Subgroups — #14478181

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91265	C₂	1	1	yes	maximal, characteristic
2	D₁₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747533	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃×#3944	C₂	1	1	yes	maximal, characteristic, complemented
7	D₅×#812	C₂	1	1	yes	maximal, characteristic, complemented
8	#11746813	C₂	1	2	yes	maximal, complemented
9	#11746812	C₂	1	2	yes	maximal, complemented
10	#11746811	C₂	1	2	yes	maximal, complemented
11	#11746810	C₂	1	2	yes	maximal, complemented
12	#10613738	—	3	1	no	maximal, Hall
13	C₂×#6771	C₄	1	1	yes	characteristic
14	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
17	C₂×#6651	C₄	1	1	yes	characteristic
18	C₂×#6650	C₄	1	1	yes	characteristic
19	C₂×#6649	C₄	1	1	yes	characteristic
20	#91265	C₄	1	1	yes	characteristic
21	#91265	C₄	1	1	yes	characteristic
22	#91265	C₄	1	1	yes	characteristic
23	#91265	C₄	1	1	yes	characteristic
24	#91265	C₂²	1	1	yes	characteristic
25	#91265	C₂²	1	1	yes	characteristic
26	#91265	C₂²	1	1	yes	characteristic
27	#91265	C₂²	1	1	yes	characteristic
28	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic
29	#91096	C₂²	1	1	yes	characteristic
30	#91082	C₂²	1	2	yes	complemented
31	C₁₆×D₁₅	C₂²	1	2	yes	complemented
32	C₅×#812	C₂²	1	1	yes	characteristic
33	C₅×#798	C₂²	1	2	yes	complemented
34	C₅×D₃×C₁₆	C₂²	1	2	yes	complemented
35	C₃×#3944	C₂²	1	1	yes	characteristic
36	C₃×#3930	C₂²	1	2	yes	complemented
37	C₃×D₅×C₁₆	C₂²	1	2	yes	complemented
38	#90936	C₂²	1	2	yes	complemented
39	#90935	C₂²	1	2	yes	complemented
40	#90934	C₂²	1	2	yes	complemented
41	#90933	C₂²	1	2	yes	complemented
42	D₃×#672	C₂²	1	2	yes	complemented
43	D₅×C₃⋊C₁₆	C₂²	1	2	yes	complemented
44	#82007	—	5	1	no	maximal, Hall
45	C₂×#4047	—	3	1	no	—
46	C₂×C₅×M₃₂	—	3	1	no	—
47	C₂×#3944	—	3	1	no	—
48	#65196	—	3	2	no	—
49	#65196	—	3	2	no	—
50	D₅×M₃₂	—	3	1	no	—
51	D₅×M₃₂	—	3	1	no	—
52	D₅×M₃₂	—	3	1	no	—
53	D₅×M₃₂	D₃	1	1	yes	characteristic, complemented
54	#65190	—	3	2	no	—
55	#65190	—	3	2	no	—
56	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×#1204	C₈	1	1	yes	characteristic
60	C₂×#1203	C₈	1	1	yes	characteristic
61	C₂×#1202	C₈	1	1	yes	characteristic
62	C₂×#1201	C₈	1	1	yes	characteristic
63	#6771	C₈	1	1	yes	characteristic
64	#6771	C₈	1	1	yes	characteristic
65	#6771	C₈	1	1	yes	characteristic
66	#6771	C₈	1	1	yes	characteristic
67	#6771	C₂×C₄	1	1	yes	characteristic
68	#6771	C₂×C₄	1	1	yes	characteristic
69	#6771	C₂×C₄	1	1	yes	characteristic
