Subgroups — #14294665

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6649	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅×#208	C₂	1	1	yes	maximal, characteristic
4	#11746379	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4558	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745983	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745982	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599731	—	3	1	no	maximal, Hall
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×#6710	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
13	C₂×C₅×#208	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	1	yes	characteristic
16	C₃×D₅×M₁₆	—	2	2	no	—
17	C₃×D₅×M₁₆	C₄	1	4	yes	—
18	C₂×C₃×#676	—	2	1	no	—
19	C₂×C₃×C₈×D₅	—	2	1	no	—
20	C₂×#6649	—	2	1	no	—
21	C₂×#6649	—	2	2	no	—
22	C₂×#6649	—	2	2	no	—
23	C₂×#6649	C₄	1	2	yes	—
24	C₂×#6649	C₄	1	2	yes	—
25	D₅×#208	—	2	2	no	—
26	D₅×#208	C₄	1	4	yes	—
27	C₂×D₅×C₃⋊C₈	—	2	1	no	—
28	#71994	—	5	1	no	maximal, Hall
29	C₂×D₅×M₁₆	—	3	1	no	—
30	C₂×D₅×M₁₆	D₃	1	1	yes	characteristic
31	C₂²×#676	—	3	1	no	—
32	C₅×#341	—	3	1	no	—
33	#64778	—	3	1	no	—
34	#64778	—	3	1	no	—
35	#64772	—	3	1	no	—
36	C₂³×C₃×D₅	Q₈	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₃×Dic₅	Q₈	1	1	yes	characteristic
39	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	#6710	—	2	1	no	—
51	#6710	C₂×C₄	1	2	yes	—
52	C₂×C₃⋊#168	—	2	1	no	—
53	C₂×C₃⋊#168	—	2	1	no	—
54	C₂×C₃⋊#168	—	2	1	no	—
55	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
56	C₅×#208	—	2	1	no	—
57	C₅×#208	C₂×C₄	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
62	C₃×#681	—	2	1	no	—
63	C₃×#681	C₂×C₄	1	2	yes	—
64	C₂×C₃×#168	—	2	1	no	—
65	C₃×#676	—	2	4	no	—
66	C₃×C₈×D₅	—	2	4	no	—
67	#6649	—	2	4	no	—
68	#6649	—	2	4	no	—
69	#6649	—	2	4	no	—
70	D₅×C₃⋊C₈	—	2	4	no	—
71	C₂²×C₃×M₁₆	—	5	1	no	—
72	C₂²×#208	—	5	1	no	—
73	C₂²×#208	—	5	1	no	—
74	#4558	—	5	1	no	—
75	#4558	—	5	1	no	—
76	#4558	—	5	1	no	—
77	#4558	D₅	1	1	yes	characteristic, complemented
78	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	—	3	1	no	—
80	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₅×C₈	—	3	1	no	—
82	C₂×#681	—	3	1	no	—
83	C₂×#681	C₂×D₃	1	1	yes	characteristic
84	C₂²×#168	—	3	1	no	—
85	D₅×M₁₆	—	2	2	no	—
86	D₅×M₁₆	—	3	4	no	—
87	D₅×M₁₆	—	6	2	no	—
88	D₅×M₁₆	Dic₃	1	4	yes	—
89	C₂×#676	—	2	1	no	—
90	C₂×#676	—	3	2	no	—
91	C₂×#676	—	3	2	no	—
92	C₂×#676	—	6	2	no	—
93	C₂×#676	—	6	2	no	—
94	C₂×#676	—	6	1	no	—
95	C₂×C₈×D₅	—	2	1	no	—
96	C₂×C₈×D₅	—	6	1	no	—
97	#1738	—	15	1	no	Sylow
98	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₃×D₅	—	4	2	no	—
100	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
