Subgroups — #14478148

Order 1920.

736 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	#11754017	C₂	1	1	yes	maximal, characteristic
2	#11752384	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65725	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751741	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#91164	C₂	1	1	yes	maximal, characteristic, complemented
6	#11751738	C₂	1	1	yes	maximal, characteristic, complemented
7	#11751736	C₂	1	1	yes	maximal, characteristic, complemented
8	#11751646	C₂	1	2	yes	maximal, complemented
9	#11751644	C₂	1	2	yes	maximal, complemented
10	#11751642	C₂	1	2	yes	maximal, complemented
11	D₃×D₅⋊C₁₆	C₂	1	2	yes	maximal, complemented
12	D₅⋊#504	—	3	1	no	maximal, Hall
13	#92016	C₄	1	1	yes	characteristic
14	M₁₆×D₁₅	C₄	1	1	yes	characteristic
15	C₅×#907	C₄	1	1	yes	characteristic
16	C₃×#4053	C₂²	1	1	yes	characteristic
17	C₂×#6648	C₂²	1	1	yes	characteristic
18	#91286	C₂²	1	1	yes	characteristic
19	#91283	C₄	1	1	yes	characteristic
20	#91267	C₄	1	2	yes	—
21	#91266	C₂²	1	2	yes	—
22	#91246	C₄	1	2	yes	—
23	D₃×C₈×D₅	C₂²	1	2	yes	—
24	#91227	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃⋊#674	C₂²	1	1	yes	characteristic, complemented
26	#91219	C₂²	1	2	yes	complemented
27	D₅⋊(C₃⋊C₁₆)	C₂²	1	2	yes	complemented
28	C₃×#3998	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×#674	C₂²	1	1	yes	characteristic, complemented
30	C₃×#3990	C₂²	1	2	yes	complemented
31	C₃×D₅⋊C₁₆	C₂²	1	2	yes	complemented
32	#91166	C₂²	1	2	yes	complemented
33	#91165	C₂²	1	2	yes	complemented
34	#91165	C₂²	1	2	yes	complemented
35	#91164	C₂²	1	1	yes	characteristic
36	#91164	C₂²	1	1	yes	characteristic
37	#91164	C₂²	1	2	yes	—
38	#91164	C₂²	1	1	yes	characteristic, complemented
39	#91164	C₂²	1	1	yes	characteristic, complemented
40	D₃×#674	C₂²	1	2	yes	complemented
41	D₃×#674	C₂²	1	2	yes	complemented
42	D₃×#504	—	5	1	no	maximal, Hall
43	D₅×#131	—	3	1	no	—
44	#65791	—	3	1	no	—
45	#65791	—	3	1	no	—
46	#65725	—	3	1	no	—
47	#65725	—	3	2	no	—
48	#65725	—	3	2	no	—
49	#65725	D₃	1	1	yes	characteristic, complemented
50	D₅⋊M₃₂	—	3	1	no	—
51	D₅⋊M₃₂	—	3	2	no	—
52	C₂×D₅⋊C₁₆	—	3	1	no	—
53	C₂×D₅⋊C₁₆	—	3	2	no	—
54	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
55	C₅×#235	C₂×C₄	1	1	yes	characteristic
