Subgroups — #14297632

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91782	C₂	1	1	yes	maximal, characteristic
2	C₂×#91105	C₂	1	1	yes	maximal, characteristic
3	C₂×#91098	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751076	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#91093	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746350	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599685	—	3	1	no	maximal, Hall
9	C₂²×D₆₀	C₂²	1	1	yes	characteristic
10	C₂²×C₄×D₁₅	—	2	1	no	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×#6714	—	2	1	no	—
15	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
16	C₂×#6712	—	2	1	no	—
17	C₂×#6712	—	2	1	no	—
18	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
20	#91782	—	2	2	no	—
21	#91782	C₄	1	4	yes	complemented
22	#91105	—	2	2	no	—
23	#91098	—	2	2	no	—
24	#91093	—	2	2	no	—
25	#68892	—	5	1	no	maximal, Hall
26	C₂×#4039	—	3	1	no	—
27	C₂×#3953	—	3	1	no	—
28	C₂×#3946	—	3	1	no	—
29	#65265	—	3	1	no	—
30	C₂×#3941	—	3	1	no	—
31	C₅×#340	D₃	1	1	yes	characteristic, complemented
32	#64749	—	3	1	no	—
33	C₂³×D₁₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₅	—	2	1	no	—
38	C₂²×Dic₁₅	D₄	1	1	yes	characteristic
39	C₂²×Dic₁₅	D₄	1	1	yes	characteristic
40	C₂×D₆₀	—	2	1	no	—
41	C₂×D₆₀	—	2	1	no	—
42	C₂×D₆₀	—	2	1	no	—
43	C₂×D₆₀	C₂×C₄	1	2	yes	—
44	C₂×D₆₀	D₄	1	2	yes	—
45	C₂×D₆₀	Q₈	1	2	yes	—
46	C₂×C₄×D₁₅	—	2	4	no	—
47	C₂×C₄×D₁₅	—	4	2	no	—
48	C₂×C₄×D₁₅	—	4	2	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₂×C₃×C₅×C₈	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	#6714	—	2	4	no	—
57	C₄⋊Dic₁₅	—	2	1	no	—
58	C₄⋊Dic₁₅	—	2	1	no	—
59	#6712	—	4	2	no	—
60	#6712	—	4	2	no	—
61	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
62	C₄×Dic₁₅	D₄	1	2	yes	—
63	C₂×C₃⋊#168	—	2	1	no	—
64	C₂×C₃⋊#168	—	2	1	no	—
65	C₂×C₃⋊#168	—	2	1	no	—
66	C₂×#893	—	5	1	no	—
67	C₂×#821	—	5	1	no	—
68	C₂×Dic₃⋊C₈	—	5	1	no	—
69	#4975	—	5	1	no	—
70	C₂×#809	—	5	1	no	—
71	C₃×#340	D₅	1	1	yes	characteristic, complemented
72	#4529	—	5	1	no	—
73	C₂²×D₂₀	—	3	1	no	—
74	C₂²×C₄×D₅	—	6	1	no	—
75	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
78	C₂×#685	—	6	1	no	—
79	C₂×C₄⋊Dic₅	—	3	1	no	—
80	C₂×#683	—	6	1	no	—
81	C₂×#683	—	6	1	no	—
82	C₂×C₄×Dic₅	—	3	1	no	—
83	C₂²×#168	—	3	1	no	—
84	#4039	—	3	4	no	—
85	#4039	—	6	2	no	—
86	#3953	—	6	2	no	—
87	#3946	—	6	2	no	—
88	#3941	—	6	2	no	—
89	#1802	—	15	1	no	Sylow
90	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×D₁₅	—	2	2	no	—
92	C₂²×D₁₅	—	2	2	no	—
93	C₂²×D₁₅	—	2	2	no	—
94	C₂²×D₁₅	—	4	1	no	—
95	C₂²×D₁₅	—	4	1	no	—
96	C₂²×D₁₅	—	4	1	no	—
97	C₂²×D₁₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	—	4	1	no	—
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×Dic₁₅	—	2	1	no	—
111	C₂×Dic₁₅	—	2	1	no	—
112	C₂×Dic₁₅	—	4	1	no	—
113	C₂×Dic₁₅	—	4	1	no	—
114	C₂×Dic₁₅	—	4	1	no	—
