Subgroups — #14300229

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91837	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic
3	C₂×#91121	C₂	1	1	yes	maximal, characteristic
4	C₂×#91103	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751100	C₂	1	1	yes	maximal, characteristic, complemented
6	#11746371	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746353	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601085	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×#117	C₂²	1	1	yes	characteristic
12	#91837	—	2	2	no	—
13	#91837	—	2	2	no	—
14	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
15	C₂×#6710	—	2	1	no	—
16	C₂×#6710	C₂²	1	1	yes	characteristic
17	C₂×#6710	C₂²	1	1	yes	characteristic
18	C₂²×C₃⋊#168	—	2	1	no	—
19	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
20	C₃×C₅×#103	C₄	1	1	yes	characteristic, complemented
21	C₃×C₅×#103	C₄	1	1	yes	characteristic, complemented
22	C₃×C₅×#102	C₄	1	1	yes	characteristic, complemented
23	C₃×C₅×#102	C₄	1	1	yes	characteristic, complemented
24	#91121	—	2	2	no	—
25	#91103	—	2	2	no	—
26	C₄⋊(C₃⋊#168)	—	2	1	no	—
27	C₄⋊(C₃⋊#168)	—	2	1	no	—
28	#70292	—	5	1	no	maximal, Hall
29	C₂×#4094	—	3	1	no	—
30	C₅×#416	D₃	1	1	yes	characteristic
31	C₂×#3969	—	3	1	no	—
32	C₂×#3951	—	3	1	no	—
33	#65288	—	3	1	no	—
34	#64770	—	3	1	no	—
35	#64752	—	3	1	no	—
36	C₃×C₅×#41	—	2	1	no	—
37	C₃×C₅×#41	—	2	1	no	—
38	C₃×C₅×#41	D₄	1	2	yes	—
39	C₃×C₅×#41	Q₈	1	2	yes	—
40	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	—	2	1	no	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×Dic₁₅	—	2	1	no	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₄×Dic₁₅	—	2	1	no	—
55	C₄×Dic₁₅	—	2	1	no	—
56	#6710	—	2	4	no	—
57	#6710	—	2	1	no	—
58	#6710	—	2	1	no	—
59	#6710	—	2	1	no	—
60	#6710	D₄	1	2	yes	—
61	C₂×C₃⋊#168	—	2	4	no	—
62	C₂×C₃⋊#168	—	2	1	no	—
63	C₂×C₃⋊#168	—	2	1	no	—
64	C₂×C₃⋊#168	—	2	1	no	—
65	C₂×C₃⋊#168	—	2	1	no	—
66	C₂×C₃⋊#168	D₄	1	1	yes	characteristic
67	C₂×C₃⋊#168	D₄	1	1	yes	characteristic
68	C₂×#948	—	5	1	no	—
69	C₃×#416	D₅	1	1	yes	characteristic
70	C₂×#837	—	5	1	no	—
71	C₂×#819	—	5	1	no	—
72	#4999	—	5	1	no	—
73	#4550	—	5	1	no	—
74	#4532	—	5	1	no	—
75	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
77	C₅×#117	C₂×D₃	1	1	yes	characteristic
78	#4094	—	6	2	no	—
79	#4094	—	6	2	no	—
80	C₂×C₄×Dic₅	—	3	1	no	—
81	C₂×#681	—	3	1	no	—
82	C₂×#681	—	3	1	no	—
83	C₂×#681	—	6	1	no	—
84	C₂²×#168	—	3	1	no	—
85	C₂²×#168	—	6	1	no	—
86	C₅×#103	Dic₃	1	1	yes	characteristic, complemented
87	C₅×#103	Dic₃	1	1	yes	characteristic, complemented
88	C₅×#102	Dic₃	1	1	yes	characteristic, complemented
89	C₅×#102	Dic₃	1	1	yes	characteristic, complemented
90	#3969	—	6	2	no	—
91	#3951	—	6	2	no	—
92	C₄⋊#168	—	6	1	no	—
93	C₄⋊#168	—	6	1	no	—
94	#1866	—	15	1	no	Sylow
95	C₂³×C₃×C₅	—	2	1	no	—
96	C₂³×C₃×C₅	#41	1	1	yes	characteristic
97	C₃×C₅×Q₈	—	2	1	no	—
98	C₃×C₅×Q₈	C₄⋊C₄	1	2	yes	—
99	C₃×C₅×D₄	—	2	2	no	—
100	C₃×C₅×D₄	—	2	2	no	—
101	C₃×C₅×D₄	—	2	1	no	—
102	C₃×C₅×D₄	C₄⋊C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	1	no	—
107	C₂×C₃×C₄×C₅	—	2	1	no	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
114	C₂×Dic₁₅	—	2	2	no	—
115	C₂×Dic₁₅	—	4	1	no	—
116	C₂×Dic₁₅	—	4	1	no	—
117	C₃×C₅×C₈	—	2	1	no	—
118	C₃×C₅×C₈	—	2	1	no	—
