Subgroups — #14414919

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×#91837	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751335	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751308	C₂	1	1	yes	maximal, characteristic, complemented
6	#11751112	C₂	1	4	yes	maximal, complemented
7	D₄×C₃⋊#168	C₂	1	4	yes	maximal, complemented
8	#11751100	C₂	1	1	yes	maximal, characteristic, complemented
9	#11751098	C₂	1	1	yes	maximal, characteristic, complemented
10	#10614647	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#123	C₄	1	2	yes	—
14	C₃×C₅×C₂²⋊Q₈	C₄	1	2	yes	—
15	C₃×C₅×#121	C₄	1	2	yes	—
16	C₃×C₅×#120	C₄	1	2	yes	—
17	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
18	C₃×C₅×#117	C₂²	1	1	yes	characteristic
19	#91837	—	2	4	no	—
20	C₂×#6710	C₂²	1	1	yes	characteristic
21	C₂×#6710	C₂²	1	1	yes	characteristic
22	C₂×#6710	C₂²	1	2	yes	complemented
23	C₂²×C₃⋊#168	—	2	4	no	—
24	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
25	C₂²×C₃⋊#168	C₂²	1	2	yes	—
26	C₂²×C₃⋊#168	C₂²	1	2	yes	—
27	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
28	C₂²×C₃⋊#168	C₂²	1	2	yes	complemented
29	#91114	C₂²	1	4	yes	—
30	#91114	C₂²	1	4	yes	complemented
31	C₄⋊(C₃⋊#168)	C₂²	1	4	yes	complemented
32	#91087	C₂²	1	2	yes	complemented
33	C₄×C₃⋊#168	C₂²	1	2	yes	complemented
34	#82916	—	5	1	no	maximal, Hall
35	C₅×#525	D₃	1	1	yes	characteristic
36	C₂×#4094	—	3	1	no	—
37	C₂³×#168	—	3	1	no	—
38	#65523	—	3	1	no	—
39	#65496	—	3	1	no	—
40	#65300	—	3	4	no	—
41	D₄×#168	—	3	4	no	—
42	#65288	—	3	1	no	—
43	#65286	—	3	1	no	—
44	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×#41	—	2	2	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
49	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
50	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	—	2	2	no	—
52	C₂²×C₃×C₄×C₅	—	2	2	no	—
53	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
60	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
62	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
63	C₃×C₄²×C₅	C₂³	1	2	yes	—
64	#6710	—	2	2	no	—
65	#6710	—	2	2	no	—
66	#6710	—	2	4	no	—
67	C₂×C₃⋊#168	—	2	2	no	—
68	C₂×C₃⋊#168	—	2	4	no	—
69	C₂×C₃⋊#168	—	2	4	no	—
70	C₂×C₃⋊#168	—	2	4	no	—
71	C₂×C₃⋊#168	D₄	1	4	yes	complemented
72	C₂×C₃⋊#168	C₂³	1	2	yes	—
73	C₂×C₃⋊#168	C₂³	1	2	yes	—
74	C₂×C₃⋊#168	C₂³	1	2	yes	—
75	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
76	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
77	C₃×#525	D₅	1	1	yes	characteristic
78	C₂×#948	—	5	1	no	—
79	C₂³×C₃⋊C₈	—	5	1	no	—
80	#5234	—	5	1	no	—
81	#5207	—	5	1	no	—
82	#5011	—	5	4	no	—
83	D₄×C₃⋊C₈	—	5	4	no	—
84	#4999	—	5	1	no	—
85	#4997	—	5	1	no	—
86	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
87	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
88	C₅×#123	Dic₃	1	2	yes	—
89	C₅×C₂²⋊Q₈	Dic₃	1	2	yes	—
90	C₅×#121	Dic₃	1	2	yes	—
91	C₅×#120	Dic₃	1	2	yes	—
92	C₄×C₅×D₄	C₂×D₃	1	4	yes	—
93	C₅×#117	C₂×D₃	1	1	yes	characteristic
94	#4094	—	6	4	no	—
95	C₂×#681	—	3	1	no	—
96	C₂×#681	—	3	1	no	—
97	C₂×#681	—	3	2	no	—
98	C₂²×#168	—	3	1	no	—
99	C₂²×#168	—	3	1	no	—
100	C₂²×#168	—	3	2	no	—
101	C₂²×#168	—	3	2	no	—
102	C₂²×#168	—	3	2	no	—
103	C₂²×#168	—	6	4	no	—
104	C₂²⋊#168	—	3	4	no	—
105	C₂²⋊#168	—	3	4	no	—
106	C₄⋊#168	—	3	4	no	—
107	#3935	—	3	2	no	—
108	C₄×#168	—	3	2	no	—
109	#2929	—	15	1	no	Sylow
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	4	no	—
112	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
113	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
115	C₃×C₅×Q₈	—	2	2	no	—
