Subgroups — #11754629

Order 960.

676 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6790	C₂	1	1	yes	maximal, characteristic
2	C₂×#6714	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	#91561	C₂	1	1	yes	maximal, characteristic, complemented
6	#67⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
7	#91559	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×#685	C₂	1	1	yes	maximal, characteristic, complemented
9	D₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#91446	C₂	1	1	yes	maximal, characteristic, complemented
11	#91444	C₂	1	1	yes	maximal, characteristic, complemented
12	#91405	C₂	1	1	yes	maximal, characteristic, complemented
13	#91403	C₂	1	1	yes	maximal, characteristic, complemented
14	#91402	C₂	1	1	yes	maximal, characteristic, complemented
15	#91395	C₂	1	1	yes	maximal, characteristic, complemented
16	#65879	—	3	1	no	maximal, Hall
17	C₂³×D₁₅	C₂²	1	1	yes	characteristic
18	C₂²×D₃×D₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
20	C₂²×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
25	#6790	C₄	1	8	yes	complemented
26	C₂×#1203	C₂²	1	1	yes	characteristic
27	C₂×#1202	C₂²	1	1	yes	characteristic
28	C₂×#1200	C₂²	1	1	yes	characteristic
29	C₂×#1200	C₂²	1	1	yes	characteristic, complemented
30	C₂×#1200	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
32	C₂×D₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
33	#6714	C₂²	1	1	yes	characteristic
34	#6714	C₂²	1	1	yes	characteristic
35	#6714	C₂²	1	1	yes	characteristic, complemented
36	#6714	C₂²	1	1	yes	characteristic, complemented
37	C₅×#217	C₂²	1	1	yes	characteristic, complemented
38	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
42	C₃×#685	C₂²	1	1	yes	characteristic, complemented
43	C₃×#683	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
45	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
46	#6668	C₂²	1	1	yes	characteristic, complemented
47	#6667	C₂²	1	1	yes	characteristic
48	#6667	C₂²	1	1	yes	characteristic
49	(C₂×D₃)⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
50	#6665	C₂²	1	1	yes	characteristic, complemented
51	Dic₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
52	Dic₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
53	#5545	—	5	1	no	maximal, Hall
54	C₂×D₄×D₅	—	3	1	no	—
55	C₄×C₅×D₄	—	3	1	no	—
56	D₄×Dic₅	—	3	1	no	—
57	C₄×C₂²⋊D₅	—	3	1	no	—
58	C₄×C₂²⋊D₅	D₃	1	1	yes	characteristic, complemented
