Subgroups — #14479171

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×#91815	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic, complemented
4	#11755410	C₂	1	4	yes	maximal, complemented
5	#11754513	C₂	1	4	yes	maximal, complemented
6	#11754503	C₂	1	2	yes	maximal, complemented
7	#11754492	C₂	1	4	yes	maximal, complemented
8	#11754455	C₂	1	4	yes	maximal, complemented
9	D₃×#4072	C₂	1	4	yes	maximal, complemented
10	Dic₅×#235	C₂	1	4	yes	maximal, complemented
11	#11754211	C₂	1	2	yes	maximal, complemented
12	#10619161	—	3	1	no	maximal, Hall
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₅×#67	C₂²	1	2	yes	—
15	C₂×C₅×#235	C₄	1	16	yes	complemented
16	C₂×C₅×#235	C₂²	1	2	yes	—
17	C₂×C₅×#235	C₂²	1	2	yes	—
18	C₂×C₅×#235	C₂²	1	2	yes	—
19	C₂×C₅×#235	C₂²	1	2	yes	—
20	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
22	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
23	C₂×#6719	C₂²	1	2	yes	—
24	#91815	C₂²	1	2	yes	—
25	#91815	C₂²	1	2	yes	—
26	#91815	C₂²	1	2	yes	complemented
27	#91815	C₂²	1	2	yes	complemented
28	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	complemented
29	C₂×C₄×Dic₁₅	C₂²	1	2	yes	complemented
30	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
31	C₃×#4072	C₂²	1	2	yes	—
32	C₃×#4072	C₂²	1	2	yes	—
33	C₃×#4072	C₂²	1	2	yes	complemented
34	C₃×#4072	C₂²	1	2	yes	complemented
35	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
36	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
37	#67⋊Dic₅	C₂²	1	16	yes	complemented
38	D₃×C₂²⋊Dic₅	C₂²	1	8	yes	—
39	Dic₅×#67	C₂²	1	16	yes	complemented
40	#91529	C₂²	1	8	yes	—
41	#91435	C₂²	1	8	yes	complemented
42	D₃×C₄⋊Dic₅	C₂²	1	8	yes	complemented
43	Dic₅×D₁₂	C₂²	1	8	yes	complemented
44	C₄×D₃×Dic₅	C₂²	1	8	yes	complemented
45	#91371	C₂²	1	8	yes	complemented
46	#91344	C₂²	1	8	yes	complemented
47	#91338	C₂²	1	8	yes	complemented
48	Dic₅×Dic₆	C₂²	1	8	yes	complemented
49	#85731	—	5	1	no	maximal, Hall
50	C₂²×C₅×#41	—	3	1	no	—
51	#66161	—	3	4	no	—
52	#66161	—	3	4	no	—
53	#41×Dic₅	—	3	4	no	—
54	#41×Dic₅	—	3	4	no	—
55	#66146	—	3	2	no	—
56	#66132	—	3	2	no	—
57	#66132	—	3	4	no	—
58	C₂×#4072	—	3	4	no	—
59	C₂×#4072	—	3	1	no	—
60	C₂×#4072	D₃	1	1	yes	characteristic, complemented
61	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
62	C₂³×C₅×D₃	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	complemented
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×Dic₁₅	C₂³	1	4	yes	—
71	C₂×C₅×#67	C₂×C₄	1	16	yes	complemented
72	C₂×C₅×#67	C₂³	1	4	yes	—
73	C₂×C₅×#67	C₂³	1	4	yes	—
74	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
75	C₅×#235	C₂×C₄	1	16	yes	complemented