116	C₃×C₅×D₄	—	2	4	no	—
117	C₃×C₅×D₄	—	2	8	no	—
118	C₃×C₅×D₄	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	4	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	#41	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₃⋊#168	—	2	2	no	—
133	C₃⋊#168	—	2	2	no	—
134	C₃⋊#168	—	2	2	no	—
135	C₃⋊#168	C₂×D₄	1	2	yes	—
136	C₃⋊#168	C₂×D₄	1	2	yes	—
137	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
138	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
139	C₃×#123	Dic₅	1	2	yes	—
140	C₃×C₂²⋊Q₈	Dic₅	1	2	yes	—
141	C₃×#121	Dic₅	1	2	yes	—
142	C₃×#120	Dic₅	1	2	yes	—
143	C₃×C₄×D₄	C₂×D₅	1	4	yes	—
144	C₃×#117	C₂×D₅	1	1	yes	characteristic
145	#948	—	10	4	no	—
146	C₂×#208	—	5	1	no	—
147	C₂×#208	—	5	1	no	—
148	C₂×#208	—	5	2	no	—
149	C₂²×C₃⋊C₈	—	5	1	no	—
150	C₂²×C₃⋊C₈	—	5	1	no	—
151	C₂²×C₃⋊C₈	—	5	2	no	—
152	C₂²×C₃⋊C₈	—	5	2	no	—
153	C₂²×C₃⋊C₈	—	5	2	no	—
154	C₂²×C₃⋊C₈	—	10	4	no	—
155	#830	—	5	4	no	—
156	#830	—	5	4	no	—
157	C₄⋊(C₃⋊C₈)	—	5	4	no	—
158	#803	—	5	2	no	—
159	C₄×C₃⋊C₈	—	5	2	no	—
160	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
161	C₅×#41	—	2	2	no	—
162	C₅×#41	—	2	2	no	—
163	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
164	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	—
165	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
166	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	—	2	2	no	—
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
170	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
172	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
173	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
175	C₅×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
176	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
177	C₅×C₂²⋊C₄	C₂×Dic₃	1	4	yes	—
178	C₅×C₂²⋊C₄	C₂×Dic₃	1	4	yes	—
179	C₄²×C₅	C₂²×D₃	1	2	yes	—
180	#681	—	6	4	no	—
181	#681	—	6	2	no	—
182	#681	—	6	2	no	—
183	C₂×#168	—	3	4	no	—
184	C₂×#168	—	3	1	no	—
185	C₂×#168	—	3	1	no	—
186	C₂×#168	—	3	2	no	—
187	C₂×#168	—	3	2	no	—
188	C₂×#168	—	3	2	no	—
189	C₂×#168	—	6	4	no	—
190	C₂×#168	—	6	4	no	—
191	C₂×#168	—	6	4	no	—
192	C₂×#168	—	6	2	no	—
193	C₂×#131	—	15	1	no	—
194	C₂³×C₈	—	15	1	no	—
195	#525	D₁₅	1	1	yes	characteristic
196	#435	—	15	4	no	—
197	C₈×D₄	—	15	4	no	—
198	#424	—	15	1	no	—
199	#408	—	15	1	no	—
200	#407	—	15	1	no	—
201	#405	—	15	1	no	—
202	C₂²×C₃×C₅	—	2	8	no	—
203	C₂²×C₃×C₅	—	2	2	no	—
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	2	2	no	—
206	C₂²×C₃×C₅	—	2	2	no	—
207	C₂²×C₃×C₅	—	2	4	no	—
208	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
209	C₂²×C₃×C₅	#131	1	4	yes	complemented
210	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	2	4	no	—
214	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
215	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
217	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
218	C₃×#41	—	2	2	no	—
219	C₃×#41	—	2	2	no	—
220	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
221	C₂×C₃×D₄	C₂×Dic₅	1	4	yes	—
222	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
223	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	—	2	2	no	—
225	C₂²×C₃×C₄	—	2	2	no	—
226	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
227	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
229	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
230	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
231	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
232	C₃×C₄⋊C₄	C₂×Dic₅	1	4	yes	—
233	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