56	C₃×#709	C₂×C₄	1	1	yes	characteristic
57	#6790	C₈	1	2	yes	—
58	#6780	C₈	1	2	yes	—
59	#6777	C₈	1	1	yes	characteristic
60	C₄×D₃×D₅	C₂×C₄	1	2	yes	—
61	#6771	C₂×C₄	1	2	yes	—
62	D₁₅⋊Q₈	C₈	1	1	yes	characteristic
63	#6768	C₈	1	1	yes	characteristic
64	#6766	C₈	1	1	yes	characteristic
65	C₃×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
66	#6710	C₂×C₄	1	1	yes	characteristic
67	#6705	C₂×C₄	1	2	yes	—
68	C₈×D₁₅	C₂×C₄	1	2	yes	—
69	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	—
71	C₅×D₃×C₈	C₂×C₄	1	2	yes	—
72	C₂×C₃×#168	C₂³	1	1	yes	characteristic
73	C₃×#676	C₂×C₄	1	2	yes	—
74	C₃×C₈×D₅	C₂³	1	2	yes	—
75	#6650	C₂×C₄	1	2	yes	—
76	#6649	C₂×C₄	1	2	yes	—
77	#6648	C₂×C₄	1	1	yes	characteristic
78	#6648	C₂×C₄	1	1	yes	characteristic
79	#6648	C₂³	1	1	yes	characteristic
80	#6648	C₂³	1	1	yes	characteristic
81	D₃×#168	C₂³	1	2	yes	—
82	D₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
83	C₃⋊#674	C₂³	1	1	yes	characteristic
84	C₃⋊#674	C₂³	1	2	yes	—
85	C₃⋊#674	C₂³	1	1	yes	characteristic
86	C₃×#674	C₂³	1	1	yes	characteristic
87	C₃×#674	C₂³	1	2	yes	—
88	C₃×#674	C₂³	1	1	yes	characteristic
89	D₃×#131	—	5	1	no	—
90	C₃×#504	—	5	1	no	—
91	#5140	—	5	1	no	—
92	#4907	—	5	1	no	—
93	#4907	—	5	2	no	—
94	D₃×M₃₂	—	5	1	no	—
95	D₃×M₃₂	—	5	2	no	—
96	#4901	—	5	1	no	—
97	#4901	—	5	2	no	—
98	C₂×D₃×C₁₆	—	5	1	no	—
99	C₂×D₃×C₁₆	—	5	2	no	—
100	D₅×#41	—	3	1	no	—
101	C₅×#131	—	3	1	no	—
102	#4094	—	3	1	no	—
103	#4053	—	3	2	no	—
104	#4053	C₂×D₃	1	1	yes	characteristic
105	D₅×M₁₆	—	3	1	no	—
106	D₅×M₁₆	—	3	2	no	—
107	#4047	—	3	1	no	—
108	#4047	—	3	2	no	—
109	C₂×C₈×D₅	—	3	1	no	—
110	C₂×C₈×D₅	—	3	2	no	—
111	#3998	—	3	1	no	—
112	#3998	—	3	2	no	—
113	#3998	—	3	2	no	—
114	#3998	C₂×D₃	1	1	yes	characteristic, complemented
115	C₂×#674	—	3	1	no	—
116	C₂×#674	—	3	2	no	—
117	C₂×#674	—	3	2	no	—
118	C₂×#674	C₂×D₃	1	1	yes	characteristic, complemented
119	#3990	—	3	2	no	—
120	#3990	—	3	2	no	—
121	#3990	C₂×D₃	1	2	yes	complemented
122	D₅⋊C₁₆	—	3	2	no	—
123	D₅⋊C₁₆	—	3	1	no	—
124	D₅⋊C₁₆	—	3	1	no	—
125	D₅⋊C₁₆	—	3	2	no	—
126	D₅⋊C₁₆	—	3	1	no	—
127	D₅⋊C₁₆	—	3	1	no	—
128	D₅⋊C₁₆	C₂×D₃	1	2	yes	complemented
129	C₂×#504	—	15	1	no	Sylow
130	C₂²×D₁₅	C₂×C₈	1	1	yes	characteristic
131	C₂×D₃×D₅	C₂×C₈	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×Dic₁₅	C₂×C₈	1	1	yes	characteristic
