Subgroups — #14295322

Order 1920.

696 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6710	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×#90952	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745966	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745966	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600742	—	3	1	no	maximal, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×#6710	—	2	2	no	—
11	C₂×#6710	—	2	2	no	—
12	C₂×#6710	C₄	1	4	yes	complemented
13	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
14	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₂²⋊Dic₅	C₄	1	2	yes	—
18	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
20	C₅×#830	C₄	1	4	yes	complemented
21	C₃×#3963	C₄	1	2	yes	—
22	#90952	—	2	2	no	—
23	Dic₅×C₃⋊C₈	—	2	2	no	—
24	#69448	—	5	1	no	maximal, Hall
25	C₂²×#681	—	3	1	no	—
26	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
27	C₄×C₂²⋊Dic₅	D₃	1	1	yes	characteristic
28	C₂×#3947	—	3	1	no	—
29	C₂×C₈×Dic₅	—	3	1	no	—
30	#64770	—	3	1	no	—
31	#64770	—	3	1	no	—
32	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
42	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
43	#6710	—	2	8	no	—
44	C₂×C₃⋊#168	—	2	1	no	—
45	C₂×C₃⋊#168	—	2	1	no	—
46	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
47	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
48	C₂×C₃⋊#168	D₄	1	2	yes	—
49	C₂×C₃⋊#168	D₄	1	2	yes	—
50	C₂×C₅×C₃⋊C₈	—	2	1	no	—
51	C₂×C₅×C₃⋊C₈	—	2	1	no	—
52	C₂×C₅×C₃⋊C₈	—	2	1	no	—
53	C₂×C₅×C₃⋊C₈	—	2	1	no	—
54	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
55	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
56	C₃×C₂²⋊Dic₅	—	2	4	no	—
57	C₃×C₄×Dic₅	—	2	1	no	—
58	C₃×C₄×Dic₅	—	2	1	no	—
59	C₃×C₄×Dic₅	—	2	1	no	—
60	C₃×C₄×Dic₅	—	2	1	no	—
61	C₂²×#208	—	5	1	no	—
62	C₃×C₄×C₂²⋊C₄	—	5	1	no	—
63	C₂×#830	D₅	1	1	yes	characteristic
64	C₂×#803	—	5	1	no	—
65	C₂×C₄×C₃⋊C₈	—	5	1	no	—
66	#4524	—	5	1	no	—
67	#4524	—	5	1	no	—
68	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
69	C₂²×C₅×C₈	—	3	1	no	—
70	C₂²×C₅×C₈	—	3	1	no	—
71	C₂×C₂²⋊Dic₅	Dic₃	1	2	yes	—
72	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
73	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
74	C₂×#681	—	3	4	no	—
75	C₂×#681	—	6	2	no	—
76	C₂×#681	—	6	2	no	—
77	C₂²×#168	—	3	1	no	—
78	C₂²×#168	—	3	1	no	—
79	C₅×C₂²⋊C₈	—	3	4	no	—
80	#3963	Dic₃	1	2	yes	—
81	#3947	—	6	2	no	—
82	C₈×Dic₅	—	6	2	no	—
83	#1753	—	15	1	no	Sylow
84	C₂³×C₃×C₅	—	2	1	no	—
85	C₂³×C₃×C₅	—	2	1	no	—
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	C₄²	1	2	yes	—
89	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₃×Dic₅	—	2	2	no	—
104	C₂×C₃×Dic₅	—	2	2	no	—
105	C₂×C₃×Dic₅	—	2	2	no	—
106	C₂×C₃×Dic₅	—	2	2	no	—
107	C₂×C₃×Dic₅	—	2	2	no	—
108	C₂×C₃×Dic₅	M₁₆	1	4	yes	complemented
109	C₃⋊#168	—	2	2	no	—
110	C₃⋊#168	C₂²⋊C₄	1	4	yes	complemented
111	C₅×C₃⋊C₈	—	2	2	no	—
112	C₅×C₃⋊C₈	—	2	2	no	—
