Subgroups — #14479169

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×C₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₂×#91815	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
4	#11755406	C₂	1	4	yes	maximal, complemented
5	#11754509	C₂	1	4	yes	maximal, complemented
6	#11754499	C₂	1	4	yes	maximal, complemented
7	#11754488	C₂	1	2	yes	maximal, complemented
8	#11754444	C₂	1	4	yes	maximal, complemented
9	Dic₃×#709	C₂	1	4	yes	maximal, complemented
10	D₅×#926	C₂	1	4	yes	maximal, complemented
11	#11754188	C₂	1	2	yes	maximal, complemented
12	#10617632	—	3	1	no	maximal, Hall
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
15	C₂×C₃×#709	C₄	1	16	yes	complemented
16	C₂×C₃×#709	C₂²	1	2	yes	—
17	C₂×C₃×#709	C₂²	1	2	yes	—
18	C₂×C₃×#709	C₂²	1	2	yes	—
19	C₂×C₃×#709	C₂²	1	2	yes	—
20	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
22	C₂²×C₃×Dic₁₀	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×C₅×#217	C₂²	1	2	yes	—
31	C₅×#926	C₂²	1	2	yes	—
32	C₅×#926	C₂²	1	2	yes	—
33	C₅×#926	C₂²	1	2	yes	complemented
34	C₅×#926	C₂²	1	2	yes	complemented
35	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
36	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
37	#91559	C₂²	1	16	yes	complemented
38	Dic₃×C₂²⋊D₅	C₂²	1	16	yes	complemented
39	D₅×#217	C₂²	1	8	yes	—
40	#91528	C₂²	1	8	yes	—
41	#91434	C₂²	1	8	yes	complemented
42	Dic₃×D₂₀	C₂²	1	8	yes	complemented
43	D₅×C₄⋊Dic₃	C₂²	1	8	yes	complemented
44	C₄×D₅×Dic₃	C₂²	1	8	yes	complemented
45	#91358	C₂²	1	8	yes	complemented
46	#91357	C₂²	1	8	yes	complemented
47	#91331	C₂²	1	8	yes	complemented
48	Dic₃×Dic₁₀	C₂²	1	8	yes	complemented
49	#87260	—	5	1	no	maximal, Hall
50	C₂²×#709	D₃	1	1	yes	characteristic
51	C₂×C₅×#117	—	3	1	no	—
52	C₂×#4072	—	3	1	no	—
53	#65857	—	3	4	no	—
54	#65856	—	3	4	no	—
55	#65855	—	3	2	no	—
56	D₅×#117	—	3	4	no	—
57	#65850	—	3	2	no	—
58	#65838	—	3	4	no	—
59	#65820	—	3	4	no	—
60	C₄×#709	—	3	4	no	—
61	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
62	C₂³×C₃×D₅	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	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
72	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	16	yes	complemented
73	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
74	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
75	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
76	C₃×#709	C₂×C₄	1	16	yes	complemented
77	C₃×#709	C₂×C₄	1	16	yes	complemented
78	C₃×#709	C₂×C₄	1	16	yes	complemented
79	C₃×#709	C₂×C₄	1	16	yes	complemented
80	C₂×C₃×D₂₀	C₂×C₄	1	8	yes	complemented
