Subgroups — C₃×#10610811 #14413111

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×#676	C₂	1	1	yes	maximal, characteristic
3	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65391	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65288	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65128	C₂	1	4	yes	maximal, complemented
9	C₃×#65126	C₂	1	4	yes	maximal, complemented
10	#10610811	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₃×#4072	C₂²	1	1	yes	characteristic
16	C₂×C₃×#681	C₂²	1	1	yes	characteristic
17	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
18	C₃×D₅×M₁₆	—	2	4	no	—
19	C₂×C₃×#676	—	2	4	no	—
20	C₂×C₃×#676	C₂²	1	2	yes	—
21	C₂×C₃×#676	C₂²	1	2	yes	—
22	C₂×C₃×#676	C₂²	1	2	yes	—
23	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
24	C₃×#4038	C₄	1	2	yes	—
25	C₃×D₅×C₄⋊C₄	C₄	1	2	yes	—
26	C₃×D₅×C₂²⋊C₄	C₄	1	2	yes	—
27	C₃×#4023	C₄	1	2	yes	—
28	C₃×#4018	C₂²	1	2	yes	—
29	C₃×C₄²×D₅	C₂²	1	2	yes	—
30	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
31	C₃×#3946	C₂²	1	4	yes	complemented
32	C₃×#3946	C₂²	1	4	yes	complemented
33	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
34	C₃×#2905	—	5	1	no	maximal, Hall
35	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic
36	C₂²×#676	C₂×C₃	1	1	yes	characteristic
37	D₅×#117	C₂×C₃	1	1	yes	characteristic
38	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
39	#65408	C₂×C₃	1	1	yes	characteristic, complemented
40	#65391	C₂×C₃	1	1	yes	characteristic, complemented
41	#65288	C₂×C₃	1	1	yes	characteristic, complemented
42	#65128	C₂×C₃	1	4	yes	complemented
43	#65126	C₂×C₃	1	4	yes	complemented
44	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	D₄	1	4	yes	—
51	C₂×C₃×C₄×D₅	Q₈	1	4	yes	—
52	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
54	C₃×C₅×M₁₆	—	2	2	no	—
55	C₂×C₃×C₅×C₈	—	2	2	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₃×C₄²×C₅	C₂³	1	2	yes	—
61	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
62	C₃×#685	C₂×C₄	1	4	yes	—
63	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
64	C₃×#683	C₂×C₄	1	4	yes	—
65	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
66	C₃×C₄×Dic₅	C₂³	1	2	yes	—
67	C₃×#681	—	2	2	no	—
68	C₂×C₃×#168	—	2	2	no	—
69	C₂×C₃×#168	C₂³	1	2	yes	—
70	C₂×C₃×#168	C₂³	1	2	yes	—
71	C₃×#676	—	2	4	no	—
72	C₃×#676	—	2	4	no	—
73	C₃×#676	—	2	4	no	—
74	C₃×C₈×D₅	—	2	4	no	—
75	C₂²×C₃×M₁₆	—	5	1	no	—
76	C₂²×C₃×M₁₆	—	5	1	no	—
77	C₂×C₃×#117	—	5	1	no	—
78	C₃×#424	—	5	1	no	—
79	C₃×#424	—	5	1	no	—
80	C₃×#424	—	5	1	no	—
81	C₃×#424	—	5	4	no	—
82	C₃×#424	D₅	1	1	yes	characteristic, complemented
83	C₃×#423	—	5	4	no	—
84	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
87	C₅×#117	C₂²×C₃	1	1	yes	characteristic
88	#4072	C₂²×C₃	1	1	yes	characteristic
89	C₂×#681	C₂²×C₃	1	1	yes	characteristic
90	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
91	D₅×M₁₆	—	2	4	no	—
92	C₂×#676	—	2	4	no	—
93	C₂×#676	C₂²×C₃	1	2	yes	—
94	C₂×#676	C₂²×C₃	1	2	yes	—
95	C₂×#676	C₂²×C₃	1	2	yes	—
96	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
97	#4038	C₃×C₄	1	2	yes	—
98	D₅×C₄⋊C₄	C₃×C₄	1	2	yes	—
