Subgroups — C₃×#10610253 #14415847

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4053	C₂	1	2	yes	maximal, complemented
2	C₃×#65811	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65418	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64995	C₂	1	4	yes	maximal, complemented
7	C₃×#64977	C₂	1	2	yes	maximal, complemented
8	C₃×C₈×D₂₀	C₂	1	2	yes	maximal, complemented
9	#10610253	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#709	C₂²	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₃×#4076	C₄	1	2	yes	—
15	C₃×#4076	C₄	1	2	yes	—
16	C₂²×C₃×#168	C₂²	1	2	yes	—
17	C₃×#4053	—	2	8	no	—
18	C₂×C₃×#676	C₂²	1	4	yes	—
19	C₂×C₃×C₈×D₅	C₂²	1	4	yes	—
20	C₃×#4021	C₄	1	2	yes	—
21	C₃×#4020	C₄	1	1	yes	characteristic
22	C₃×C₄×D₂₀	C₂²	1	2	yes	—
23	C₃×C₄×D₂₀	C₂²	1	2	yes	—
24	C₃×#4015	C₄	1	1	yes	characteristic
25	C₃×C₅×#97	C₂²	1	2	yes	—
26	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
27	C₃×#3952	C₂²	1	4	yes	—
28	C₃×#3952	C₂²	1	4	yes	—
29	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
30	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊#168	C₂²	1	2	yes	—
32	C₃×#2935	—	5	1	no	maximal, Hall
33	C₂×#4053	C₂×C₃	1	2	yes	complemented
34	#65811	C₂×C₃	1	1	yes	characteristic
35	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
36	#65418	C₂×C₃	1	2	yes	complemented
37	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
38	#64995	C₂×C₃	1	4	yes	complemented
39	#64977	C₂×C₃	1	2	yes	complemented
40	C₈×D₂₀	C₂×C₃	1	2	yes	complemented
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	—
45	C₃×#709	—	2	4	no	—
46	C₃×#709	—	2	4	no	—
47	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
48	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
49	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
50	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
51	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
52	C₃×C₅×M₁₆	—	2	2	no	—
53	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
54	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₃×#685	C₂×C₄	1	4	yes	—
61	C₃×#685	C₂×C₄	1	4	yes	—
62	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
63	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
64	C₂×C₃×#168	—	2	4	no	—
65	C₂×C₃×#168	C₂³	1	2	yes	—
66	C₂×C₃×#168	C₂³	1	2	yes	—
67	C₃×#676	—	2	8	no	—
68	C₃×C₈×D₅	—	2	8	no	—
69	C₂×C₃×#131	—	5	2	no	—
70	C₃×#532	—	5	1	no	—
71	C₃×#436	—	5	2	no	—
72	C₃×#435	—	5	4	no	—
73	C₃×C₈×D₄	—	5	2	no	—
74	C₂×C₃×C₄⋊C₈	—	5	1	no	—
75	C₃×#408	—	5	2	no	—
76	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic, complemented
77	C₂×#709	C₂²×C₃	1	2	yes	—
78	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
81	#4076	C₃×C₄	1	2	yes	—
82	#4076	C₃×C₄	1	2	yes	—
83	C₂²×#168	C₂²×C₃	1	2	yes	—
84	#4053	—	2	8	no	—
85	C₂×#676	C₂²×C₃	1	4	yes	—
86	C₂×C₈×D₅	C₂²×C₃	1	4	yes	—
87	#4021	C₃×C₄	1	2	yes	—
88	#4020	C₃×C₄	1	1	yes	characteristic
89	C₄×D₂₀	C₂²×C₃	1	2	yes	—
90	C₄×D₂₀	C₂²×C₃	1	2	yes	—
91	#4015	C₃×C₄	1	1	yes	characteristic
92	C₅×#97	C₂²×C₃	1	2	yes	—
93	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
94	#3952	C₂²×C₃	1	4	yes	—
95	#3952	C₂²×C₃	1	4	yes	—
96	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
97	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
98	C₄⋊#168	C₂²×C₃	1	2	yes	—
99	#2935	—	5	1	no	Sylow