102	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
103	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
111	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
114	C₃×C₄×D₅	C₄²	1	2	yes	—
115	C₃×C₄×D₅	C₄²	1	2	yes	—
116	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
117	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
118	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
119	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
120	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
121	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
122	C₃×C₅×C₈	—	2	2	no	—
123	C₃⋊#168	—	2	2	no	—
124	C₃⋊#168	—	2	2	no	—
125	C₃×#168	—	2	2	no	—
126	C₅×C₃⋊C₈	—	2	2	no	—
127	C₅×C₃⋊C₈	—	2	2	no	—
128	C₂³×C₃×C₄	—	5	1	no	—
129	C₂×C₃×M₁₆	—	5	1	no	—
130	C₂×C₃×M₁₆	—	5	4	no	—
131	C₂×C₃×M₁₆	—	10	1	no	—
132	C₂×C₃×M₁₆	—	10	2	no	—
133	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
134	C₂²×C₃×C₈	—	10	1	no	—
135	C₂×#208	—	5	2	no	—
136	C₂×#208	—	5	2	no	—
137	C₂×#208	—	5	1	no	—
138	C₂×#208	—	5	4	no	—
139	C₂×#208	—	10	1	no	—
140	C₂×#208	—	10	2	no	—
141	C₂×#208	—	10	2	no	—
142	C₂×#208	—	10	2	no	—
143	C₂×#208	C₂×D₅	1	1	yes	characteristic
144	C₂²×C₃⋊C₈	—	5	1	no	—
145	C₂²×C₃⋊C₈	—	10	1	no	—
146	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
147	C₂³×D₅	Dic₆	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₂²×Dic₅	Dic₆	1	1	yes	characteristic
150	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
151	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
152	C₂×C₄×D₅	C₄×D₃	1	2	yes	—
153	C₂×C₄×D₅	D₁₂	1	2	yes	—
154	C₂×C₄×D₅	C₂×Dic₃	1	2	yes	—
155	C₂×C₄×D₅	#67	1	1	yes	characteristic
156	C₂×C₄×D₅	#67	1	1	yes	characteristic
157	C₂×C₄×D₅	#67	1	2	yes	—
158	C₅×M₁₆	—	2	1	no	—
159	C₅×M₁₆	—	3	2	no	—
160	C₅×M₁₆	—	6	1	no	—
161	C₅×M₁₆	C₂×Dic₃	1	2	yes	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	3	2	no	—
164	C₂×C₅×C₈	—	6	1	no	—
165	C₂×C₅×C₈	—	6	1	no	—
166	C₂×C₅×C₈	—	6	1	no	—
167	#681	—	2	1	no	—
168	#681	—	3	2	no	—
169	#681	—	6	1	no	—
170	#681	C₂×Dic₃	1	2	yes	—
171	C₂×#168	—	2	1	no	—
172	C₂×#168	—	3	2	no	—
173	C₂×#168	—	6	1	no	—
174	C₂×#168	—	6	1	no	—
175	C₂×#168	—	6	1	no	—
176	#676	—	2	4	no	—
177	#676	—	6	4	no	—
178	#676	—	6	4	no	—
179	#676	—	6	4	no	—
180	C₈×D₅	—	2	4	no	—
181	C₈×D₅	—	6	4	no	—
182	C₂²×M₁₆	—	5	1	no	—
183	C₂²×M₁₆	—	15	1	no	—
184	C₂²×M₁₆	—	15	1	no	—
185	#341	—	3	1	no	—
186	#341	—	15	1	no	—
187	#341	—	15	1	no	—
188	#341	—	15	1	no	—
189	C₂²×C₃×C₅	—	2	2	no	—
190	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₃×D₅	—	2	2	no	—
194	C₂×C₃×D₅	—	2	2	no	—
195	C₂×C₃×D₅	—	4	2	no	—
196	C₂×C₃×D₅	—	4	2	no	—
