Subgroups — #14419073

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×C₅×#239	C₂	1	1	yes	maximal, characteristic
2	#11751125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65313	C₂	1	1	yes	maximal, characteristic, complemented
4	#11747014	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747008	C₂	1	1	yes	maximal, characteristic, complemented
6	#11747005	C₂	1	2	yes	maximal, complemented
7	#11746999	C₂	1	2	yes	maximal, complemented
8	#11746987	C₂	1	2	yes	maximal, complemented
9	C₄×D₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746853	C₂	1	1	yes	maximal, characteristic, complemented
11	#11746853	C₂	1	2	yes	maximal, complemented
12	#10614248	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic
16	C₅×#893	C₄	1	2	yes	—
17	C₅×#893	C₄	1	1	yes	characteristic
18	C₅×#892	C₄	1	2	yes	—
19	C₅×#892	C₄	1	1	yes	characteristic
20	C₄×C₅×D₁₂	C₂²	1	2	yes	—
21	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
22	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₄²×C₅×D₃	C₂²	1	2	yes	—
24	C₂×#6650	C₂²	1	2	yes	—
25	C₂×#6650	C₂²	1	2	yes	—
26	C₂×D₃×#168	C₂²	1	1	yes	characteristic
27	C₂×D₃×#168	C₂²	1	1	yes	characteristic
28	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
29	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
30	#91087	C₂²	1	2	yes	—
31	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
32	C₃×C₄⋊#168	C₂²	1	2	yes	—
33	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
34	C₃×#3935	C₂²	1	2	yes	—
35	C₃×C₄×#168	C₂²	1	1	yes	characteristic
36	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
37	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
38	(C₂×D₃)⋊#168	C₂²	1	2	yes	—
39	Dic₃×#168	C₂²	1	1	yes	characteristic
40	Dic₃×#168	C₂²	1	2	yes	—
41	Dic₃×#168	C₂²	1	1	yes	characteristic
42	#79938	—	5	1	no	maximal, Hall
43	C₄×C₅×#41	—	3	1	no	—
44	#65313	—	3	1	no	—
45	#65313	D₃	1	1	yes	characteristic, complemented
46	#65301	—	3	1	no	—
47	#65301	—	3	1	no	—
48	#65300	—	3	2	no	—
49	#65300	—	3	2	no	—
50	#65214	—	3	1	no	—
51	#65214	—	3	2	no	—
52	C₄×#681	—	3	2	no	—
53	C₂×C₄×#168	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₅×#239	—	2	4	no	—
56	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
57	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
60	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₄²×C₅	C₂³	1	2	yes	—
68	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
69	C₂×C₃⋊#168	C₂³	1	2	yes	—
70	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
71	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
72	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
73	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
74	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
75	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
78	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