59	C₂×#685	—	3	1	no	—
60	C₂×#685	—	3	1	no	—
61	#4039	—	3	1	no	—
62	#4038	—	3	1	no	—
63	#4027	—	3	1	no	—
64	#4027	—	3	1	no	—
65	D₅×C₂²⋊C₄	—	3	1	no	—
66	D₅×C₂²⋊C₄	—	3	1	no	—
67	C₄×D₂₀	—	3	1	no	—
68	#4018	—	3	1	no	—
69	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂²×D₁₅	—	4	1	no	—
71	C₂²×D₁₅	—	4	1	no	—
72	C₂²×D₁₅	C₂×C₄	1	4	yes	complemented
73	C₂²×D₁₅	C₂³	1	1	yes	characteristic
74	C₂²×D₁₅	C₂³	1	1	yes	characteristic
75	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
76	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
77	C₂×D₃×D₅	—	4	1	no	—
78	C₂×D₃×D₅	—	4	1	no	—
79	C₂×D₃×D₅	C₂×C₄	1	4	yes	complemented
80	C₂×C₃×C₄×C₅	—	4	1	no	—
81	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂×Dic₁₅	—	4	1	no	—
84	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
85	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
86	C₅×#67	C₂×C₄	1	4	yes	complemented
87	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
88	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
89	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
90	C₄×C₅×D₃	—	4	1	no	—
91	C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	complemented
92	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
93	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
94	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
95	C₃×C₄×D₅	—	4	1	no	—
96	#1203	C₂×C₄	1	4	yes	complemented
97	#1202	C₂×C₄	1	4	yes	complemented
98	#1200	—	4	1	no	—
99	#1200	—	4	1	no	—
100	#1200	C₂×C₄	1	4	yes	complemented
101	D₃×Dic₅	—	4	1	no	—
102	D₅×Dic₃	—	4	1	no	—
103	C₂×D₃×D₄	—	5	1	no	—
104	C₃×C₄×D₄	—	5	1	no	—
105	D₄×Dic₃	—	5	1	no	—
106	C₄×#67	—	5	1	no	—
107	C₄×#67	D₅	1	1	yes	characteristic, complemented
108	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
109	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
110	#893	—	5	1	no	—
111	#892	—	5	1	no	—
112	#67⋊C₄	—	5	1	no	—
113	#67⋊C₄	—	5	1	no	—
114	D₃×C₂²⋊C₄	—	5	1	no	—
115	D₃×C₂²⋊C₄	—	5	1	no	—
116	C₄×D₁₂	—	5	1	no	—
117	#872	—	5	1	no	—
118	C₂³×D₅	—	3	1	no	—
119	C₂³×D₅	—	3	1	no	—
120	C₂×C₅×D₄	—	3	1	no	—
121	C₂²×C₄×C₅	—	3	1	no	—
122	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
123	C₂×C₂²⋊D₅	—	3	1	no	—
124	C₂×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
125	C₂²×Dic₅	—	3	1	no	—
126	C₂²×Dic₅	—	3	1	no	—
127	D₄×D₅	—	3	8	no	—
128	C₂×D₂₀	—	3	1	no	—
129	C₂×C₄×D₅	—	3	1	no	—