115	C₂×Dic₁₅	C₂²⋊C₄	1	2	yes	—
116	C₂×Dic₁₅	C₂²⋊C₄	1	2	yes	—
117	C₂×Dic₁₅	D₈	1	2	yes	—
118	C₂×Dic₁₅	SD₁₆	1	2	yes	—
119	D₆₀	—	2	2	no	—
120	D₆₀	—	2	2	no	—
121	D₆₀	—	2	2	no	—
122	D₆₀	C₄⋊C₄	1	4	yes	complemented
123	C₄×D₁₅	—	4	8	no	—
124	C₃×C₅×C₈	—	4	1	no	—
125	C₃⋊#168	—	4	1	no	—
126	C₂²×D₁₂	—	5	1	no	—
127	C₂²×C₄×D₃	—	10	1	no	—
128	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
131	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
132	C₂×C₄⋊Dic₃	—	5	1	no	—
133	C₂×Dic₃⋊C₄	—	10	1	no	—
134	C₂×Dic₃⋊C₄	—	10	1	no	—
135	C₂×C₄×Dic₃	—	5	1	no	—
136	C₂²×C₃⋊C₈	—	5	1	no	—
137	#893	—	5	4	no	—
138	#893	—	10	2	no	—
139	#821	—	10	2	no	—
140	Dic₃⋊C₈	—	10	2	no	—
141	#809	—	10	2	no	—
142	C₂³×D₅	—	6	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
146	C₂²×Dic₅	—	3	1	no	—
147	C₂²×Dic₅	—	3	1	no	—
148	C₂²×Dic₅	—	6	1	no	—
149	C₂×D₂₀	—	3	2	no	—
150	C₂×D₂₀	—	3	2	no	—
151	C₂×D₂₀	—	3	2	no	—
152	C₂×D₂₀	—	6	1	no	—
153	C₂×D₂₀	—	6	1	no	—
154	C₂×D₂₀	—	6	1	no	—
155	C₂×C₄×D₅	—	6	4	no	—
156	C₂×C₄×D₅	—	12	2	no	—
157	C₂×C₄×D₅	—	12	2	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
165	#685	—	6	4	no	—
166	C₄⋊Dic₅	—	6	1	no	—
167	C₄⋊Dic₅	—	6	1	no	—
168	#683	—	12	2	no	—
169	#683	—	12	2	no	—
170	C₄×Dic₅	—	3	2	no	—
171	C₄×Dic₅	—	3	2	no	—
172	C₂×#168	—	6	1	no	—
173	C₂×#168	—	6	1	no	—
174	C₂×#168	—	6	1	no	—
175	C₂×C₄×D₄	—	15	1	no	—
176	C₂×C₄⋊C₈	—	15	1	no	—
177	C₂×#102	—	15	1	no	—
178	C₂×#102	—	15	1	no	—
179	#384	—	15	1	no	—
180	#340	—	15	1	no	—
181	#340	D₁₅	1	1	yes	characteristic, complemented
182	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₃×C₅	#121	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
186	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
187	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂²×C₃×C₅	#137	1	1	yes	characteristic
189	C₂×D₁₅	—	2	4	no	—
190	C₂×D₁₅	—	4	2	no	—
191	C₂×D₁₅	—	4	2	no	—
192	C₂×D₁₅	—	4	2	no	—
193	C₂×D₁₅	—	4	2	no	—
194	C₂×D₁₅	—	4	2	no	—
195	C₂×D₁₅	—	4	2	no	—
196	C₃×C₄×C₅	—	4	2	no	—
197	C₃×C₄×C₅	—	8	1	no	—
198	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₃×C₄×C₅	#117	1	1	yes	characteristic
200	C₃×C₄×C₅	#121	1	1	yes	characteristic
201	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
202	Dic₁₅	—	2	2	no	—
203	Dic₁₅	—	8	1	no	—
204	Dic₁₅	#102	1	4	yes	complemented
205	C₂³×D₃	—	10	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
209	C₂²×Dic₃	—	5	1	no	—
210	C₂²×Dic₃	—	5	1	no	—
211	C₂²×Dic₃	—	10	1	no	—
212	C₂×D₁₂	—	5	2	no	—
213	C₂×D₁₂	—	5	2	no	—
214	C₂×D₁₂	—	5	2	no	—
215	C₂×D₁₂	—	10	1	no	—
216	C₂×D₁₂	—	10	1	no	—
217	C₂×D₁₂	—	10	1	no	—
218	C₂×C₄×D₃	—	10	4	no	—
219	C₂×C₄×D₃	—	20	2	no	—
220	C₂×C₄×D₃	—	20	2	no	—
221	C₂×C₃×C₈	—	2	1	no	—
222	C₂×C₃×C₈	—	2	1	no	—
223	C₂×C₃×C₈	—	2	1	no	—
224	C₃×C₄⋊C₄	—	2	1	no	—
225	C₃×C₄⋊C₄	—	2	1	no	—
226	C₃×C₄⋊C₄	—	2	1	no	—