134	C₄×D₁₅	C₂×C₈	1	1	yes	characteristic
135	C₄×D₁₅	C₂×C₈	1	1	yes	characteristic
136	C₄×D₁₅	C₂²×C₄	1	1	yes	characteristic
137	C₄×D₁₅	C₂²×C₄	1	1	yes	characteristic
138	C₅×#67	C₂×C₈	1	2	yes	—
139	C₅×D₁₂	C₂×C₈	1	1	yes	characteristic
140	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
141	C₅×Dic₆	C₂×C₈	1	1	yes	characteristic
142	C₃×C₂²⋊D₅	C₂×C₈	1	2	yes	—
143	C₃×D₂₀	C₂×C₈	1	1	yes	characteristic
144	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
145	C₃×Dic₁₀	C₂×C₈	1	1	yes	characteristic
146	#1204	C₂×C₈	1	2	yes	—
147	#1203	C₂×C₈	1	2	yes	—
148	#1202	C₂×C₈	1	2	yes	—
149	#1201	C₂×C₈	1	2	yes	—
150	#1200	C₂×C₈	1	2	yes	—
151	D₃×Dic₅	C₂×C₈	1	2	yes	—
152	D₅×Dic₃	C₂×C₈	1	2	yes	—
153	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
154	C₃⋊#168	C₂²×C₄	1	2	yes	—
155	C₃×#168	C₂²×C₄	1	1	yes	characteristic
156	C₃×#168	C₂⁴	1	1	yes	characteristic
157	C₅×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
158	C₅×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
159	D₃×#41	—	5	1	no	—
160	C₃×#131	—	5	1	no	—
161	#948	—	5	1	no	—
162	#907	—	5	2	no	—
163	#907	AGL(1,𝔽₅)	1	1	yes	characteristic
164	D₃×M₁₆	—	5	1	no	—
165	D₃×M₁₆	—	5	2	no	—
166	#901	—	5	1	no	—
167	#901	—	5	2	no	—
168	C₂×D₃×C₈	—	5	1	no	—
169	C₂×D₃×C₈	—	5	2	no	—
170	C₃×M₃₂	—	5	2	no	—
171	C₃×M₃₂	—	5	1	no	—
172	C₂×C₃×C₁₆	—	5	2	no	—
173	C₂×C₃×C₁₆	—	5	1	no	—
174	#812	—	5	2	no	—
175	#812	—	5	1	no	—
176	C₂×C₃⋊C₁₆	—	5	2	no	—
177	C₂×C₃⋊C₁₆	—	5	1	no	—
178	#798	—	5	2	no	—
179	#798	—	5	2	no	—
180	#798	—	5	2	no	—
181	D₃×C₁₆	—	5	2	no	—
182	D₃×C₁₆	—	5	2	no	—
183	D₃×C₁₆	—	5	1	no	—
184	D₃×C₁₆	—	5	1	no	—
185	D₃×C₁₆	—	5	2	no	—
186	D₃×C₁₆	—	5	1	no	—
187	D₃×C₁₆	—	5	1	no	—
188	C₅×#41	—	3	1	no	—
189	#713	—	3	1	no	—
190	Q₈×D₅	—	3	1	no	—
191	#711	—	3	2	no	—
192	#711	—	3	1	no	—
193	D₄×D₅	—	3	2	no	—
194	D₄×D₅	—	3	1	no	—
195	#709	—	3	2	no	—
196	#709	C₄×D₃	1	1	yes	characteristic
197	C₂×C₄×D₅	—	3	1	no	—
198	C₂×C₄×D₅	—	3	2	no	—
199	C₅×M₁₆	—	3	2	no	—
200	C₅×M₁₆	C₄×D₃	1	1	yes	characteristic
201	C₂×C₅×C₈	—	3	1	no	—
202	C₂×C₅×C₈	—	3	2	no	—
203	#681	—	3	1	no	—
204	#681	—	3	2	no	—
205	C₂×#168	—	3	2	no	—
206	C₂×#168	C₂²×D₃	1	1	yes	characteristic
207	#676	—	3	2	no	—
208	#676	—	3	2	no	—
209	#676	C₄×D₃	1	2	yes	—
210	C₈×D₅	—	3	2	no	—