81	C₂×C₃×D₂₀	C₂³	1	2	yes	—
82	C₂×C₃×D₂₀	C₂³	1	2	yes	—
83	C₂×C₃×C₄×D₅	C₂×C₄	1	16	yes	complemented
84	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
85	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
86	C₂×C₃×Dic₁₀	C₂×C₄	1	8	yes	complemented
87	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
88	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
89	C₂×D₅×Dic₃	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	C₅×#217	C₂³	1	4	yes	—
97	C₅×#217	C₂³	1	4	yes	—
98	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
99	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
100	C₄×C₅×Dic₃	C₂³	1	4	yes	—
101	C₄×C₅×Dic₃	C₂³	1	4	yes	—
102	#6668	C₂³	1	16	yes	—
103	#6665	C₂³	1	16	yes	—
104	Dic₃×Dic₅	C₂³	1	16	yes	—
105	C₂²×C₃×#41	—	5	1	no	—
106	#5827	—	5	4	no	—
107	#5827	—	5	4	no	—
108	Dic₃×#41	—	5	4	no	—
109	Dic₃×#41	—	5	4	no	—
110	#5812	—	5	2	no	—
111	#5798	—	5	4	no	—
112	#5798	—	5	2	no	—
113	C₂×#926	—	5	1	no	—
114	C₂×#926	—	5	4	no	—
115	C₂×#926	D₅	1	1	yes	characteristic, complemented
116	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
117	C₂²×C₂²⋊D₅	C₂×D₃	1	2	yes	—
118	C₂×#709	Dic₃	1	16	yes	complemented
119	C₂×#709	C₂×D₃	1	2	yes	—
120	C₂×#709	C₂×D₃	1	2	yes	—
121	C₂×#709	C₂×D₃	1	2	yes	—
122	C₂×#709	C₂×D₃	1	2	yes	—
123	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
124	C₂²×C₄×D₅	C₂×D₃	1	2	yes	—
125	C₂²×Dic₁₀	C₂×D₃	1	1	yes	characteristic
126	C₅×#117	—	3	2	no	—
127	C₅×#117	—	3	2	no	—
128	C₅×#117	—	3	2	no	—
129	C₅×#117	—	3	2	no	—
130	C₂×C₅×C₄⋊C₄	—	3	2	no	—
131	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
132	C₂×C₄²×C₅	—	3	2	no	—
133	C₂×C₂²⋊Dic₅	—	3	2	no	—
134	C₄×C₂²⋊D₅	—	3	16	no	—
135	#4072	—	3	2	no	—
136	#4072	—	3	2	no	—
137	#4072	—	3	2	no	—
138	#4072	—	3	2	no	—
139	C₂×C₄⋊Dic₅	—	3	2	no	—
140	C₂×C₄×Dic₅	—	3	2	no	—
141	#4039	—	3	8	no	—
142	#4038	—	3	8	no	—
143	D₅×C₄⋊C₄	—	3	8	no	—
144	#4033	—	3	8	no	—
145	#4027	—	3	16	no	—
146	D₅×C₂²⋊C₄	—	3	8	no	—
147	#4023	—	3	8	no	—
148	C₄×D₂₀	—	3	8	no	—
149	#4018	—	3	8	no	—
150	C₄²×D₅	—	3	8	no	—
151	C₄×Dic₁₀	—	3	8	no	—
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×C₃×D₅	—	4	4	no	—
159	C₂²×C₃×D₅	C₂²×C₄	1	8	yes	—
160	C₂²×C₃×D₅	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	C₂×C₅×Dic₃	—	4	4	no	—
174	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
175	C₃×C₂²⋊D₅	C₂²×C₄	1	16	yes	—
176	C₃×C₂²⋊D₅	C₂²×C₄	1	16	yes	—
177	C₂×C₃×Dic₅	C₂²×C₄	1	8	yes	—
178	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
179	C₃×D₂₀	C₂²×C₄	1	8	yes	—
180	C₃×D₂₀	C₂²×C₄	1	8	yes	—
181	C₃×C₄×D₅	C₂²×C₄	1	16	yes	—