100	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	4	1	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	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	#41	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₃×C₂²⋊D₅	—	2	8	no	—
113	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
114	C₃×D₂₀	—	2	4	no	—
115	C₃×D₂₀	—	2	4	no	—
116	C₃×D₂₀	—	4	2	no	—
117	C₃×C₄×D₅	—	2	4	no	—
118	C₃×C₄×D₅	—	2	4	no	—
119	C₃×Dic₁₀	—	2	4	no	—
120	C₃×C₅×C₈	—	2	2	no	—
121	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
122	C₃×#168	—	2	2	no	—
123	C₃×#168	—	2	2	no	—
124	C₂×C₃×#41	—	5	2	no	—
125	C₃×#131	—	10	8	no	—
126	C₂×C₃×M₁₆	—	5	4	no	—
127	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
128	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
129	C₂²×C₃×C₈	—	5	2	no	—
130	C₂²×C₃×C₈	—	5	4	no	—
131	C₃×C₄⋊Q₈	—	5	1	no	—
132	C₃×#127	—	5	1	no	—
133	C₃×#124	—	5	2	no	—
134	C₃×#121	—	5	2	no	—
135	C₃×#121	—	5	2	no	—
136	C₃×C₄×D₄	—	5	2	no	—
137	C₃×C₄×D₄	—	5	2	no	—
138	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
139	C₃×C₄⋊C₈	—	5	1	no	—
140	C₃×C₄⋊C₈	—	5	2	no	—
141	C₃×C₄⋊C₈	—	5	1	no	—
142	C₃×C₂²⋊C₈	—	5	4	no	—
143	C₃×C₂²⋊C₈	—	5	4	no	—
144	C₃×#97	C₂×D₅	1	2	yes	—
145	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
146	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	4	yes	—
150	#709	—	2	4	no	—
151	#709	—	2	4	no	—
152	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
153	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
154	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
155	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
156	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
157	C₅×M₁₆	—	2	2	no	—
158	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
159	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
160	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
161	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
162	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
163	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
165	#685	C₂×C₃×C₄	1	4	yes	—
166	#685	C₂×C₃×C₄	1	4	yes	—
167	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
168	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
169	C₂×#168	—	2	4	no	—
170	C₂×#168	C₂³×C₃	1	2	yes	—
171	C₂×#168	C₂³×C₃	1	2	yes	—
172	#676	—	2	8	no	—
173	C₈×D₅	—	2	8	no	—
174	C₂×#131	—	5	2	no	—
175	#532	—	5	1	no	—
176	#436	—	5	2	no	—
177	#435	—	5	4	no	—
178	C₈×D₄	—	5	2	no	—
179	C₂×C₄⋊C₈	—	5	1	no	—
180	#408	—	5	2	no	—
181	C₄×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
185	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₃×D₅	—	2	4	no	—
187	C₂×C₃×D₅	—	2	4	no	—
188	C₂×C₃×D₅	—	2	4	no	—
189	C₃×C₄×C₅	—	2	1	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
193	C₃×C₄×C₅	#131	1	2	yes	complemented
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
196	C₃×Dic₅	—	2	4	no	—
197	C₃×#41	—	10	4	no	—
198	C₃×#41	—	10	4	no	—
199	C₂×C₃×Q₈	—	5	2	no	—
200	C₂×C₃×D₄	—	5	4	no	—
201	C₂×C₃×D₄	—	5	2	no	—
202	C₂×C₃×D₄	—	5	2	no	—
203	C₂×C₃×D₄	—	5	2	no	—
204	C₂²×C₃×C₄	—	5	4	no	—
205	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
208	C₃×M₁₆	—	2	2	no	—
209	C₃×M₁₆	—	10	8	no	—
210	C₃×M₁₆	D₂₀	1	4	yes	complemented
211	C₂×C₃×C₈	—	5	2	no	—
212	C₂×C₃×C₈	—	5	2	no	—
213	C₂×C₃×C₈	—	10	4	no	—
214	C₂×C₃×C₈	—	10	8	no	—
215	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
216	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
217	C₃×C₄⋊C₄	—	5	2	no	—
218	C₃×C₄⋊C₄	—	5	2	no	—
219	C₃×C₂²⋊C₄	—	5	4	no	—