211	C₈×D₅	—	3	2	no	—
212	C₈×D₅	—	3	1	no	—
213	C₈×D₅	—	3	1	no	—
214	C₈×D₅	—	3	1	no	—
215	C₈×D₅	—	3	1	no	—
216	C₈×D₅	C₂²×D₃	1	2	yes	—
217	#674	—	3	1	no	—
218	#674	—	3	2	no	—
219	#674	—	3	1	no	—
220	#674	C₂²×D₃	1	1	yes	characteristic
221	#674	C₂²×D₃	1	1	yes	characteristic
222	#674	C₂²×D₃	1	2	yes	—
223	C₂×#131	—	15	1	no	—
224	#504	—	5	1	no	—
225	#504	—	15	2	no	—
226	#504	—	15	1	no	—
227	#504	—	15	2	no	—
228	#504	—	15	1	no	—
229	#504	—	15	1	no	—
230	C₂×M₃₂	—	15	2	no	—
231	C₂×M₃₂	—	15	1	no	—
232	C₂²×C₁₆	—	15	2	no	—
233	C₂²×C₁₆	—	15	1	no	—
234	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
235	C₂×D₁₅	—	2	2	no	—
236	C₂×D₁₅	C₂²×C₈	1	1	yes	characteristic
237	C₂×D₁₅	C₂²×C₈	1	1	yes	characteristic
238	C₂×C₅×D₃	C₂²×C₈	1	2	yes	—
239	C₂×C₃×D₅	C₂²×C₈	1	2	yes	—
240	D₃×D₅	—	2	4	no	—
241	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
243	Dic₁₅	C₂²×C₈	1	1	yes	characteristic
244	Dic₁₅	C₂²×C₈	1	1	yes	characteristic
245	C₃×Dic₅	C₂²×C₈	1	2	yes	—
246	C₅×Dic₃	C₂²×C₈	1	2	yes	—
247	C₃×#41	—	5	1	no	—
248	#239	—	5	1	no	—
249	D₃×Q₈	—	5	1	no	—
250	#237	—	5	2	no	—
251	#237	—	5	1	no	—
252	D₃×D₄	—	5	2	no	—
253	D₃×D₄	—	5	1	no	—
254	#235	—	5	2	no	—
255	#235	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
256	C₂×C₄×D₃	—	5	1	no	—
257	C₂×C₄×D₃	—	5	2	no	—
258	C₃×M₁₆	—	5	2	no	—
259	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
260	C₂×C₃×C₈	—	5	1	no	—
261	C₂×C₃×C₈	—	5	2	no	—
262	#208	—	5	1	no	—
263	#208	—	5	2	no	—
264	C₂×C₃⋊C₈	—	5	2	no	—
265	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
266	ΓL(1,𝔽₂₅)	—	5	2	no	—
267	ΓL(1,𝔽₂₅)	—	5	2	no	—
268	ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	1	2	yes	—
269	D₃×C₈	—	5	2	no	—
270	D₃×C₈	—	5	2	no	—
271	D₃×C₈	—	5	1	no	—
272	D₃×C₈	—	5	1	no	—
273	D₃×C₈	—	5	1	no	—
274	D₃×C₈	—	5	1	no	—
275	D₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
276	C₃×C₁₆	—	5	1	no	—
277	C₃×C₁₆	—	5	2	no	—
278	C₃×C₁₆	—	5	1	no	—
279	C₃⋊C₁₆	—	5	1	no	—
280	C₃⋊C₁₆	—	5	2	no	—
281	C₃⋊C₁₆	—	5	1	no	—
282	C₂²×D₅	—	3	1	no	—
283	C₂²×D₅	—	3	2	no	—
284	C₅×Q₈	—	3	1	no	—
285	C₅×D₄	—	3	2	no	—
286	C₅×D₄	—	3	1	no	—
287	C₂×C₄×C₅	—	3	2	no	—
288	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
289	C₂²⋊D₅	—	3	2	no	—
290	C₂²⋊D₅	—	3	2	no	—
291	C₂²⋊D₅	D₃×C₈	1	2	yes	—
292	C₂×Dic₅	—	3	1	no	—