70	#6771	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
73	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
74	C₈×D₁₅	C₂×C₄	1	1	yes	characteristic
75	C₈×D₁₅	C₂³	1	1	yes	characteristic
76	C₈×D₁₅	C₂³	1	1	yes	characteristic
77	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₅×D₃×C₈	C₂×C₄	1	1	yes	characteristic
79	C₅×D₃×C₈	C₂×C₄	1	1	yes	characteristic
80	C₅×D₃×C₈	C₂³	1	1	yes	characteristic
81	C₅×D₃×C₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
83	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
84	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
85	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
86	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
87	#6651	C₂×C₄	1	1	yes	characteristic
88	#6651	C₂×C₄	1	1	yes	characteristic
89	#6651	C₂×C₄	1	1	yes	characteristic
90	#6651	C₂×C₄	1	1	yes	characteristic
91	#6650	C₂×C₄	1	1	yes	characteristic
92	#6650	C₂×C₄	1	1	yes	characteristic
93	#6650	C₂×C₄	1	1	yes	characteristic
94	#6650	C₂×C₄	1	1	yes	characteristic
95	#6649	C₂×C₄	1	1	yes	characteristic
96	#6649	C₂×C₄	1	1	yes	characteristic
97	#6649	C₂×C₄	1	1	yes	characteristic
98	#6649	C₂×C₄	1	1	yes	characteristic
99	C₃×C₅×C₁₆	C₂³	1	2	yes	—
100	C₃⋊#672	C₂³	1	2	yes	—
101	C₃×#672	C₂³	1	2	yes	—
102	C₅×C₃⋊C₁₆	C₂³	1	2	yes	—
103	C₂×#901	—	5	1	no	—
104	C₂×C₃×M₃₂	—	5	1	no	—
105	C₂×#812	—	5	1	no	—
106	#4907	—	5	2	no	—
107	#4907	—	5	2	no	—
108	D₃×M₃₂	—	5	1	no	—
109	D₃×M₃₂	—	5	1	no	—
110	D₃×M₃₂	—	5	1	no	—
111	D₃×M₃₂	D₅	1	1	yes	characteristic, complemented
112	#4901	—	5	2	no	—
113	#4901	—	5	2	no	—
114	C₂×#709	—	3	1	no	—
115	C₂²×C₅×C₈	—	3	1	no	—
116	C₂×#681	—	3	1	no	—
117	#4047	—	3	1	no	—
118	#4047	—	3	1	no	—
119	#4047	—	3	1	no	—
120	#4047	—	3	1	no	—
121	#4047	—	3	1	no	—
122	#4047	—	3	1	no	—
123	#4047	—	3	1	no	—
124	#4047	—	3	1	no	—
125	C₂×#676	—	3	1	no	—
126	C₂×#676	—	3	1	no	—
127	C₂×C₈×D₅	—	3	1	no	—
128	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
129	C₅×M₃₂	—	3	1	no	—
130	C₅×M₃₂	—	3	2	no	—
131	C₅×M₃₂	C₂×D₃	1	1	yes	characteristic
132	C₂×C₅×C₁₆	—	3	2	no	—
133	#3944	—	3	1	no	—
134	#3944	—	3	2	no	—
135	#3944	C₂×D₃	1	1	yes	characteristic
136	C₂×#672	—	3	2	no	—
137	#3930	—	3	2	no	—
138	#3930	—	3	2	no	—
139	#3930	—	3	2	no	—
140	#3930	C₂×D₃	1	2	yes	complemented
141	D₅×C₁₆	—	3	2	no	—
142	D₅×C₁₆	—	3	2	no	—
143	D₅×C₁₆	—	3	2	no	—
144	D₅×C₁₆	C₂×D₃	1	2	yes	complemented
145	#3407	—	15	1	no	Sylow
146	C₂²×D₁₅	C₂×C₈	1	1	yes	characteristic
147	C₂²×C₅×D₃	C₂×C₈	1	1	yes	characteristic
148	C₂²×C₃×D₅	C₂×C₈	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₁₅	C₂×C₈	1	1	yes	characteristic