99	D₅×C₂²⋊C₄	C₃×C₄	1	2	yes	—
100	#4023	C₃×C₄	1	2	yes	—
101	#4018	C₂²×C₃	1	2	yes	—
102	C₄²×D₅	C₂²×C₃	1	2	yes	—
103	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
104	#3946	C₂²×C₃	1	4	yes	complemented
105	#3946	C₂²×C₃	1	4	yes	complemented
106	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
107	#2905	—	5	1	no	Sylow
108	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₃×D₅	—	4	2	no	—
110	C₂²×C₃×D₅	C₄⋊C₄	1	4	yes	—
111	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₂×C₃×Dic₅	C₄⋊C₄	1	4	yes	—
119	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
120	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
122	C₃×C₄×D₅	—	4	4	no	—
123	C₃×C₄×D₅	C₄⋊C₄	1	4	yes	—
124	C₃×C₄×D₅	C₄⋊C₄	1	4	yes	—
125	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
126	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
127	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
128	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
129	C₃×C₅×C₈	—	2	2	no	—
130	C₃×C₅×C₈	—	2	2	no	—
131	C₃×#168	—	2	2	no	—
132	C₃×#168	—	2	2	no	—
133	C₂³×C₃×C₄	—	5	1	no	—
134	C₂×C₃×M₁₆	—	5	1	no	—
135	C₂×C₃×M₁₆	—	5	2	no	—
136	C₂×C₃×M₁₆	—	5	2	no	—
137	C₂×C₃×M₁₆	—	5	2	no	—
138	C₂×C₃×M₁₆	—	10	4	no	—
139	C₂×C₃×M₁₆	—	10	4	no	—
140	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
141	C₂²×C₃×C₈	—	5	1	no	—
142	C₂²×C₃×C₈	—	5	2	no	—
143	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
144	C₃×#117	—	5	1	no	—
145	C₃×#117	—	5	2	no	—
146	C₃×#117	—	5	2	no	—
147	C₃×#117	—	5	2	no	—
148	C₃×#117	C₂×D₅	1	1	yes	characteristic
149	C₂×C₃×C₄⋊C₄	—	5	2	no	—
150	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
151	C₂×C₃×C₄²	—	5	2	no	—
152	C₃×C₄⋊C₈	—	5	4	no	—
153	C₃×C₄⋊C₈	—	5	4	no	—
154	C₃×C₄⋊C₈	—	5	4	no	—
155	C₃×C₄⋊C₈	C₂×D₅	1	4	yes	complemented
156	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
159	C₂×C₄×D₅	C₂×C₃×C₄	1	4	yes	—
160	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
161	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
162	C₂×C₄×D₅	C₃×D₄	1	4	yes	—
163	C₂×C₄×D₅	C₃×Q₈	1	4	yes	—
164	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
166	C₅×M₁₆	—	2	2	no	—
167	C₂×C₅×C₈	—	2	2	no	—
168	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
169	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
170	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
171	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
172	C₄²×C₅	C₂³×C₃	1	2	yes	—
173	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
174	#685	C₂×C₃×C₄	1	4	yes	—
175	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
176	#683	C₂×C₃×C₄	1	4	yes	—
177	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
178	C₄×Dic₅	C₂³×C₃	1	2	yes	—
179	#681	—	2	2	no	—
180	C₂×#168	—	2	2	no	—
181	C₂×#168	C₂³×C₃	1	2	yes	—
182	C₂×#168	C₂³×C₃	1	2	yes	—
183	#676	—	2	4	no	—
184	#676	—	2	4	no	—
185	#676	—	2	4	no	—
186	C₈×D₅	—	2	4	no	—
187	C₂²×M₁₆	—	5	1	no	—
188	C₂²×M₁₆	—	5	1	no	—
189	C₂×#117	—	5	1	no	—
190	#424	—	5	1	no	—
191	#424	—	5	1	no	—
192	#424	—	5	1	no	—
193	#424	—	5	4	no	—
194	#424	C₃×D₅	1	1	yes	characteristic, complemented