182	C₃×C₄×D₅	C₂²×C₄	1	16	yes	—
183	C₃×Dic₁₀	C₂²×C₄	1	8	yes	—
184	C₃×Dic₁₀	C₂²×C₄	1	8	yes	—
185	D₅×Dic₃	—	4	16	no	—
186	C₂×C₃×#41	—	5	16	no	—
187	C₂×C₃×#41	—	5	2	no	—
188	C₂×C₃×#41	—	5	2	no	—
189	C₂×C₃×#41	—	5	2	no	—
190	C₂×C₃×#41	—	5	2	no	—
191	C₂²×C₃×Q₈	—	5	1	no	—
192	C₂²×C₃×D₄	—	5	2	no	—
193	C₂²×C₃×D₄	—	5	1	no	—
194	C₂³×C₃×C₄	—	5	2	no	—
195	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
196	C₂×#217	—	5	2	no	—
197	C₂×#217	—	5	8	no	—
198	C₂×#217	C₂×D₅	1	2	yes	—
199	Q₈×Dic₃	—	5	8	no	—
200	Q₈×Dic₃	—	5	8	no	—
201	D₄×Dic₃	—	5	16	no	—
202	D₄×Dic₃	—	5	16	no	—
203	D₄×Dic₃	—	5	8	no	—
204	D₄×Dic₃	—	5	8	no	—
205	#926	—	5	2	no	—
206	#926	—	5	2	no	—
207	#926	—	5	2	no	—
208	#926	—	5	2	no	—
209	#926	—	5	8	no	—
210	#926	—	5	8	no	—
211	#926	—	5	8	no	—
212	#926	C₂×D₅	1	2	yes	—
213	#926	C₂×D₅	1	2	yes	—
214	#926	C₂×D₅	1	2	yes	complemented
215	#926	C₂×D₅	1	2	yes	complemented
216	C₂×C₄⋊Dic₃	—	5	2	no	—
217	C₂×C₄⋊Dic₃	—	5	8	no	—
218	C₂×C₄⋊Dic₃	C₂×D₅	1	2	yes	complemented
219	C₂×C₄×Dic₃	—	5	2	no	—
220	C₂×C₄×Dic₃	—	5	8	no	—
221	C₂×C₄×Dic₃	C₂×D₅	1	2	yes	complemented
222	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
223	C₂³×D₅	C₂²×D₃	1	2	yes	—
224	C₂²×C₄×C₅	—	3	4	no	—
225	C₂²×C₄×C₅	C₂×Dic₃	1	8	yes	complemented
226	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
227	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
229	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₂²⋊D₅	C₂×Dic₃	1	16	yes	complemented
233	C₂×C₂²⋊D₅	C₂²×D₃	1	4	yes	—
234	C₂×C₂²⋊D₅	C₂²×D₃	1	4	yes	—
235	C₂²×Dic₅	—	3	4	no	—
236	C₂²×Dic₅	C₂²×D₃	1	2	yes	—
237	#709	C₂×Dic₃	1	16	yes	complemented
238	#709	C₂×Dic₃	1	16	yes	complemented
239	#709	C₂×Dic₃	1	16	yes	complemented
240	#709	C₂×Dic₃	1	16	yes	complemented
241	C₂×D₂₀	C₂×Dic₃	1	8	yes	complemented
242	C₂×D₂₀	C₂²×D₃	1	2	yes	—
243	C₂×D₂₀	C₂²×D₃	1	2	yes	—
244	C₂×C₄×D₅	—	3	16	no	—
245	C₂×C₄×D₅	C₂×Dic₃	1	16	yes	complemented
246	C₂×C₄×D₅	C₂²×D₃	1	4	yes	—
247	C₂×C₄×D₅	C₂²×D₃	1	4	yes	—
248	C₂×Dic₁₀	C₂×Dic₃	1	8	yes	complemented
249	C₂×Dic₁₀	C₂²×D₃	1	2	yes	—
250	C₂×Dic₁₀	C₂²×D₃	1	2	yes	—
251	C₅×C₄⋊C₄	—	3	4	no	—
252	C₅×C₄⋊C₄	—	3	4	no	—
253	C₅×C₂²⋊C₄	—	3	4	no	—
254	C₅×C₂²⋊C₄	—	3	4	no	—
255	C₄²×C₅	—	3	4	no	—
256	C₄²×C₅	—	3	4	no	—
257	C₂²⋊Dic₅	—	3	4	no	—
258	C₂²⋊Dic₅	—	3	4	no	—
259	#685	—	3	16	no	—
260	C₄⋊Dic₅	—	3	4	no	—
261	C₄⋊Dic₅	—	3	4	no	—
262	#683	—	3	16	no	—
263	C₄×Dic₅	—	3	4	no	—
264	C₄×Dic₅	—	3	4	no	—
265	C₄×Dic₅	—	3	16	no	—
266	C₂²×#41	—	5	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	—	3	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×C₃×D₅	—	2	8	no	—