113	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
114	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
115	C₂×C₃×C₄²	—	5	1	no	—
116	C₂×C₃×C₄²	—	5	1	no	—
117	C₂×#208	—	5	4	no	—
118	C₂×#208	—	10	2	no	—
119	C₂×#208	—	10	2	no	—
120	C₂²×C₃⋊C₈	—	5	1	no	—
121	C₂²×C₃⋊C₈	—	5	1	no	—
122	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
123	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
124	C₃×#95	—	5	2	no	—
125	#830	Dic₅	1	4	yes	complemented
126	#803	—	10	2	no	—
127	C₄×C₃⋊C₈	—	10	2	no	—
128	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
134	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
135	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
137	C₂²×Dic₅	C₂×Dic₃	1	2	yes	—
138	C₂²×Dic₅	C₂×Dic₃	1	2	yes	—
139	C₂×C₅×C₈	—	3	2	no	—
140	C₂×C₅×C₈	—	3	2	no	—
141	C₂×C₅×C₈	—	6	1	no	—
142	C₂×C₅×C₈	—	6	1	no	—
143	C₂×C₅×C₈	—	6	1	no	—
144	C₂×C₅×C₈	—	6	1	no	—
145	C₂²⋊Dic₅	—	2	4	no	—
146	C₄×Dic₅	—	2	1	no	—
147	C₄×Dic₅	—	2	1	no	—
148	C₄×Dic₅	—	2	1	no	—
149	C₄×Dic₅	—	2	1	no	—
150	#681	—	6	8	no	—
151	C₂×#168	—	3	2	no	—
152	C₂×#168	—	3	2	no	—
153	C₂×#168	—	3	2	no	—
154	C₂×#168	—	3	2	no	—
155	C₂×#168	—	6	1	no	—
156	C₂×#168	—	6	1	no	—
157	C₂²×M₁₆	—	15	1	no	—
158	C₂×C₂²⋊C₈	—	3	1	no	—
159	C₂×#97	—	15	1	no	—
160	C₂×C₄×C₈	—	15	1	no	—
161	C₄×C₂²⋊C₄	—	5	1	no	—
162	#336	—	15	1	no	—
163	#336	—	15	1	no	—
164	C₂²×C₃×C₅	—	2	2	no	—
165	C₂²×C₃×C₅	—	2	2	no	—
166	C₂²×C₃×C₅	—	2	2	no	—
167	C₂²×C₃×C₅	—	4	2	no	—
168	C₂²×C₃×C₅	—	4	2	no	—
169	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
173	C₂²×C₃×C₅	#131	1	2	yes	—
174	C₃×C₄×C₅	—	2	2	no	—
175	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₃×C₄×C₅	#117	1	1	yes	characteristic
177	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
179	C₃×Dic₅	—	2	4	no	—
180	C₃×Dic₅	—	4	2	no	—
181	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂²×C₃×C₄	—	5	2	no	—
187	C₂²×C₃×C₄	—	5	2	no	—
188	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
190	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
191	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
192	C₃×C₂²⋊C₄	—	10	4	no	—
193	C₃×C₄²	—	10	1	no	—
194	C₃×C₄²	—	10	1	no	—
195	C₃×C₄²	—	10	1	no	—
196	C₃×C₄²	—	10	1	no	—
197	#208	—	10	8	no	—
198	C₂×C₃⋊C₈	—	2	1	no	—
199	C₂×C₃⋊C₈	—	2	1	no	—
200	C₂×C₃⋊C₈	—	2	1	no	—
201	C₂×C₃⋊C₈	—	2	1	no	—
202	C₂×C₃⋊C₈	—	5	2	no	—
203	C₂×C₃⋊C₈	—	5	2	no	—
204	C₂×C₃⋊C₈	—	5	2	no	—
205	C₂×C₃⋊C₈	—	5	2	no	—
206	C₂×C₃⋊C₈	—	10	1	no	—
207	C₂×C₃⋊C₈	—	10	1	no	—
208	C₂×C₃⋊C₈	C₂×Dic₅	1	2	yes	—
209	C₂×C₃⋊C₈	C₂×Dic₅	1	2	yes	—
210	C₂³×C₅	—	2	2	no	—
211	C₂³×C₅	—	2	1	no	—
212	C₂³×C₅	—	2	1	no	—
213	C₂³×C₅	—	2	2	no	—
214	C₂³×C₅	C₄×Dic₃	1	2	yes	—
215	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
223	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
225	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	#237	1	1	yes	characteristic
228	C₂×C₄×C₅	#237	1	1	yes	characteristic