79	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₅×Dic₃	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	#6650	—	2	4	no	—
85	#6650	—	2	4	no	—
86	D₃×#168	—	2	2	no	—
87	D₃×#168	—	2	2	no	—
88	C₄×#239	D₅	1	1	yes	characteristic
89	C₃×#446	—	5	1	no	—
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×C₅×#41	—	3	1	no	—
100	C₄×C₅×Q₈	—	3	1	no	—
101	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
102	C₄×C₅×D₄	—	3	2	no	—
103	C₄×C₅×D₄	—	3	1	no	—
104	C₄×C₅×D₄	—	3	2	no	—
105	C₄×C₅×D₄	—	3	1	no	—
106	C₅×#117	—	3	1	no	—
107	C₅×#117	—	3	2	no	—
108	C₂×C₄²×C₅	—	3	1	no	—
109	C₂×C₄²×C₅	—	3	2	no	—
110	C₂×#681	—	3	2	no	—
111	C₂×#681	—	3	2	no	—
112	C₂²×#168	—	3	1	no	—
113	C₂²×#168	—	3	1	no	—
114	C₂²⋊#168	—	3	2	no	—
115	C₂²⋊#168	—	3	2	no	—
116	C₂²⋊#168	—	3	2	no	—
117	C₄⋊#168	—	3	2	no	—
118	C₄⋊#168	—	3	1	no	—
119	C₄⋊#168	C₂×D₃	1	2	yes	—
120	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
121	#3935	—	3	2	no	—
122	#3935	C₂×D₃	1	2	yes	—
123	C₄×#168	—	3	1	no	—
124	C₄×#168	—	3	1	no	—
125	C₄×#168	—	3	1	no	—
126	C₄×#168	—	3	2	no	—
127	C₄×#168	C₂×D₃	1	1	yes	characteristic
128	#2965	—	15	1	no	Sylow
129	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
130	C₂²×C₅×D₃	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×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
139	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
141	C₅×D₁₂	—	2	4	no	—
142	C₅×D₁₂	—	2	2	no	—
143	C₄×C₅×D₃	—	2	1	no	—
144	C₄×C₅×D₃	—	2	1	no	—
145	C₄×C₅×D₃	—	2	2	no	—
146	C₄×C₅×D₃	—	2	2	no	—
147	C₄×C₅×D₃	—	2	4	no	—
148	C₄×C₅×D₃	—	2	2	no	—
149	C₄×C₅×D₃	—	2	4	no	—
150	C₄×C₅×D₃	M₁₆	1	4	yes	complemented
151	C₃⋊#168	—	2	1	no	—
152	C₃⋊#168	—	2	2	no	—
153	C₃⋊#168	#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	Dic₅	1	1	yes	characteristic
158	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
159	Q₈×Dic₃	Dic₅	1	1	yes	characteristic
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	Dic₅	1	2	yes	—
165	#893	Dic₅	1	1	yes	characteristic
166	#892	Dic₅	1	2	yes	—
167	#892	Dic₅	1	1	yes	characteristic
168	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
169	C₄×D₁₂	C₂×D₅	1	2	yes	—
170	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
171	C₄²×D₃	C₂×D₅	1	2	yes	—
172	C₃×C₄⋊C₈	—	5	2	no	—
173	C₃×C₄⋊C₈	—	5	1	no	—
174	C₃×#97	—	5	2	no	—
175	C₃×C₄×C₈	—	5	1	no	—
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	C₅×#41	—	6	4	no	—
187	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
188	C₂×C₅×D₄	—	3	2	no	—
189	C₂×C₅×D₄	—	3	1	no	—
190	C₂²×C₄×C₅	—	3	1	no	—
191	C₂²×C₄×C₅	—	3	2	no	—
192	C₂²×C₄×C₅	—	3	1	no	—
193	C₂²×C₄×C₅	—	3	2	no	—
194	C₂²×C₄×C₅	—	3	1	no	—
195	C₂²×C₄×C₅	—	3	2	no	—
196	C₅×C₄⋊C₄	—	3	2	no	—
197	C₅×C₄⋊C₄	—	3	1	no	—
198	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
199	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
200	C₅×C₂²⋊C₄	—	3	2	no	—
201	C₅×C₂²⋊C₄	—	3	2	no	—
202	C₅×C₂²⋊C₄	—	3	2	no	—
203	C₄²×C₅	—	3	1	no	—
204	C₄²×C₅	—	3	2	no	—
205	C₄²×C₅	—	3	2	no	—