197	C₂×C₃×D₅	#95	1	2	yes	—
198	C₂×C₃×D₅	#95	1	2	yes	—
199	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₃×Dic₅	#95	1	2	yes	—
204	C₃×Dic₅	#95	1	2	yes	—
205	C₂⁴×C₃	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	5	2	no	—
208	C₂²×C₃×C₄	—	5	1	no	—
209	C₂²×C₃×C₄	—	5	1	no	—
210	C₂²×C₃×C₄	—	5	2	no	—
211	C₂²×C₃×C₄	—	5	1	no	—
212	C₂²×C₃×C₄	—	5	2	no	—
213	C₂²×C₃×C₄	—	5	1	no	—
214	C₂²×C₃×C₄	—	5	2	no	—
215	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
216	C₃×M₁₆	—	2	1	no	—
217	C₃×M₁₆	—	5	2	no	—
218	C₃×M₁₆	—	10	4	no	—
219	C₃×M₁₆	—	10	1	no	—
220	C₃×M₁₆	C₄×D₅	1	2	yes	—
221	C₂×C₃×C₈	—	2	1	no	—
222	C₂×C₃×C₈	—	10	4	no	—
223	C₂×C₃×C₈	—	10	1	no	—
224	#208	—	2	1	no	—
225	#208	—	5	2	no	—
226	#208	—	10	4	no	—
227	#208	—	10	4	no	—
228	#208	—	10	4	no	—
229	#208	—	10	1	no	—
230	#208	C₄×D₅	1	2	yes	—
231	C₂×C₃⋊C₈	—	2	1	no	—
232	C₂×C₃⋊C₈	—	2	1	no	—
233	C₂×C₃⋊C₈	—	2	1	no	—
234	C₂×C₃⋊C₈	—	5	2	no	—
235	C₂×C₃⋊C₈	—	10	4	no	—
236	C₂×C₃⋊C₈	—	10	1	no	—
237	C₂×C₃⋊C₈	—	10	1	no	—
238	C₂×C₃⋊C₈	—	10	1	no	—
239	C₂×C₃⋊C₈	C₄×D₅	1	2	yes	—
240	C₂³×C₅	C₂×Dic₆	1	1	yes	characteristic
241	C₂²×D₅	—	4	2	no	—
242	C₂²×D₅	Dic₃⋊C₄	1	1	yes	characteristic
243	C₂²×D₅	Dic₃⋊C₄	1	1	yes	characteristic
244	C₂²×D₅	Dic₃⋊C₄	1	2	yes	—
245	C₂²×D₅	C₄⋊Dic₃	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
252	C₂×Dic₅	Dic₃⋊C₄	1	2	yes	—
253	C₂×Dic₅	Dic₃⋊C₄	1	1	yes	characteristic
254	C₂×Dic₅	Dic₃⋊C₄	1	1	yes	characteristic
255	C₂×Dic₅	C₄⋊Dic₃	1	2	yes	—
256	C₄×D₅	C₄×Dic₃	1	2	yes	—
257	C₄×D₅	C₄×Dic₃	1	2	yes	—
258	C₄×D₅	(C₂×D₃)⋊C₄	1	2	yes	—
259	C₄×D₅	(C₂×D₃)⋊C₄	1	2	yes	—
260	C₄×D₅	(C₂×D₃)⋊C₄	1	2	yes	—
261	C₄×D₅	(C₂×D₃)⋊C₄	1	2	yes	—
262	C₄×D₅	#217	1	2	yes	—
263	C₄×D₅	#217	1	2	yes	—
264	C₅×C₈	—	2	2	no	—
265	C₅×C₈	—	6	2	no	—
266	C₅×C₈	—	6	2	no	—
267	#168	—	2	2	no	—
268	#168	—	6	2	no	—
269	#168	—	6	2	no	—
270	C₂³×C₄	—	5	1	no	—
271	C₂×M₁₆	—	3	1	no	—
272	C₂×M₁₆	—	5	1	no	—
273	C₂×M₁₆	—	5	4	no	—
274	C₂×M₁₆	—	10	1	no	—
275	C₂×M₁₆	—	10	2	no	—
276	C₂×M₁₆	—	15	2	no	—
277	C₂×M₁₆	—	15	2	no	—
278	C₂×M₁₆	—	15	4	no	—
279	C₂×M₁₆	—	15	1	no	—
280	C₂×M₁₆	—	30	2	no	—
281	C₂×M₁₆	—	30	2	no	—
282	C₂×M₁₆	—	30	1	no	—
283	C₂×M₁₆	—	30	2	no	—
284	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
285	C₂²×C₈	—	3	1	no	—
286	C₂²×C₈	—	10	1	no	—
287	C₂²×C₈	—	15	1	no	—
288	C₂²×C₈	—	30	1	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	—	2	1	no	—
291	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
292	C₂×C₃×C₅	#430	1	2	yes	—
293	C₃×D₅	—	2	2	no	—
294	C₃×D₅	—	2	2	no	—
295	C₂³×C₃	—	5	1	no	—
296	C₂³×C₃	—	5	1	no	—
297	C₂³×C₃	—	5	2	no	—
298	C₂³×C₃	—	5	2	no	—
299	C₂³×C₃	—	20	2	no	—
300	C₂³×C₃	Q₈×D₅	1	1	yes	characteristic