130	C₂×C₄×D₅	—	3	1	no	—
131	C₂×C₄×D₅	—	3	1	no	—
132	C₂×C₄×D₅	—	3	1	no	—
133	C₂×C₄×D₅	C₂×D₃	1	1	yes	characteristic, complemented
134	C₅×C₄⋊C₄	—	3	1	no	—
135	C₅×C₂²⋊C₄	—	3	1	no	—
136	C₅×C₂²⋊C₄	—	3	1	no	—
137	C₄²×C₅	—	3	1	no	—
138	C₂²⋊Dic₅	—	3	1	no	—
139	C₂²⋊Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
140	#685	—	3	1	no	—
141	#685	—	3	1	no	—
142	#685	—	3	1	no	—
143	#685	—	3	1	no	—
144	#685	—	3	1	no	—
145	#685	—	3	1	no	—
146	#685	—	3	1	no	—
147	#685	C₂×D₃	1	1	yes	characteristic, complemented
148	C₄⋊Dic₅	—	3	1	no	—
149	#683	—	3	1	no	—
150	#683	C₂×D₃	1	1	yes	characteristic, complemented
151	C₄×Dic₅	—	3	1	no	—
152	C₄×Dic₅	—	3	1	no	—
153	C₄×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
154	#518	—	15	1	no	Sylow
155	C₂²×C₃×C₅	—	2	1	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	C₂²×C₄	1	2	yes	—
158	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
159	C₂×D₁₅	—	2	1	no	—
160	C₂×D₁₅	—	2	1	no	—
161	C₂×D₁₅	—	2	1	no	—
162	C₂×D₁₅	—	2	1	no	—
163	C₂×D₁₅	—	4	4	no	—
164	C₂×D₁₅	C₂²×C₄	1	2	yes	—
165	C₂×D₁₅	C₂²×C₄	1	2	yes	—
166	C₂×C₅×D₃	—	2	1	no	—
167	C₂×C₅×D₃	—	2	1	no	—
168	C₂×C₅×D₃	C₂²×C₄	1	2	yes	—
169	C₂×C₃×D₅	—	2	1	no	—
170	C₂×C₃×D₅	—	2	1	no	—
171	C₂×C₃×D₅	C₂²×C₄	1	2	yes	—
172	D₃×D₅	—	4	4	no	—
173	C₃×C₄×C₅	—	2	1	no	—
174	C₃×C₄×C₅	—	2	1	no	—
175	Dic₁₅	—	2	1	no	—
176	Dic₁₅	—	2	1	no	—
177	C₃×Dic₅	—	2	1	no	—
178	C₃×Dic₅	—	2	1	no	—
179	C₃×Dic₅	C₂²×C₄	1	2	yes	—
180	C₅×Dic₃	—	2	1	no	—
181	C₅×Dic₃	—	2	1	no	—
182	C₅×Dic₃	C₂²×C₄	1	2	yes	—
183	C₂³×D₃	—	5	1	no	—
184	C₂³×D₃	—	5	1	no	—
185	C₂×C₃×D₄	—	5	1	no	—
186	C₂²×C₃×C₄	—	5	1	no	—
187	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
188	C₂×#67	—	5	1	no	—
189	C₂×#67	C₂×D₅	1	1	yes	characteristic
190	C₂²×Dic₃	—	5	1	no	—
191	C₂²×Dic₃	—	5	1	no	—
192	D₃×D₄	—	5	8	no	—
193	C₂×D₁₂	—	5	1	no	—
194	C₂×C₄×D₃	—	5	1	no	—
195	C₂×C₄×D₃	—	5	1	no	—
196	C₂×C₄×D₃	—	5	1	no	—
197	C₂×C₄×D₃	—	5	1	no	—
198	C₂×C₄×D₃	C₂×D₅	1	1	yes	characteristic, complemented
199	C₃×C₄⋊C₄	—	5	1	no	—
200	C₃×C₂²⋊C₄	—	5	1	no	—
201	C₃×C₂²⋊C₄	—	5	1	no	—
202	C₃×C₄²	—	5	1	no	—
203	#217	—	5	1	no	—
204	#217	C₂×D₅	1	1	yes	characteristic, complemented
205	(C₂×D₃)⋊C₄	—	5	1	no	—
206	(C₂×D₃)⋊C₄	—	5	1	no	—
207	(C₂×D₃)⋊C₄	—	5	1	no	—
208	(C₂×D₃)⋊C₄	—	5	1	no	—
209	(C₂×D₃)⋊C₄	—	5	1	no	—
210	(C₂×D₃)⋊C₄	—	5	1	no	—
211	(C₂×D₃)⋊C₄	—	5	1	no	—
212	(C₂×D₃)⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
213	C₄⋊Dic₃	—	5	1	no	—