195	#423	—	5	4	no	—
196	C₂²×C₃×C₅	—	2	2	no	—
197	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
198	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₃×D₅	—	2	2	no	—
200	C₂×C₃×D₅	—	2	2	no	—
201	C₂×C₃×D₅	—	4	4	no	—
202	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
203	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
204	C₃×C₄×C₅	—	2	4	no	—
205	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
206	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
208	C₃×Dic₅	—	2	4	no	—
209	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
210	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
211	C₂⁴×C₃	—	5	1	no	—
212	C₂²×C₃×C₄	—	5	1	no	—
213	C₂²×C₃×C₄	—	5	1	no	—
214	C₂²×C₃×C₄	—	5	1	no	—
215	C₂²×C₃×C₄	—	5	4	no	—
216	C₂²×C₃×C₄	—	5	4	no	—
217	C₂²×C₃×C₄	—	5	1	no	—
218	C₂²×C₃×C₄	—	5	1	no	—
219	C₂²×C₃×C₄	—	5	4	no	—
220	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
221	C₃×M₁₆	—	2	2	no	—
222	C₃×M₁₆	—	10	4	no	—
223	C₃×M₁₆	—	10	4	no	—
224	C₃×M₁₆	—	10	4	no	—
225	C₃×M₁₆	—	10	2	no	—
226	C₂×C₃×C₈	—	2	2	no	—
227	C₂×C₃×C₈	—	5	2	no	—
228	C₂×C₃×C₈	—	5	2	no	—
229	C₂×C₃×C₈	—	10	4	no	—
230	C₂×C₃×C₈	—	10	2	no	—
231	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
232	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
233	C₃×C₄⋊C₄	—	5	4	no	—
234	C₃×C₄⋊C₄	—	5	2	no	—
235	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
236	C₃×C₂²⋊C₄	—	5	2	no	—
237	C₃×C₂²⋊C₄	—	5	4	no	—
238	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
239	C₃×C₄²	—	5	4	no	—
240	C₃×C₄²	—	5	2	no	—
241	C₃×C₄²	C₂²×D₅	1	2	yes	—
242	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
243	C₂²×D₅	—	4	2	no	—
244	C₂²×D₅	C₃×C₄⋊C₄	1	4	yes	—
245	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
246	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
248	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
250	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
251	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
252	C₂×Dic₅	C₃×C₄⋊C₄	1	4	yes	—
253	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
254	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
255	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
256	C₄×D₅	—	4	4	no	—
257	C₄×D₅	C₃×C₄⋊C₄	1	4	yes	—
258	C₄×D₅	C₃×C₄⋊C₄	1	4	yes	—
259	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
260	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
261	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
262	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
263	C₅×C₈	—	2	2	no	—
264	C₅×C₈	—	2	2	no	—
265	#168	—	2	2	no	—
266	#168	—	2	2	no	—
267	C₂³×C₄	—	5	1	no	—
268	C₂×M₁₆	—	5	1	no	—
269	C₂×M₁₆	—	5	2	no	—
270	C₂×M₁₆	—	5	2	no	—
271	C₂×M₁₆	—	5	2	no	—
272	C₂×M₁₆	—	10	4	no	—
273	C₂×M₁₆	—	10	4	no	—
274	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
275	C₂²×C₈	—	5	1	no	—
276	C₂²×C₈	—	5	2	no	—
277	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
278	#117	—	5	1	no	—
279	#117	—	5	2	no	—
280	#117	—	5	2	no	—
281	#117	—	5	2	no	—
282	#117	C₂×C₃×D₅	1	1	yes	characteristic
283	C₂×C₄⋊C₄	—	5	2	no	—
284	C₂×C₂²⋊C₄	—	5	2	no	—
