Subgroups — #14419664

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65813	C₂	1	1	yes	maximal, characteristic
2	#11751026	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
4	#11748503	C₂	1	2	yes	maximal, complemented
5	C₃⋊C₈×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
6	#11746991	C₂	1	2	yes	maximal, complemented
7	#11746975	C₂	1	2	yes	maximal, complemented
8	#11746874	C₂	1	2	yes	maximal, complemented
9	#11746847	C₂	1	2	yes	maximal, complemented
10	#10610212	—	3	1	no	maximal, Hall
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
13	C₃×#4076	C₄	1	1	yes	characteristic
14	C₃×#4075	C₄	1	2	yes	—
15	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
16	C₃×#4070	C₄	1	1	yes	characteristic
17	C₃×#4022	C₄	1	2	yes	—
18	C₃×#4021	C₄	1	1	yes	characteristic
19	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
20	C₃×#4018	C₂²	1	2	yes	—
21	C₃×#4016	C₄	1	1	yes	characteristic
22	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
23	C₂×#6649	C₂²	1	2	yes	—
24	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
25	#91114	C₂²	1	1	yes	characteristic
26	#91114	C₂²	1	1	yes	characteristic
27	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
28	C₄×C₃⋊#168	C₂²	1	2	yes	—
29	C₅×#803	C₂²	1	2	yes	—
30	C₅×#803	C₂²	1	1	yes	characteristic
31	C₅×#803	C₂²	1	1	yes	characteristic
32	#90982	C₂²	1	2	yes	—
33	#90982	C₂²	1	2	yes	—
34	#90955	C₂²	1	2	yes	—
35	#90955	C₂²	1	2	yes	—
36	#90952	C₂²	1	2	yes	—
37	Dic₅×C₃⋊C₈	C₂²	1	2	yes	—
38	#83128	—	5	1	no	maximal, Hall
39	#65813	D₃	1	1	yes	characteristic
40	C₂×C₅×#97	—	3	1	no	—
41	#65400	—	3	2	no	—
42	C₈×C₂²⋊D₅	—	3	2	no	—
43	#65214	—	3	1	no	—
44	#64998	—	3	2	no	—
45	#64997	—	3	2	no	—
46	#64995	—	3	2	no	—
47	#64990	—	3	2	no	—
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
52	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
54	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃⋊#168	C₂³	1	2	yes	—
60	C₂×C₃⋊#168	C₂³	1	2	yes	—
61	C₂×C₅×C₃⋊C₈	—	2	4	no	—
62	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
63	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
64	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
65	C₃×#685	C₂×C₄	1	2	yes	—
66	C₃×#685	C₂×C₄	1	2	yes	—
67	C₃×#685	C₂×C₄	1	2	yes	—
68	C₃×#685	C₂×C₄	1	2	yes	—
69	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
70	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₃×#683	C₂×C₄	1	2	yes	—
72	C₃×#683	C₂×C₄	1	2	yes	—
73	C₃×#683	C₂×C₄	1	2	yes	—
74	C₃×#683	C₂×C₄	1	2	yes	—
75	C₃×C₄×Dic₅	C₂³	1	2	yes	—
76	#6649	—	2	4	no	—
77	D₅×C₃⋊C₈	—	2	4	no	—
78	C₃×#529	—	5	1	no	—
79	#5024	—	5	2	no	—
80	#5011	—	5	2	no	—
81	#5011	—	5	2	no	—
82	D₄×C₃⋊C₈	—	5	2	no	—
83	#5000	—	5	2	no	—
84	#4997	—	5	2	no	—
85	#4925	—	5	1	no	—
86	C₂×#803	D₅	1	1	yes	characteristic, complemented
87	C₂²×C₅×C₈	—	3	2	no	—
88	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
89	#4076	Dic₃	1	1	yes	characteristic
90	#4075	Dic₃	1	2	yes	—
91	C₄×C₂²⋊D₅	C₂×D₃	1	2	yes	—
92	#4070	Dic₃	1	1	yes	characteristic
93	C₂×#676	—	3	2	no	—
94	C₂×C₈×D₅	—	3	2	no	—
95	#4022	Dic₃	1	2	yes	—
96	#4021	Dic₃	1	1	yes	characteristic
97	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