234	C₃×C₂²⋊C₄	C₂×Dic₅	1	4	yes	—
235	C₃×C₂²⋊C₄	C₂×Dic₅	1	4	yes	—
236	C₃×C₄²	C₂²×D₅	1	2	yes	—
237	#208	—	10	4	no	—
238	#208	—	10	2	no	—
239	#208	—	10	2	no	—
240	C₂×C₃⋊C₈	—	5	4	no	—
241	C₂×C₃⋊C₈	—	5	1	no	—
242	C₂×C₃⋊C₈	—	5	1	no	—
243	C₂×C₃⋊C₈	—	5	2	no	—
244	C₂×C₃⋊C₈	—	5	2	no	—
245	C₂×C₃⋊C₈	—	5	2	no	—
246	C₂×C₃⋊C₈	—	10	4	no	—
247	C₂×C₃⋊C₈	—	10	4	no	—
248	C₂×C₃⋊C₈	—	10	4	no	—
249	C₂×C₃⋊C₈	—	10	2	no	—
250	C₂³×C₅	—	2	2	no	—
251	C₂³×C₅	—	2	4	no	—
252	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
253	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
254	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
255	C₅×Q₈	—	2	2	no	—
256	C₅×D₄	—	2	4	no	—
257	C₅×D₄	—	2	8	no	—
258	C₅×D₄	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	4	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
266	C₂×C₄×C₅	#237	1	2	yes	—
267	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
268	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
269	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
270	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
272	#168	—	3	2	no	—
273	#168	—	3	2	no	—
274	#168	—	6	2	no	—
275	#168	—	6	2	no	—
276	#168	—	6	2	no	—
277	C₂×#41	C₂×D₁₅	1	1	yes	characteristic
278	C₂³×C₄	C₂×D₁₅	1	1	yes	characteristic
279	#131	—	30	4	no	—
280	C₂×M₁₆	—	15	1	no	—
281	C₂×M₁₆	—	15	2	no	—
282	C₂×M₁₆	—	15	1	no	—
283	C₂²×C₈	—	15	1	no	—
284	C₂²×C₈	—	15	1	no	—
285	C₂²×C₈	—	15	2	no	—
286	C₂²×C₈	—	15	2	no	—
287	C₂²×C₈	—	15	2	no	—
288	C₂²×C₈	—	30	4	no	—
289	#123	Dic₁₅	1	2	yes	—
290	C₂²⋊Q₈	Dic₁₅	1	2	yes	—
291	#121	Dic₁₅	1	2	yes	—
292	#120	Dic₁₅	1	2	yes	—
293	C₄×D₄	C₂×D₁₅	1	4	yes	—
294	#117	C₂×D₁₅	1	1	yes	characteristic
295	C₄⋊C₈	—	15	4	no	—
296	C₂²⋊C₈	—	15	4	no	—
297	C₂²⋊C₈	—	15	4	no	—
298	#97	—	15	2	no	—
299	C₄×C₈	—	15	2	no	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	—	2	4	no	—
302	C₂×C₃×C₅	—	4	2	no	—
303	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂×C₃×C₅	C₂×#131	1	2	yes	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	2	4	no	—
307	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
308	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
309	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×D₄	—	2	4	no	—
312	C₃×D₄	—	2	8	no	—
313	C₃×D₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
321	C₂×C₃×C₄	#711	1	2	yes	—
322	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
323	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
324	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
325	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
327	C₃⋊C₈	—	5	2	no	—
328	C₃⋊C₈	—	5	2	no	—
329	C₃⋊C₈	—	10	2	no	—
330	C₃⋊C₈	—	10	2	no	—
331	C₃⋊C₈	—	10	2	no	—
332	C₂²×C₅	—	2	8	no	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	2	2	no	—
335	C₂²×C₅	—	2	2	no	—
336	C₂²×C₅	—	2	2	no	—
337	C₂²×C₅	—	2	4	no	—
338	C₂²×C₅	D₄×Dic₃	1	2	yes	—
339	C₂²×C₅	#948	1	4	yes	complemented
340	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	2	4	no	—
344	C₄×C₅	D₄×Dic₃	1	2	yes	—
345	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
346	C₄×C₅	C₂×#237	1	1	yes	characteristic
347	C₂⁴	C₂×Dic₁₅	1	1	yes	characteristic
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	C₂×Q₈	C₂×Dic₁₅	1	1	yes	characteristic
351	C₂×D₄	C₂×Dic₁₅	1	4	yes	—
352	C₂×D₄	C₂×Dic₁₅	1	2	yes	—
353	C₂×D₄	C₂×Dic₁₅	1	1	yes	characteristic
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	C₂×Dic₁₅	1	2	yes	—
357	C₂²×C₄	C₂×Dic₁₅	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
359	C₂²×C₄	C₂²×D₁₅	1	2	yes	—
360	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