286	C₂×C₃×D₅	—	4	8	no	—
287	C₂×C₃×D₅	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	C₂³×C₄	1	8	yes	—
294	C₅×Dic₃	—	2	8	no	—
295	C₂⁴×C₃	—	5	2	no	—
296	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
297	C₃×#41	—	5	16	no	—
298	C₃×#41	—	5	16	no	—
299	C₃×#41	—	5	16	no	—
300	C₃×#41	—	5	16	no	—
301	C₂×C₃×Q₈	—	5	8	no	—
302	C₂×C₃×Q₈	—	5	2	no	—
303	C₂×C₃×Q₈	—	5	2	no	—
304	C₂×C₃×D₄	—	5	16	no	—
305	C₂×C₃×D₄	—	5	4	no	—
306	C₂×C₃×D₄	—	5	4	no	—
307	C₂×C₃×D₄	—	5	8	no	—
308	C₂×C₃×D₄	—	5	2	no	—
309	C₂×C₃×D₄	—	5	2	no	—
310	C₂²×C₃×C₄	—	5	2	no	—
311	C₂²×C₃×C₄	—	5	16	no	—
312	C₂²×C₃×C₄	—	5	4	no	—
313	C₂²×C₃×C₄	—	5	4	no	—
314	C₂²×C₃×C₄	C₄×D₅	1	8	yes	complemented
315	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
316	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
317	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
318	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
321	C₂²×Dic₃	—	5	4	no	—
322	C₂²×Dic₃	—	5	16	no	—
323	C₂²×Dic₃	C₂²×D₅	1	4	yes	—
324	#217	—	5	4	no	—
325	#217	—	5	4	no	—
326	#217	—	5	16	no	—
327	#217	C₂²×D₅	1	4	yes	—
328	#217	C₂²×D₅	1	4	yes	—
329	C₄⋊Dic₃	—	5	4	no	—
330	C₄⋊Dic₃	—	5	4	no	—
331	C₄⋊Dic₃	—	5	16	no	—
332	C₄⋊Dic₃	C₂²×D₅	1	4	yes	—
333	C₄⋊Dic₃	C₂²×D₅	1	4	yes	—
334	C₄×Dic₃	—	5	4	no	—
335	C₄×Dic₃	—	5	4	no	—
336	C₄×Dic₃	—	5	16	no	—
337	C₄×Dic₃	C₂²×D₅	1	4	yes	—
338	C₄×Dic₃	C₂²×D₅	1	4	yes	—
339	C₂³×C₅	—	4	2	no	—
340	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
341	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
342	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
343	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
344	C₂²×D₅	—	4	4	no	—
345	C₂²×D₅	C₂²×Dic₃	1	8	yes	—
346	C₂²×D₅	C₂³×D₃	1	4	yes	—
347	C₂×C₄×C₅	—	3	8	no	—
348	C₂×C₄×C₅	—	12	4	no	—
349	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
350	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
351	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
352	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
353	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
354	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
355	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
356	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
357	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
359	C₂²⋊D₅	C₂²×Dic₃	1	16	yes	—
360	C₂²⋊D₅	C₂²×Dic₃	1	16	yes	—
361	C₂×Dic₅	—	3	8	no	—
362	C₂×Dic₅	—	12	4	no	—
363	C₂×Dic₅	C₂²×Dic₃	1	8	yes	—
364	C₂×Dic₅	C₂³×D₃	1	4	yes	—
365	D₂₀	C₂²×Dic₃	1	8	yes	—
366	D₂₀	C₂²×Dic₃	1	8	yes	—
367	C₄×D₅	—	12	16	no	—