301	C₂×C₃×C₄	—	5	2	no	—
302	C₂×C₃×C₄	—	5	1	no	—
303	C₂×C₃×C₄	—	5	1	no	—
304	C₂×C₃×C₄	—	5	2	no	—
305	C₂×C₃×C₄	—	5	2	no	—
306	C₂×C₃×C₄	—	5	2	no	—
307	C₂×C₃×C₄	—	5	2	no	—
308	C₂×C₃×C₄	—	5	2	no	—
309	C₂×C₃×C₄	—	5	2	no	—
310	C₂×C₃×C₄	—	5	2	no	—
311	C₂×C₃×C₄	—	5	2	no	—
312	C₂×C₃×C₄	—	5	2	no	—
313	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
316	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
317	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
318	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
319	C₃×C₈	—	2	2	no	—
320	C₃×C₈	—	10	2	no	—
321	C₃⋊C₈	—	2	2	no	—
322	C₃⋊C₈	—	2	2	no	—
323	C₃⋊C₈	—	10	2	no	—
324	C₃⋊C₈	—	10	2	no	—
325	C₂²×C₅	—	2	2	no	—
326	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
327	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
328	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
329	C₂×D₅	—	2	2	no	—
330	C₂×D₅	—	2	2	no	—
331	C₂×D₅	—	4	2	no	—
332	C₂×D₅	—	4	2	no	—
333	C₂×D₅	C₃⋊#95	1	2	yes	—
334	C₂×D₅	C₃⋊#95	1	2	yes	—
335	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
336	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
337	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
338	C₄×C₅	C₂×#217	1	1	yes	characteristic
339	Dic₅	C₃⋊#95	1	2	yes	—
340	Dic₅	C₃⋊#95	1	2	yes	—
341	C₂⁴	—	5	1	no	—
342	C₂²×C₄	—	5	1	no	—
343	C₂²×C₄	—	5	2	no	—
344	C₂²×C₄	—	5	1	no	—
345	C₂²×C₄	—	5	1	no	—
346	C₂²×C₄	—	5	2	no	—
347	C₂²×C₄	—	5	2	no	—
348	C₂²×C₄	—	5	2	no	—
349	C₂²×C₄	—	5	1	no	—
350	C₂²×C₄	—	5	1	no	—
351	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
352	M₁₆	—	2	1	no	—
353	M₁₆	—	3	2	no	—
354	M₁₆	—	5	2	no	—
355	M₁₆	—	6	1	no	—
356	M₁₆	—	10	4	no	—
357	M₁₆	—	10	1	no	—
358	M₁₆	—	15	2	no	—
359	M₁₆	—	30	4	no	—
360	M₁₆	—	30	4	no	—
361	M₁₆	—	30	4	no	—
362	M₁₆	—	30	1	no	—
363	M₁₆	D₅×Dic₃	1	2	yes	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	3	2	no	—
366	C₂×C₈	—	6	1	no	—
367	C₂×C₈	—	6	1	no	—
368	C₂×C₈	—	6	1	no	—
369	C₂×C₈	—	10	4	no	—
370	C₂×C₈	—	10	1	no	—
371	C₂×C₈	—	15	2	no	—
372	C₂×C₈	—	30	4	no	—
373	C₂×C₈	—	30	1	no	—
374	C₂×C₈	—	30	1	no	—
375	C₂×C₈	—	30	1	no	—
376	C₃×C₅	#1738	1	1	yes	characteristic, complemented, Hall
377	C₂²×C₃	—	2	2	no	—
378	C₂²×C₃	—	5	2	no	—
379	C₂²×C₃	—	5	2	no	—
380	C₂²×C₃	—	10	2	no	—
381	C₂²×C₃	—	10	2	no	—
382	C₂²×C₃	—	20	2	no	—
383	C₂²×C₃	—	20	2	no	—
384	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
385	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
386	C₂²×C₃	D₅×C₄⋊C₄	1	1	yes	characteristic
387	C₃×C₄	—	5	2	no	—
388	C₃×C₄	—	5	2	no	—
389	C₃×C₄	C₄²×D₅	1	1	yes	characteristic
390	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