285	C₂×C₄²	—	5	2	no	—
286	C₄⋊C₈	—	5	4	no	—
287	C₄⋊C₈	—	5	4	no	—
288	C₄⋊C₈	—	5	4	no	—
289	C₄⋊C₈	C₂×C₃×D₅	1	4	yes	complemented
290	C₂×C₃×C₅	—	2	2	no	—
291	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
292	C₂×C₃×C₅	#568	1	2	yes	—
293	C₃×D₅	—	2	2	no	—
294	C₃×D₅	—	2	2	no	—
295	C₂³×C₃	—	5	1	no	—
296	C₂³×C₃	—	5	1	no	—
297	C₂³×C₃	—	5	4	no	—
298	C₂³×C₃	—	20	2	no	—
299	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
300	C₂×C₃×C₄	—	5	1	no	—
301	C₂×C₃×C₄	—	5	1	no	—
302	C₂×C₃×C₄	—	5	4	no	—
303	C₂×C₃×C₄	—	5	2	no	—
304	C₂×C₃×C₄	—	5	2	no	—
305	C₂×C₃×C₄	—	5	2	no	—
306	C₂×C₃×C₄	—	5	2	no	—
307	C₂×C₃×C₄	—	5	4	no	—
308	C₂×C₃×C₄	—	5	4	no	—
309	C₂×C₃×C₄	—	5	4	no	—
310	C₂×C₃×C₄	—	20	4	no	—
311	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
312	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
313	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
314	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
315	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
316	C₃×C₈	—	2	2	no	—
317	C₃×C₈	—	2	2	no	—
318	C₃×C₈	—	10	2	no	—
319	C₃×C₈	—	10	2	no	—
320	C₂²×C₅	—	2	2	no	—
321	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
322	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
323	C₂×D₅	—	2	2	no	—
324	C₂×D₅	—	2	2	no	—
325	C₂×D₅	—	4	4	no	—
326	C₂×D₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
327	C₂×D₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
330	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
331	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
332	Dic₅	—	2	4	no	—
333	Dic₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
334	Dic₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
335	C₂⁴	—	5	1	no	—
336	C₂²×C₄	—	5	1	no	—
337	C₂²×C₄	—	5	1	no	—
338	C₂²×C₄	—	5	1	no	—
339	C₂²×C₄	—	5	4	no	—
340	C₂²×C₄	—	5	4	no	—
341	C₂²×C₄	—	5	1	no	—
342	C₂²×C₄	—	5	1	no	—
343	C₂²×C₄	—	5	4	no	—
344	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
345	M₁₆	—	2	2	no	—
346	M₁₆	—	10	4	no	—
347	M₁₆	—	10	4	no	—
348	M₁₆	—	10	4	no	—
349	M₁₆	—	10	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	5	2	no	—
352	C₂×C₈	—	5	2	no	—
353	C₂×C₈	—	10	4	no	—
354	C₂×C₈	—	10	2	no	—
355	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
356	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
357	C₄⋊C₄	—	5	4	no	—
358	C₄⋊C₄	—	5	2	no	—
359	C₄⋊C₄	C₃×C₄×D₅	1	2	yes	—
360	C₂²⋊C₄	—	5	2	no	—
361	C₂²⋊C₄	—	5	4	no	—
362	C₂²⋊C₄	C₃×C₄×D₅	1	2	yes	—
363	C₄²	—	5	4	no	—
364	C₄²	—	5	2	no	—
365	C₄²	C₂²×C₃×D₅	1	2	yes	—
366	C₃×C₅	#2905	1	1	yes	characteristic, complemented, Hall
367	C₂²×C₃	—	2	2	no	—
368	C₂²×C₃	—	5	2	no	—
369	C₂²×C₃	—	5	2	no	—
370	C₂²×C₃	—	10	2	no	—
371	C₂²×C₃	—	10	2	no	—
372	C₂²×C₃	—	20	4	no	—
373	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
374	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
375	C₃×C₄	—	2	4	no	—
376	C₃×C₄	—	5	2	no	—
377	C₃×C₄	—	5	2	no	—
378	C₃×C₄	—	10	4	no	—
379	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
380	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
381	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