293	C₂×Dic₅	—	3	2	no	—
294	D₂₀	—	3	2	no	—
295	D₂₀	D₃×C₈	1	1	yes	characteristic
296	C₄×D₅	—	3	2	no	—
297	C₄×D₅	—	3	1	no	—
298	C₄×D₅	—	3	1	no	—
299	C₄×D₅	—	3	1	no	—
300	C₄×D₅	—	3	1	no	—
301	C₄×D₅	—	3	2	no	—
302	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
303	Dic₁₀	—	3	2	no	—
304	Dic₁₀	D₃×C₈	1	1	yes	characteristic
305	C₅×C₈	—	3	1	no	—
306	C₅×C₈	—	3	1	no	—
307	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
308	#168	—	3	2	no	—
309	#168	C₂×C₄×D₃	1	1	yes	characteristic
310	#168	C₂³×D₃	1	1	yes	characteristic
311	C₂×#41	—	15	1	no	—
312	#131	—	3	1	no	—
313	#131	—	5	1	no	—
314	#131	—	15	2	no	—
315	#131	—	15	1	no	—
316	#131	—	15	2	no	—
317	#131	—	15	1	no	—
318	C₂×M₁₆	—	15	2	no	—
319	C₂×M₁₆	—	15	1	no	—
320	C₂²×C₈	—	15	1	no	—
321	C₂²×C₈	—	15	2	no	—
322	M₃₂	—	5	2	no	—
323	M₃₂	—	5	1	no	—
324	M₃₂	—	15	2	no	—
325	M₃₂	—	15	2	no	—
326	M₃₂	—	15	2	no	—
327	M₃₂	—	15	2	no	—
328	M₃₂	—	15	1	no	—
329	C₂×C₁₆	—	5	2	no	—
330	C₂×C₁₆	—	5	1	no	—
331	C₂×C₁₆	—	15	1	no	—
332	C₂×C₁₆	—	15	2	no	—
333	C₂×C₁₆	—	15	1	no	—
334	C₂×C₁₆	—	15	1	no	—
335	C₂×C₁₆	—	15	1	no	—
336	C₂×C₁₆	—	15	2	no	—
337	C₂×C₁₆	—	15	2	no	—
338	C₂×C₁₆	—	15	2	no	—
339	C₂×C₁₆	—	15	1	no	—
340	C₂×C₃×C₅	—	2	1	no	—
341	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
342	D₁₅	—	2	1	no	—
343	D₁₅	#504	1	2	yes	complemented
344	C₃×D₅	—	2	2	no	—
345	C₅×D₃	—	2	2	no	—
346	C₂²×D₃	—	5	1	no	—
347	C₂²×D₃	—	5	2	no	—
348	C₃×Q₈	—	5	1	no	—
349	C₃×D₄	—	5	2	no	—
350	C₃×D₄	—	5	1	no	—
351	C₂×C₃×C₄	—	5	2	no	—
352	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
353	#67	—	5	2	no	—
354	#67	—	5	2	no	—
355	#67	D₅⋊C₈	1	2	yes	—
356	C₂×Dic₃	—	5	1	no	—
357	C₂×Dic₃	—	5	2	no	—
358	D₁₂	—	5	2	no	—
359	D₁₂	D₅⋊C₈	1	1	yes	characteristic
360	C₄×D₃	—	5	2	no	—
361	C₄×D₃	—	5	1	no	—
362	C₄×D₃	—	5	1	no	—
363	C₄×D₃	—	5	1	no	—
364	C₄×D₃	—	5	1	no	—
365	C₄×D₃	—	5	2	no	—
366	C₄×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
367	Dic₆	—	5	2	no	—
368	Dic₆	D₅⋊C₈	1	1	yes	characteristic
369	C₃×C₈	—	5	1	no	—
370	C₃×C₈	—	5	1	no	—
371	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
372	C₃⋊C₈	—	5	2	no	—
373	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
375	C₂²×C₅	—	3	2	no	—
376	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
377	C₂×D₅	—	3	1	no	—