227	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
228	(C₂×D₃)⋊C₄	—	10	4	no	—
229	C₄⋊Dic₃	—	10	1	no	—
230	C₄⋊Dic₃	—	10	1	no	—
231	Dic₃⋊C₄	—	20	2	no	—
232	Dic₃⋊C₄	—	20	2	no	—
233	C₄×Dic₃	—	5	2	no	—
234	C₄×Dic₃	—	5	2	no	—
235	C₂×C₃⋊C₈	—	10	1	no	—
236	C₂×C₃⋊C₈	—	10	1	no	—
237	C₂×C₃⋊C₈	—	10	1	no	—
238	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
239	C₂²×D₅	—	6	2	no	—
240	C₂²×D₅	—	6	2	no	—
241	C₂²×D₅	—	6	2	no	—
242	C₂²×D₅	—	12	1	no	—
243	C₂²×D₅	—	12	1	no	—
244	C₂²×D₅	—	12	1	no	—
245	C₂²×D₅	—	12	1	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
253	C₂×C₄×C₅	#235	1	1	yes	characteristic
254	C₂×C₄×C₅	#235	1	1	yes	characteristic
255	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
258	C₂×Dic₅	—	3	2	no	—
259	C₂×Dic₅	—	3	2	no	—
260	C₂×Dic₅	—	3	2	no	—
261	C₂×Dic₅	—	3	2	no	—
262	C₂×Dic₅	—	6	1	no	—
263	C₂×Dic₅	—	6	1	no	—
264	C₂×Dic₅	—	12	1	no	—
265	C₂×Dic₅	—	12	1	no	—
266	C₂×Dic₅	—	12	1	no	—
267	D₂₀	—	3	4	no	—
268	D₂₀	—	6	2	no	—
269	D₂₀	—	6	2	no	—
270	D₂₀	—	6	2	no	—
271	C₄×D₅	—	12	8	no	—
272	C₅×C₈	—	4	1	no	—
273	#168	—	12	1	no	—
274	C₂²×D₄	—	15	1	no	—
275	C₂³×C₄	—	30	1	no	—
276	C₂²×C₈	—	15	1	no	—
277	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
278	C₄×D₄	—	15	4	no	—
279	C₄×D₄	—	30	2	no	—
280	C₂×C₄⋊C₄	—	15	1	no	—
281	C₂×C₄⋊C₄	—	30	1	no	—
282	C₂×C₄⋊C₄	—	30	1	no	—
283	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	30	1	no	—
286	C₂×C₄²	—	15	1	no	—
287	C₄⋊C₈	—	30	2	no	—
288	#102	—	30	2	no	—
289	#102	—	30	2	no	—
290	C₂×C₃×C₅	#380	1	1	yes	characteristic
291	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
292	C₂×C₃×C₅	#417	1	1	yes	characteristic
293	C₂×C₃×C₅	#459	1	1	yes	characteristic
294	C₂×C₃×C₅	#461	1	1	yes	characteristic
295	C₂×C₃×C₅	#474	1	1	yes	characteristic
296	C₂×C₃×C₅	#476	1	1	yes	characteristic
297	D₁₅	—	4	4	no	—
298	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
299	C₂²×D₃	—	10	2	no	—
300	C₂²×D₃	—	10	2	no	—
301	C₂²×D₃	—	10	2	no	—
302	C₂²×D₃	—	20	1	no	—
303	C₂²×D₃	—	20	1	no	—
304	C₂²×D₃	—	20	1	no	—
305	C₂²×D₃	—	20	1	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	4	1	no	—
308	C₂×C₃×C₄	—	4	1	no	—
309	C₂×C₃×C₄	—	4	1	no	—
310	C₂×C₃×C₄	—	4	1	no	—
311	C₂×C₃×C₄	—	4	1	no	—
312	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
313	C₂×C₃×C₄	#709	1	1	yes	characteristic
314	C₂×C₃×C₄	#709	1	1	yes	characteristic
315	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
316	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
317	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
318	C₂×Dic₃	—	5	2	no	—
319	C₂×Dic₃	—	5	2	no	—
320	C₂×Dic₃	—	5	2	no	—
321	C₂×Dic₃	—	5	2	no	—
322	C₂×Dic₃	—	10	1	no	—
323	C₂×Dic₃	—	10	1	no	—
324	C₂×Dic₃	—	20	1	no	—
325	C₂×Dic₃	—	20	1	no	—
326	C₂×Dic₃	—	20	1	no	—
327	D₁₂	—	5	4	no	—
328	D₁₂	—	10	2	no	—
329	D₁₂	—	10	2	no	—
330	D₁₂	—	10	2	no	—
331	C₄×D₃	—	20	8	no	—
