Subgroups — #14297449

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×#90982	C₂	1	2	yes	maximal, complemented
3	C₂×#90955	C₂	1	2	yes	maximal
4	#11746345	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4524	C₂	1	1	yes	maximal, characteristic, complemented
6	#10599455	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊#168	C₂²	1	2	yes	—
12	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
13	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	C₃×C₄²×D₅	—	2	4	no	—
17	#90982	—	2	4	no	—
18	#90955	—	2	4	no	—
19	#71530	—	5	1	no	maximal, Hall
20	C₂×C₄²×D₅	D₃	1	1	yes	characteristic
21	C₂×#3952	—	3	2	no	—
22	C₂×#3946	—	3	2	no	—
23	C₅×#336	—	3	1	no	—
24	#64744	—	3	1	no	—
25	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃×C₄×D₅	—	2	2	no	—
33	C₂×C₃×C₄×D₅	—	2	2	no	—
34	C₂×C₃×C₄×D₅	—	2	2	no	—
35	C₂×C₃×C₄×D₅	—	2	2	no	—
36	C₂×C₃×C₄×D₅	—	2	2	no	—
37	C₂×C₃×C₄×D₅	—	2	2	no	—
38	C₂×C₃×C₄×D₅	—	2	2	no	—
39	C₂×C₃×C₄×D₅	C₈	1	4	yes	complemented
40	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
41	C₂×C₃×C₄×D₅	Q₈	1	2	yes	—
42	C₃×C₄²×C₅	—	2	2	no	—
43	C₂×C₃⋊#168	—	2	2	no	—
44	C₂×C₃⋊#168	—	2	2	no	—
45	C₂×C₃⋊#168	—	2	2	no	—
46	C₂×C₅×C₃⋊C₈	—	2	2	no	—
47	C₂×C₅×C₃⋊C₈	—	2	2	no	—
48	C₂×C₅×C₃⋊C₈	—	2	2	no	—
49	C₃×C₄×Dic₅	—	2	2	no	—
50	C₃×C₄×Dic₅	—	2	2	no	—
51	C₃×C₄×Dic₅	D₄	1	4	yes	—
52	C₂²×C₃×C₄²	—	5	1	no	—
53	C₂×#830	—	5	2	no	—
54	C₂×C₄⋊(C₃⋊C₈)	—	5	2	no	—
55	#4524	—	5	1	no	—
56	#4524	D₅	1	1	yes	characteristic, complemented
57	C₂²×C₄×D₅	Dic₃	1	1	yes	characteristic
58	C₂²×C₄×D₅	Dic₃	1	1	yes	characteristic
59	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
60	C₂²×C₅×C₈	—	3	2	no	—
61	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
62	C₂×C₄×Dic₅	Dic₃	1	1	yes	characteristic
63	C₂×C₄×Dic₅	Dic₃	1	1	yes	characteristic
64	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
65	C₂²×#168	—	3	2	no	—
66	C₄²×D₅	—	2	4	no	—
67	#3952	—	6	4	no	—
68	#3946	—	6	4	no	—
69	#1797	—	15	1	no	Sylow
70	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₃×D₅	—	2	1	no	—
72	C₂²×C₃×D₅	—	2	1	no	—
73	C₂²×C₃×D₅	—	2	1	no	—
74	C₂²×C₃×D₅	—	2	1	no	—
75	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
76	C₂²×C₃×D₅	C₂×C₈	1	2	yes	—
77	C₂²×C₃×D₅	M₁₆	1	2	yes	—
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	2	1	no	—
82	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
83	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	#41	1	2	yes	—
88	C₂×C₃×Dic₅	—	2	1	no	—
89	C₂×C₃×Dic₅	—	2	1	no	—
90	C₂×C₃×Dic₅	—	2	1	no	—
91	C₂×C₃×Dic₅	—	2	1	no	—
92	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