206	C₄²×C₅	—	3	1	no	—
207	C₄²×C₅	—	3	1	no	—
208	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
209	C₄²×C₅	C₂²×D₃	1	2	yes	—
210	#681	—	6	4	no	—
211	#681	—	6	4	no	—
212	C₂×#168	—	3	1	no	—
213	C₂×#168	—	3	1	no	—
214	C₂×#168	—	3	2	no	—
215	C₂×#168	—	6	2	no	—
216	C₂×#168	—	6	2	no	—
217	C₂×#168	C₂²×D₃	1	1	yes	characteristic
218	C₂×#168	C₂²×D₃	1	2	yes	—
219	C₂×#168	C₂²×D₃	1	1	yes	characteristic
220	C₄×#41	—	3	1	no	—
221	#446	—	5	1	no	—
222	#446	—	15	1	no	—
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×C₅×D₃	—	2	1	no	—
233	C₂×C₅×D₃	—	2	1	no	—
234	C₂×C₅×D₃	—	2	2	no	—
235	C₂×C₅×D₃	—	2	2	no	—
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	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	C₅×Dic₃	—	2	1	no	—
245	C₅×Dic₃	—	2	2	no	—
246	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
247	C₅×Dic₃	#131	1	2	yes	—
248	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
249	#239	—	2	4	no	—
250	C₂×D₁₂	C₂×Dic₅	1	2	yes	—
251	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
252	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
253	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
254	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
255	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
256	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
257	C₂×C₄×D₃	C₂²×D₅	1	2	yes	—
258	C₂×C₃×C₈	—	5	1	no	—
259	C₂×C₃×C₈	—	5	1	no	—
260	C₂×C₃×C₈	—	5	2	no	—
261	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
262	C₃×C₄⋊C₄	C₂×Dic₅	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	C₂×Dic₅	1	2	yes	—
266	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
267	(C₂×D₃)⋊C₄	C₂×Dic₅	1	2	yes	—
268	C₄⋊Dic₃	C₂×Dic₅	1	2	yes	—
269	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
270	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
271	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
272	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
273	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
274	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
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	C₂³×C₅	—	3	1	no	—
283	C₂³×C₅	—	3	2	no	—
284	C₅×Q₈	—	2	2	no	—
285	C₅×D₄	—	6	4	no	—
286	C₅×D₄	—	6	2	no	—
287	C₂×C₄×C₅	—	3	1	no	—
288	C₂×C₄×C₅	—	3	1	no	—
289	C₂×C₄×C₅	—	3	4	no	—
290	C₂×C₄×C₅	—	3	1	no	—
291	C₂×C₄×C₅	—	3	2	no	—
292	C₂×C₄×C₅	—	6	2	no	—
293	C₂×C₄×C₅	—	6	4	no	—
294	C₂×C₄×C₅	—	6	4	no	—
295	C₂×C₄×C₅	—	6	1	no	—
296	C₂×C₄×C₅	—	6	2	no	—
297	C₂×C₄×C₅	—	6	1	no	—
298	C₂×C₄×C₅	—	6	2	no	—
299	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
301	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
302	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
304	#168	—	2	1	no	—
305	#168	—	2	2	no	—
306	#168	—	3	2	no	—
307	#168	—	6	1	no	—
308	#168	—	6	2	no	—
309	#168	#239	1	2	yes	complemented
310	C₂×#41	—	3	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	—	3	1	no	—