151	C₄×D₁₅	C₂×C₈	1	1	yes	characteristic
152	C₄×D₁₅	C₂×C₈	1	1	yes	characteristic
153	C₄×D₁₅	C₂²×C₄	1	1	yes	characteristic
154	C₄×D₁₅	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₅×Dic₃	C₂×C₈	1	1	yes	characteristic
156	C₄×C₅×D₃	C₂×C₈	1	1	yes	characteristic
157	C₄×C₅×D₃	C₂×C₈	1	1	yes	characteristic
158	C₄×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
159	C₄×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₃×Dic₅	C₂×C₈	1	1	yes	characteristic
161	C₃×C₄×D₅	C₂×C₈	1	1	yes	characteristic
162	C₃×C₄×D₅	C₂×C₈	1	1	yes	characteristic
163	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
164	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
165	#1204	C₂×C₈	1	1	yes	characteristic
166	#1204	C₂×C₈	1	1	yes	characteristic
167	#1204	C₂×C₈	1	1	yes	characteristic
168	#1204	C₂×C₈	1	1	yes	characteristic
169	#1203	C₂×C₈	1	1	yes	characteristic
170	#1203	C₂×C₈	1	1	yes	characteristic
171	#1203	C₂×C₈	1	1	yes	characteristic
172	#1203	C₂×C₈	1	1	yes	characteristic
173	#1202	C₂×C₈	1	1	yes	characteristic
174	#1202	C₂×C₈	1	1	yes	characteristic
175	#1202	C₂×C₈	1	1	yes	characteristic
176	#1202	C₂×C₈	1	1	yes	characteristic
177	#1201	C₂×C₈	1	1	yes	characteristic
178	#1201	C₂×C₈	1	1	yes	characteristic
179	#1201	C₂×C₈	1	1	yes	characteristic
180	#1201	C₂×C₈	1	1	yes	characteristic
181	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
182	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
183	C₃⋊#168	C₂²×C₄	1	1	yes	characteristic
184	C₃⋊#168	C₂²×C₄	1	1	yes	characteristic
185	C₃×#168	C₂²×C₄	1	1	yes	characteristic
186	C₃×#168	C₂²×C₄	1	1	yes	characteristic
187	C₅×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
188	C₅×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×#235	—	5	1	no	—
190	C₂²×C₃×C₈	—	5	1	no	—
191	C₂×#208	—	5	1	no	—
192	#901	—	5	1	no	—
193	#901	—	5	1	no	—
194	#901	—	5	1	no	—
195	#901	—	5	1	no	—
196	#901	—	5	1	no	—
197	#901	—	5	1	no	—
198	#901	—	5	1	no	—
199	#901	—	5	1	no	—
200	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
201	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
202	C₂×D₃×C₈	—	5	1	no	—
203	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
204	C₃×M₃₂	—	5	1	no	—
205	C₃×M₃₂	—	5	2	no	—
206	C₃×M₃₂	C₂×D₅	1	1	yes	characteristic
207	C₂×C₃×C₁₆	—	5	2	no	—
208	#812	—	5	1	no	—
209	#812	—	5	2	no	—
210	#812	C₂×D₅	1	1	yes	characteristic
211	C₂×C₃⋊C₁₆	—	5	2	no	—
212	#798	—	5	2	no	—
213	#798	—	5	2	no	—
214	#798	—	5	2	no	—
215	#798	C₂×D₅	1	2	yes	complemented
