Subgroups — #14418980

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6821	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	#11751125	C₂	1	1	yes	maximal, characteristic, complemented
4	#11750939	C₂	1	1	yes	maximal, characteristic, complemented
5	#11750937	C₂	1	2	yes	maximal, complemented
6	#11750934	C₂	1	1	yes	maximal, characteristic, complemented
7	#11750934	C₂	1	2	yes	maximal, complemented
8	#11750808	C₂	1	2	yes	maximal, complemented
9	#11750807	C₂	1	2	yes	maximal, complemented
10	#11750789	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₈×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611669	—	3	1	no	maximal, Hall
13	C₂×#6821	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	Q₈×Dic₁₅	C₄	1	1	yes	characteristic
16	C₂×#6705	C₂²	1	2	yes	—
17	C₂×#6705	C₂²	1	2	yes	—
18	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₁₅	C₂²	1	1	yes	characteristic
20	#91782	C₄	1	2	yes	—
21	#91782	C₄	1	1	yes	characteristic
22	#91781	C₄	1	2	yes	—
23	#91781	C₄	1	1	yes	characteristic
24	C₄×D₆₀	C₂²	1	2	yes	—
25	C₄×D₆₀	C₂²	1	1	yes	characteristic
26	C₄²×D₁₅	C₂²	1	1	yes	characteristic
27	C₄²×D₁₅	C₂²	1	2	yes	—
28	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
29	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₃×C₅×#97	C₂²	1	2	yes	—
31	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	#91104	C₂²	1	2	yes	—
33	#91104	C₂²	1	2	yes	—
34	#91104	C₂²	1	2	yes	—
35	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
36	C₈×Dic₁₅	C₂²	1	2	yes	—
37	C₈×Dic₁₅	C₂²	1	1	yes	characteristic
38	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
39	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
40	#91087	C₂²	1	2	yes	—
41	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
42	#79938	—	5	1	no	maximal, Hall
43	C₄×#713	—	3	1	no	—
44	C₅×#446	D₃	1	1	yes	characteristic, complemented
45	#65313	—	3	1	no	—
46	#65127	—	3	1	no	—
47	#65125	—	3	2	no	—
48	#65122	—	3	1	no	—
49	#65122	—	3	2	no	—
50	#64996	—	3	2	no	—
51	#64995	—	3	2	no	—
52	#64977	—	3	1	no	—
53	C₄×C₈×D₅	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	#6821	—	2	4	no	—
56	C₂×D₆₀	C₂×C₄	1	2	yes	—
57	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
59	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
60	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
63	C₂×C₄×D₁₅	C₂³	1	2	yes	—
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
68	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₄²×C₅	C₂³	1	2	yes	—
71	#6714	C₂×C₄	1	2	yes	—
72	#6714	C₂×C₄	1	2	yes	—
73	#6714	C₂×C₄	1	2	yes	—
74	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
75	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
76	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
78	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
79	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
81	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
82	C₂×C₃⋊#168	C₂³	1	2	yes	—
83	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
84	#6705	—	2	4	no	—
85	#6705	—	2	4	no	—
86	C₈×D₁₅	—	2	2	no	—
87	C₈×D₁₅	—	2	2	no	—
88	C₄×#239	—	5	1	no	—