214	Dic₃⋊C₄	—	5	1	no	—
215	Dic₃⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
216	C₄×Dic₃	—	5	1	no	—
217	C₄×Dic₃	—	5	1	no	—
218	C₄×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
219	C₂³×C₅	—	3	1	no	—
220	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
221	C₂²×D₅	—	3	1	no	—
222	C₂²×D₅	—	3	1	no	—
223	C₂²×D₅	—	3	4	no	—
224	C₂²×D₅	—	3	4	no	—
225	C₂²×D₅	—	12	1	no	—
226	C₂²×D₅	—	12	1	no	—
227	C₂²×D₅	—	12	1	no	—
228	C₂²×D₅	—	12	1	no	—
229	C₂²×D₅	C₂²×D₃	1	1	yes	characteristic
230	C₅×D₄	—	3	4	no	—
231	C₂×C₄×C₅	—	3	1	no	—
232	C₂×C₄×C₅	—	3	1	no	—
233	C₂×C₄×C₅	—	3	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	12	1	no	—
236	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
238	C₂²⋊D₅	—	3	4	no	—
239	C₂²⋊D₅	C₄×D₃	1	4	yes	complemented
240	C₂×Dic₅	—	3	1	no	—
241	C₂×Dic₅	—	3	1	no	—
242	C₂×Dic₅	—	12	1	no	—
243	C₂×Dic₅	—	12	1	no	—
244	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
245	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
246	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
247	D₂₀	—	3	4	no	—
248	C₄×D₅	—	3	4	no	—
249	C₄×D₅	—	4	1	no	—
250	C₄×D₅	—	12	1	no	—
251	C₄×D₅	—	12	1	no	—
252	C₄×D₅	—	12	1	no	—
253	C₂²×D₄	—	15	1	no	—
254	C₄×D₄	—	3	1	no	—
255	C₄×D₄	—	5	1	no	—
256	C₄×D₄	—	15	1	no	—
257	C₄×D₄	—	15	1	no	—
258	C₄×D₄	—	15	1	no	—
259	C₄×D₄	—	15	1	no	—
260	C₄×D₄	—	15	1	no	—
261	C₄×D₄	—	15	1	no	—
262	#117	—	15	1	no	—
263	#117	—	15	1	no	—
264	C₂×C₂²⋊C₄	—	15	1	no	—
265	C₂×C₂²⋊C₄	—	15	1	no	—
266	C₂×C₂²⋊C₄	—	15	1	no	—
267	C₂×C₂²⋊C₄	—	15	1	no	—
268	C₂×C₃×C₅	—	2	2	no	—
269	C₂×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
271	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
272	D₁₅	—	2	2	no	—
273	D₁₅	—	2	2	no	—
274	C₃×D₅	—	2	2	no	—
275	C₅×D₃	—	2	2	no	—
276	C₂³×C₃	—	5	1	no	—
277	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
278	C₂²×D₃	—	5	1	no	—
279	C₂²×D₃	—	5	1	no	—
280	C₂²×D₃	—	5	4	no	—
281	C₂²×D₃	—	5	4	no	—
282	C₂²×D₃	—	20	1	no	—
283	C₂²×D₃	—	20	1	no	—
284	C₂²×D₃	—	20	1	no	—
285	C₂²×D₃	—	20	1	no	—
286	C₂²×D₃	C₂²×D₅	1	1	yes	characteristic
287	C₃×D₄	—	5	4	no	—
288	C₂×C₃×C₄	—	4	1	no	—
289	C₂×C₃×C₄	—	5	1	no	—
290	C₂×C₃×C₄	—	5	1	no	—
291	C₂×C₃×C₄	—	5	1	no	—
292	C₂×C₃×C₄	—	20	1	no	—
293	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
295	#67	—	5	4	no	—
296	#67	C₄×D₅	1	4	yes	complemented
297	C₂×Dic₃	—	5	1	no	—
298	C₂×Dic₃	—	5	1	no	—