216	D₃×C₁₆	—	5	2	no	—
217	D₃×C₁₆	—	5	2	no	—
218	D₃×C₁₆	—	5	2	no	—
219	D₃×C₁₆	C₂×D₅	1	2	yes	complemented
220	C₂²×C₄×C₅	—	3	1	no	—
221	C₂×C₂²⋊D₅	—	3	1	no	—
222	C₂×C₂²⋊D₅	—	3	1	no	—
223	#709	—	3	1	no	—
224	#709	—	3	1	no	—
225	#709	—	3	1	no	—
226	#709	—	3	1	no	—
227	#709	—	3	1	no	—
228	#709	—	3	1	no	—
229	#709	—	3	1	no	—
230	#709	—	3	1	no	—
231	C₂×D₂₀	—	3	1	no	—
232	C₂×C₄×D₅	—	3	1	no	—
233	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
234	C₂×Dic₁₀	—	3	1	no	—
235	C₂×C₅×C₈	—	3	1	no	—
236	C₂×C₅×C₈	—	3	1	no	—
237	C₂×C₅×C₈	—	3	1	no	—
238	C₂×C₅×C₈	—	3	1	no	—
239	C₂×C₅×C₈	—	3	1	no	—
240	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
241	#681	—	3	1	no	—
242	#681	—	3	1	no	—
243	#681	—	3	1	no	—
244	#681	—	3	1	no	—
245	C₂×#168	—	3	1	no	—
246	C₂×#168	C₄×D₃	1	1	yes	characteristic
247	#676	—	3	1	no	—
248	#676	—	3	1	no	—
249	#676	—	3	1	no	—
250	#676	—	3	1	no	—
251	#676	—	3	1	no	—
252	#676	—	3	1	no	—
253	#676	—	3	1	no	—
254	#676	—	3	1	no	—
255	C₈×D₅	—	3	1	no	—
256	C₈×D₅	—	3	1	no	—
257	C₈×D₅	—	3	1	no	—
258	C₈×D₅	—	3	1	no	—
259	C₈×D₅	C₄×D₃	1	1	yes	characteristic
260	C₈×D₅	C₄×D₃	1	1	yes	characteristic
261	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
262	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
263	C₅×C₁₆	—	3	2	no	—
264	C₅×C₁₆	C₂²×D₃	1	2	yes	—
265	#672	—	3	2	no	—
266	#672	C₂²×D₃	1	2	yes	—
267	C₂×#131	—	15	1	no	—
268	#504	—	15	2	no	—
269	#504	—	15	2	no	—
270	#504	—	15	2	no	—
271	#504	—	15	2	no	—
272	C₂×M₃₂	—	3	1	no	—
273	C₂×M₃₂	—	5	1	no	—
274	C₂×M₃₂	—	15	1	no	—
275	C₂×M₃₂	—	15	1	no	—
276	C₂×M₃₂	—	15	1	no	—
277	C₂×M₃₂	—	15	1	no	—
278	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
279	C₂×D₁₅	—	4	1	no	—
280	C₂×D₁₅	C₂²×C₈	1	1	yes	characteristic
281	C₂×D₁₅	C₂²×C₈	1	1	yes	characteristic
282	C₂×C₅×D₃	—	4	1	no	—
283	C₂×C₅×D₃	C₂²×C₈	1	1	yes	characteristic
284	C₂×C₅×D₃	C₂²×C₈	1	1	yes	characteristic
285	C₂×C₃×D₅	—	4	1	no	—
286	C₂×C₃×D₅	C₂²×C₈	1	1	yes	characteristic
287	C₂×C₃×D₅	C₂²×C₈	1	1	yes	characteristic
288	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
289	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
290	Dic₁₅	C₂²×C₈	1	1	yes	characteristic
291	Dic₁₅	C₂²×C₈	1	1	yes	characteristic
292	C₃×Dic₅	C₂²×C₈	1	1	yes	characteristic
293	C₃×Dic₅	C₂²×C₈	1	1	yes	characteristic
294	C₅×Dic₃	C₂²×C₈	1	1	yes	characteristic
295	C₅×Dic₃	C₂²×C₈	1	1	yes	characteristic
296	C₂²×C₃×C₄	—	5	1	no	—
297	C₂×#67	—	5	1	no	—
298	C₂×#67	—	5	1	no	—
299	#235	—	5	1	no	—
300	#235	—	5	1	no	—
301	#235	—	5	1	no	—
302	#235	—	5	1	no	—