76	C₅×#235	C₂×C₄	1	16	yes	complemented
77	C₅×#235	C₂×C₄	1	16	yes	complemented
78	C₅×#235	C₂×C₄	1	16	yes	complemented
79	C₂×C₅×D₁₂	C₂×C₄	1	8	yes	complemented
80	C₂×C₅×D₁₂	C₂³	1	2	yes	—
81	C₂×C₅×D₁₂	C₂³	1	2	yes	—
82	C₂×C₄×C₅×D₃	C₂×C₄	1	16	yes	complemented
83	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
84	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
85	C₂×C₅×Dic₆	C₂×C₄	1	8	yes	complemented
86	C₂×C₅×Dic₆	C₂³	1	2	yes	—
87	C₂×C₅×Dic₆	C₂³	1	2	yes	—
88	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
89	C₂×D₃×Dic₅	C₂³	1	16	yes	—
90	#6719	C₂³	1	4	yes	—
91	#6719	C₂³	1	4	yes	—
92	C₄⋊Dic₁₅	C₂³	1	4	yes	—
93	C₄⋊Dic₁₅	C₂³	1	4	yes	—
94	C₄×Dic₁₅	C₂³	1	4	yes	—
95	C₄×Dic₁₅	C₂³	1	4	yes	—
96	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
97	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
98	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
99	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
100	C₃×C₄×Dic₅	C₂³	1	4	yes	—
101	C₃×C₄×Dic₅	C₂³	1	4	yes	—
102	Dic₃⋊Dic₅	C₂³	1	16	yes	—
103	(C₂×D₃)⋊Dic₅	C₂³	1	16	yes	—
104	Dic₃×Dic₅	C₂³	1	16	yes	—
105	C₂²×#235	D₅	1	1	yes	characteristic
106	C₂×C₃×#117	—	5	1	no	—
107	C₂×#926	—	5	1	no	—
108	#5523	—	5	4	no	—
109	#5522	—	5	4	no	—
110	#5521	—	5	2	no	—
111	D₃×#117	—	5	4	no	—
112	#5516	—	5	2	no	—
113	#5504	—	5	4	no	—
114	#5486	—	5	4	no	—
115	C₄×#235	—	5	4	no	—
116	C₂×C₅×#41	—	3	16	no	—
117	C₂×C₅×#41	—	3	2	no	—
118	C₂×C₅×#41	—	3	2	no	—
119	C₂×C₅×#41	—	3	2	no	—
120	C₂×C₅×#41	—	3	2	no	—
121	C₂²×C₅×Q₈	—	3	1	no	—
122	C₂²×C₅×D₄	—	3	2	no	—
123	C₂²×C₅×D₄	—	3	1	no	—
124	C₂³×C₄×C₅	—	3	2	no	—
125	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
126	C₂×C₂²⋊Dic₅	—	3	2	no	—
127	C₂×C₂²⋊Dic₅	—	3	8	no	—
128	C₂×C₂²⋊Dic₅	C₂×D₃	1	2	yes	—
129	Q₈×Dic₅	—	3	8	no	—
130	Q₈×Dic₅	—	3	8	no	—
131	D₄×Dic₅	—	3	16	no	—
132	D₄×Dic₅	—	3	16	no	—
133	D₄×Dic₅	—	3	8	no	—
134	D₄×Dic₅	—	3	8	no	—
135	#4072	—	3	2	no	—
136	#4072	—	3	2	no	—
137	#4072	—	3	2	no	—
138	#4072	—	3	2	no	—
139	#4072	—	3	8	no	—
140	#4072	—	3	8	no	—
141	#4072	—	3	8	no	—
142	#4072	C₂×D₃	1	2	yes	—
143	#4072	C₂×D₃	1	2	yes	—
144	#4072	C₂×D₃	1	2	yes	complemented
145	#4072	C₂×D₃	1	2	yes	complemented
146	C₂×C₄⋊Dic₅	—	3	2	no	—
147	C₂×C₄⋊Dic₅	—	3	8	no	—
148	C₂×C₄⋊Dic₅	C₂×D₃	1	2	yes	complemented
149	C₂×C₄×Dic₅	—	3	2	no	—
150	C₂×C₄×Dic₅	—	3	8	no	—
151	C₂×C₄×Dic₅	C₂×D₃	1	2	yes	complemented
152	#3428	—	15	1	no	Sylow
153	C₂³×C₃×C₅	—	4	2	no	—
154	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
155	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
156	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
157	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