220	C₃×C₂²⋊C₄	—	5	4	no	—
221	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
222	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
223	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
224	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
225	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
226	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
235	C₂×C₄×C₅	C₃×#41	1	2	yes	—
236	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
237	C₂²⋊D₅	—	2	8	no	—
238	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
239	D₂₀	—	2	4	no	—
240	D₂₀	—	2	4	no	—
241	D₂₀	—	4	2	no	—
242	C₄×D₅	—	2	4	no	—
243	C₄×D₅	—	2	4	no	—
244	Dic₁₀	—	2	4	no	—
245	C₅×C₈	—	2	2	no	—
246	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
247	#168	—	2	2	no	—
248	#168	—	2	2	no	—
249	C₂×#41	—	5	2	no	—
250	#131	—	10	8	no	—
251	C₂×M₁₆	—	5	4	no	—
252	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
253	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
254	C₂²×C₈	—	5	2	no	—
255	C₂²×C₈	—	5	4	no	—
256	C₄⋊Q₈	—	5	1	no	—
257	#127	—	5	1	no	—
258	#124	—	5	2	no	—
259	#121	—	5	2	no	—
260	#121	—	5	2	no	—
261	C₄×D₄	—	5	2	no	—
262	C₄×D₄	—	5	2	no	—
263	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
264	C₄⋊C₈	—	5	1	no	—
265	C₄⋊C₈	—	5	2	no	—
266	C₄⋊C₈	—	5	1	no	—
267	C₂²⋊C₈	—	5	4	no	—
268	C₂²⋊C₈	—	5	4	no	—
269	#97	C₂×C₃×D₅	1	2	yes	—
270	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
274	C₂×C₃×C₅	#568	1	1	yes	characteristic
275	C₃×D₅	—	4	4	no	—
276	C₂³×C₃	—	5	4	no	—
277	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
278	C₃×Q₈	—	10	4	no	—
279	C₃×D₄	—	10	8	no	—
280	C₃×D₄	—	10	4	no	—
281	C₃×D₄	—	10	4	no	—
282	C₃×D₄	—	20	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	4	1	no	—
285	C₂×C₃×C₄	—	5	4	no	—
286	C₂×C₃×C₄	—	10	4	no	—
287	C₂×C₃×C₄	—	10	4	no	—
288	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
294	C₂×C₃×C₄	#709	1	2	yes	—
295	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	—	10	2	no	—
298	C₃×C₈	—	10	2	no	—
299	C₃×C₈	C₂×D₂₀	1	4	yes	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
303	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
304	C₂×D₅	—	2	4	no	—
305	C₂×D₅	—	2	4	no	—
306	C₂×D₅	—	2	4	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
311	C₄×C₅	C₃×#131	1	2	yes	complemented
312	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
313	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
314	Dic₅	—	2	4	no	—
315	#41	—	10	4	no	—
316	#41	—	10	4	no	—
317	C₂×Q₈	—	5	2	no	—
318	C₂×D₄	—	5	4	no	—
319	C₂×D₄	—	5	2	no	—
320	C₂×D₄	—	5	2	no	—
321	C₂×D₄	—	5	2	no	—
322	C₂²×C₄	—	5	4	no	—
323	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
324	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
326	M₁₆	—	2	2	no	—
327	M₁₆	—	10	8	no	—
328	M₁₆	C₃×D₂₀	1	4	yes	complemented
329	C₂×C₈	—	5	2	no	—
330	C₂×C₈	—	5	2	no	—
331	C₂×C₈	—	10	4	no	—
332	C₂×C₈	—	10	8	no	—
333	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
334	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
335	C₄⋊C₄	—	5	2	no	—
336	C₄⋊C₄	—	5	2	no	—
337	C₂²⋊C₄	—	5	4	no	—
338	C₂²⋊C₄	—	5	4	no	—
339	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
340	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
341	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
342	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
343	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	10	4	no	—