89	C₃×#446	D₅	1	1	yes	characteristic, complemented
90	#5024	—	5	1	no	—
91	#4838	—	5	1	no	—
92	#4836	—	5	2	no	—
93	#4833	—	5	1	no	—
94	#4833	—	5	2	no	—
95	#4707	—	5	2	no	—
96	#4706	—	5	2	no	—
97	#4688	—	5	1	no	—
98	C₄×D₃×C₈	—	5	1	no	—
99	C₂×#713	—	3	1	no	—
100	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
101	Q₈×Dic₅	—	3	1	no	—
102	C₂×#676	—	3	2	no	—
103	C₂×#676	—	3	2	no	—
104	C₂×C₈×D₅	—	3	1	no	—
105	C₂×C₈×D₅	—	3	1	no	—
106	#4039	—	3	2	no	—
107	#4039	—	3	1	no	—
108	#4038	—	3	1	no	—
109	#4038	—	3	2	no	—
110	C₄×D₂₀	—	3	2	no	—
111	C₄×D₂₀	—	3	1	no	—
112	C₄²×D₅	—	3	1	no	—
113	C₄²×D₅	—	3	2	no	—
114	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
115	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
116	C₅×#97	C₂×D₃	1	2	yes	—
117	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
118	#3952	—	3	2	no	—
119	#3952	—	3	2	no	—
120	#3952	—	3	2	no	—
121	C₈×Dic₅	—	3	1	no	—
122	C₈×Dic₅	—	3	2	no	—
123	C₈×Dic₅	—	3	1	no	—
124	C₄⋊#168	—	3	1	no	—
125	C₄⋊#168	—	3	2	no	—
126	#3935	—	3	2	no	—
127	C₄×#168	—	3	1	no	—
128	#2965	—	15	1	no	Sylow
129	C₂²×D₁₅	C₂²×C₄	1	2	yes	—
130	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
131	C₃×C₅×Q₈	—	2	2	no	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
139	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
140	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
141	D₆₀	—	2	4	no	—
142	D₆₀	—	2	2	no	—
143	C₄×D₁₅	—	2	1	no	—
144	C₄×D₁₅	—	2	1	no	—
145	C₄×D₁₅	—	2	2	no	—
146	C₄×D₁₅	—	2	2	no	—
147	C₄×D₁₅	—	2	4	no	—
148	C₄×D₁₅	—	2	2	no	—
149	C₄×D₁₅	—	2	4	no	—
150	C₄×D₁₅	M₁₆	1	4	yes	complemented
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×C₅×C₈	—	2	2	no	—
153	C₃×C₅×C₈	#41	1	2	yes	complemented
154	C₃⋊#168	—	2	1	no	—
155	C₃⋊#168	—	2	2	no	—
156	C₃⋊#168	#41	1	2	yes	complemented
157	C₂×#239	—	5	1	no	—
158	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
159	Q₈×Dic₃	—	5	1	no	—
160	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
161	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
162	C₂×D₃×C₈	—	5	1	no	—
163	C₂×D₃×C₈	—	5	1	no	—
164	#893	—	5	2	no	—
165	#893	—	5	1	no	—
166	#892	—	5	1	no	—
167	#892	—	5	2	no	—
168	C₄×D₁₂	—	5	1	no	—
169	C₄×D₁₂	—	5	2	no	—
170	C₄²×D₃	—	5	1	no	—
171	C₄²×D₃	—	5	2	no	—
172	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
173	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
174	C₃×#97	C₂×D₅	1	2	yes	—
175	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
176	(C₂×D₃)⋊C₈	—	5	2	no	—
177	(C₂×D₃)⋊C₈	—	5	2	no	—
178	(C₂×D₃)⋊C₈	—	5	2	no	—
179	C₈×Dic₃	—	5	1	no	—
180	C₈×Dic₃	—	5	1	no	—
181	C₈×Dic₃	—	5	2	no	—
182	C₄⋊(C₃⋊C₈)	—	5	1	no	—
183	C₄⋊(C₃⋊C₈)	—	5	2	no	—
184	#803	—	5	2	no	—
185	C₄×C₃⋊C₈	—	5	1	no	—
186	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
187	#713	—	6	4	no	—
188	C₂×D₂₀	—	3	2	no	—
189	C₂×D₂₀	—	3	1	no	—
190	C₂×C₄×D₅	—	3	1	no	—
191	C₂×C₄×D₅	—	3	2	no	—
192	C₂×C₄×D₅	—	3	1	no	—
193	C₂×C₄×D₅	—	3	2	no	—
194	C₂×C₄×D₅	—	3	1	no	—
195	C₂×C₄×D₅	—	3	2	no	—
196	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
198	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