98	#4018	C₂×D₃	1	2	yes	—
99	#4016	Dic₃	1	1	yes	characteristic
100	C₄×Dic₁₀	C₂×D₃	1	1	yes	characteristic
101	C₅×#97	—	3	2	no	—
102	C₅×#97	—	3	1	no	—
103	C₅×#97	—	3	1	no	—
104	C₂²⋊#168	—	3	1	no	—
105	C₂²⋊#168	—	3	1	no	—
106	#3952	—	3	2	no	—
107	#3952	—	3	2	no	—
108	#3947	—	3	2	no	—
109	#3946	—	3	2	no	—
110	#3946	—	3	2	no	—
111	C₈×Dic₅	—	3	2	no	—
112	C₄⋊#168	—	3	2	no	—
113	C₄×#168	—	3	2	no	—
114	#2968	—	15	1	no	Sylow
115	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	4	1	no	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₃×C₂²⋊D₅	—	2	4	no	—
127	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
130	C₃×D₂₀	—	4	1	no	—
131	C₃×C₄×D₅	—	2	2	no	—
132	C₃×C₄×D₅	—	2	2	no	—
133	C₃×Dic₁₀	—	4	1	no	—
134	C₃⋊#168	—	2	2	no	—
135	C₃⋊#168	—	2	2	no	—
136	C₅×C₃⋊C₈	—	2	2	no	—
137	C₅×C₃⋊C₈	#41	1	4	yes	—
138	C₃×#126	—	5	2	no	—
139	C₃×#125	—	5	1	no	—
140	C₃×#124	—	5	1	no	—
141	C₃×#123	—	5	2	no	—
142	C₃×C₂²⋊Q₈	—	5	1	no	—
143	C₃×#121	—	5	1	no	—
144	C₃×C₄×Q₈	—	5	1	no	—
145	C₃×C₄×D₄	—	5	2	no	—
146	C₃×C₄×D₄	—	5	1	no	—
147	C₃×#117	—	5	2	no	—
148	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
149	C₂×#208	—	5	2	no	—
150	C₂²×C₃⋊C₈	—	5	2	no	—
151	C₂²×C₃⋊C₈	C₂×D₅	1	2	yes	—
152	#830	—	5	1	no	—
153	#830	—	5	1	no	—
154	#830	—	5	2	no	—
155	#830	—	5	2	no	—
156	C₄⋊(C₃⋊C₈)	—	5	2	no	—
157	C₄⋊(C₃⋊C₈)	—	5	2	no	—
158	C₄⋊(C₃⋊C₈)	—	5	2	no	—
159	#803	—	5	2	no	—
160	#803	C₂×D₅	1	1	yes	characteristic
161	#803	C₂×D₅	1	1	yes	characteristic
162	#803	C₂×D₅	1	2	yes	—
163	C₄×C₃⋊C₈	—	5	2	no	—
164	C₄×C₃⋊C₈	—	5	2	no	—
165	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
168	C₂×C₂²⋊D₅	C₂×Dic₃	1	2	yes	—
169	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
171	C₂×Dic₁₀	C₂×Dic₃	1	1	yes	characteristic
172	C₂×C₅×C₈	—	3	2	no	—
173	C₂×C₅×C₈	—	3	2	no	—
174	C₂×C₅×C₈	—	6	4	no	—
175	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
176	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
177	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
178	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₂²⋊Dic₅	C₂×Dic₃	1	2	yes	—
180	#685	C₂×Dic₃	1	2	yes	—
181	#685	C₂×Dic₃	1	2	yes	—
182	#685	C₂×Dic₃	1	2	yes	—
183	#685	C₂×Dic₃	1	2	yes	—
184	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
185	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
186	#683	C₂×Dic₃	1	2	yes	—
187	#683	C₂×Dic₃	1	2	yes	—
188	#683	C₂×Dic₃	1	2	yes	—
189	#683	C₂×Dic₃	1	2	yes	—
190	C₄×Dic₅	C₂²×D₃	1	2	yes	—
191	C₂×#168	—	3	2	no	—
192	C₂×#168	—	3	2	no	—
193	#676	—	6	4	no	—
194	C₈×D₅	—	6	4	no	—
195	#529	—	5	1	no	—
196	#446	—	15	2	no	—
197	#435	—	15	2	no	—
198	#435	—	15	2	no	—
199	C₈×D₄	—	15	2	no	—
200	#433	—	15	2	no	—
201	#431	—	15	1	no	—
202	#405	—	15	2	no	—
203	C₂×#97	—	3	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	#131	1	2	yes	—
207	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₃×D₅	—	2	2	no	—
209	C₂×C₃×D₅	—	2	2	no	—
210	C₂×C₃×D₅	—	2	2	no	—
211	C₃×C₄×C₅	—	2	1	no	—
212	C₃×C₄×C₅	—	2	1	no	—
213	C₃×C₄×C₅	—	2	1	no	—
214	C₃×C₄×C₅	—	2	1	no	—
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	C₂×#41	1	2	yes	—
217	C₃×Dic₅	—	2	2	no	—
218	C₃×Dic₅	—	2	2	no	—
219	C₃×Dic₅	—	2	2	no	—
