C₃×#64775	2
C₃×#64743	2
#10601147	3
C₃×#1759	5

Subgroups — C3×#10601147 #14295637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601147 #14295637