158	C₂²×C₅×D₃	—	4	4	no	—
159	C₂²×C₅×D₃	C₂²×C₄	1	8	yes	—
160	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
161	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
162	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
163	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
164	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
165	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
166	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
169	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
170	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
171	C₂×Dic₁₅	—	4	4	no	—
172	C₂×Dic₁₅	C₂⁴	1	8	yes	—
173	C₅×#67	C₂²×C₄	1	16	yes	—
174	C₅×#67	C₂²×C₄	1	16	yes	—
175	C₂×C₅×Dic₃	C₂²×C₄	1	8	yes	—
176	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
177	C₅×D₁₂	C₂²×C₄	1	8	yes	—
178	C₅×D₁₂	C₂²×C₄	1	8	yes	—
179	C₄×C₅×D₃	C₂²×C₄	1	16	yes	—
180	C₄×C₅×D₃	C₂²×C₄	1	16	yes	—
181	C₅×Dic₆	C₂²×C₄	1	8	yes	—
182	C₅×Dic₆	C₂²×C₄	1	8	yes	—
183	C₂×C₃×Dic₅	—	4	4	no	—
184	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
185	D₃×Dic₅	—	4	16	no	—
186	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
187	C₂²×#67	C₂×D₅	1	2	yes	—
188	C₂×#235	Dic₅	1	16	yes	complemented
189	C₂×#235	C₂×D₅	1	2	yes	—
190	C₂×#235	C₂×D₅	1	2	yes	—
191	C₂×#235	C₂×D₅	1	2	yes	—
192	C₂×#235	C₂×D₅	1	2	yes	—
193	C₂²×D₁₂	C₂×D₅	1	1	yes	characteristic
194	C₂²×C₄×D₃	C₂×D₅	1	2	yes	—
195	C₂²×Dic₆	C₂×D₅	1	1	yes	characteristic
196	C₃×#117	—	5	2	no	—
197	C₃×#117	—	5	2	no	—
198	C₃×#117	—	5	2	no	—
199	C₃×#117	—	5	2	no	—
200	C₂×C₃×C₄⋊C₄	—	5	2	no	—
201	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
202	C₂×C₃×C₄²	—	5	2	no	—
203	C₂×#217	—	5	2	no	—
204	C₄×#67	—	5	16	no	—
205	#926	—	5	2	no	—
206	#926	—	5	2	no	—
207	#926	—	5	2	no	—
208	#926	—	5	2	no	—
209	C₂×C₄⋊Dic₃	—	5	2	no	—
210	C₂×C₄×Dic₃	—	5	2	no	—
211	#893	—	5	8	no	—
212	#892	—	5	8	no	—
213	D₃×C₄⋊C₄	—	5	8	no	—
214	#887	—	5	8	no	—
215	#67⋊C₄	—	5	16	no	—
216	D₃×C₂²⋊C₄	—	5	8	no	—
217	#877	—	5	8	no	—
218	C₄×D₁₂	—	5	8	no	—
219	#872	—	5	8	no	—
220	C₄²×D₃	—	5	8	no	—
221	C₄×Dic₆	—	5	8	no	—
222	C₂⁴×C₅	—	3	2	no	—
223	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
224	C₅×#41	—	3	16	no	—
225	C₅×#41	—	3	16	no	—
226	C₅×#41	—	3	16	no	—
227	C₅×#41	—	3	16	no	—
228	C₂×C₅×Q₈	—	3	8	no	—
229	C₂×C₅×Q₈	—	3	2	no	—
230	C₂×C₅×Q₈	—	3	2	no	—
231	C₂×C₅×D₄	—	3	16	no	—
232	C₂×C₅×D₄	—	3	4	no	—
233	C₂×C₅×D₄	—	3	4	no	—
234	C₂×C₅×D₄	—	3	8	no	—
235	C₂×C₅×D₄	—	3	2	no	—
236	C₂×C₅×D₄	—	3	2	no	—
237	C₂²×C₄×C₅	—	3	2	no	—
238	C₂²×C₄×C₅	—	3	16	no	—
239	C₂²×C₄×C₅	—	3	4	no	—
240	C₂²×C₄×C₅	—	3	4	no	—
241	C₂²×C₄×C₅	C₄×D₃	1	8	yes	complemented