93	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
94	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
95	C₂×C₃×Dic₅	C₂×C₈	1	2	yes	—
96	C₂×C₃×Dic₅	M₁₆	1	2	yes	—
97	C₃×C₄×D₅	—	2	8	no	—
98	C₃×C₄×D₅	—	2	4	no	—
99	C₃×C₄×D₅	—	2	4	no	—
100	C₃×C₄×D₅	—	2	8	no	—
101	C₃⋊#168	—	4	2	no	—
102	C₅×C₃⋊C₈	—	4	2	no	—
103	C₂³×C₃×C₄	—	5	1	no	—
104	C₂³×C₃×C₄	—	5	1	no	—
105	C₂³×C₃×C₄	—	5	1	no	—
106	C₂×C₃×C₄²	—	5	1	no	—
107	C₂×C₃×C₄²	—	5	1	no	—
108	C₂×C₃×C₄²	—	5	1	no	—
109	C₂×C₃×C₄²	—	10	4	no	—
110	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
111	C₂²×C₃⋊C₈	—	5	2	no	—
112	C₂²×C₃⋊C₈	C₂×D₅	1	2	yes	—
113	#830	—	10	4	no	—
114	C₄⋊(C₃⋊C₈)	—	10	4	no	—
115	C₂³×D₅	C₂×Dic₃	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
119	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
120	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
121	C₂²×Dic₅	C₂×Dic₃	1	1	yes	characteristic
122	C₂×C₄×D₅	—	2	2	no	—
123	C₂×C₄×D₅	—	2	2	no	—
124	C₂×C₄×D₅	—	2	2	no	—
125	C₂×C₄×D₅	—	2	2	no	—
126	C₂×C₄×D₅	—	2	2	no	—
127	C₂×C₄×D₅	—	2	2	no	—
128	C₂×C₄×D₅	—	2	2	no	—
129	C₂×C₄×D₅	C₃⋊C₈	1	4	yes	complemented
130	C₂×C₄×D₅	Dic₆	1	2	yes	—
131	C₂×C₄×D₅	D₁₂	1	2	yes	—
132	C₂×C₅×C₈	—	6	2	no	—
133	C₂×C₅×C₈	—	6	2	no	—
134	C₂×C₅×C₈	—	6	2	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄×Dic₅	—	2	2	no	—
137	C₄×Dic₅	—	2	2	no	—
138	C₄×Dic₅	#67	1	4	yes	—
139	C₂×#168	—	6	2	no	—
140	C₂×#168	—	6	2	no	—
141	C₂×#168	—	6	2	no	—
142	C₂²×C₄²	—	5	1	no	—
143	C₂×C₄⋊C₈	—	15	2	no	—
144	C₂×C₂²⋊C₈	—	15	2	no	—
145	#336	—	3	1	no	—
146	#336	—	15	1	no	—
147	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂²×C₃×C₅	#117	1	1	yes	characteristic
150	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
152	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
153	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
154	C₂×C₃×D₅	—	2	2	no	—
155	C₂×C₃×D₅	—	2	2	no	—
156	C₂×C₃×D₅	—	2	2	no	—
157	C₂×C₃×D₅	—	2	2	no	—
158	C₂×C₃×D₅	—	2	2	no	—
159	C₂×C₃×D₅	—	2	2	no	—
160	C₂×C₃×D₅	C₄⋊C₈	1	4	yes	complemented
161	C₃×C₄×C₅	—	2	2	no	—
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	#121	1	2	yes	—
164	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
165	C₃×Dic₅	—	2	2	no	—
166	C₃×Dic₅	—	2	2	no	—
167	C₃×Dic₅	C₂²⋊C₈	1	4	yes	complemented
168	C₂⁴×C₃	—	5	1	no	—
169	C₂²×C₃×C₄	—	5	1	no	—
170	C₂²×C₃×C₄	—	5	1	no	—
171	C₂²×C₃×C₄	—	5	1	no	—
172	C₂²×C₃×C₄	—	5	4	no	—
173	C₂²×C₃×C₄	—	5	2	no	—
174	C₂²×C₃×C₄	—	5	2	no	—
175	C₂²×C₃×C₄	—	10	2	no	—
176	C₂²×C₃×C₄	—	10	2	no	—
177	C₂²×C₃×C₄	—	10	2	no	—
178	C₂²×C₃×C₄	—	10	2	no	—
179	C₂²×C₃×C₄	—	10	2	no	—