303	#235	—	5	1	no	—
304	#235	—	5	1	no	—
305	#235	—	5	1	no	—
306	#235	—	5	1	no	—
307	C₂×D₁₂	—	5	1	no	—
308	C₂×C₄×D₃	—	5	1	no	—
309	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
310	C₂×Dic₆	—	5	1	no	—
311	C₂×C₃×C₈	—	5	1	no	—
312	C₂×C₃×C₈	—	5	1	no	—
313	C₂×C₃×C₈	—	5	1	no	—
314	C₂×C₃×C₈	—	5	1	no	—
315	C₂×C₃×C₈	—	5	1	no	—
316	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
317	#208	—	5	1	no	—
318	#208	—	5	1	no	—
319	#208	—	5	1	no	—
320	#208	—	5	1	no	—
321	C₂×C₃⋊C₈	—	5	1	no	—
322	C₂×C₃⋊C₈	C₄×D₅	1	1	yes	characteristic
323	ΓL(1,𝔽₂₅)	—	5	1	no	—
324	ΓL(1,𝔽₂₅)	—	5	1	no	—
325	ΓL(1,𝔽₂₅)	—	5	1	no	—
326	ΓL(1,𝔽₂₅)	—	5	1	no	—
327	ΓL(1,𝔽₂₅)	—	5	1	no	—
328	ΓL(1,𝔽₂₅)	—	5	1	no	—
329	ΓL(1,𝔽₂₅)	—	5	1	no	—
330	ΓL(1,𝔽₂₅)	—	5	1	no	—
331	D₃×C₈	—	5	1	no	—
332	D₃×C₈	—	5	1	no	—
333	D₃×C₈	—	5	1	no	—
334	D₃×C₈	—	5	1	no	—
335	D₃×C₈	C₄×D₅	1	1	yes	characteristic
336	D₃×C₈	C₄×D₅	1	1	yes	characteristic
337	D₃×C₈	C₂²×D₅	1	1	yes	characteristic
338	D₃×C₈	C₂²×D₅	1	1	yes	characteristic
339	C₃×C₁₆	—	5	2	no	—
340	C₃×C₁₆	C₂²×D₅	1	2	yes	—
341	C₃⋊C₁₆	—	5	2	no	—
342	C₃⋊C₁₆	C₂²×D₅	1	2	yes	—
343	C₂³×C₅	—	3	1	no	—
344	C₂²×D₅	—	3	1	no	—
345	C₂²×D₅	D₃×C₈	1	1	yes	characteristic
346	C₂×C₄×C₅	—	3	1	no	—
347	C₂×C₄×C₅	—	3	1	no	—
348	C₂×C₄×C₅	—	3	1	no	—
349	C₂×C₄×C₅	—	3	1	no	—
350	C₂×C₄×C₅	—	3	1	no	—
351	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
352	C₂²⋊D₅	—	3	1	no	—
353	C₂²⋊D₅	—	3	1	no	—
354	C₂²⋊D₅	—	3	1	no	—
355	C₂²⋊D₅	—	3	1	no	—
356	C₂²⋊D₅	—	3	1	no	—
357	C₂²⋊D₅	—	3	1	no	—
358	C₂²⋊D₅	—	3	1	no	—
359	C₂²⋊D₅	—	3	1	no	—
360	C₂×Dic₅	—	3	1	no	—
361	C₂×Dic₅	D₃×C₈	1	1	yes	characteristic
362	D₂₀	—	3	1	no	—
363	D₂₀	—	3	1	no	—
364	D₂₀	—	3	1	no	—
365	D₂₀	—	3	1	no	—
366	C₄×D₅	—	3	1	no	—
367	C₄×D₅	—	3	1	no	—
368	C₄×D₅	—	3	1	no	—
369	C₄×D₅	—	3	1	no	—
370	C₄×D₅	D₃×C₈	1	1	yes	characteristic
371	C₄×D₅	D₃×C₈	1	1	yes	characteristic
372	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
373	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
374	Dic₁₀	—	3	1	no	—
375	Dic₁₀	—	3	1	no	—
376	Dic₁₀	—	3	1	no	—
377	Dic₁₀	—	3	1	no	—
378	C₅×C₈	—	3	1	no	—
379	C₅×C₈	—	3	1	no	—
380	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
381	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
382	#168	—	3	1	no	—
383	#168	—	3	1	no	—
384	#168	C₂×C₄×D₃	1	1	yes	characteristic
385	#168	C₂×C₄×D₃	1	1	yes	characteristic
386	C₂×#41	—	15	1	no	—
387	#131	—	15	1	no	—
388	#131	—	15	1	no	—
389	#131	—	15	1	no	—
390	#131	—	15	1	no	—
391	#131	—	15	1	no	—
392	#131	—	15	1	no	—
393	#131	—	15	1	no	—
394	#131	—	15	1	no	—