242	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
244	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
245	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
246	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
247	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
248	C₂²×Dic₅	—	3	4	no	—
249	C₂²×Dic₅	—	3	16	no	—
250	C₂²×Dic₅	C₂²×D₃	1	4	yes	—
251	C₂²⋊Dic₅	—	3	4	no	—
252	C₂²⋊Dic₅	—	3	4	no	—
253	C₂²⋊Dic₅	—	3	16	no	—
254	C₂²⋊Dic₅	C₂²×D₃	1	4	yes	—
255	C₂²⋊Dic₅	C₂²×D₃	1	4	yes	—
256	C₄⋊Dic₅	—	3	4	no	—
257	C₄⋊Dic₅	—	3	4	no	—
258	C₄⋊Dic₅	—	3	16	no	—
259	C₄⋊Dic₅	C₂²×D₃	1	4	yes	—
260	C₄⋊Dic₅	C₂²×D₃	1	4	yes	—
261	C₄×Dic₅	—	3	4	no	—
262	C₄×Dic₅	—	3	4	no	—
263	C₄×Dic₅	—	3	16	no	—
264	C₄×Dic₅	C₂²×D₃	1	4	yes	—
265	C₄×Dic₅	C₂²×D₃	1	4	yes	—
266	C₂²×#41	—	3	1	no	—
267	#520	—	15	4	no	—
268	#520	—	15	4	no	—
269	#519	—	15	2	no	—
270	#518	—	15	4	no	—
271	#518	—	15	2	no	—
272	C₄×#41	—	15	4	no	—
273	C₄×#41	—	15	4	no	—
274	C₂×#117	—	5	1	no	—
275	C₂×#117	—	15	4	no	—
276	C₂×#117	—	15	1	no	—
277	C₂²×C₃×C₅	—	2	2	no	—
278	C₂²×C₃×C₅	—	2	2	no	—
279	C₂²×C₃×C₅	—	2	2	no	—
280	C₂²×C₃×C₅	—	4	4	no	—
281	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
282	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
283	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
284	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
285	C₂×C₅×D₃	—	2	8	no	—
286	C₂×C₅×D₃	—	4	8	no	—
287	C₂×C₅×D₃	C₂³×C₄	1	8	yes	—
288	C₃×C₄×C₅	C₂³×C₄	1	2	yes	—
289	C₃×C₄×C₅	C₂³×C₄	1	2	yes	—
290	C₃×C₄×C₅	C₂³×C₄	1	2	yes	—
291	C₃×C₄×C₅	C₂³×C₄	1	2	yes	—
292	Dic₁₅	—	2	8	no	—
293	C₃×Dic₅	—	2	8	no	—
294	C₅×Dic₃	C₂³×C₄	1	8	yes	—
295	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
296	C₂³×D₃	C₂²×D₅	1	2	yes	—
297	C₂²×C₃×C₄	—	5	4	no	—
298	C₂²×C₃×C₄	C₂×Dic₅	1	8	yes	complemented
299	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
300	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
301	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
302	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
303	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
304	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
305	C₂×#67	C₂×Dic₅	1	16	yes	complemented
306	C₂×#67	C₂²×D₅	1	4	yes	—
307	C₂×#67	C₂²×D₅	1	4	yes	—
308	C₂²×Dic₃	—	5	4	no	—
309	C₂²×Dic₃	C₂²×D₅	1	2	yes	—
310	#235	C₂×Dic₅	1	16	yes	complemented
311	#235	C₂×Dic₅	1	16	yes	complemented
312	#235	C₂×Dic₅	1	16	yes	complemented
313	#235	C₂×Dic₅	1	16	yes	complemented
314	C₂×D₁₂	C₂×Dic₅	1	8	yes	complemented
315	C₂×D₁₂	C₂²×D₅	1	2	yes	—
316	C₂×D₁₂	C₂²×D₅	1	2	yes	—
317	C₂×C₄×D₃	—	5	16	no	—
318	C₂×C₄×D₃	C₂×Dic₅	1	16	yes	complemented