382	C₂×C₅	—	2	2	no	—
383	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
384	C₂×C₅	C₃×#568	1	2	yes	—
385	D₅	—	2	2	no	—
386	D₅	—	2	2	no	—
387	C₂³	—	5	1	no	—
388	C₂³	—	5	1	no	—
389	C₂³	—	5	4	no	—
390	C₂³	—	20	2	no	—
391	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
392	C₂×C₄	—	5	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	4	no	—
395	C₂×C₄	—	5	2	no	—
396	C₂×C₄	—	5	2	no	—
397	C₂×C₄	—	5	2	no	—
398	C₂×C₄	—	5	2	no	—
399	C₂×C₄	—	5	4	no	—
400	C₂×C₄	—	5	4	no	—
401	C₂×C₄	—	5	4	no	—
402	C₂×C₄	—	20	4	no	—
403	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
404	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
405	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
406	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
407	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	2	2	no	—
410	C₈	—	10	2	no	—
411	C₈	—	10	2	no	—
412	C₂×C₃	—	2	2	no	—
413	C₂×C₃	—	10	2	no	—
414	C₂×C₃	—	10	2	no	—
415	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
416	C₂×C₃	#66084	1	2	yes	—
417	C₅	C₃×#2905	1	1	yes	characteristic, complemented, Sylow
418	C₂²	—	2	2	no	—
419	C₂²	—	5	2	no	—
420	C₂²	—	5	2	no	—
421	C₂²	—	10	2	no	—
422	C₂²	—	10	2	no	—
423	C₂²	—	20	4	no	—
424	C₂²	C₃×D₅×C₄⋊C₄	1	2	yes	—
425	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	5	2	no	—
428	C₄	—	5	2	no	—
429	C₄	—	10	4	no	—
430	C₄	C₃×D₅×C₄⋊C₄	1	2	yes	—
431	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
432	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
433	C₃	#10610811	1	1	yes	characteristic, direct product factor, Sylow
434	C₂	—	2	2	no	—
435	C₂	—	10	2	no	—
436	C₂	—	10	2	no	—
437	C₂	C₂×C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
438	C₂	C₃×#66084	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#424	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#424	D₅
hypocenter	C₅	C₃×#2905
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#424

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#424	C₂	semidirect
5. C₃×#65408	C₂	semidirect
6. C₃×#65391	C₂	semidirect
7. C₃×#65288	C₂	semidirect
8. C₃×#65128	C₂	semidirect
9. C₃×#65126	C₂	semidirect
10. #10610811	C₃	direct (N × H)
30. C₃×C₅×C₄⋊C₈	C₂²	semidirect
31. C₃×#3946	C₂²	semidirect
32. C₃×#3946	C₂²	semidirect
33. C₃×C₄⋊#168	C₂²	semidirect
38. C₅×#424	C₂×C₃	semidirect
39. #65408	C₂×C₃	semidirect
40. #65391	C₂×C₃	semidirect
41. #65288	C₂×C₃	semidirect
42. #65128	C₂×C₃	semidirect
43. #65126	C₂×C₃	semidirect
82. C₃×#424	D₅	semidirect
103. C₅×C₄⋊C₈	C₂²×C₃	semidirect
104. #3946	C₂²×C₃	semidirect
105. #3946	C₂²×C₃	semidirect
106. C₄⋊#168	C₂²×C₃	semidirect
155. C₃×C₄⋊C₈	C₂×D₅	semidirect
194. #424	C₃×D₅	semidirect
289. C₄⋊C₈	C₂×C₃×D₅	semidirect
366. C₃×C₅	#2905	semidirect
417. C₅	C₃×#2905	semidirect
433. C₃	#10610811	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×D₅×M₁₆	2
C₂²×C₃×#676	2
C₃×D₅×#117	2
C₃×C₅×#424	2
C₃×#65408	2
C₃×#65391	2
C₃×#65288	2
C₃×#65128	2
C₃×#65126	2
#10610811	3
C₃×#2905	5

Subgroups — C3×#10610811 #14413111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610811 #14413111