220	C₂×C₃×Q₈	—	5	1	no	—
221	C₂×C₃×D₄	—	5	2	no	—
222	C₂×C₃×D₄	—	5	1	no	—
223	C₂²×C₃×C₄	—	5	2	no	—
224	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
227	C₃×C₄⋊C₄	—	5	2	no	—
228	C₃×C₄⋊C₄	—	5	2	no	—
229	C₃×C₄⋊C₄	—	5	2	no	—
230	C₃×C₄⋊C₄	—	5	2	no	—
231	C₃×C₄⋊C₄	—	5	1	no	—
232	C₃×C₄⋊C₄	—	5	1	no	—
233	C₃×C₂²⋊C₄	—	5	2	no	—
234	C₃×C₂²⋊C₄	—	5	2	no	—
235	C₃×C₂²⋊C₄	—	5	2	no	—
236	C₃×C₂²⋊C₄	—	5	2	no	—
237	C₃×C₂²⋊C₄	—	5	2	no	—
238	C₃×C₄²	—	5	2	no	—
239	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
240	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
241	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
242	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
243	#208	—	10	4	no	—
244	C₂×C₃⋊C₈	—	2	4	no	—
245	C₂×C₃⋊C₈	—	5	2	no	—
246	C₂×C₃⋊C₈	—	5	2	no	—
247	C₂×C₃⋊C₈	—	10	4	no	—
248	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
249	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
250	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
251	C₂²×D₅	C₂²×Dic₃	1	2	yes	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
261	C₂²⋊D₅	—	2	4	no	—
262	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
263	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
264	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
265	D₂₀	—	4	1	no	—
266	C₄×D₅	—	2	2	no	—
267	C₄×D₅	—	2	2	no	—
268	Dic₁₀	—	4	1	no	—
269	C₅×C₈	—	3	4	no	—
270	C₅×C₈	—	6	2	no	—
271	#168	—	6	2	no	—
272	#168	—	6	2	no	—
273	C₂×M₁₆	—	15	2	no	—
274	C₂²×C₈	—	3	2	no	—
275	C₂²×C₈	—	15	2	no	—
276	#126	—	5	2	no	—
277	#125	—	5	1	no	—
278	#124	—	5	1	no	—
279	#123	—	5	2	no	—
280	C₂²⋊Q₈	—	5	1	no	—
281	#121	—	5	1	no	—
282	C₄×Q₈	—	5	1	no	—
283	C₄×D₄	—	5	2	no	—
284	C₄×D₄	—	5	1	no	—
285	#117	—	5	2	no	—
286	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
287	C₄⋊C₈	—	15	2	no	—
288	C₄⋊C₈	—	15	2	no	—
289	C₄⋊C₈	—	15	2	no	—
290	C₂²⋊C₈	—	15	2	no	—
291	C₂²⋊C₈	—	15	2	no	—
292	C₂²⋊C₈	—	15	1	no	—
293	C₂²⋊C₈	—	15	1	no	—
294	#97	—	3	1	no	—
295	#97	—	3	1	no	—
296	#97	—	3	2	no	—
297	#97	—	15	2	no	—
298	C₄×C₈	—	15	2	no	—
299	C₄×C₈	—	15	2	no	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
303	C₂×C₃×C₅	#568	1	1	yes	characteristic
304	C₃×D₅	—	4	2	no	—
305	C₂³×C₃	—	5	2	no	—
306	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
307	C₃×Q₈	—	20	1	no	—
308	C₃×D₄	—	10	4	no	—
309	C₃×D₄	—	20	1	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	4	1	no	—
313	C₂×C₃×C₄	—	5	2	no	—
314	C₂×C₃×C₄	—	5	2	no	—
315	C₂×C₃×C₄	—	5	2	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
324	C₃⋊C₈	—	2	2	no	—
325	C₃⋊C₈	—	10	2	no	—
326	C₃⋊C₈	—	10	2	no	—
327	C₃⋊C₈	#709	1	4	yes	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	#948	1	2	yes	—
331	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
332	C₂×D₅	—	2	2	no	—
333	C₂×D₅	—	2	2	no	—
334	C₂×D₅	—	2	2	no	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	1	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	D₃×#41	1	2	yes	—
341	Dic₅	—	2	2	no	—
342	Dic₅	—	2	2	no	—
343	Dic₅	—	2	2	no	—
344	C₂×Q₈	—	5	1	no	—
345	C₂×D₄	—	5	2	no	—
346	C₂×D₄	—	5	1	no	—
347	C₂²×C₄	—	5	2	no	—
348	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