119	C₃⋊#168	—	2	1	no	—
120	C₃⋊#168	—	2	2	no	—
121	C₃⋊#168	—	2	1	no	—
122	C₃⋊#168	—	4	1	no	—
123	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
124	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
125	C₃×#117	C₂×D₅	1	1	yes	characteristic
126	#948	—	10	2	no	—
127	#948	—	10	2	no	—
128	C₂×C₄×Dic₃	—	5	1	no	—
129	C₂×#208	—	5	1	no	—
130	C₂×#208	—	5	1	no	—
131	C₂×#208	—	10	1	no	—
132	C₂²×C₃⋊C₈	—	5	1	no	—
133	C₂²×C₃⋊C₈	—	10	1	no	—
134	C₃×#103	Dic₅	1	1	yes	characteristic, complemented
135	C₃×#103	Dic₅	1	1	yes	characteristic, complemented
136	C₃×#102	Dic₅	1	1	yes	characteristic, complemented
137	C₃×#102	Dic₅	1	1	yes	characteristic, complemented
138	#837	—	10	2	no	—
139	#819	—	10	2	no	—
140	C₄⋊(C₃⋊C₈)	—	10	1	no	—
141	C₄⋊(C₃⋊C₈)	—	10	1	no	—
142	C₅×#41	—	2	1	no	—
143	C₅×#41	—	2	1	no	—
144	C₅×#41	Dic₆	1	2	yes	—
145	C₅×#41	D₁₂	1	2	yes	—
146	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
151	C₂²×Dic₅	—	6	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
158	C₅×C₂²⋊C₄	—	2	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄×Dic₅	—	6	1	no	—
161	C₄×Dic₅	—	6	1	no	—
162	#681	—	3	2	no	—
163	#681	—	6	4	no	—
164	#681	—	6	1	no	—
165	#681	—	6	1	no	—
166	#681	—	6	1	no	—
167	C₂×#168	—	3	1	no	—
168	C₂×#168	—	3	1	no	—
169	C₂×#168	—	6	4	no	—
170	C₂×#168	—	6	1	no	—
171	C₂×#168	—	6	1	no	—
172	C₂×#168	—	6	1	no	—
173	C₂×#168	—	6	1	no	—
174	C₂×#131	—	15	1	no	—
175	C₂×#108	—	15	1	no	—
176	#424	—	15	1	no	—
177	C₂×#104	—	15	1	no	—
178	#416	D₁₅	1	1	yes	characteristic
179	#339	—	15	1	no	—
180	#336	—	15	1	no	—
181	C₂²×C₃×C₅	—	2	1	no	—
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	—	2	2	no	—
184	C₂²×C₃×C₅	—	4	1	no	—
185	C₂²×C₃×C₅	—	4	1	no	—
186	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
187	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂²×C₃×C₅	#123	1	1	yes	characteristic
189	C₃×C₄×C₅	—	2	2	no	—
190	C₃×C₄×C₅	—	4	1	no	—
191	C₃×C₄×C₅	—	4	1	no	—
192	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
194	C₃×C₄×C₅	#120	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
196	Dic₁₅	—	4	2	no	—
197	C₃×#41	—	2	1	no	—
198	C₃×#41	—	2	1	no	—
199	C₃×#41	Dic₁₀	1	2	yes	—
200	C₃×#41	D₂₀	1	2	yes	—
201	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
206	C₂²×Dic₃	—	10	1	no	—
207	C₂×C₃×C₈	—	2	1	no	—
208	C₂×C₃×C₈	—	2	1	no	—
209	C₂×C₃×C₈	C₂×Dic₅	1	1	yes	characteristic
210	C₂×C₃×C₈	C₂×Dic₅	1	1	yes	characteristic
211	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
212	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
213	C₃×C₂²⋊C₄	—	2	1	no	—
214	C₃×C₄²	—	2	1	no	—
215	C₄×Dic₃	—	10	1	no	—
216	C₄×Dic₃	—	10	1	no	—
217	#208	—	5	2	no	—
218	#208	—	10	4	no	—
219	#208	—	10	1	no	—
220	#208	—	10	1	no	—
221	#208	—	10	1	no	—
222	C₂×C₃⋊C₈	—	5	1	no	—
223	C₂×C₃⋊C₈	—	5	1	no	—
224	C₂×C₃⋊C₈	—	10	4	no	—
225	C₂×C₃⋊C₈	—	10	1	no	—
226	C₂×C₃⋊C₈	—	10	1	no	—
227	C₂×C₃⋊C₈	—	10	1	no	—
228	C₂×C₃⋊C₈	—	10	1	no	—
229	C₂³×C₅	—	2	1	no	—
230	C₂³×C₅	#237	1	1	yes	characteristic
231	C₅×Q₈	—	2	1	no	—
232	C₅×Q₈	C₄⋊Dic₃	1	2	yes	—
233	C₅×D₄	—	2	2	no	—
234	C₅×D₄	—	2	2	no	—
235	C₅×D₄	—	2	1	no	—
236	C₅×D₄	C₄⋊Dic₃	1	2	yes	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
244	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	#237	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