347	C₂²×C₃	—	10	4	no	—
348	C₂²×C₃	—	10	4	no	—
349	C₂²×C₃	C₄×D₂₀	1	2	yes	—
350	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	10	4	no	—
355	C₃×C₄	C₄×D₂₀	1	2	yes	—
356	C₃×C₄	#4053	1	2	yes	complemented
357	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
358	C₃×C₄	C₂×#709	1	1	yes	characteristic
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
361	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
362	C₂×C₅	C₃×#568	1	1	yes	characteristic
363	D₅	—	4	4	no	—
364	C₂³	—	5	4	no	—
365	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
366	Q₈	—	10	4	no	—
367	D₄	—	10	8	no	—
368	D₄	—	10	4	no	—
369	D₄	—	10	4	no	—
370	D₄	—	20	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	5	4	no	—
374	C₂×C₄	—	10	4	no	—
375	C₂×C₄	—	10	4	no	—
376	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
377	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
378	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
379	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
380	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
381	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
382	C₂×C₄	C₃×#709	1	2	yes	—
383	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	10	2	no	—
386	C₈	—	10	2	no	—
387	C₈	C₂×C₃×D₂₀	1	4	yes	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	—	20	4	no	—
390	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
391	C₂×C₃	C₂×#4053	1	1	yes	characteristic
392	C₂×C₃	#66079	1	1	yes	characteristic
393	C₅	C₃×#2935	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	10	4	no	—
397	C₂²	—	10	4	no	—
398	C₂²	—	10	4	no	—
399	C₂²	C₃×C₄×D₂₀	1	2	yes	—
400	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	10	4	no	—
405	C₄	C₃×C₄×D₂₀	1	2	yes	—
406	C₄	C₃×#4053	1	2	yes	complemented
407	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
408	C₄	C₂×C₃×#709	1	1	yes	characteristic
409	C₃	#10610253	1	1	yes	characteristic, direct product factor, Sylow
410	C₂	—	2	2	no	—
411	C₂	—	20	4	no	—
412	C₂	C₂×C₃×C₄×D₂₀	1	1	yes	characteristic
413	C₂	C₂×C₃×#4053	1	1	yes	characteristic
414	C₂	C₃×#66079	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#65811	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×M₁₆	D₅
hypocenter	C₅	C₃×#2935
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4053	C₂	semidirect
3. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. C₃×#65418	C₂	semidirect
5. C₂×C₃×C₄⋊#168	C₂	semidirect
6. C₃×#64995	C₂	semidirect
7. C₃×#64977	C₂	semidirect
8. C₃×C₈×D₂₀	C₂	semidirect
9. #10610253	C₃	direct (N × H)
33. C₂×#4053	C₂×C₃	semidirect
35. C₄×C₅×M₁₆	C₂×C₃	semidirect
36. #65418	C₂×C₃	semidirect
37. C₂×C₄⋊#168	C₂×C₃	semidirect
38. #64995	C₂×C₃	semidirect
39. #64977	C₂×C₃	semidirect
40. C₈×D₂₀	C₂×C₃	semidirect
53. C₃×C₅×M₁₆	D₄	semidirect
76. C₃×C₄×M₁₆	D₅	semidirect
158. C₅×M₁₆	C₃×D₄	semidirect
181. C₄×M₁₆	C₃×D₅	semidirect
193. C₃×C₄×C₅	#131	semidirect
210. C₃×M₁₆	D₂₀	semidirect
311. C₄×C₅	C₃×#131	semidirect
328. M₁₆	C₃×D₂₀	semidirect
343. C₃×C₅	#2935	semidirect
356. C₃×C₄	#4053	semidirect
393. C₅	C₃×#2935	semidirect
406. C₄	C₃×#4053	semidirect
409. C₃	#10610253	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×#4053	2
C₃×#65811	2
C₃×C₄×C₅×M₁₆	2
C₃×#65418	2
C₂×C₃×C₄⋊#168	2
C₃×#64995	2
C₃×#64977	2
C₃×C₈×D₂₀	2
#10610253	3
C₃×#2935	5

Subgroups — C3×#10610253 #14415847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610253 #14415847