349	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
351	M₁₆	—	30	4	no	—
352	C₂×C₈	—	3	2	no	—
353	C₂×C₈	—	3	2	no	—
354	C₂×C₈	—	6	4	no	—
355	C₂×C₈	—	15	2	no	—
356	C₂×C₈	—	15	2	no	—
357	C₂×C₈	—	30	4	no	—
358	C₄⋊C₄	—	5	2	no	—
359	C₄⋊C₄	—	5	2	no	—
360	C₄⋊C₄	—	5	1	no	—
361	C₄⋊C₄	—	5	2	no	—
362	C₄⋊C₄	—	5	1	no	—
363	C₄⋊C₄	—	5	2	no	—
364	C₂²⋊C₄	—	5	2	no	—
365	C₂²⋊C₄	—	5	2	no	—
366	C₂²⋊C₄	—	5	2	no	—
367	C₂²⋊C₄	—	5	2	no	—
368	C₂²⋊C₄	—	5	2	no	—
369	C₄²	—	5	2	no	—
370	C₄²	D₅×Dic₃	1	1	yes	characteristic
371	C₄²	D₅×Dic₃	1	1	yes	characteristic
372	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
373	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
374	C₃×C₅	#2968	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	—	10	2	no	—
378	C₂²×C₃	—	10	2	no	—
379	C₂²×C₃	—	10	2	no	—
380	C₂²×C₃	#4053	1	2	yes	—
381	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	10	2	no	—
388	C₃×C₄	—	10	2	no	—
389	C₃×C₄	—	10	2	no	—
390	C₃×C₄	C₂×#709	1	2	yes	—
391	C₂×C₅	—	2	2	no	—
392	C₂×C₅	C₂×#948	1	1	yes	characteristic
393	C₂×C₅	#5819	1	1	yes	characteristic
394	C₂×C₅	Dic₃×#41	1	1	yes	characteristic
395	D₅	—	4	2	no	—
396	C₂³	—	5	2	no	—
397	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
398	Q₈	—	20	1	no	—
399	D₄	—	10	4	no	—
400	D₄	—	20	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	5	2	no	—
405	C₂×C₄	—	5	2	no	—
406	C₂×C₄	—	5	2	no	—
407	C₂×C₄	—	10	2	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
410	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
411	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
412	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
413	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
415	C₈	—	3	4	no	—
416	C₈	—	6	2	no	—
417	C₈	—	30	2	no	—
418	C₈	—	30	2	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	20	2	no	—
421	C₂×C₃	C₄×#709	1	1	yes	characteristic
422	C₂×C₃	C₂×#4053	1	1	yes	characteristic
423	C₂×C₃	#66079	1	1	yes	characteristic
424	C₅	#83128	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	10	2	no	—
428	C₂²	—	10	2	no	—
429	C₂²	—	10	2	no	—
430	C₂²	#91284	1	2	yes	—
431	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	10	2	no	—
438	C₄	—	10	2	no	—
439	C₄	—	10	2	no	—
440	C₄	D₃×#709	1	2	yes	—
441	C₃	#10610212	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	20	2	no	—
444	C₂	C₂×#91284	1	1	yes	characteristic
445	C₂	#11754120	1	1	yes	characteristic
446	C₂	Dic₃×#709	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂×C₃×C₄²×C₅	C₂²
prime radical	C₃×#4076	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	#2968
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #11751026	C₂	semidirect
3. C₂×C₅×#803	C₂	semidirect
4. #11748503	C₂	semidirect
5. C₃⋊C₈×C₂²⋊D₅	C₂	semidirect
6. #11746991	C₂	semidirect
7. #11746975	C₂	semidirect
8. #11746874	C₂	semidirect
9. #11746847	C₂	semidirect
86. C₂×#803	D₅	semidirect
374. C₃×C₅	#2968	semidirect
424. C₅	#83128	semidirect
441. C₃	#10610212	semidirect

Maximal subgroups

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

subgroup	index
C₃×#65813	2
#11751026	2
C₂×C₅×#803	2
#11748503	2
C₃⋊C₈×C₂²⋊D₅	2
#11746991	2
#11746975	2
#11746874	2
#11746847	2
#10610212	3
#83128	5