248	C₂×Dic₅	—	6	2	no	—
249	C₂×Dic₅	—	12	1	no	—
250	C₂×Dic₅	—	12	1	no	—
251	C₅×C₈	—	2	1	no	—
252	C₅×C₈	—	2	1	no	—
253	#168	—	6	1	no	—
254	#168	—	6	1	no	—
255	#168	—	6	2	no	—
256	#168	—	12	1	no	—
257	C₂×#41	C₂×D₁₅	1	1	yes	characteristic
258	#131	—	30	2	no	—
259	#131	—	30	2	no	—
260	C₂×M₁₆	—	15	1	no	—
261	C₂×M₁₆	—	15	1	no	—
262	C₂×M₁₆	—	30	1	no	—
263	C₂²×C₈	—	15	1	no	—
264	C₂²×C₈	—	30	1	no	—
265	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
266	#117	C₂×D₁₅	1	1	yes	characteristic
267	C₂×C₄²	—	15	1	no	—
268	#108	—	30	2	no	—
269	C₄⋊C₈	—	30	1	no	—
270	C₄⋊C₈	—	30	1	no	—
271	#104	—	30	2	no	—
272	#103	Dic₁₅	1	1	yes	characteristic, complemented
273	#103	Dic₁₅	1	1	yes	characteristic, complemented
274	#102	Dic₁₅	1	1	yes	characteristic, complemented
275	#102	Dic₁₅	1	1	yes	characteristic, complemented
276	C₂×C₃×C₅	—	2	1	no	—
277	C₂×C₃×C₅	—	2	1	no	—
278	C₂×C₃×C₅	—	4	2	no	—
279	C₂×C₃×C₅	#385	1	1	yes	characteristic
280	C₂×C₃×C₅	#443	1	1	yes	characteristic
281	C₂×C₃×C₅	#444	1	1	yes	characteristic
282	C₂³×C₃	—	2	1	no	—
283	C₂³×C₃	#711	1	1	yes	characteristic
284	C₃×Q₈	—	2	1	no	—
285	C₃×Q₈	C₄⋊Dic₅	1	2	yes	—
286	C₃×D₄	—	2	2	no	—
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	—	2	1	no	—
289	C₃×D₄	C₄⋊Dic₅	1	2	yes	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
297	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
298	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
299	C₂×C₃×C₄	#711	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
301	C₂×Dic₃	—	10	2	no	—
302	C₂×Dic₃	—	20	1	no	—
303	C₂×Dic₃	—	20	1	no	—
304	C₃×C₈	—	2	1	no	—
305	C₃×C₈	—	2	1	no	—
306	C₃⋊C₈	—	10	1	no	—
307	C₃⋊C₈	—	10	1	no	—
308	C₃⋊C₈	—	10	2	no	—
309	C₃⋊C₈	—	20	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	2	2	no	—
313	C₂²×C₅	—	4	1	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	#878	1	1	yes	characteristic
316	C₂²×C₅	#886	1	1	yes	characteristic
317	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	4	1	no	—
320	C₄×C₅	—	4	1	no	—
321	C₄×C₅	#878	1	1	yes	characteristic
322	C₄×C₅	#882	1	1	yes	characteristic
323	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
324	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
325	Dic₅	—	12	2	no	—
326	#41	—	2	1	no	—
327	#41	—	2	1	no	—
328	#41	Dic₃₀	1	2	yes	—
329	#41	D₆₀	1	2	yes	—
330	C₂×Q₈	C₂×Dic₁₅	1	1	yes	characteristic
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂×Dic₁₅	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	30	1	no	—
335	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
336	M₁₆	—	15	2	no	—
337	M₁₆	—	30	4	no	—
338	M₁₆	—	30	1	no	—
339	M₁₆	—	30	1	no	—
340	M₁₆	—	30	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	15	1	no	—
344	C₂×C₈	—	15	1	no	—
345	C₂×C₈	—	30	4	no	—
346	C₂×C₈	—	30	1	no	—
347	C₂×C₈	—	30	1	no	—
348	C₂×C₈	—	30	1	no	—
349	C₂×C₈	—	30	1	no	—
350	C₂×C₈	C₂×Dic₁₅	1	1	yes	characteristic
351	C₂×C₈	C₂×Dic₁₅	1	1	yes	characteristic
352	C₄⋊C₄	C₂×Dic₁₅	1	1	yes	characteristic
353	C₄⋊C₄	C₂×Dic₁₅	1	1	yes	characteristic
354	C₂²⋊C₄	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	30	1	no	—
357	C₄²	—	30	1	no	—
358	C₃×C₅	#1866	1	1	yes	characteristic, complemented, Hall
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	—	2	2	no	—
362	C₂²×C₃	—	4	1	no	—