299	C₂×Dic₃	—	20	1	no	—
300	C₂×Dic₃	—	20	1	no	—
301	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
302	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
303	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
304	D₁₂	—	5	4	no	—
305	C₄×D₃	—	4	1	no	—
306	C₄×D₃	—	5	4	no	—
307	C₄×D₃	—	20	1	no	—
308	C₄×D₃	—	20	1	no	—
309	C₄×D₃	—	20	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	3	2	no	—
313	C₂²×C₅	—	6	1	no	—
314	C₂²×C₅	—	6	1	no	—
315	C₂²×C₅	C₂×C₄×D₃	1	2	yes	—
316	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
317	C₂×D₅	—	2	1	no	—
318	C₂×D₅	—	2	1	no	—
319	C₂×D₅	—	3	2	no	—
320	C₂×D₅	—	3	2	no	—
321	C₂×D₅	—	6	1	no	—
322	C₂×D₅	—	6	1	no	—
323	C₂×D₅	—	6	1	no	—
324	C₂×D₅	—	6	1	no	—
325	C₂×D₅	—	12	4	no	—
326	C₂×D₅	—	12	4	no	—
327	C₂×D₅	C₂×C₄×D₃	1	2	yes	—
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	3	2	no	—
331	C₄×C₅	—	6	1	no	—
332	C₄×C₅	—	6	1	no	—
333	Dic₅	—	2	1	no	—
334	Dic₅	—	2	1	no	—
335	Dic₅	—	6	1	no	—
336	Dic₅	—	6	1	no	—
337	Dic₅	C₂×C₄×D₃	1	2	yes	—
338	C₂⁴	—	15	1	no	—
339	C₂⁴	—	15	1	no	—
340	C₂×D₄	—	3	1	no	—
341	C₂×D₄	—	5	1	no	—
342	C₂×D₄	—	15	1	no	—
343	C₂×D₄	—	15	1	no	—
344	C₂×D₄	—	15	8	no	—
345	C₂²×C₄	—	3	1	no	—
346	C₂²×C₄	—	5	1	no	—
347	C₂²×C₄	—	15	1	no	—
348	C₂²×C₄	—	15	1	no	—
349	C₂²×C₄	—	15	1	no	—
350	C₂²×C₄	—	15	1	no	—
351	C₂²×C₄	—	15	1	no	—
352	C₂²×C₄	—	15	1	no	—
353	C₂²×C₄	D₃×D₅	1	1	yes	characteristic, complemented
354	C₄⋊C₄	—	3	1	no	—
355	C₄⋊C₄	—	5	1	no	—
356	C₄⋊C₄	—	15	1	no	—
357	C₄⋊C₄	—	15	1	no	—
358	C₂²⋊C₄	—	3	1	no	—
359	C₂²⋊C₄	—	3	1	no	—
360	C₂²⋊C₄	—	5	1	no	—
361	C₂²⋊C₄	—	5	1	no	—
362	C₂²⋊C₄	—	15	1	no	—
363	C₂²⋊C₄	—	15	1	no	—
364	C₂²⋊C₄	—	15	1	no	—
365	C₂²⋊C₄	—	15	1	no	—
366	C₂²⋊C₄	—	15	1	no	—
367	C₂²⋊C₄	—	15	1	no	—
368	C₂²⋊C₄	—	15	1	no	—
369	C₂²⋊C₄	—	15	1	no	—
370	C₄²	—	3	1	no	—
371	C₄²	—	5	1	no	—
372	C₄²	—	15	1	no	—
373	C₄²	—	15	1	no	—
374	C₃×C₅	#518	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	—	5	2	no	—
378	C₂²×C₃	—	10	1	no	—
379	C₂²×C₃	—	10	1	no	—
380	C₂²×C₃	C₂×C₄×D₅	1	2	yes	—
381	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
382	C₂×D₃	—	2	1	no	—
383	C₂×D₃	—	2	1	no	—
384	C₂×D₃	—	5	2	no	—
385	C₂×D₃	—	5	2	no	—
386	C₂×D₃	—	10	1	no	—
387	C₂×D₃	—	10	1	no	—
388	C₂×D₃	—	10	1	no	—
389	C₂×D₃	—	10	1	no	—
390	C₂×D₃	—	20	4	no	—
391	C₂×D₃	—	20	4	no	—
392	C₂×D₃	C₂×C₄×D₅	1	2	yes	—
393	C₃×C₄	—	2	1	no	—
394	C₃×C₄	—	2	1	no	—
395	C₃×C₄	—	5	2	no	—
396	C₃×C₄	—	10	1	no	—