395	C₂×M₁₆	—	15	1	no	—
396	C₂×M₁₆	—	15	1	no	—
397	C₂×M₁₆	—	15	1	no	—
398	C₂²×C₈	—	3	1	no	—
399	C₂²×C₈	—	5	1	no	—
400	C₂²×C₈	—	15	1	no	—
401	M₃₂	—	3	1	no	—
402	M₃₂	—	3	2	no	—
403	M₃₂	—	5	1	no	—
404	M₃₂	—	5	2	no	—
405	M₃₂	—	15	2	no	—
406	M₃₂	—	15	2	no	—
407	M₃₂	—	15	2	no	—
408	M₃₂	—	15	1	no	—
409	M₃₂	—	15	2	no	—
410	M₃₂	D₃×D₅	1	1	yes	characteristic
411	C₂×C₁₆	—	3	2	no	—
412	C₂×C₁₆	—	5	2	no	—
413	C₂×C₁₆	—	15	2	no	—
414	C₂×C₁₆	—	15	2	no	—
415	C₂×C₁₆	—	15	2	no	—
416	C₂×C₁₆	—	15	2	no	—
417	C₂×C₃×C₅	—	2	1	no	—
418	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
419	D₁₅	—	2	1	no	—
420	D₁₅	—	2	1	no	—
421	C₃×D₅	—	2	1	no	—
422	C₃×D₅	—	2	1	no	—
423	C₅×D₃	—	2	1	no	—
424	C₅×D₃	—	2	1	no	—
425	C₂³×C₃	—	5	1	no	—
426	C₂²×D₃	—	5	1	no	—
427	C₂²×D₃	C₈×D₅	1	1	yes	characteristic
428	C₂×C₃×C₄	—	5	1	no	—
429	C₂×C₃×C₄	—	5	1	no	—
430	C₂×C₃×C₄	—	5	1	no	—
431	C₂×C₃×C₄	—	5	1	no	—
432	C₂×C₃×C₄	—	5	1	no	—
433	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
434	#67	—	5	1	no	—
435	#67	—	5	1	no	—
436	#67	—	5	1	no	—
437	#67	—	5	1	no	—
438	#67	—	5	1	no	—
439	#67	—	5	1	no	—
440	#67	—	5	1	no	—
441	#67	—	5	1	no	—
442	C₂×Dic₃	—	5	1	no	—
443	C₂×Dic₃	C₈×D₅	1	1	yes	characteristic
444	D₁₂	—	5	1	no	—
445	D₁₂	—	5	1	no	—
446	D₁₂	—	5	1	no	—
447	D₁₂	—	5	1	no	—
448	C₄×D₃	—	5	1	no	—
449	C₄×D₃	—	5	1	no	—
450	C₄×D₃	—	5	1	no	—
451	C₄×D₃	—	5	1	no	—
452	C₄×D₃	C₈×D₅	1	1	yes	characteristic
453	C₄×D₃	C₈×D₅	1	1	yes	characteristic
454	C₄×D₃	C₂×C₄×D₅	1	1	yes	characteristic
455	C₄×D₃	C₂×C₄×D₅	1	1	yes	characteristic
456	Dic₆	—	5	1	no	—
457	Dic₆	—	5	1	no	—
458	Dic₆	—	5	1	no	—
459	Dic₆	—	5	1	no	—
460	C₃×C₈	—	5	1	no	—
461	C₃×C₈	—	5	1	no	—
462	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
463	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
464	C₃⋊C₈	—	5	1	no	—
465	C₃⋊C₈	—	5	1	no	—
466	C₃⋊C₈	C₂×C₄×D₅	1	1	yes	characteristic
467	C₃⋊C₈	C₂×C₄×D₅	1	1	yes	characteristic
468	C₂²×C₅	—	3	1	no	—
469	C₂²×C₅	—	3	1	no	—
470	C₂²×C₅	—	12	1	no	—
471	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
472	C₂×D₅	—	3	1	no	—
473	C₂×D₅	—	3	1	no	—
474	C₂×D₅	—	4	1	no	—
475	C₂×D₅	—	12	1	no	—
476	C₂×D₅	C₂×D₃×C₈	1	1	yes	characteristic
477	C₂×D₅	C₂×D₃×C₈	1	1	yes	characteristic
478	C₄×C₅	—	3	1	no	—
479	C₄×C₅	—	3	1	no	—
480	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
481	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
482	Dic₅	—	3	1	no	—
483	Dic₅	—	3	1	no	—
484	Dic₅	C₂×D₃×C₈	1	1	yes	characteristic
485	Dic₅	C₂×D₃×C₈	1	1	yes	characteristic
486	#41	—	15	1	no	—