378	C₂×D₅	—	3	1	no	—
379	C₂×D₅	—	6	4	no	—
380	C₂×D₅	—	6	2	no	—
381	C₂×D₅	C₂×D₃×C₈	1	2	yes	—
382	C₄×C₅	—	3	2	no	—
383	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
384	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
385	Dic₅	—	3	1	no	—
386	Dic₅	—	3	1	no	—
387	Dic₅	C₂×D₃×C₈	1	2	yes	—
388	#41	—	3	1	no	—
389	#41	—	5	1	no	—
390	#41	—	15	2	no	—
391	#41	—	15	2	no	—
392	#41	—	15	1	no	—
393	#41	—	15	1	no	—
394	C₂×Q₈	—	15	1	no	—
395	C₂×D₄	—	15	2	no	—
396	C₂×D₄	—	15	1	no	—
397	C₂²×C₄	—	15	2	no	—
398	C₂²×C₄	—	15	1	no	—
399	M₁₆	—	3	2	no	—
400	M₁₆	—	5	2	no	—
401	M₁₆	—	15	2	no	—
402	M₁₆	—	15	2	no	—
403	M₁₆	—	15	1	no	—
404	M₁₆	—	15	2	no	—
405	M₁₆	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
406	C₂×C₈	—	3	1	no	—
407	C₂×C₈	—	3	2	no	—
408	C₂×C₈	—	5	1	no	—
409	C₂×C₈	—	5	2	no	—
410	C₂×C₈	—	15	1	no	—
411	C₂×C₈	—	15	1	no	—
412	C₂×C₈	—	15	1	no	—
413	C₂×C₈	—	15	1	no	—
414	C₂×C₈	—	15	2	no	—
415	C₂×C₈	—	15	2	no	—
416	C₂×C₈	—	15	2	no	—
417	C₁₆	—	5	1	no	—
418	C₁₆	—	5	2	no	—
419	C₁₆	—	5	1	no	—
420	C₁₆	—	15	1	no	—
421	C₁₆	—	15	1	no	—
422	C₁₆	—	15	2	no	—
423	C₃×C₅	C₂×#504	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	5	2	no	—
425	C₂²×C₃	C₂×D₅⋊C₈	1	1	yes	characteristic
426	C₂×D₃	—	5	1	no	—
427	C₂×D₃	—	5	1	no	—
428	C₂×D₃	—	10	4	no	—
429	C₂×D₃	—	10	2	no	—
430	C₂×D₃	C₂×D₅⋊C₈	1	2	yes	—
431	C₃×C₄	—	5	2	no	—
432	C₃×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
433	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
434	Dic₃	—	5	1	no	—
435	Dic₃	—	5	1	no	—
436	Dic₃	C₂×D₅⋊C₈	1	2	yes	—
437	C₂×C₅	—	2	1	no	—
438	C₂×C₅	—	6	2	no	—
439	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
440	D₅	—	2	2	no	—
441	D₅	—	3	2	no	—
442	D₅	—	6	1	no	—
443	C₂³	—	15	2	no	—
444	C₂³	—	15	1	no	—
445	Q₈	—	3	1	no	—
446	Q₈	—	5	1	no	—
447	Q₈	—	15	2	no	—
448	D₄	—	3	2	no	—
449	D₄	—	3	1	no	—
450	D₄	—	5	2	no	—
451	D₄	—	5	1	no	—
452	D₄	—	15	2	no	—
453	D₄	—	15	2	no	—
454	D₄	—	15	2	no	—
455	C₂×C₄	—	3	2	no	—
456	C₂×C₄	—	5	2	no	—
457	C₂×C₄	—	15	2	no	—
458	C₂×C₄	—	15	2	no	—
459	C₂×C₄	—	15	2	no	—
460	C₂×C₄	—	15	1	no	—
461	C₂×C₄	—	15	1	no	—
462	C₂×C₄	—	15	1	no	—
463	C₂×C₄	—	15	1	no	—
464	C₂×C₄	—	15	1	no	—
465	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
466	C₈	—	3	1	no	—
467	C₈	—	3	1	no	—
468	C₈	—	5	1	no	—