199	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
200	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
201	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₄²×C₅	C₂²×D₃	1	2	yes	—
203	#685	—	3	2	no	—
204	#685	—	3	2	no	—
205	#685	—	3	2	no	—
206	C₄⋊Dic₅	—	3	2	no	—
207	C₄⋊Dic₅	—	3	1	no	—
208	C₄×Dic₅	—	3	1	no	—
209	C₄×Dic₅	—	3	2	no	—
210	C₄×Dic₅	—	3	2	no	—
211	C₄×Dic₅	—	3	1	no	—
212	C₄×Dic₅	—	3	1	no	—
213	C₂×#168	—	3	1	no	—
214	C₂×#168	—	3	1	no	—
215	C₂×#168	—	3	2	no	—
216	#676	—	6	4	no	—
217	#676	—	6	4	no	—
218	C₈×D₅	—	6	2	no	—
219	C₈×D₅	—	6	2	no	—
220	C₄×#41	—	15	1	no	—
221	#446	—	15	1	no	—
222	#446	D₁₅	1	1	yes	characteristic, complemented
223	#436	—	15	1	no	—
224	#436	—	15	1	no	—
225	#435	—	15	2	no	—
226	#435	—	15	2	no	—
227	#431	—	15	2	no	—
228	#431	—	15	1	no	—
229	C₄×M₁₆	—	15	2	no	—
230	C₂×C₄×C₈	—	15	1	no	—
231	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂×D₁₅	—	2	1	no	—
233	C₂×D₁₅	—	2	1	no	—
234	C₂×D₁₅	—	2	2	no	—
235	C₂×D₁₅	—	2	2	no	—
236	C₂×D₁₅	—	2	2	no	—
237	C₂×D₁₅	C₂×M₁₆	1	2	yes	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	2	1	no	—
240	C₃×C₄×C₅	—	2	2	no	—
241	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
242	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
244	Dic₁₅	—	2	1	no	—
245	Dic₁₅	—	2	2	no	—
246	Dic₁₅	C₂×M₁₆	1	2	yes	—
247	Dic₁₅	#131	1	2	yes	—
248	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
249	#239	—	10	4	no	—
250	C₂×D₁₂	—	5	2	no	—
251	C₂×D₁₂	—	5	1	no	—
252	C₂×C₄×D₃	—	5	1	no	—
253	C₂×C₄×D₃	—	5	2	no	—
254	C₂×C₄×D₃	—	5	1	no	—
255	C₂×C₄×D₃	—	5	2	no	—
256	C₂×C₄×D₃	—	5	1	no	—
257	C₂×C₄×D₃	—	5	2	no	—
258	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
259	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
260	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
261	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
262	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
263	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
264	C₃×C₄²	C₂²×D₅	1	2	yes	—
265	(C₂×D₃)⋊C₄	—	5	2	no	—
266	(C₂×D₃)⋊C₄	—	5	2	no	—
267	(C₂×D₃)⋊C₄	—	5	2	no	—
268	C₄⋊Dic₃	—	5	2	no	—
269	C₄⋊Dic₃	—	5	1	no	—
270	C₄×Dic₃	—	5	1	no	—
271	C₄×Dic₃	—	5	2	no	—
272	C₄×Dic₃	—	5	2	no	—
273	C₄×Dic₃	—	5	1	no	—
274	C₄×Dic₃	—	5	1	no	—
275	C₂×C₃⋊C₈	—	5	1	no	—
276	C₂×C₃⋊C₈	—	5	1	no	—
277	C₂×C₃⋊C₈	—	5	2	no	—
278	ΓL(1,𝔽₂₅)	—	10	4	no	—
279	ΓL(1,𝔽₂₅)	—	10	4	no	—
280	D₃×C₈	—	10	2	no	—
281	D₃×C₈	—	10	2	no	—
282	C₂²×D₅	—	3	1	no	—
283	C₂²×D₅	—	3	2	no	—
284	C₅×Q₈	—	2	2	no	—
285	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
286	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
288	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
290	C₂×Dic₅	—	3	1	no	—
291	C₂×Dic₅	—	3	1	no	—
292	C₂×Dic₅	—	3	1	no	—
293	C₂×Dic₅	—	3	2	no	—
294	D₂₀	—	6	4	no	—
295	D₂₀	—	6	2	no	—
296	C₄×D₅	—	3	4	no	—
297	C₄×D₅	—	6	2	no	—
298	C₄×D₅	—	6	4	no	—
299	C₄×D₅	—	6	4	no	—
300	C₄×D₅	—	6	1	no	—
301	C₄×D₅	—	6	2	no	—
302	C₄×D₅	—	6	1	no	—
303	C₄×D₅	—	6	2	no	—
304	C₅×C₈	—	2	1	no	—
305	C₅×C₈	—	2	2	no	—
306	C₅×C₈	#239	1	2	yes	complemented
307	#168	—	3	2	no	—
308	#168	—	6	1	no	—
309	#168	—	6	2	no	—