316	C₄×Q₈	D₃×D₅	1	1	yes	characteristic
317	C₄×D₄	—	3	2	no	—
318	C₄×D₄	—	3	1	no	—
319	C₄×D₄	—	3	2	no	—
320	C₄×D₄	—	3	1	no	—
321	#117	—	3	1	no	—
322	#117	—	3	2	no	—
323	C₂×C₄²	—	3	1	no	—
324	C₂×C₄²	—	3	2	no	—
325	C₄⋊C₈	—	5	2	no	—
326	C₄⋊C₈	—	5	1	no	—
327	C₄⋊C₈	—	15	2	no	—
328	C₄⋊C₈	—	15	1	no	—
329	C₂²⋊C₈	—	15	2	no	—
330	C₂²⋊C₈	—	15	2	no	—
331	C₂²⋊C₈	—	15	2	no	—
332	#97	—	5	2	no	—
333	#97	—	15	2	no	—
334	C₄×C₈	—	5	1	no	—
335	C₄×C₈	—	15	1	no	—
336	C₄×C₈	—	15	1	no	—
337	C₄×C₈	—	15	2	no	—
338	C₄×C₈	—	15	1	no	—
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	C₅×D₃	—	2	2	no	—
343	C₅×D₃	—	4	2	no	—
344	C₂²×D₃	C₂²×Dic₅	1	2	yes	—
345	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
346	C₃×Q₈	—	2	2	no	—
347	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
348	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
350	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
352	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
353	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
354	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
355	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
356	D₁₂	—	2	4	no	—
357	D₁₂	—	2	2	no	—
358	C₄×D₃	—	2	1	no	—
359	C₄×D₃	—	2	1	no	—
360	C₄×D₃	—	2	2	no	—
361	C₄×D₃	—	2	2	no	—
362	C₄×D₃	—	2	4	no	—
363	C₄×D₃	—	2	2	no	—
364	C₄×D₃	—	2	4	no	—
365	C₄×D₃	#681	1	4	yes	complemented
366	C₃×C₈	—	5	2	no	—
367	C₃×C₈	—	10	1	no	—
368	C₃×C₈	—	10	2	no	—
369	C₃⋊C₈	—	5	2	no	—
370	C₃⋊C₈	—	10	1	no	—
371	C₃⋊C₈	—	10	2	no	—
372	C₂²×C₅	—	3	2	no	—
373	C₂²×C₅	—	6	1	no	—
374	C₂²×C₅	—	6	1	no	—
375	C₂²×C₅	—	6	2	no	—
376	C₂²×C₅	—	6	2	no	—
377	C₂²×C₅	—	6	2	no	—
378	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	2	1	no	—
381	C₄×C₅	—	2	2	no	—
382	C₄×C₅	—	3	2	no	—
383	C₄×C₅	—	3	2	no	—
384	C₄×C₅	—	6	1	no	—
385	C₄×C₅	—	6	2	no	—
386	C₄×C₅	D₃×M₁₆	1	2	yes	—
387	C₄×C₅	C₂×#239	1	1	yes	characteristic
388	C₄×C₅	D₃×#41	1	1	yes	characteristic
389	#41	—	6	4	no	—
390	C₂×Q₈	D₃×Dic₅	1	1	yes	characteristic
391	C₂×D₄	—	3	2	no	—
392	C₂×D₄	—	3	1	no	—
393	C₂²×C₄	—	3	1	no	—
394	C₂²×C₄	—	3	2	no	—
395	C₂²×C₄	—	3	1	no	—
396	C₂²×C₄	—	3	2	no	—
397	C₂²×C₄	—	3	1	no	—
398	C₂²×C₄	—	3	2	no	—
399	M₁₆	—	30	4	no	—
400	M₁₆	—	30	4	no	—
401	C₂×C₈	—	5	1	no	—
402	C₂×C₈	—	5	1	no	—
403	C₂×C₈	—	5	2	no	—
404	C₂×C₈	—	15	1	no	—
405	C₂×C₈	—	15	1	no	—
406	C₂×C₈	—	15	2	no	—
407	C₂×C₈	—	30	2	no	—
408	C₂×C₈	—	30	2	no	—
409	C₄⋊C₄	—	3	2	no	—
410	C₄⋊C₄	—	3	1	no	—
411	C₄⋊C₄	D₃×Dic₅	1	2	yes	—
412	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
413	C₂²⋊C₄	—	3	2	no	—
414	C₂²⋊C₄	—	3	2	no	—
415	C₂²⋊C₄	—	3	2	no	—
416	C₄²	—	3	1	no	—
417	C₄²	—	3	2	no	—
418	C₄²	—	3	2	no	—
419	C₄²	—	3	1	no	—
420	C₄²	—	3	1	no	—
421	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
422	C₄²	C₂×D₃×D₅	1	2	yes	—
423	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
425	C₂×D₃	—	2	1	no	—
426	C₂×D₃	—	2	1	no	—
427	C₂×D₃	—	2	2	no	—
428	C₂×D₃	—	2	2	no	—