397	C₃×C₄	—	10	1	no	—
398	Dic₃	—	2	1	no	—
399	Dic₃	—	2	1	no	—
400	Dic₃	—	10	1	no	—
401	Dic₃	—	10	1	no	—
402	Dic₃	C₂×C₄×D₅	1	2	yes	—
403	C₂×C₅	—	2	2	no	—
404	C₂×C₅	—	6	2	no	—
405	C₂×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
406	C₂×C₅	#1004	1	1	yes	characteristic
407	C₂×C₅	#1009	1	1	yes	characteristic
408	D₅	—	2	2	no	—
409	D₅	—	6	2	no	—
410	D₅	—	6	2	no	—
411	C₂³	—	3	1	no	—
412	C₂³	—	5	1	no	—
413	C₂³	—	15	4	no	—
414	C₂³	—	15	1	no	—
415	C₂³	—	15	1	no	—
416	C₂³	—	15	4	no	—
417	C₂³	—	60	1	no	—
418	C₂³	—	60	1	no	—
419	C₂³	—	60	1	no	—
420	C₂³	—	60	1	no	—
421	C₂³	C₂×D₃×D₅	1	1	yes	characteristic
422	D₄	—	3	4	no	—
423	D₄	—	5	4	no	—
424	D₄	—	15	4	no	—
425	D₄	—	15	4	no	—
426	C₂×C₄	—	3	1	no	—
427	C₂×C₄	—	3	1	no	—
428	C₂×C₄	—	3	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	5	1	no	—
431	C₂×C₄	—	5	1	no	—
432	C₂×C₄	—	5	1	no	—
433	C₂×C₄	—	12	1	no	—
434	C₂×C₄	—	15	4	no	—
435	C₂×C₄	—	15	1	no	—
436	C₂×C₄	—	15	1	no	—
437	C₂×C₄	—	20	1	no	—
438	C₂×C₄	—	60	1	no	—
439	C₂×C₄	—	60	1	no	—
440	C₂×C₄	—	60	1	no	—
441	C₂×C₄	—	60	1	no	—
442	C₂×C₄	—	60	1	no	—
443	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
444	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
445	C₂×C₃	—	2	2	no	—
446	C₂×C₃	—	10	2	no	—
447	C₂×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
448	C₂×C₃	#4144	1	1	yes	characteristic
449	C₂×C₃	#4149	1	1	yes	characteristic
450	D₃	—	2	2	no	—
451	D₃	—	10	2	no	—
452	D₃	—	10	2	no	—
453	C₅	#5545	1	1	yes	characteristic, complemented, Sylow
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	3	2	no	—
457	C₂²	—	5	2	no	—
458	C₂²	—	6	1	no	—
459	C₂²	—	6	1	no	—
460	C₂²	—	10	1	no	—
461	C₂²	—	10	1	no	—
462	C₂²	—	15	2	no	—
463	C₂²	—	15	2	no	—
464	C₂²	—	30	1	no	—
465	C₂²	—	30	1	no	—
466	C₂²	—	30	1	no	—
467	C₂²	—	30	1	no	—
468	C₂²	—	60	4	no	—
469	C₂²	—	60	4	no	—
470	C₂²	C₄×D₃×D₅	1	2	yes	—
471	C₂²	C₂²×D₃×D₅	1	1	yes	characteristic
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	3	2	no	—
475	C₄	—	5	2	no	—
476	C₄	—	6	1	no	—
477	C₄	—	6	1	no	—
478	C₄	—	10	1	no	—
479	C₄	—	10	1	no	—
480	C₄	—	30	1	no	—
481	C₄	—	30	1	no	—
482	C₃	#65879	1	1	yes	characteristic, complemented, Sylow
483	C₂	—	2	2	no	—
484	C₂	—	6	2	no	—
485	C₂	—	10	2	no	—
486	C₂	—	30	2	no	—
487	C₂	—	30	2	no	—
488	C₂	C₂×C₄×D₃×D₅	1	1	yes	characteristic
489	C₂	#92019	1	1	yes	characteristic
490	C₂	#92049	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₄