319	C₂×C₄×D₃	C₂²×D₅	1	4	yes	—
320	C₂×C₄×D₃	C₂²×D₅	1	4	yes	—
321	C₂×Dic₆	C₂×Dic₅	1	8	yes	complemented
322	C₂×Dic₆	C₂²×D₅	1	2	yes	—
323	C₂×Dic₆	C₂²×D₅	1	2	yes	—
324	C₃×C₄⋊C₄	—	5	4	no	—
325	C₃×C₄⋊C₄	—	5	4	no	—
326	C₃×C₂²⋊C₄	—	5	4	no	—
327	C₃×C₂²⋊C₄	—	5	4	no	—
328	C₃×C₄²	—	5	4	no	—
329	C₃×C₄²	—	5	4	no	—
330	#217	—	5	4	no	—
331	#217	—	5	4	no	—
332	(C₂×D₃)⋊C₄	—	5	16	no	—
333	C₄⋊Dic₃	—	5	4	no	—
334	C₄⋊Dic₃	—	5	4	no	—
335	Dic₃⋊C₄	—	5	16	no	—
336	C₄×Dic₃	—	5	4	no	—
337	C₄×Dic₃	—	5	4	no	—
338	C₄×Dic₃	—	5	16	no	—
339	C₂³×C₅	—	3	4	no	—
340	C₂³×C₅	—	3	8	no	—
341	C₂³×C₅	—	4	2	no	—
342	C₂³×C₅	—	12	4	no	—
343	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
344	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
345	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
346	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
347	C₅×Q₈	—	3	8	no	—
348	C₅×Q₈	—	3	8	no	—
349	C₅×D₄	—	3	16	no	—
350	C₅×D₄	—	3	16	no	—
351	C₅×D₄	—	3	8	no	—
352	C₅×D₄	—	3	8	no	—
353	C₂×C₄×C₅	—	3	8	no	—
354	C₂×C₄×C₅	—	3	4	no	—
355	C₂×C₄×C₅	—	3	16	no	—
356	C₂×C₄×C₅	—	3	16	no	—
357	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
358	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
359	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
360	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
361	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
362	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
363	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
364	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
365	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
366	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
367	C₂×Dic₅	—	3	8	no	—
368	C₂×Dic₅	—	4	4	no	—
369	C₂×Dic₅	—	12	16	no	—
370	C₂×Dic₅	—	12	4	no	—
371	C₂×Dic₅	C₂³×D₃	1	8	yes	—
372	C₂×#41	—	3	16	no	—
373	C₂×#41	—	3	2	no	—
374	C₂×#41	—	3	2	no	—
375	C₂×#41	—	3	2	no	—
376	C₂×#41	—	3	2	no	—
377	C₂²×Q₈	—	3	1	no	—
378	C₂²×D₄	—	3	2	no	—
379	C₂²×D₄	—	3	1	no	—
380	C₂³×C₄	—	3	2	no	—
381	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
382	C₄×Q₈	—	15	8	no	—
383	C₄×Q₈	—	15	8	no	—
384	C₄×D₄	—	15	8	no	—
385	C₄×D₄	—	15	16	no	—
386	C₄×D₄	—	15	8	no	—
387	C₄×D₄	—	15	16	no	—
388	#117	—	5	2	no	—
389	#117	—	5	2	no	—
390	#117	—	5	2	no	—
391	#117	—	5	2	no	—
392	#117	—	15	8	no	—
393	#117	—	15	8	no	—
394	#117	—	15	8	no	—
395	#117	—	15	2	no	—
396	#117	—	15	2	no	—
397	#117	—	15	2	no	—
398	#117	—	15	2	no	—
399	C₂×C₄⋊C₄	—	5	2	no	—
400	C₂×C₄⋊C₄	—	15	8	no	—
401	C₂×C₄⋊C₄	—	15	2	no	—
402	C₂×C₂²⋊C₄	—	5	2	no	—
403	C₂×C₂²⋊C₄	—	15	8	no	—
404	C₂×C₂²⋊C₄	—	15	2	no	—
405	C₂×C₄²	—	5	2	no	—