363	C₂²×C₃	—	4	1	no	—
364	C₂²×C₃	#4024	1	1	yes	characteristic
365	C₂²×C₃	#4032	1	1	yes	characteristic
366	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	4	1	no	—
369	C₃×C₄	—	4	1	no	—
370	C₃×C₄	#4024	1	1	yes	characteristic
371	C₃×C₄	#4028	1	1	yes	characteristic
372	C₃×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
373	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
374	Dic₃	—	20	2	no	—
375	C₂×C₅	—	2	1	no	—
376	C₂×C₅	—	2	1	no	—
377	C₂×C₅	—	4	2	no	—
378	C₂×C₅	#4950	1	1	yes	characteristic
379	C₂×C₅	#5196	1	1	yes	characteristic
380	C₂×C₅	#5197	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	#6819	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	C₄⋊Dic₁₅	1	2	yes	—
385	D₄	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	1	no	—
388	D₄	C₄⋊Dic₁₅	1	2	yes	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	30	2	no	—
395	C₂×C₄	—	60	1	no	—
396	C₂×C₄	—	60	1	no	—
397	C₂×C₄	C₂×Dic₃₀	1	1	yes	characteristic
398	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
399	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
400	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
401	C₂×C₄	#6819	1	1	yes	characteristic
402	C₂×C₄	C₂²×Dic₁₅	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	30	1	no	—
406	C₈	—	30	1	no	—
407	C₈	—	30	2	no	—
408	C₈	—	60	1	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	—	4	2	no	—
412	C₂×C₃	#65239	1	1	yes	characteristic
413	C₂×C₃	#65485	1	1	yes	characteristic
414	C₂×C₃	#65486	1	1	yes	characteristic
415	C₅	#70292	1	1	yes	characteristic, complemented, Sylow
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	#91767	1	1	yes	characteristic
422	C₂²	#91775	1	1	yes	characteristic
423	C₂²	D₄×Dic₁₅	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	60	2	no	—
428	C₄	#91767	1	1	yes	characteristic
429	C₄	#91771	1	1	yes	characteristic
430	C₄	C₂×C₄⋊Dic₁₅	1	1	yes	characteristic
431	C₄	D₄×Dic₁₅	1	1	yes	characteristic
432	C₃	#10601085	1	1	yes	characteristic, complemented, Sylow
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	4	2	no	—
436	C₂	#11751051	1	1	yes	characteristic
437	C₂	#11751297	1	1	yes	characteristic
438	C₂	#11751298	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₃×C₅×#416	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	#416	D₁₅
hypocenter	C₃×C₅	#1866
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #416

Complements

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

N	H ≅ G/N	type
4. C₂×#91103	C₂	semidirect
5. #11751100	C₂	semidirect
6. #11746371	C₂	semidirect
7. #11746353	C₂	semidirect
20. C₃×C₅×#103	C₄	semidirect
21. C₃×C₅×#103	C₄	semidirect
22. C₃×C₅×#102	C₄	semidirect
23. C₃×C₅×#102	C₄	semidirect
86. C₅×#103	Dic₃	semidirect
87. C₅×#103	Dic₃	semidirect
88. C₅×#102	Dic₃	semidirect
89. C₅×#102	Dic₃	semidirect
134. C₃×#103	Dic₅	semidirect
135. C₃×#103	Dic₅	semidirect
136. C₃×#102	Dic₅	semidirect
137. C₃×#102	Dic₅	semidirect
272. #103	Dic₁₅	semidirect
273. #103	Dic₁₅	semidirect
274. #102	Dic₁₅	semidirect
275. #102	Dic₁₅	semidirect
358. C₃×C₅	#1866	semidirect
415. C₅	#70292	semidirect
432. C₃	#10601085	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91837	2
C₃×C₅×#416	2
C₂×#91121	2
C₂×#91103	2
#11751100	2
#11746371	2
#11746353	2
#10601085	3
#70292	5