361	M₁₆	—	30	4	no	—
362	M₁₆	—	30	2	no	—
363	M₁₆	—	30	2	no	—
364	C₂×C₈	—	15	4	no	—
365	C₂×C₈	—	15	1	no	—
366	C₂×C₈	—	15	1	no	—
367	C₂×C₈	—	15	2	no	—
368	C₂×C₈	—	15	2	no	—
369	C₂×C₈	—	15	2	no	—
370	C₂×C₈	—	30	4	no	—
371	C₂×C₈	—	30	4	no	—
372	C₂×C₈	—	30	4	no	—
373	C₂×C₈	—	30	2	no	—
374	C₄⋊C₄	C₂×Dic₁₅	1	2	yes	—
375	C₄⋊C₄	C₂×Dic₁₅	1	4	yes	—
376	C₂²⋊C₄	C₂×Dic₁₅	1	2	yes	—
377	C₂²⋊C₄	C₂×Dic₁₅	1	4	yes	—
378	C₂²⋊C₄	C₂×Dic₁₅	1	4	yes	—
379	C₄²	C₂²×D₁₅	1	2	yes	—
380	C₃×C₅	#2929	1	1	yes	characteristic, complemented, Hall
381	C₂²×C₃	—	2	8	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	2	no	—
385	C₂²×C₃	—	2	2	no	—
386	C₂²×C₃	—	2	4	no	—
387	C₂²×C₃	D₄×Dic₅	1	2	yes	—
388	C₂²×C₃	#4094	1	4	yes	complemented
389	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
390	C₃×C₄	—	2	2	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	4	no	—
393	C₃×C₄	D₄×Dic₅	1	2	yes	—
394	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
395	C₃×C₄	C₂×#711	1	1	yes	characteristic
396	C₂×C₅	—	2	2	no	—
397	C₂×C₅	—	2	4	no	—
398	C₂×C₅	—	4	2	no	—
399	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
400	C₂×C₅	C₂×#948	1	2	yes	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	4	no	—
403	C₂³	C₂²×Dic₁₅	1	2	yes	—
404	C₂³	C₂²×Dic₁₅	1	1	yes	characteristic
405	C₂³	C₂²×Dic₁₅	1	2	yes	—
406	Q₈	—	2	2	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	8	no	—
409	D₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	D₄×D₁₅	1	2	yes	—
417	C₂×C₄	#6819	1	2	yes	—
418	C₂×C₄	C₂²×Dic₁₅	1	4	yes	—
419	C₂×C₄	C₂²×Dic₁₅	1	2	yes	—
420	C₂×C₄	C₂²×Dic₁₅	1	2	yes	—
421	C₂×C₄	C₂²×Dic₁₅	1	1	yes	characteristic
422	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
423	C₈	—	15	2	no	—
424	C₈	—	15	2	no	—
425	C₈	—	30	2	no	—
426	C₈	—	30	2	no	—
427	C₈	—	30	2	no	—
428	C₂×C₃	—	2	2	no	—
429	C₂×C₃	—	2	4	no	—
430	C₂×C₃	—	4	2	no	—
431	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
432	C₂×C₃	C₂×#4094	1	2	yes	—
433	C₅	#82916	1	1	yes	characteristic, complemented, Sylow
434	C₂²	—	2	8	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	D₄×Dic₁₅	1	2	yes	—
441	C₂²	#91837	1	4	yes	complemented
442	C₂²	C₂³×Dic₁₅	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	4	no	—
446	C₄	D₄×Dic₁₅	1	2	yes	—
447	C₄	C₂×D₄×D₁₅	1	1	yes	characteristic
448	C₄	C₂×#6819	1	1	yes	characteristic
449	C₃	#10614647	1	1	yes	characteristic, complemented, Sylow
450	C₂	—	2	2	no	—
451	C₂	—	2	4	no	—
452	C₂	—	4	2	no	—
453	C₂	C₂×D₄×Dic₁₅	1	1	yes	characteristic
454	C₂	C₂×#91837	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting, prime radical	C₃×C₅×#525	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#525	D₁₅
hypocenter	C₃×C₅	#2929
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
2. C₂×#91837	C₂	semidirect
3. C₂³×C₃⋊#168	C₂	semidirect
4. #11751335	C₂	semidirect
5. #11751308	C₂	semidirect
6. #11751112	C₂	semidirect
7. D₄×C₃⋊#168	C₂	semidirect
8. #11751100	C₂	semidirect
9. #11751098	C₂	semidirect
22. C₂×#6710	C₂²	semidirect
28. C₂²×C₃⋊#168	C₂²	semidirect
30. #91114	C₂²	semidirect
31. C₄⋊(C₃⋊#168)	C₂²	semidirect
32. #91087	C₂²	semidirect
33. C₄×C₃⋊#168	C₂²	semidirect
71. C₂×C₃⋊#168	D₄	semidirect
209. C₂²×C₃×C₅	#131	semidirect
339. C₂²×C₅	#948	semidirect
380. C₃×C₅	#2929	semidirect
388. C₂²×C₃	#4094	semidirect
433. C₅	#82916	semidirect
441. C₂²	#91837	semidirect
449. C₃	#10614647	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#525	2
C₂×#91837	2
C₂³×C₃⋊#168	2
#11751335	2
#11751308	2
#11751112	2
D₄×C₃⋊#168	2
#11751100	2
#11751098	2
#10614647	3
#82916	5