229	C₂×Dic₅	—	2	2	no	—
230	C₂×Dic₅	—	2	2	no	—
231	C₂×Dic₅	—	2	2	no	—
232	C₂×Dic₅	—	2	2	no	—
233	C₂×Dic₅	—	2	2	no	—
234	C₂×Dic₅	#208	1	4	yes	complemented
235	C₅×C₈	—	6	2	no	—
236	C₅×C₈	—	6	2	no	—
237	#168	—	3	4	no	—
238	#168	—	6	2	no	—
239	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
240	C₂×M₁₆	—	15	4	no	—
241	C₂×M₁₆	—	30	2	no	—
242	C₂×M₁₆	—	30	2	no	—
243	C₂²×C₈	—	3	1	no	—
244	C₂²×C₈	—	3	1	no	—
245	C₂²×C₈	—	15	1	no	—
246	C₂²×C₈	—	15	1	no	—
247	C₂×C₂²⋊C₄	—	5	2	no	—
248	C₂×C₄²	—	5	1	no	—
249	C₂×C₄²	—	5	1	no	—
250	C₂²⋊C₈	—	3	4	no	—
251	#97	—	30	2	no	—
252	C₄×C₈	—	30	2	no	—
253	#95	—	5	2	no	—
254	C₂×C₃×C₅	—	4	2	no	—
255	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
257	C₂×C₃×C₅	#405	1	1	yes	characteristic
258	C₂×C₃×C₅	#435	1	2	yes	—
259	C₂×C₃×C₅	#436	1	2	yes	—
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂³×C₃	—	2	2	no	—
263	C₂³×C₃	—	2	2	no	—
264	C₂³×C₃	C₄×Dic₅	1	2	yes	—
265	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	5	4	no	—
273	C₂×C₃×C₄	—	10	2	no	—
274	C₂×C₃×C₄	—	10	2	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	—	10	2	no	—
277	C₂×C₃×C₄	—	10	2	no	—
278	C₂×C₃×C₄	C₄×Dic₅	1	2	yes	—
279	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
280	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
281	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
282	C₂×C₃×C₄	#711	1	1	yes	characteristic
283	C₂×C₃×C₄	#711	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
285	C₃⋊C₈	—	2	2	no	—
286	C₃⋊C₈	—	2	2	no	—
287	C₃⋊C₈	—	5	4	no	—
288	C₃⋊C₈	—	10	2	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	—	2	2	no	—
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	C₂×#208	1	2	yes	—
295	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
296	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
297	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
298	C₂²×C₅	#948	1	2	yes	—
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	#877	1	1	yes	characteristic
301	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
302	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
303	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
304	Dic₅	—	2	4	no	—
305	Dic₅	—	4	2	no	—
306	C₂⁴	D₅×Dic₃	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	5	2	no	—
312	C₂²×C₄	—	5	2	no	—
313	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
314	C₂²×C₄	D₃×Dic₅	1	2	yes	—
315	C₂²×C₄	#1200	1	2	yes	—
316	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
317	M₁₆	—	30	8	no	—
318	C₂×C₈	—	3	2	no	—
319	C₂×C₈	—	3	2	no	—
320	C₂×C₈	—	6	1	no	—
321	C₂×C₈	—	6	1	no	—
322	C₂×C₈	—	6	1	no	—
323	C₂×C₈	—	6	1	no	—
324	C₂×C₈	—	15	2	no	—
325	C₂×C₈	—	15	2	no	—
326	C₂×C₈	—	15	2	no	—
327	C₂×C₈	—	15	2	no	—
328	C₂×C₈	—	30	1	no	—
329	C₂×C₈	—	30	1	no	—
330	C₂²⋊C₄	—	10	4	no	—
331	C₄²	—	10	1	no	—
332	C₄²	—	10	1	no	—
333	C₄²	—	10	1	no	—
334	C₄²	—	10	1	no	—