180	C₂²×C₃×C₄	—	10	2	no	—
181	C₂²×C₃×C₄	—	10	2	no	—
182	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
185	C₃×C₄²	—	2	2	no	—
186	C₃×C₄²	—	5	4	no	—
187	C₃×C₄²	—	10	2	no	—
188	C₃×C₄²	—	10	2	no	—
189	C₂×C₃⋊C₈	—	2	2	no	—
190	C₂×C₃⋊C₈	—	2	2	no	—
191	C₂×C₃⋊C₈	—	2	2	no	—
192	C₂×C₃⋊C₈	—	10	2	no	—
193	C₂×C₃⋊C₈	—	10	2	no	—
194	C₂×C₃⋊C₈	—	10	2	no	—
195	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
196	C₂²×D₅	—	2	1	no	—
197	C₂²×D₅	—	2	1	no	—
198	C₂²×D₅	—	2	1	no	—
199	C₂²×D₅	—	2	1	no	—
200	C₂²×D₅	C₂×C₃⋊C₈	1	2	yes	—
201	C₂²×D₅	#208	1	2	yes	—
202	C₂²×D₅	C₄⋊Dic₃	1	2	yes	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
208	C₂×C₄×C₅	#208	1	2	yes	—
209	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
211	C₂×C₄×C₅	#235	1	2	yes	—
212	C₂×C₄×C₅	C₂×#67	1	2	yes	—
213	C₂×Dic₅	—	2	1	no	—
214	C₂×Dic₅	—	2	1	no	—
215	C₂×Dic₅	—	2	1	no	—
216	C₂×Dic₅	—	2	1	no	—
217	C₂×Dic₅	C₂×C₃⋊C₈	1	2	yes	—
218	C₂×Dic₅	#208	1	2	yes	—
219	C₂×Dic₅	C₄⋊Dic₃	1	2	yes	—
220	C₂×Dic₅	#217	1	2	yes	—
221	C₂×Dic₅	#217	1	2	yes	—
222	C₄×D₅	—	2	8	no	—
223	C₄×D₅	—	2	4	no	—
224	C₄×D₅	—	2	4	no	—
225	C₄×D₅	—	2	8	no	—
226	C₅×C₈	—	12	2	no	—
227	#168	—	12	2	no	—
228	C₂³×C₄	—	5	1	no	—
229	C₂³×C₄	—	5	1	no	—
230	C₂³×C₄	—	5	1	no	—
231	C₂²×C₈	—	3	2	no	—
232	C₂²×C₈	—	15	2	no	—
233	C₂×C₄²	—	5	1	no	—
234	C₂×C₄²	—	5	1	no	—
235	C₂×C₄²	—	5	1	no	—
236	C₂×C₄²	—	10	4	no	—
237	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
238	C₄⋊C₈	—	30	4	no	—
239	C₂²⋊C₈	—	30	4	no	—
240	C₂×C₃×C₅	#380	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
242	C₂×C₃×C₅	#407	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
244	C₂×C₃×C₅	#423	1	1	yes	characteristic
245	C₂×C₃×C₅	#431	1	1	yes	characteristic
246	C₂×C₃×C₅	#432	1	1	yes	characteristic
247	C₃×D₅	—	2	4	no	—
248	C₂³×C₃	—	5	2	no	—
249	C₂³×C₃	—	5	2	no	—
250	C₂³×C₃	—	5	2	no	—
251	C₂³×C₃	—	10	1	no	—
252	C₂³×C₃	—	10	1	no	—
253	C₂³×C₃	—	10	1	no	—
254	C₂³×C₃	—	10	1	no	—
255	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	5	2	no	—
261	C₂×C₃×C₄	—	5	2	no	—
262	C₂×C₃×C₄	—	5	2	no	—
263	C₂×C₃×C₄	—	5	2	no	—
264	C₂×C₃×C₄	—	5	2	no	—
265	C₂×C₃×C₄	—	10	8	no	—
266	C₂×C₃×C₄	—	10	8	no	—
267	C₂×C₃×C₄	—	10	1	no	—
268	C₂×C₃×C₄	—	10	1	no	—
269	C₂×C₃×C₄	—	10	1	no	—
270	C₂×C₃×C₄	—	10	1	no	—
271	C₂×C₃×C₄	—	10	4	no	—
272	C₂×C₃×C₄	—	10	4	no	—
273	C₂×C₃×C₄	C₈×D₅	1	2	yes	—
274	C₂×C₃×C₄	#676	1	2	yes	—
275	C₂×C₃×C₄	#709	1	2	yes	—
276	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
277	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
278	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