310	C₂×#41	—	15	1	no	—
311	C₂×M₁₆	—	15	2	no	—
312	C₂×M₁₆	—	15	2	no	—
313	C₂²×C₈	—	15	1	no	—
314	C₂²×C₈	—	15	1	no	—
315	C₄×Q₈	—	15	1	no	—
316	C₄×Q₈	C₂×D₁₅	1	1	yes	characteristic
317	C₄×D₄	—	15	2	no	—
318	C₄×D₄	—	15	1	no	—
319	C₄×D₄	—	15	2	no	—
320	C₄×D₄	—	15	1	no	—
321	#117	—	15	1	no	—
322	#117	—	15	2	no	—
323	C₂×C₄²	—	15	1	no	—
324	C₂×C₄²	—	15	2	no	—
325	C₄⋊C₈	—	15	2	no	—
326	C₄⋊C₈	—	15	1	no	—
327	C₄⋊C₈	C₂×D₁₅	1	2	yes	—
328	C₄⋊C₈	C₂×D₁₅	1	1	yes	characteristic
329	C₂²⋊C₈	—	15	2	no	—
330	C₂²⋊C₈	—	15	2	no	—
331	C₂²⋊C₈	—	15	2	no	—
332	#97	—	15	2	no	—
333	#97	C₂×D₁₅	1	2	yes	—
334	C₄×C₈	—	15	1	no	—
335	C₄×C₈	—	15	1	no	—
336	C₄×C₈	—	15	2	no	—
337	C₄×C₈	—	15	1	no	—
338	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
339	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
341	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
342	D₁₅	—	2	2	no	—
343	D₁₅	—	4	2	no	—
344	C₂²×D₃	—	5	1	no	—
345	C₂²×D₃	—	5	2	no	—
346	C₃×Q₈	—	2	2	no	—
347	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
348	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
350	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
352	C₂×Dic₃	—	5	1	no	—
353	C₂×Dic₃	—	5	1	no	—
354	C₂×Dic₃	—	5	1	no	—
355	C₂×Dic₃	—	5	2	no	—
356	D₁₂	—	10	4	no	—
357	D₁₂	—	10	2	no	—
358	C₄×D₃	—	5	4	no	—
359	C₄×D₃	—	10	2	no	—
360	C₄×D₃	—	10	4	no	—
361	C₄×D₃	—	10	4	no	—
362	C₄×D₃	—	10	1	no	—
363	C₄×D₃	—	10	2	no	—
364	C₄×D₃	—	10	1	no	—
365	C₄×D₃	—	10	2	no	—
366	C₃×C₈	—	2	1	no	—
367	C₃×C₈	—	2	2	no	—
368	C₃×C₈	#713	1	2	yes	complemented
369	C₃⋊C₈	—	5	2	no	—
370	C₃⋊C₈	—	10	1	no	—
371	C₃⋊C₈	—	10	2	no	—
372	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
373	C₂×D₅	—	3	2	no	—
374	C₂×D₅	—	6	1	no	—
375	C₂×D₅	—	6	1	no	—
376	C₂×D₅	—	6	2	no	—
377	C₂×D₅	—	6	2	no	—
378	C₂×D₅	—	6	2	no	—
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	2	1	no	—
381	C₄×C₅	—	2	2	no	—
382	C₄×C₅	D₃×M₁₆	1	2	yes	—
383	C₄×C₅	C₂×#239	1	1	yes	characteristic
384	C₄×C₅	D₃×#41	1	1	yes	characteristic
385	Dic₅	—	3	2	no	—
386	Dic₅	—	3	2	no	—
387	Dic₅	—	6	1	no	—
388	Dic₅	—	6	2	no	—
389	#41	—	30	4	no	—
390	C₂×Q₈	C₄×D₁₅	1	1	yes	characteristic
391	C₂×D₄	—	15	2	no	—
392	C₂×D₄	—	15	1	no	—
393	C₂²×C₄	—	15	1	no	—
394	C₂²×C₄	—	15	2	no	—
395	C₂²×C₄	—	15	1	no	—
396	C₂²×C₄	—	15	2	no	—
397	C₂²×C₄	—	15	1	no	—
398	C₂²×C₄	—	15	2	no	—
399	M₁₆	—	30	4	no	—
400	M₁₆	—	30	4	no	—
401	C₂×C₈	—	15	1	no	—
402	C₂×C₈	—	15	1	no	—
403	C₂×C₈	—	15	2	no	—
404	C₂×C₈	—	30	2	no	—
405	C₂×C₈	—	30	2	no	—
406	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
407	C₂×C₈	C₂²×D₁₅	1	2	yes	—
408	C₂×C₈	C₂²×D₁₅	1	1	yes	characteristic
409	C₄⋊C₄	—	15	2	no	—
410	C₄⋊C₄	—	15	1	no	—
411	C₄⋊C₄	C₄×D₁₅	1	2	yes	—
412	C₄⋊C₄	C₄×D₁₅	1	1	yes	characteristic
413	C₂²⋊C₄	—	15	2	no	—
414	C₂²⋊C₄	—	15	2	no	—
415	C₂²⋊C₄	—	15	2	no	—
416	C₄²	—	15	1	no	—
417	C₄²	—	15	2	no	—
418	C₄²	—	15	2	no	—
419	C₄²	—	15	1	no	—
420	C₄²	—	15	1	no	—
421	C₄²	C₂²×D₁₅	1	1	yes	characteristic
422	C₄²	C₂²×D₁₅	1	2	yes	—
423	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
425	C₂×D₃	—	5	2	no	—
426	C₂×D₃	—	10	1	no	—
427	C₂×D₃	—	10	1	no	—