335	C₃×C₅	#1753	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	—	4	2	no	—
341	C₂²×C₃	#4027	1	1	yes	characteristic
342	C₂²×C₃	#4027	1	1	yes	characteristic
343	C₂²×C₃	#4047	1	2	yes	—
344	C₂²×C₃	D₅×M₁₆	1	2	yes	—
345	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	10	4	no	—
348	C₃×C₄	—	20	2	no	—
349	C₃×C₄	#4023	1	1	yes	characteristic
350	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
351	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
352	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
353	C₂×C₅	—	4	2	no	—
354	C₂×C₅	C₄×#208	1	1	yes	characteristic
355	C₂×C₅	Dic₃×C₂²⋊C₄	1	1	yes	characteristic
356	C₂×C₅	#4997	1	1	yes	characteristic
357	C₂×C₅	#5011	1	2	yes	—
358	C₂×C₅	#5012	1	2	yes	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	Dic₃×Dic₅	1	2	yes	—
364	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	5	4	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	Dic₃×Dic₅	1	2	yes	—
378	C₂×C₄	#6780	1	1	yes	characteristic
379	C₂×C₄	#6780	1	1	yes	characteristic
380	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
381	C₂×C₄	C₂×#1200	1	1	yes	characteristic
382	C₂×C₄	#6790	1	1	yes	characteristic
383	C₂×C₄	#6790	1	1	yes	characteristic
384	C₈	—	6	2	no	—
385	C₈	—	6	2	no	—
386	C₈	—	15	4	no	—
387	C₈	—	30	2	no	—
388	C₂×C₃	—	4	2	no	—
389	C₂×C₃	#65017	1	2	yes	—
390	C₂×C₃	#65018	1	2	yes	—
391	C₂×C₃	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
392	C₂×C₃	#65390	1	1	yes	characteristic
393	C₂×C₃	M₁₆×Dic₅	1	1	yes	characteristic
394	C₅	#69448	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	D₅×#208	1	2	yes	—
401	C₂²	#91283	1	2	yes	—
402	C₂²	C₂×Dic₃×Dic₅	1	1	yes	characteristic
403	C₂²	#91559	1	1	yes	characteristic
404	C₂²	#91559	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	10	4	no	—
407	C₄	—	20	2	no	—
408	C₄	#91532	1	1	yes	characteristic
409	C₄	#67⋊Dic₅	1	1	yes	characteristic
410	C₄	#67⋊Dic₅	1	1	yes	characteristic
411	C₄	#91561	1	1	yes	characteristic
412	C₃	#10600742	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	4	2	no	—
414	C₂	Dic₅×#208	1	1	yes	characteristic
415	C₂	#11748318	1	1	yes	characteristic
416	C₂	#11748339	1	2	yes	—
417	C₂	#11748494	1	2	yes	—
418	C₂	#11749487	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂×C₄²
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	#1753
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
4. C₂×#90952	C₂	semidirect
5. C₂×Dic₅×C₃⋊C₈	C₂	semidirect
6. #11745966	C₂	semidirect
7. #11745966	C₂	semidirect
12. C₂×#6710	C₄	semidirect
20. C₅×#830	C₄	semidirect
108. C₂×C₃×Dic₅	M₁₆	semidirect
110. C₃⋊#168	C₂²⋊C₄	semidirect
125. #830	Dic₅	semidirect
234. C₂×Dic₅	#208	semidirect
335. C₃×C₅	#1753	semidirect
394. C₅	#69448	semidirect
412. C₃	#10600742	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#6710	2
C₂×C₅×#830	2
C₃×C₄×C₂²⋊Dic₅	2
C₂×#90952	2
C₂×Dic₅×C₃⋊C₈	2
#11745966	2
#10600742	3
#69448	5