279	C₃⋊C₈	—	4	2	no	—
280	C₃⋊C₈	—	20	2	no	—
281	C₂²×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
282	C₂²×C₅	C₂×#208	1	1	yes	characteristic
283	C₂²×C₅	C₂×#208	1	1	yes	characteristic
284	C₂²×C₅	C₂×#208	1	1	yes	characteristic
285	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
286	C₂²×C₅	#926	1	1	yes	characteristic
287	C₂²×C₅	C₂×#217	1	1	yes	characteristic
288	C₂×D₅	—	2	2	no	—
289	C₂×D₅	—	2	2	no	—
290	C₂×D₅	—	2	2	no	—
291	C₂×D₅	—	2	2	no	—
292	C₂×D₅	—	2	2	no	—
293	C₂×D₅	—	2	2	no	—
294	C₂×D₅	C₄⋊(C₃⋊C₈)	1	4	yes	complemented
295	C₄×C₅	—	2	2	no	—
296	C₄×C₅	—	2	2	no	—
297	C₄×C₅	#924	1	2	yes	—
298	C₄×C₅	#930	1	2	yes	—
299	Dic₅	—	2	2	no	—
300	Dic₅	—	2	2	no	—
301	Dic₅	#830	1	4	yes	complemented
302	C₂⁴	—	5	1	no	—
303	C₂²×C₄	—	5	1	no	—
304	C₂²×C₄	—	5	1	no	—
305	C₂²×C₄	—	5	1	no	—
306	C₂²×C₄	—	5	2	no	—
307	C₂²×C₄	—	5	2	no	—
308	C₂²×C₄	—	5	4	no	—
309	C₂²×C₄	—	10	2	no	—
310	C₂²×C₄	—	10	2	no	—
311	C₂²×C₄	—	10	2	no	—
312	C₂²×C₄	—	10	2	no	—
313	C₂²×C₄	—	10	2	no	—
314	C₂²×C₄	—	10	2	no	—
315	C₂²×C₄	—	10	2	no	—
316	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
317	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
319	C₂×C₈	—	6	2	no	—
320	C₂×C₈	—	6	2	no	—
321	C₂×C₈	—	6	2	no	—
322	C₂×C₈	—	30	2	no	—
323	C₂×C₈	—	30	2	no	—
324	C₂×C₈	—	30	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	5	4	no	—
327	C₄²	—	10	2	no	—
328	C₄²	—	10	2	no	—
329	C₃×C₅	#1797	1	1	yes	characteristic, complemented, Hall
330	C₂²×C₃	—	5	4	no	—
331	C₂²×C₃	—	10	2	no	—
332	C₂²×C₃	—	10	2	no	—
333	C₂²×C₃	—	10	2	no	—
334	C₂²×C₃	—	10	2	no	—
335	C₂²×C₃	—	10	2	no	—
336	C₂²×C₃	—	10	2	no	—
337	C₂²×C₃	#4018	1	1	yes	characteristic
338	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
339	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
340	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
341	C₂²×C₃	C₂×#676	1	1	yes	characteristic
342	C₂²×C₃	D₅×M₁₆	1	1	yes	characteristic
343	C₂²×C₃	D₅×M₁₆	1	1	yes	characteristic
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	—	5	4	no	—
347	C₃×C₄	—	10	2	no	—
348	C₃×C₄	—	10	2	no	—
349	C₃×C₄	#4030	1	2	yes	—
350	C₃×C₄	#4042	1	2	yes	—
351	C₂×C₅	C₂×C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
352	C₂×C₅	#4924	1	1	yes	characteristic
353	C₂×C₅	#4925	1	1	yes	characteristic
354	C₂×C₅	#4926	1	1	yes	characteristic
355	C₂×C₅	C₂×#830	1	1	yes	characteristic
356	C₂×C₅	#5207	1	1	yes	characteristic
357	C₂×C₅	#5212	1	1	yes	characteristic
358	D₅	—	2	4	no	—
359	C₂³	—	5	2	no	—
360	C₂³	—	5	2	no	—
361	C₂³	—	5	2	no	—
362	C₂³	—	10	1	no	—
363	C₂³	—	10	1	no	—
364	C₂³	—	10	1	no	—