Fitting	C₂²×C₃×C₄×C₅	C₂²
socle, cosocle	C₂²×C₃×C₅	C₂⁴
prime radical	C₂×#6790	C₂
hypercenter	C₂²×C₄	D₃×D₅
hypocenter	C₃×C₅	#518
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#6714	C₂	semidirect
3. C₄×C₅×#67	C₂	semidirect
4. C₃×C₄×C₂²⋊D₅	C₂	semidirect
5. #91561	C₂	semidirect
6. #67⋊Dic₅	C₂	semidirect
7. #91559	C₂	semidirect
8. D₃×#685	C₂	semidirect
9. D₅×(C₂×D₃)⋊C₄	C₂	semidirect
10. #91446	C₂	semidirect
11. #91444	C₂	semidirect
12. #91405	C₂	semidirect
13. #91403	C₂	semidirect
14. #91402	C₂	semidirect
15. #91395	C₂	semidirect
19. C₂²×C₃×C₄×C₅	C₂²	semidirect
20. C₂²×Dic₁₅	C₂²	semidirect
22. C₂×C₄×C₅×D₃	C₂²	semidirect
24. C₂×C₃×C₄×D₅	C₂²	semidirect
25. #6790	C₄	semidirect
29. C₂×#1200	C₂²	semidirect
30. C₂×#1200	C₂²	semidirect
31. C₂×D₃×Dic₅	C₂²	semidirect
32. C₂×D₅×Dic₃	C₂²	semidirect
35. #6714	C₂²	semidirect
36. #6714	C₂²	semidirect
37. C₅×#217	C₂²	semidirect
38. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
39. C₅×Dic₃⋊C₄	C₂²	semidirect
40. C₄×C₅×Dic₃	C₂²	semidirect
41. C₃×C₂²⋊Dic₅	C₂²	semidirect
42. C₃×#685	C₂²	semidirect
43. C₃×#683	C₂²	semidirect
44. C₃×C₄×Dic₅	C₂²	semidirect
45. Dic₃⋊Dic₅	C₂²	semidirect
46. #6668	C₂²	semidirect
49. (C₂×D₃)⋊Dic₅	C₂²	semidirect
50. #6665	C₂²	semidirect
51. Dic₃×Dic₅	C₂²	semidirect
52. Dic₃×Dic₅	C₂²	semidirect
58. C₄×C₂²⋊D₅	D₃	semidirect
72. C₂²×D₁₅	C₂×C₄	semidirect
79. C₂×D₃×D₅	C₂×C₄	semidirect
86. C₅×#67	C₂×C₄	semidirect
91. C₃×C₂²⋊D₅	C₂×C₄	semidirect
96. #1203	C₂×C₄	semidirect
97. #1202	C₂×C₄	semidirect
100. #1200	C₂×C₄	semidirect
107. C₄×#67	D₅	semidirect
122. C₂²×C₄×C₅	C₂×D₃	semidirect
133. C₂×C₄×D₅	C₂×D₃	semidirect
139. C₂²⋊Dic₅	C₂×D₃	semidirect
147. #685	C₂×D₃	semidirect
150. #683	C₂×D₃	semidirect
153. C₄×Dic₅	C₂×D₃	semidirect
187. C₂²×C₃×C₄	C₂×D₅	semidirect
198. C₂×C₄×D₃	C₂×D₅	semidirect
204. #217	C₂×D₅	semidirect
212. (C₂×D₃)⋊C₄	C₂×D₅	semidirect
215. Dic₃⋊C₄	C₂×D₅	semidirect
218. C₄×Dic₃	C₂×D₅	semidirect
239. C₂²⋊D₅	C₄×D₃	semidirect
296. #67	C₄×D₅	semidirect
353. C₂²×C₄	D₃×D₅	semidirect
374. C₃×C₅	#518	semidirect
453. C₅	#5545	semidirect
482. C₃	#65879	semidirect

Maximal subgroups

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

subgroup	index
C₂×#6790	2
C₂×#6714	2
C₄×C₅×#67	2
C₃×C₄×C₂²⋊D₅	2
#91561	2
#67⋊Dic₅	2
#91559	2
D₃×#685	2
D₅×(C₂×D₃)⋊C₄	2
#91446	2
#91444	2
#91405	2
#91403	2
#91402	2
#91395	2
#65879	3
#5545	5