406	C₂×C₄²	—	15	8	no	—
407	C₂×C₄²	—	15	2	no	—
408	C₂×C₃×C₅	—	2	2	no	—
409	C₂×C₃×C₅	—	2	2	no	—
410	C₂×C₃×C₅	—	2	2	no	—
411	C₂×C₃×C₅	C₂⁴×C₄	1	1	yes	characteristic
412	C₂×C₃×C₅	#585	1	2	yes	—
413	C₅×D₃	—	2	8	no	—
414	C₂³×C₃	—	4	2	no	—
415	C₂³×C₃	C₂²×Dic₅	1	4	yes	—
416	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
417	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
418	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
419	C₂²×D₃	—	4	4	no	—
420	C₂²×D₃	C₂²×Dic₅	1	8	yes	—
421	C₂²×D₃	C₂³×D₅	1	4	yes	—
422	C₂×C₃×C₄	—	5	8	no	—
423	C₂×C₃×C₄	—	20	4	no	—
424	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
425	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
426	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
427	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
428	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
429	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
430	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
431	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
432	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
433	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
434	#67	C₂²×Dic₅	1	16	yes	—
435	#67	C₂²×Dic₅	1	16	yes	—
436	C₂×Dic₃	—	5	8	no	—
437	C₂×Dic₃	—	20	4	no	—
438	C₂×Dic₃	C₂²×Dic₅	1	8	yes	—
439	C₂×Dic₃	C₂³×D₅	1	4	yes	—
440	D₁₂	C₂²×Dic₅	1	8	yes	—
441	D₁₂	C₂²×Dic₅	1	8	yes	—
442	C₄×D₃	—	20	16	no	—
443	C₄×D₃	C₂²×Dic₅	1	16	yes	—
444	C₄×D₃	C₂²×Dic₅	1	16	yes	—
445	Dic₆	C₂²×Dic₅	1	8	yes	—
446	Dic₆	C₂²×Dic₅	1	8	yes	—
447	C₂²×C₅	—	2	2	no	—
448	C₂²×C₅	—	2	2	no	—
449	C₂²×C₅	—	2	2	no	—
450	C₂²×C₅	—	3	8	no	—
451	C₂²×C₅	—	4	4	no	—
452	C₂²×C₅	—	6	8	no	—
453	C₂²×C₅	—	12	8	no	—
454	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
455	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
456	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
457	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
458	C₄×C₅	—	3	8	no	—
459	C₄×C₅	C₂²×C₄×D₃	1	2	yes	—
460	C₄×C₅	C₂²×C₄×D₃	1	2	yes	—
461	C₄×C₅	C₂²×C₄×D₃	1	2	yes	—
462	C₄×C₅	C₂²×C₄×D₃	1	2	yes	—
463	Dic₅	—	2	8	no	—
464	Dic₅	—	6	8	no	—
465	C₂⁴	—	3	2	no	—
466	C₂⁴	C₂×D₃×D₅	1	1	yes	characteristic
467	#41	—	3	16	no	—
468	#41	—	3	16	no	—
469	#41	—	3	16	no	—
470	#41	—	3	16	no	—
471	C₂×Q₈	—	3	8	no	—
472	C₂×Q₈	—	3	2	no	—
473	C₂×Q₈	—	3	2	no	—
474	C₂×D₄	—	3	16	no	—
475	C₂×D₄	—	3	4	no	—
476	C₂×D₄	—	3	4	no	—
477	C₂×D₄	—	3	8	no	—
478	C₂×D₄	—	3	2	no	—
479	C₂×D₄	—	3	2	no	—
480	C₂²×C₄	—	3	2	no	—
481	C₂²×C₄	—	3	16	no	—
482	C₂²×C₄	—	3	4	no	—
483	C₂²×C₄	—	3	4	no	—
484	C₂²×C₄	—	5	4	no	—
485	C₂²×C₄	—	15	16	no	—
486	C₂²×C₄	—	15	4	no	—