368	C₄×D₅	C₂²×Dic₃	1	16	yes	—
369	C₄×D₅	C₂²×Dic₃	1	16	yes	—
370	Dic₁₀	C₂²×Dic₃	1	8	yes	—
371	Dic₁₀	C₂²×Dic₃	1	8	yes	—
372	C₂×#41	—	5	16	no	—
373	C₂×#41	—	5	2	no	—
374	C₂×#41	—	5	2	no	—
375	C₂×#41	—	5	2	no	—
376	C₂×#41	—	5	2	no	—
377	C₂²×Q₈	—	5	1	no	—
378	C₂²×D₄	—	5	2	no	—
379	C₂²×D₄	—	5	1	no	—
380	C₂³×C₄	—	5	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	—	3	2	no	—
389	#117	—	3	2	no	—
390	#117	—	3	2	no	—
391	#117	—	3	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	—	3	2	no	—
400	C₂×C₄⋊C₄	—	15	8	no	—
401	C₂×C₄⋊C₄	—	15	2	no	—
402	C₂×C₂²⋊C₄	—	3	2	no	—
403	C₂×C₂²⋊C₄	—	15	8	no	—
404	C₂×C₂²⋊C₄	—	15	2	no	—
405	C₂×C₄²	—	3	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	C₃×D₅	—	2	8	no	—
414	C₂³×C₃	—	4	2	no	—
415	C₂³×C₃	—	5	4	no	—
416	C₂³×C₃	—	5	8	no	—
417	C₂³×C₃	—	20	4	no	—
418	C₂³×C₃	C₂×C₄×D₅	1	4	yes	—
419	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
420	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
421	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
422	C₃×Q₈	—	5	8	no	—
423	C₃×Q₈	—	5	8	no	—
424	C₃×D₄	—	5	16	no	—
425	C₃×D₄	—	5	16	no	—
426	C₃×D₄	—	5	8	no	—
427	C₃×D₄	—	5	8	no	—
428	C₂×C₃×C₄	—	5	8	no	—
429	C₂×C₃×C₄	—	5	4	no	—
430	C₂×C₃×C₄	—	5	16	no	—
431	C₂×C₃×C₄	—	5	16	no	—
432	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
433	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
434	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
435	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
436	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
437	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
438	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
439	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
440	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
441	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
442	C₂×Dic₃	—	4	4	no	—
443	C₂×Dic₃	—	5	8	no	—
444	C₂×Dic₃	—	20	16	no	—
445	C₂×Dic₃	—	20	4	no	—
446	C₂×Dic₃	C₂³×D₅	1	8	yes	—
447	C₂²×C₅	—	2	2	no	—
448	C₂²×C₅	—	2	2	no	—
449	C₂²×C₅	—	2	2	no	—
450	C₂²×C₅	—	4	4	no	—
451	C₂²×C₅	C₂³×Dic₃	1	2	yes	—
452	C₂²×C₅	C₂³×Dic₃	1	2	yes	—
453	C₂²×C₅	C₂³×Dic₃	1	2	yes	—
454	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
455	C₂×D₅	—	2	8	no	—
456	C₂×D₅	—	4	8	no	—
457	C₂×D₅	C₂³×Dic₃	1	8	yes	—
458	C₄×C₅	—	6	8	no	—
459	C₄×C₅	C₂³×Dic₃	1	2	yes	—
460	C₄×C₅	C₂³×Dic₃	1	2	yes	—
461	C₄×C₅	C₂³×Dic₃	1	2	yes	—
462	C₄×C₅	C₂³×Dic₃	1	2	yes	—
463	Dic₅	—	6	8	no	—
464	Dic₅	C₂³×Dic₃	1	8	yes	—
465	C₂⁴	—	5	2	no	—
466	C₂⁴	C₂×D₃×D₅	1	1	yes	characteristic
467	#41	—	5	16	no	—
468	#41	—	5	16	no	—