487	#41	—	15	1	no	—
488	#41	—	15	1	no	—
489	#41	—	15	1	no	—
490	#41	—	15	1	no	—
491	#41	—	15	1	no	—
492	#41	—	15	1	no	—
493	#41	—	15	1	no	—
494	C₂×Q₈	—	15	1	no	—
495	C₂×D₄	—	15	1	no	—
496	C₂×D₄	—	15	1	no	—
497	C₂×D₄	—	15	1	no	—
498	C₂²×C₄	—	3	1	no	—
499	C₂²×C₄	—	5	1	no	—
500	C₂²×C₄	—	15	1	no	—
501	M₁₆	—	15	1	no	—
502	M₁₆	—	15	1	no	—
503	M₁₆	—	15	1	no	—
504	M₁₆	—	15	1	no	—
505	M₁₆	—	15	1	no	—
506	M₁₆	—	15	1	no	—
507	M₁₆	—	15	1	no	—
508	M₁₆	—	15	1	no	—
509	M₁₆	—	15	1	no	—
510	M₁₆	—	15	1	no	—
511	M₁₆	—	15	1	no	—
512	M₁₆	—	15	1	no	—
513	C₂×C₈	—	3	1	no	—
514	C₂×C₈	—	3	1	no	—
515	C₂×C₈	—	3	1	no	—
516	C₂×C₈	—	3	1	no	—
517	C₂×C₈	—	3	1	no	—
518	C₂×C₈	—	5	1	no	—
519	C₂×C₈	—	5	1	no	—
520	C₂×C₈	—	5	1	no	—
521	C₂×C₈	—	5	1	no	—
522	C₂×C₈	—	5	1	no	—
523	C₂×C₈	—	15	1	no	—
524	C₂×C₈	—	15	1	no	—
525	C₂×C₈	—	15	1	no	—
526	C₂×C₈	—	15	1	no	—
527	C₂×C₈	—	15	1	no	—
528	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
529	C₁₆	—	3	2	no	—
530	C₁₆	—	5	2	no	—
531	C₁₆	—	15	2	no	—
532	C₁₆	C₂×D₃×D₅	1	2	yes	—
533	C₃×C₅	#3407	1	1	yes	characteristic, complemented, Hall
534	C₂²×C₃	—	5	1	no	—
535	C₂²×C₃	—	5	1	no	—
536	C₂²×C₃	—	20	1	no	—
537	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
538	C₂×D₃	—	4	1	no	—
539	C₂×D₃	—	5	1	no	—
540	C₂×D₃	—	5	1	no	—
541	C₂×D₃	—	20	1	no	—
542	C₂×D₃	C₂×C₈×D₅	1	1	yes	characteristic
543	C₂×D₃	C₂×C₈×D₅	1	1	yes	characteristic
544	C₃×C₄	—	5	1	no	—
545	C₃×C₄	—	5	1	no	—
546	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
547	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
548	Dic₃	—	5	1	no	—
549	Dic₃	—	5	1	no	—
550	Dic₃	C₂×C₈×D₅	1	1	yes	characteristic
551	Dic₃	C₂×C₈×D₅	1	1	yes	characteristic
552	C₂×C₅	—	2	1	no	—
553	C₂×C₅	—	6	1	no	—
554	C₂×C₅	—	6	1	no	—
555	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
556	D₅	—	2	1	no	—
557	D₅	—	2	1	no	—
558	D₅	—	6	1	no	—
559	D₅	—	6	1	no	—
560	C₂³	—	3	1	no	—
561	C₂³	—	5	1	no	—
562	C₂³	—	15	1	no	—
563	Q₈	—	15	1	no	—
564	Q₈	—	15	1	no	—
565	Q₈	—	15	1	no	—
566	Q₈	—	15	1	no	—
567	D₄	—	15	1	no	—
568	D₄	—	15	1	no	—
569	D₄	—	15	1	no	—
570	D₄	—	15	1	no	—
571	D₄	—	15	1	no	—
572	D₄	—	15	1	no	—
573	D₄	—	15	1	no	—
574	D₄	—	15	1	no	—
575	D₄	—	15	1	no	—
576	D₄	—	15	1	no	—
577	D₄	—	15	1	no	—
578	D₄	—	15	1	no	—
579	C₂×C₄	—	3	1	no	—
580	C₂×C₄	—	3	1	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	1	no	—
583	C₂×C₄	—	3	1	no	—
584	C₂×C₄	—	5	1	no	—
585	C₂×C₄	—	5	1	no	—
586	C₂×C₄	—	5	1	no	—
587	C₂×C₄	—	5	1	no	—
588	C₂×C₄	—	5	1	no	—
589	C₂×C₄	—	15	1	no	—
590	C₂×C₄	—	15	1	no	—
591	C₂×C₄	—	15	1	no	—