429	C₂×D₃	—	2	2	no	—
430	C₂×D₃	C₂×#681	1	2	yes	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	C₂×#681	1	2	yes	—
435	C₃×C₄	D₅×#41	1	1	yes	characteristic
436	C₃×C₄	D₅×#41	1	1	yes	characteristic
437	Dic₃	—	2	1	no	—
438	Dic₃	—	2	2	no	—
439	Dic₃	C₂×#681	1	2	yes	—
440	Dic₃	#4094	1	2	yes	—
441	C₂×C₅	—	6	2	no	—
442	C₂×C₅	—	12	2	no	—
443	C₂×C₅	C₄×#239	1	1	yes	characteristic
444	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
445	C₂×C₅	D₃×#131	1	1	yes	characteristic
446	C₂³	—	3	1	no	—
447	C₂³	—	3	2	no	—
448	Q₈	—	2	2	no	—
449	D₄	—	6	4	no	—
450	D₄	—	6	2	no	—
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	3	1	no	—
453	C₂×C₄	—	3	4	no	—
454	C₂×C₄	—	3	1	no	—
455	C₂×C₄	—	3	2	no	—
456	C₂×C₄	—	6	4	no	—
457	C₂×C₄	—	6	2	no	—
458	C₂×C₄	—	6	4	no	—
459	C₂×C₄	—	6	1	no	—
460	C₂×C₄	—	6	2	no	—
461	C₂×C₄	—	6	1	no	—
462	C₂×C₄	—	6	2	no	—
463	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
464	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
465	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
466	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
468	C₈	—	5	2	no	—
469	C₈	—	10	1	no	—
470	C₈	—	10	2	no	—
471	C₈	—	15	2	no	—
472	C₈	—	30	1	no	—
473	C₈	—	30	2	no	—
474	C₂×C₃	C₂²×#681	1	1	yes	characteristic
475	C₂×C₃	C₂×#4094	1	1	yes	characteristic
476	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
477	D₃	—	2	2	no	—
478	D₃	—	4	2	no	—
479	C₅	#79938	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	3	2	no	—
481	C₂²	—	6	1	no	—
482	C₂²	—	6	1	no	—
483	C₂²	—	6	2	no	—
484	C₂²	—	6	2	no	—
485	C₂²	—	6	2	no	—
486	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	3	2	no	—
491	C₄	—	3	2	no	—
492	C₄	—	6	1	no	—
493	C₄	—	6	2	no	—
494	C₄	D₃×#681	1	2	yes	—
495	C₄	D₅×#239	1	1	yes	characteristic
496	C₄	#92034	1	1	yes	characteristic
497	C₃	#10614248	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	6	2	no	—
499	C₂	—	12	2	no	—
500	C₂	C₂×D₃×#681	1	1	yes	characteristic
501	C₂	Dic₅×#239	1	1	yes	characteristic
502	C₂	D₃×#4094	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×Q₈	C₂²
prime radical	C₂×C₅×#239	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	#2965
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #11751125	C₂	semidirect
3. C₃×#65313	C₂	semidirect
4. #11747014	C₂	semidirect
5. #11747008	C₂	semidirect
6. #11747005	C₂	semidirect
7. #11746999	C₂	semidirect
8. #11746987	C₂	semidirect
9. C₄×D₃×#168	C₂	semidirect
10. #11746853	C₂	semidirect
11. #11746853	C₂	semidirect
45. #65313	D₃	semidirect
150. C₄×C₅×D₃	M₁₆	semidirect
153. C₃⋊#168	#41	semidirect
156. C₃×#168	#41	semidirect
309. #168	#239	semidirect
365. C₄×D₃	#681	semidirect
423. C₃×C₅	#2965	semidirect
479. C₅	#79938	semidirect
497. C₃	#10614248	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#239	2
#11751125	2
C₃×#65313	2
#11747014	2
#11747008	2
#11747005	2
#11746999	2
#11746987	2
C₄×D₃×#168	2
#11746853	2
#10614248	3
#79938	5