469	#41	—	5	16	no	—
470	#41	—	5	16	no	—
471	C₂×Q₈	—	5	8	no	—
472	C₂×Q₈	—	5	2	no	—
473	C₂×Q₈	—	5	2	no	—
474	C₂×D₄	—	5	16	no	—
475	C₂×D₄	—	5	4	no	—
476	C₂×D₄	—	5	4	no	—
477	C₂×D₄	—	5	8	no	—
478	C₂×D₄	—	5	2	no	—
479	C₂×D₄	—	5	2	no	—
480	C₂²×C₄	—	3	4	no	—
481	C₂²×C₄	—	5	2	no	—
482	C₂²×C₄	—	5	16	no	—
483	C₂²×C₄	—	5	4	no	—
484	C₂²×C₄	—	5	4	no	—
485	C₂²×C₄	—	15	16	no	—
486	C₂²×C₄	—	15	4	no	—
487	C₂²×C₄	D₅×Dic₃	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	—	3	4	no	—
495	C₄⋊C₄	—	3	4	no	—
496	C₄⋊C₄	—	15	16	no	—
497	C₄⋊C₄	—	15	4	no	—
498	C₄⋊C₄	—	15	4	no	—
499	C₂²⋊C₄	—	3	4	no	—
500	C₂²⋊C₄	—	3	4	no	—
501	C₂²⋊C₄	—	15	16	no	—
502	C₂²⋊C₄	—	15	4	no	—
503	C₂²⋊C₄	—	15	4	no	—
504	C₄²	—	3	4	no	—
505	C₄²	—	3	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	—	5	8	no	—
515	C₂²×C₃	—	10	8	no	—
516	C₂²×C₃	—	20	8	no	—
517	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
518	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
519	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
520	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
521	C₃×C₄	—	5	8	no	—
522	C₃×C₄	C₂²×C₄×D₅	1	2	yes	—
523	C₃×C₄	C₂²×C₄×D₅	1	2	yes	—
524	C₃×C₄	C₂²×C₄×D₅	1	2	yes	—
525	C₃×C₄	C₂²×C₄×D₅	1	2	yes	—
526	Dic₃	—	2	8	no	—
527	Dic₃	—	10	8	no	—
528	C₂×C₅	—	2	2	no	—
529	C₂×C₅	—	2	2	no	—
530	C₂×C₅	—	2	2	no	—
531	C₂×C₅	#5964	1	2	yes	—
532	C₂×C₅	C₂⁴×Dic₃	1	1	yes	characteristic
533	D₅	—	2	8	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	5	4	no	—
536	C₂³	—	5	8	no	—
537	C₂³	—	20	4	no	—
538	C₂³	C₂×D₅×Dic₃	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	—	5	8	no	—
543	Q₈	—	5	8	no	—
544	D₄	—	5	16	no	—
545	D₄	—	5	16	no	—
546	D₄	—	5	8	no	—
547	D₄	—	5	8	no	—
548	C₂×C₄	—	3	8	no	—
549	C₂×C₄	—	5	8	no	—
550	C₂×C₄	—	5	4	no	—
551	C₂×C₄	—	5	16	no	—
552	C₂×C₄	—	5	16	no	—
553	C₂×C₄	—	12	4	no	—
554	C₂×C₄	—	15	8	no	—
555	C₂×C₄	—	60	16	no	—
556	C₂×C₄	—	60	4	no	—
557	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
558	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
559	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
560	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
561	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
562	C₂×C₄	C₂×D₅×Dic₃	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	—	10	8	no	—
571	C₂×C₃	C₂³×C₄×D₅	1	1	yes	characteristic
572	C₂×C₃	#66283	1	2	yes	—
573	C₅	#87260	1	1	yes	characteristic, complemented, Sylow
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	5	8	no	—
579	C₂²	—	10	8	no	—
580	C₂²	—	20	8	no	—
581	C₂²	C₂²×D₅×Dic₃	1	2	yes	—
582	C₂²	C₂²×D₅×Dic₃	1	2	yes	—