592	C₂×C₄	—	15	1	no	—
593	C₂×C₄	—	15	1	no	—
594	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
595	C₈	—	3	1	no	—
596	C₈	—	3	1	no	—
597	C₈	—	5	1	no	—
598	C₈	—	5	1	no	—
599	C₈	—	15	1	no	—
600	C₈	—	15	1	no	—
601	C₈	C₄×D₃×D₅	1	1	yes	characteristic
602	C₈	C₂²×D₃×D₅	1	1	yes	characteristic
603	C₂×C₃	—	2	1	no	—
604	C₂×C₃	—	10	1	no	—
605	C₂×C₃	—	10	1	no	—
606	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
607	D₃	—	2	1	no	—
608	D₃	—	2	1	no	—
609	D₃	—	10	1	no	—
610	D₃	—	10	1	no	—
611	C₅	#82007	1	1	yes	characteristic, complemented, Sylow
612	C₂²	—	3	1	no	—
613	C₂²	—	3	1	no	—
614	C₂²	—	5	1	no	—
615	C₂²	—	5	1	no	—
616	C₂²	—	12	1	no	—
617	C₂²	—	15	1	no	—
618	C₂²	—	15	1	no	—
619	C₂²	—	20	1	no	—
620	C₂²	—	60	1	no	—
621	C₂²	D₃×C₈×D₅	1	1	yes	characteristic
622	C₄	—	3	1	no	—
623	C₄	—	3	1	no	—
624	C₄	—	5	1	no	—
625	C₄	—	5	1	no	—
626	C₄	—	15	1	no	—
627	C₄	—	15	1	no	—
628	C₄	D₃×C₈×D₅	1	1	yes	characteristic
629	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
630	C₃	#10613738	1	1	yes	characteristic, complemented, Sylow
631	C₂	—	2	1	no	—
632	C₂	—	6	1	no	—
633	C₂	—	6	1	no	—
634	C₂	—	10	1	no	—
635	C₂	—	10	1	no	—
636	C₂	—	30	1	no	—
637	C₂	—	30	1	no	—
638	C₂	C₂×D₃×C₈×D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×D₃×D₅
commutator, socle	C₂×C₃×C₅	C₂³×C₈
Fitting	C₃×C₅×M₃₂	C₂²
prime radical	C₂×#6771	C₄
cosocle	C₃×C₅×C₈	C₂⁴
hypercenter	M₃₂	D₃×D₅
hypocenter	C₃×C₅	#3407
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. D₁₅×M₃₂	C₂	semidirect
3. C₅×D₃×M₃₂	C₂	semidirect
4. C₃×D₅×M₃₂	C₂	semidirect
5. #11747533	C₂	semidirect
6. D₃×#3944	C₂	semidirect
7. D₅×#812	C₂	semidirect
8. #11746813	C₂	semidirect
9. #11746812	C₂	semidirect
10. #11746811	C₂	semidirect
11. #11746810	C₂	semidirect
30. #91082	C₂²	semidirect
31. C₁₆×D₁₅	C₂²	semidirect
33. C₅×#798	C₂²	semidirect
34. C₅×D₃×C₁₆	C₂²	semidirect
36. C₃×#3930	C₂²	semidirect
37. C₃×D₅×C₁₆	C₂²	semidirect
38. #90936	C₂²	semidirect
39. #90935	C₂²	semidirect
40. #90934	C₂²	semidirect
41. #90933	C₂²	semidirect
42. D₃×#672	C₂²	semidirect
43. D₅×C₃⋊C₁₆	C₂²	semidirect
53. D₅×M₃₂	D₃	semidirect
111. D₃×M₃₂	D₅	semidirect
140. #3930	C₂×D₃	semidirect
144. D₅×C₁₆	C₂×D₃	semidirect
215. #798	C₂×D₅	semidirect
219. D₃×C₁₆	C₂×D₅	semidirect
533. C₃×C₅	#3407	semidirect
611. C₅	#82007	semidirect
630. C₃	#10613738	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91265	2
D₁₅×M₃₂	2
C₅×D₃×M₃₂	2
C₃×D₅×M₃₂	2
#11747533	2
D₃×#3944	2
D₅×#812	2
#11746813	2
#11746812	2
#11746811	2
#11746810	2
#10613738	3
#82007	5