487	C₂²×C₄	D₃×Dic₅	1	8	yes	complemented
488	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
494	C₄⋊C₄	—	5	4	no	—
495	C₄⋊C₄	—	5	4	no	—
496	C₄⋊C₄	—	15	16	no	—
497	C₄⋊C₄	—	15	4	no	—
498	C₄⋊C₄	—	15	4	no	—
499	C₂²⋊C₄	—	5	4	no	—
500	C₂²⋊C₄	—	5	4	no	—
501	C₂²⋊C₄	—	15	16	no	—
502	C₂²⋊C₄	—	15	4	no	—
503	C₂²⋊C₄	—	15	4	no	—
504	C₄²	—	5	4	no	—
505	C₄²	—	5	4	no	—
506	C₄²	—	15	16	no	—
507	C₄²	—	15	4	no	—
508	C₄²	—	15	4	no	—
509	C₃×C₅	#3428	1	1	yes	characteristic, complemented, Hall
510	C₂²×C₃	—	2	2	no	—
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	—	2	2	no	—
513	C₂²×C₃	—	4	4	no	—
514	C₂²×C₃	C₂³×Dic₅	1	2	yes	—
515	C₂²×C₃	C₂³×Dic₅	1	2	yes	—
516	C₂²×C₃	C₂³×Dic₅	1	2	yes	—
517	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
518	C₂×D₃	—	2	8	no	—
519	C₂×D₃	—	4	8	no	—
520	C₂×D₃	C₂³×Dic₅	1	8	yes	—
521	C₃×C₄	—	10	8	no	—
522	C₃×C₄	C₂³×Dic₅	1	2	yes	—
523	C₃×C₄	C₂³×Dic₅	1	2	yes	—
524	C₃×C₄	C₂³×Dic₅	1	2	yes	—
525	C₃×C₄	C₂³×Dic₅	1	2	yes	—
526	Dic₃	—	10	8	no	—
527	Dic₃	C₂³×Dic₅	1	8	yes	—
528	C₂×C₅	—	2	2	no	—
529	C₂×C₅	—	2	2	no	—
530	C₂×C₅	—	2	2	no	—
531	C₂×C₅	—	6	8	no	—
532	C₂×C₅	C₂³×C₄×D₃	1	1	yes	characteristic
533	C₂×C₅	#5964	1	2	yes	—
534	C₂³	—	3	4	no	—
535	C₂³	—	3	8	no	—
536	C₂³	—	4	2	no	—
537	C₂³	—	12	4	no	—
538	C₂³	C₂×D₃×Dic₅	1	4	yes	—
539	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
540	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
541	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
542	Q₈	—	3	8	no	—
543	Q₈	—	3	8	no	—
544	D₄	—	3	16	no	—
545	D₄	—	3	16	no	—
546	D₄	—	3	8	no	—
547	D₄	—	3	8	no	—
548	C₂×C₄	—	3	8	no	—
549	C₂×C₄	—	3	4	no	—
550	C₂×C₄	—	3	16	no	—
551	C₂×C₄	—	3	16	no	—
552	C₂×C₄	—	5	8	no	—
553	C₂×C₄	—	15	8	no	—
554	C₂×C₄	—	20	4	no	—
555	C₂×C₄	—	60	16	no	—
556	C₂×C₄	—	60	4	no	—
557	C₂×C₄	C₂×D₃×Dic₅	1	4	yes	—
558	C₂×C₄	C₂×D₃×Dic₅	1	4	yes	—
559	C₂×C₄	C₂×D₃×Dic₅	1	4	yes	—
560	C₂×C₄	C₂×D₃×Dic₅	1	4	yes	—
561	C₂×C₄	C₂×D₃×Dic₅	1	4	yes	—
562	C₂×C₄	C₂×D₃×Dic₅	1	4	yes	—
563	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
565	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
567	C₂×C₃	—	2	2	no	—
568	C₂×C₃	—	2	2	no	—
569	C₂×C₃	—	2	2	no	—
570	C₂×C₃	#66283	1	2	yes	—
571	C₂×C₃	C₂⁴×Dic₅	1	1	yes	characteristic
572	D₃	—	2	8	no	—
573	C₅	#85731	1	1	yes	characteristic, complemented, Sylow
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	3	8	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	6	8	no	—
580	C₂²	—	12	8	no	—
581	C₂²	C₂²×D₃×Dic₅	1	2	yes	—
582	C₂²	C₂²×D₃×Dic₅	1	2	yes	—
583	C₂²	C₂²×D₃×Dic₅	1	2	yes	—
584	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
585	C₄	—	3	8	no	—
586	C₄	—	10	8	no	—
587	C₄	—	30	8	no	—