391	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
392	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
393	C₂×C₅	—	2	1	no	—
394	C₂×C₅	—	2	1	no	—
395	C₂×C₅	#5124	1	2	yes	—
396	C₂×C₅	C₂×C₃⋊#95	1	1	yes	characteristic
397	D₅	—	2	2	no	—
398	D₅	—	2	2	no	—
399	C₂³	—	5	1	no	—
400	C₂³	—	5	1	no	—
401	C₂³	—	5	2	no	—
402	C₂³	—	5	2	no	—
403	C₂³	—	20	2	no	—
404	C₂³	D₅×Dic₆	1	1	yes	characteristic
405	C₂×C₄	—	5	2	no	—
406	C₂×C₄	—	5	1	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	5	2	no	—
409	C₂×C₄	—	5	2	no	—
410	C₂×C₄	—	5	2	no	—
411	C₂×C₄	—	5	2	no	—
412	C₂×C₄	—	5	2	no	—
413	C₂×C₄	—	5	2	no	—
414	C₂×C₄	—	5	2	no	—
415	C₂×C₄	—	5	2	no	—
416	C₂×C₄	—	5	2	no	—
417	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
418	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
419	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
420	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
421	C₂×C₄	D₅×#67	1	1	yes	characteristic
422	C₂×C₄	D₅×#67	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	6	2	no	—
425	C₈	—	6	2	no	—
426	C₈	—	10	2	no	—
427	C₈	—	30	2	no	—
428	C₈	—	30	2	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	—	2	1	no	—
431	C₂×C₃	—	10	2	no	—
432	C₂×C₃	—	10	2	no	—
433	C₂×C₃	D₅×#95	1	1	yes	characteristic
434	C₂×C₃	#65182	1	2	yes	—
435	C₅	#71994	1	1	yes	characteristic, complemented, Sylow
436	C₂²	—	2	2	no	—
437	C₂²	—	5	2	no	—
438	C₂²	—	5	2	no	—
439	C₂²	—	10	2	no	—
440	C₂²	—	10	2	no	—
441	C₂²	—	20	2	no	—
442	C₂²	—	20	2	no	—
443	C₂²	D₅×Dic₃⋊C₄	1	1	yes	characteristic
444	C₂²	D₅×Dic₃⋊C₄	1	1	yes	characteristic
445	C₂²	D₅×C₄⋊Dic₃	1	1	yes	characteristic
446	C₄	—	5	2	no	—
447	C₄	—	5	2	no	—
448	C₄	C₄×D₅×Dic₃	1	1	yes	characteristic
449	C₄	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
450	C₄	D₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
451	C₄	D₅×#217	1	1	yes	characteristic
452	C₃	#10599731	1	1	yes	characteristic, complemented, Sylow
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	10	2	no	—
456	C₂	—	10	2	no	—
457	C₂	#11748171	1	2	yes	—
458	C₂	D₅×C₃⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×#67
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₃×D₅	Q₈
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	#1738
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #11746379	C₂	semidirect
5. C₅×#4558	C₂	semidirect
6. #11745983	C₂	semidirect
7. #11745982	C₂	semidirect
77. #4558	D₅	semidirect
376. C₃×C₅	#1738	semidirect
435. C₅	#71994	semidirect
452. C₃	#10599731	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₅×M₁₆	2
C₂²×#6649	2
C₂×D₅×#208	2
#11746379	2
C₅×#4558	2
#11745983	2
#11745982	2
#10599731	3
#71994	5