428	C₂×D₃	—	10	2	no	—
429	C₂×D₃	—	10	2	no	—
430	C₂×D₃	—	10	2	no	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	D₅×M₁₆	1	2	yes	—
435	C₃×C₄	C₂×#713	1	1	yes	characteristic
436	C₃×C₄	D₅×#41	1	1	yes	characteristic
437	Dic₃	—	5	2	no	—
438	Dic₃	—	5	2	no	—
439	Dic₃	—	10	1	no	—
440	Dic₃	—	10	2	no	—
441	C₂×C₅	C₄×#239	1	1	yes	characteristic
442	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
443	C₂×C₅	D₃×#131	1	1	yes	characteristic
444	D₅	—	6	2	no	—
445	D₅	—	12	2	no	—
446	C₂³	—	15	1	no	—
447	C₂³	—	15	2	no	—
448	Q₈	—	2	2	no	—
449	D₄	—	30	4	no	—
450	D₄	—	30	2	no	—
451	C₂×C₄	—	15	1	no	—
452	C₂×C₄	—	15	1	no	—
453	C₂×C₄	—	15	4	no	—
454	C₂×C₄	—	15	1	no	—
455	C₂×C₄	—	15	2	no	—
456	C₂×C₄	—	30	4	no	—
457	C₂×C₄	—	30	2	no	—
458	C₂×C₄	—	30	4	no	—
459	C₂×C₄	—	30	1	no	—
460	C₂×C₄	—	30	2	no	—
461	C₂×C₄	—	30	1	no	—
462	C₂×C₄	—	30	2	no	—
463	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
464	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
465	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
466	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
467	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
468	C₈	—	2	1	no	—
469	C₈	—	2	2	no	—
470	C₈	—	15	2	no	—
471	C₈	—	30	1	no	—
472	C₈	—	30	2	no	—
473	C₈	#6821	1	2	yes	complemented
474	C₂×C₃	C₄×#713	1	1	yes	characteristic
475	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
476	C₂×C₃	D₅×#131	1	1	yes	characteristic
477	D₃	—	10	2	no	—
478	D₃	—	20	2	no	—
479	C₅	#79938	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	15	2	no	—
481	C₂²	—	30	1	no	—
482	C₂²	—	30	1	no	—
483	C₂²	—	30	2	no	—
484	C₂²	—	30	2	no	—
485	C₂²	—	30	2	no	—
486	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	2	no	—
490	C₄	—	15	2	no	—
491	C₄	—	15	2	no	—
492	C₄	—	30	1	no	—
493	C₄	—	30	2	no	—
494	C₄	M₁₆×D₁₅	1	2	yes	—
495	C₄	C₂×#6821	1	1	yes	characteristic
496	C₄	#41×D₁₅	1	1	yes	characteristic
497	C₃	#10611669	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	30	2	no	—
499	C₂	—	60	2	no	—
500	C₂	C₄×#6821	1	1	yes	characteristic
501	C₂	C₂×M₁₆×D₁₅	1	1	yes	characteristic
502	C₂	D₁₅×#131	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×#446	C₂
prime radical	C₂×#6821	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#446	D₁₅
hypocenter	C₃×C₅	#2965
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#446	C₂	semidirect
3. #11751125	C₂	semidirect
4. #11750939	C₂	semidirect
5. #11750937	C₂	semidirect
6. #11750934	C₂	semidirect
7. #11750934	C₂	semidirect
8. #11750808	C₂	semidirect
9. #11750807	C₂	semidirect
10. #11750789	C₂	semidirect
11. C₄×C₈×D₁₅	C₂	semidirect
44. C₅×#446	D₃	semidirect
89. C₃×#446	D₅	semidirect
150. C₄×D₁₅	M₁₆	semidirect
153. C₃×C₅×C₈	#41	semidirect
156. C₃⋊#168	#41	semidirect
222. #446	D₁₅	semidirect
306. C₅×C₈	#239	semidirect
368. C₃×C₈	#713	semidirect
423. C₃×C₅	#2965	semidirect
473. C₈	#6821	semidirect
479. C₅	#79938	semidirect
497. C₃	#10611669	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6821	2
C₃×C₅×#446	2
#11751125	2
#11750939	2
#11750937	2
#11750934	2
#11750808	2
#11750807	2
#11750789	2
C₄×C₈×D₁₅	2
#10611669	3
#79938	5