332	C₃×C₈	—	4	1	no	—
333	C₃⋊C₈	—	20	1	no	—
334	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
335	C₂²×C₅	#884	1	1	yes	characteristic
336	C₂²×C₅	#896	1	1	yes	characteristic
337	C₂²×C₅	D₃×D₈	1	1	yes	characteristic
338	C₂²×C₅	D₃×SD₁₆	1	1	yes	characteristic
339	C₂²×C₅	#914	1	1	yes	characteristic
340	C₂²×C₅	#918	1	1	yes	characteristic
341	C₂×D₅	—	6	4	no	—
342	C₂×D₅	—	12	2	no	—
343	C₂×D₅	—	12	2	no	—
344	C₂×D₅	—	12	2	no	—
345	C₂×D₅	—	12	2	no	—
346	C₂×D₅	—	12	2	no	—
347	C₂×D₅	—	12	2	no	—
348	C₄×C₅	—	4	2	no	—
349	C₄×C₅	—	8	1	no	—
350	C₄×C₅	#872	1	1	yes	characteristic
351	C₄×C₅	#884	1	1	yes	characteristic
352	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
353	C₄×C₅	#896	1	1	yes	characteristic
354	Dic₅	—	3	4	no	—
355	Dic₅	—	6	2	no	—
356	Dic₅	—	24	1	no	—
357	C₂⁴	—	30	1	no	—
358	C₂×D₄	—	15	2	no	—
359	C₂×D₄	—	15	2	no	—
360	C₂×D₄	—	15	2	no	—
361	C₂×D₄	—	30	1	no	—
362	C₂×D₄	—	30	1	no	—
363	C₂×D₄	—	30	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	15	1	no	—
367	C₂²×C₄	—	15	1	no	—
368	C₂²×C₄	—	30	4	no	—
369	C₂²×C₄	—	30	1	no	—
370	C₂²×C₄	—	60	2	no	—
371	C₂²×C₄	—	60	2	no	—
372	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	30	1	no	—
377	C₂×C₈	—	30	1	no	—
378	C₂×C₈	—	30	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	30	1	no	—
383	C₄⋊C₄	—	30	1	no	—
384	C₄⋊C₄	—	60	2	no	—
385	C₄⋊C₄	—	60	2	no	—
386	C₄⋊C₄	C₄×D₁₅	1	2	yes	—
387	C₂²⋊C₄	—	30	4	no	—
388	C₄²	—	15	2	no	—
389	C₄²	—	15	2	no	—
390	C₃×C₅	#1802	1	1	yes	characteristic, complemented, Hall
391	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
392	C₂²×C₃	#4030	1	1	yes	characteristic
393	C₂²×C₃	#4042	1	1	yes	characteristic
394	C₂²×C₃	D₅×D₈	1	1	yes	characteristic
395	C₂²×C₃	D₅×SD₁₆	1	1	yes	characteristic
396	C₂²×C₃	#4060	1	1	yes	characteristic
397	C₂²×C₃	#4064	1	1	yes	characteristic
398	C₂×D₃	—	10	4	no	—
399	C₂×D₃	—	20	2	no	—
400	C₂×D₃	—	20	2	no	—
401	C₂×D₃	—	20	2	no	—
402	C₂×D₃	—	20	2	no	—
403	C₂×D₃	—	20	2	no	—
404	C₂×D₃	—	20	2	no	—
405	C₃×C₄	—	4	2	no	—
406	C₃×C₄	—	8	1	no	—
407	C₃×C₄	#4018	1	1	yes	characteristic
408	C₃×C₄	#4030	1	1	yes	characteristic
409	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
410	C₃×C₄	#4042	1	1	yes	characteristic
411	Dic₃	—	5	4	no	—
412	Dic₃	—	10	2	no	—
413	Dic₃	—	40	1	no	—
414	C₂×C₅	#4667	1	1	yes	characteristic
415	C₂×C₅	D₃×#102	1	1	yes	characteristic
416	C₂×C₅	#4786	1	1	yes	characteristic
417	C₂×C₅	#4803	1	1	yes	characteristic
418	C₂×C₅	#4818	1	1	yes	characteristic
419	C₂×C₅	#4870	1	1	yes	characteristic
420	C₂×C₅	#4890	1	1	yes	characteristic
421	D₅	—	12	4	no	—
422	C₂³	—	30	2	no	—
423	C₂³	—	30	2	no	—
424	C₂³	—	30	2	no	—
425	C₂³	—	60	1	no	—
426	C₂³	—	60	1	no	—
427	C₂³	—	60	1	no	—
428	C₂³	—	60	1	no	—
429	C₂³	D₄×D₁₅	1	1	yes	characteristic
430	D₄	—	15	4	no	—
431	D₄	—	30	2	no	—
432	D₄	—	30	2	no	—