588	C₄	C₂²×D₃×Dic₅	1	2	yes	—
589	C₄	C₂²×D₃×Dic₅	1	2	yes	—
590	C₄	C₂²×D₃×Dic₅	1	2	yes	—
591	C₄	C₂²×D₃×Dic₅	1	2	yes	—
592	C₃	#10619161	1	1	yes	characteristic, complemented, Sylow
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	2	2	no	—
596	C₂	—	6	8	no	—
597	C₂	#11757022	1	2	yes	—
598	C₂	C₂³×D₃×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂⁴×C₄
Frattini	C₂²	C₂³×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle, cosocle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂²×C₅×#235	C₂
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	#3428
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#91815	C₂	semidirect
3. C₂×C₃×#4072	C₂	semidirect
4. #11755410	C₂	semidirect
5. #11754513	C₂	semidirect
6. #11754503	C₂	semidirect
7. #11754492	C₂	semidirect
8. #11754455	C₂	semidirect
9. D₃×#4072	C₂	semidirect
10. Dic₅×#235	C₂	semidirect
11. #11754211	C₂	semidirect
15. C₂×C₅×#235	C₄	semidirect
26. #91815	C₂²	semidirect
27. #91815	C₂²	semidirect
28. C₂×C₄⋊Dic₁₅	C₂²	semidirect
29. C₂×C₄×Dic₁₅	C₂²	semidirect
33. C₃×#4072	C₂²	semidirect
34. C₃×#4072	C₂²	semidirect
35. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
36. C₂×C₃×C₄×Dic₅	C₂²	semidirect
37. #67⋊Dic₅	C₂²	semidirect
39. Dic₅×#67	C₂²	semidirect
41. #91435	C₂²	semidirect
42. D₃×C₄⋊Dic₅	C₂²	semidirect
43. Dic₅×D₁₂	C₂²	semidirect
44. C₄×D₃×Dic₅	C₂²	semidirect
45. #91371	C₂²	semidirect
46. #91344	C₂²	semidirect
47. #91338	C₂²	semidirect
48. Dic₅×Dic₆	C₂²	semidirect
60. C₂×#4072	D₃	semidirect
63. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
71. C₂×C₅×#67	C₂×C₄	semidirect
75. C₅×#235	C₂×C₄	semidirect
76. C₅×#235	C₂×C₄	semidirect
77. C₅×#235	C₂×C₄	semidirect
78. C₅×#235	C₂×C₄	semidirect
79. C₂×C₅×D₁₂	C₂×C₄	semidirect
82. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
85. C₂×C₅×Dic₆	C₂×C₄	semidirect
144. #4072	C₂×D₃	semidirect
145. #4072	C₂×D₃	semidirect
148. C₂×C₄⋊Dic₅	C₂×D₃	semidirect
151. C₂×C₄×Dic₅	C₂×D₃	semidirect
188. C₂×#235	Dic₅	semidirect
241. C₂²×C₄×C₅	C₄×D₃	semidirect
298. C₂²×C₃×C₄	C₂×Dic₅	semidirect
305. C₂×#67	C₂×Dic₅	semidirect
310. #235	C₂×Dic₅	semidirect
311. #235	C₂×Dic₅	semidirect
312. #235	C₂×Dic₅	semidirect
313. #235	C₂×Dic₅	semidirect
314. C₂×D₁₂	C₂×Dic₅	semidirect
318. C₂×C₄×D₃	C₂×Dic₅	semidirect
321. C₂×Dic₆	C₂×Dic₅	semidirect
487. C₂²×C₄	D₃×Dic₅	semidirect
509. C₃×C₅	#3428	semidirect
573. C₅	#85731	semidirect
592. C₃	#10619161	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#235	2
C₂×#91815	2
C₂×C₃×#4072	2
#11755410	2
#11754513	2
#11754503	2
#11754492	2
#11754455	2
D₃×#4072	2
Dic₅×#235	2
#11754211	2
#10619161	3
#85731	5