583	C₂²	C₂²×D₅×Dic₃	1	2	yes	—
584	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
585	C₄	—	5	8	no	—
586	C₄	—	6	8	no	—
587	C₄	—	30	8	no	—
588	C₄	C₂²×D₅×Dic₃	1	2	yes	—
589	C₄	C₂²×D₅×Dic₃	1	2	yes	—
590	C₄	C₂²×D₅×Dic₃	1	2	yes	—
591	C₄	C₂²×D₅×Dic₃	1	2	yes	—
592	C₃	#10617632	1	1	yes	characteristic, complemented, Sylow
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	2	2	no	—
596	C₂	—	10	8	no	—
597	C₂	#11757022	1	2	yes	—
598	C₂	C₂³×D₅×Dic₃	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×C₃×#709	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×C₅×#926	C₂	semidirect
4. #11755406	C₂	semidirect
5. #11754509	C₂	semidirect
6. #11754499	C₂	semidirect
7. #11754488	C₂	semidirect
8. #11754444	C₂	semidirect
9. Dic₃×#709	C₂	semidirect
10. D₅×#926	C₂	semidirect
11. #11754188	C₂	semidirect
15. C₂×C₃×#709	C₄	semidirect
26. #91815	C₂²	semidirect
27. #91815	C₂²	semidirect
28. C₂×C₄⋊Dic₁₅	C₂²	semidirect
29. C₂×C₄×Dic₁₅	C₂²	semidirect
33. C₅×#926	C₂²	semidirect
34. C₅×#926	C₂²	semidirect
35. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
36. C₂×C₄×C₅×Dic₃	C₂²	semidirect
37. #91559	C₂²	semidirect
38. Dic₃×C₂²⋊D₅	C₂²	semidirect
41. #91434	C₂²	semidirect
42. Dic₃×D₂₀	C₂²	semidirect
43. D₅×C₄⋊Dic₃	C₂²	semidirect
44. C₄×D₅×Dic₃	C₂²	semidirect
45. #91358	C₂²	semidirect
46. #91357	C₂²	semidirect
47. #91331	C₂²	semidirect
48. Dic₃×Dic₁₀	C₂²	semidirect
63. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
72. C₂×C₃×C₂²⋊D₅	C₂×C₄	semidirect
76. C₃×#709	C₂×C₄	semidirect
77. C₃×#709	C₂×C₄	semidirect
78. C₃×#709	C₂×C₄	semidirect
79. C₃×#709	C₂×C₄	semidirect
80. C₂×C₃×D₂₀	C₂×C₄	semidirect
83. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
86. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
115. C₂×#926	D₅	semidirect
118. C₂×#709	Dic₃	semidirect
214. #926	C₂×D₅	semidirect
215. #926	C₂×D₅	semidirect
218. C₂×C₄⋊Dic₃	C₂×D₅	semidirect
221. C₂×C₄×Dic₃	C₂×D₅	semidirect
225. C₂²×C₄×C₅	C₂×Dic₃	semidirect
232. C₂×C₂²⋊D₅	C₂×Dic₃	semidirect
237. #709	C₂×Dic₃	semidirect
238. #709	C₂×Dic₃	semidirect
239. #709	C₂×Dic₃	semidirect
240. #709	C₂×Dic₃	semidirect
241. C₂×D₂₀	C₂×Dic₃	semidirect
245. C₂×C₄×D₅	C₂×Dic₃	semidirect
248. C₂×Dic₁₀	C₂×Dic₃	semidirect
314. C₂²×C₃×C₄	C₄×D₅	semidirect
487. C₂²×C₄	D₅×Dic₃	semidirect
509. C₃×C₅	#3428	semidirect
573. C₅	#87260	semidirect
592. C₃	#10617632	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×#709	2
C₂×#91815	2
C₂×C₅×#926	2
#11755406	2
#11754509	2
#11754499	2
#11754488	2
#11754444	2
Dic₃×#709	2
D₅×#926	2
#11754188	2
#10617632	3
#87260	5