469	C₈	—	5	1	no	—
470	C₈	—	15	2	no	—
471	C₈	C₂×D₃×AGL(1,𝔽₅)	1	2	yes	—
472	C₂×C₃	—	2	1	no	—
473	C₂×C₃	—	10	2	no	—
474	C₂×C₃	C₂²×D₅⋊C₈	1	1	yes	characteristic
475	D₃	—	2	2	no	—
476	D₃	—	5	2	no	—
477	D₃	—	10	1	no	—
478	C₅	D₃×#504	1	1	yes	characteristic, complemented, Sylow
479	C₂²	—	3	2	no	—
480	C₂²	—	5	2	no	—
481	C₂²	—	15	1	no	—
482	C₂²	—	15	1	no	—
483	C₂²	—	30	2	no	—
484	C₂²	—	30	4	no	—
485	C₂²	D₃×D₅⋊C₈	1	1	yes	characteristic
486	C₄	—	3	2	no	—
487	C₄	—	5	2	no	—
488	C₄	—	15	1	no	—
489	C₄	—	15	1	no	—
490	C₄	D₃×D₅⋊C₈	1	1	yes	characteristic
491	C₄	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
492	C₃	D₅⋊#504	1	1	yes	characteristic, complemented, Sylow
493	C₂	—	2	1	no	—
494	C₂	—	6	2	no	—
495	C₂	—	10	2	no	—
496	C₂	—	15	2	no	—
497	C₂	—	30	1	no	—
498	C₂	C₂×D₃×D₅⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
commutator, socle	C₂×C₃×C₅	C₂³×C₈
Fitting	C₃×C₅×M₁₆	C₂×C₄
prime radical	#92016	C₄
cosocle	C₃×#168	C₂⁴
hypercenter	M₁₆	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×#504
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. #11752384	C₂	semidirect
3. C₃×#65725	C₂	semidirect
4. #11751741	C₂	semidirect
5. C₂×#91164	C₂	semidirect
6. #11751738	C₂	semidirect
7. #11751736	C₂	semidirect
8. #11751646	C₂	semidirect
9. #11751644	C₂	semidirect
10. #11751642	C₂	semidirect
11. D₃×D₅⋊C₁₆	C₂	semidirect
24. #91227	C₂²	semidirect
25. C₂×C₃⋊#674	C₂²	semidirect
26. #91219	C₂²	semidirect
27. D₅⋊(C₃⋊C₁₆)	C₂²	semidirect
28. C₃×#3998	C₂²	semidirect
29. C₂×C₃×#674	C₂²	semidirect
30. C₃×#3990	C₂²	semidirect
31. C₃×D₅⋊C₁₆	C₂²	semidirect
32. #91166	C₂²	semidirect
33. #91165	C₂²	semidirect
34. #91165	C₂²	semidirect
38. #91164	C₂²	semidirect
39. #91164	C₂²	semidirect
40. D₃×#674	C₂²	semidirect
41. D₃×#674	C₂²	semidirect
49. #65725	D₃	semidirect
114. #3998	C₂×D₃	semidirect
118. C₂×#674	C₂×D₃	semidirect
121. #3990	C₂×D₃	semidirect
128. D₅⋊C₁₆	C₂×D₃	semidirect
343. D₁₅	#504	semidirect
423. C₃×C₅	C₂×#504	semidirect
478. C₅	D₃×#504	semidirect
492. C₃	D₅⋊#504	semidirect

Maximal subgroups

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

subgroup	index
#11754017	2
#11752384	2
C₃×#65725	2
#11751741	2
C₂×#91164	2
#11751738	2
#11751736	2
#11751646	2
#11751644	2
#11751642	2
D₃×D₅⋊C₁₆	2
D₅⋊#504	3
D₃×#504	5