365	C₂³	—	10	1	no	—
366	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	5	2	no	—
372	C₂×C₄	—	5	2	no	—
373	C₂×C₄	—	5	2	no	—
374	C₂×C₄	—	5	2	no	—
375	C₂×C₄	—	5	2	no	—
376	C₂×C₄	—	10	8	no	—
377	C₂×C₄	—	10	8	no	—
378	C₂×C₄	—	10	1	no	—
379	C₂×C₄	—	10	1	no	—
380	C₂×C₄	—	10	1	no	—
381	C₂×C₄	—	10	1	no	—
382	C₂×C₄	—	10	4	no	—
383	C₂×C₄	—	10	4	no	—
384	C₂×C₄	D₅×C₃⋊C₈	1	2	yes	—
385	C₂×C₄	#6649	1	2	yes	—
386	C₂×C₄	D₅×Dic₆	1	1	yes	characteristic
387	C₂×C₄	#6771	1	2	yes	—
388	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
389	C₂×C₄	D₅×#67	1	2	yes	—
390	C₈	—	12	2	no	—
391	C₈	—	60	2	no	—
392	C₂×C₃	—	10	4	no	—
393	C₂×C₃	#64956	1	1	yes	characteristic
394	C₂×C₃	#64974	1	1	yes	characteristic
395	C₂×C₃	#64994	1	1	yes	characteristic
396	C₂×C₃	D₅×C₂²⋊C₈	1	1	yes	characteristic
397	C₂×C₃	#65015	1	1	yes	characteristic
398	C₂×C₃	D₅×C₄⋊C₈	1	1	yes	characteristic
399	C₂×C₃	#65126	1	1	yes	characteristic
400	C₅	#71530	1	1	yes	characteristic, complemented, Sylow
401	C₂²	—	5	4	no	—
402	C₂²	—	10	2	no	—
403	C₂²	—	10	2	no	—
404	C₂²	—	10	2	no	—
405	C₂²	—	10	2	no	—
406	C₂²	—	10	2	no	—
407	C₂²	—	10	2	no	—
408	C₂²	C₂×D₅×C₃⋊C₈	1	1	yes	characteristic
409	C₂²	D₅×#208	1	1	yes	characteristic
410	C₂²	D₅×#208	1	1	yes	characteristic
411	C₂²	C₂×#6649	1	1	yes	characteristic
412	C₂²	#91357	1	1	yes	characteristic
413	C₂²	D₅×C₄⋊Dic₃	1	1	yes	characteristic
414	C₂²	D₅×#217	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	5	4	no	—
418	C₄	—	10	2	no	—
419	C₄	—	10	2	no	—
420	C₄	#91349	1	2	yes	—
421	C₄	#91448	1	2	yes	—
422	C₃	#10599455	1	1	yes	characteristic, complemented, Sylow
423	C₂	—	10	4	no	—
424	C₂	#11746868	1	1	yes	characteristic
425	C₂	#11746870	1	1	yes	characteristic
426	C₂	D₅×C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
427	C₂	#11747007	1	1	yes	characteristic
428	C₂	D₅×#830	1	1	yes	characteristic
429	C₂	#11748499	1	1	yes	characteristic
430	C₂	#11748738	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂²×C₈
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#1797
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×#90982	C₂	semidirect
4. #11746345	C₂	semidirect
5. C₅×#4524	C₂	semidirect
39. C₂×C₃×C₄×D₅	C₈	semidirect
56. #4524	D₅	semidirect
129. C₂×C₄×D₅	C₃⋊C₈	semidirect
160. C₂×C₃×D₅	C₄⋊C₈	semidirect
167. C₃×Dic₅	C₂²⋊C₈	semidirect
294. C₂×D₅	C₄⋊(C₃⋊C₈)	semidirect
301. Dic₅	#830	semidirect
329. C₃×C₅	#1797	semidirect
400. C₅	#71530	semidirect
422. C₃	#10599455	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×D₅	2
C₂×#90982	2
C₂×#90955	2
#11746345	2
C₅×#4524	2
#10599455	3
#71530	5