433	D₄	—	30	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	15	2	no	—
441	C₂×C₄	—	15	2	no	—
442	C₂×C₄	—	15	2	no	—
443	C₂×C₄	—	15	2	no	—
444	C₂×C₄	—	30	1	no	—
445	C₂×C₄	—	30	1	no	—
446	C₂×C₄	—	60	8	no	—
447	C₂×C₄	—	60	1	no	—
448	C₂×C₄	—	60	1	no	—
449	C₂×C₄	—	60	1	no	—
450	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
451	C₂×C₄	#6817	1	1	yes	characteristic
452	C₂×C₄	#6817	1	1	yes	characteristic
453	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
454	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
455	C₂×C₄	Q₈×D₁₅	1	1	yes	characteristic
456	C₈	—	4	1	no	—
457	C₈	—	60	1	no	—
458	C₂×C₃	#64956	1	1	yes	characteristic
459	C₂×C₃	D₅×#102	1	1	yes	characteristic
460	C₂×C₃	#65075	1	1	yes	characteristic
461	C₂×C₃	#65092	1	1	yes	characteristic
462	C₂×C₃	#65107	1	1	yes	characteristic
463	C₂×C₃	#65159	1	1	yes	characteristic
464	C₂×C₃	#65179	1	1	yes	characteristic
465	D₃	—	20	4	no	—
466	C₅	#68892	1	1	yes	characteristic, complemented, Sylow
467	C₂²	—	30	4	no	—
468	C₂²	—	60	2	no	—
469	C₂²	—	60	2	no	—
470	C₂²	—	60	2	no	—
471	C₂²	—	60	2	no	—
472	C₂²	—	60	2	no	—
473	C₂²	—	60	2	no	—
474	C₂²	C₂²⋊C₄×D₁₅	1	1	yes	characteristic
475	C₂²	#91773	1	1	yes	characteristic
476	C₂²	#91785	1	1	yes	characteristic
477	C₂²	D₈×D₁₅	1	1	yes	characteristic
478	C₂²	SD₁₆×D₁₅	1	1	yes	characteristic
479	C₂²	#91803	1	1	yes	characteristic
480	C₂²	#91807	1	1	yes	characteristic
481	C₄	—	4	2	no	—
482	C₄	—	8	1	no	—
483	C₄	—	15	4	no	—
484	C₄	—	30	2	no	—
485	C₄	—	120	1	no	—
486	C₄	#91761	1	1	yes	characteristic
487	C₄	#91773	1	1	yes	characteristic
488	C₄	C₄⋊C₄×D₁₅	1	1	yes	characteristic
489	C₄	#91785	1	1	yes	characteristic
490	C₃	#10599685	1	1	yes	characteristic, complemented, Sylow
491	C₂	—	60	4	no	—
492	C₂	#11750768	1	1	yes	characteristic
493	C₂	D₁₅×#102	1	1	yes	characteristic
494	C₂	#11750887	1	1	yes	characteristic
495	C₂	#11750904	1	1	yes	characteristic
496	C₂	#11750919	1	1	yes	characteristic
497	C₂	#11750971	1	1	yes	characteristic
498	C₂	#11750991	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₃×C₅×#340	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×D₆₀	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	#340	D₁₅
hypocenter	C₃×C₅	#1802
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

Complements

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

N	H ≅ G/N	type
3. C₂×#91098	C₂	semidirect
4. #11751076	C₂	semidirect
6. C₃×C₅×#340	C₂	semidirect
7. #11746350	C₂	semidirect
21. #91782	C₄	semidirect
31. C₅×#340	D₃	semidirect
71. C₃×#340	D₅	semidirect
122. D₆₀	C₄⋊C₄	semidirect
181. #340	D₁₅	semidirect
204. Dic₁₅	#102	semidirect
390. C₃×C₅	#1802	semidirect
466. C₅	#68892	semidirect
490. C₃	#10599685	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91782	2
C₂×#91105	2
C₂×#91098	2
#11751076	2
C₂×#91093	2
C₃×C₅×#340	2
#11746350	2
#10599685	3
#68892	5