Subgroups — #14419259

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65914	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₃⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5024	C₂	1	1	yes	maximal, characteristic, complemented
4	#11747010	C₂	1	1	yes	maximal, characteristic, complemented
5	#11746996	C₂	1	2	yes	maximal, complemented
6	#11746996	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746991	C₂	1	2	yes	maximal, complemented
8	#11746975	C₂	1	2	yes	maximal, complemented
9	C₄×D₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746873	C₂	1	2	yes	maximal, complemented
11	#11746871	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611670	—	3	1	no	maximal, Hall
13	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×#4093	C₄	1	1	yes	characteristic
15	C₃×#4092	C₄	1	1	yes	characteristic
16	C₃×#4044	C₄	1	2	yes	—
17	C₃×#4041	C₄	1	1	yes	characteristic
18	C₃×#4040	C₄	1	2	yes	—
19	C₃×#4036	C₄	1	1	yes	characteristic
20	C₃×C₄×D₂₀	C₂²	1	2	yes	—
21	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
22	C₃×#4018	C₂²	1	2	yes	—
23	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
24	C₂×#6649	C₂²	1	2	yes	—
25	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
28	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
29	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
30	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
31	C₄×C₃⋊#168	C₂²	1	2	yes	—
32	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
33	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
34	C₅×#803	C₂²	1	2	yes	—
35	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
36	#90955	C₂²	1	2	yes	—
37	#90955	C₂²	1	2	yes	—
38	#90955	C₂²	1	2	yes	—
39	#90952	C₂²	1	2	yes	—
40	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
41	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	#83126	—	5	1	no	maximal, Hall
43	#65914	D₃	1	1	yes	characteristic
44	C₅×#446	—	3	1	no	—
45	Q₈×#168	—	3	1	no	—
46	#65129	—	3	2	no	—
47	#65124	—	3	1	no	—
48	#65123	—	3	1	no	—
49	#65123	—	3	2	no	—
50	#64997	—	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	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
57	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
61	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₃×C₄²×C₅	C₂³	1	2	yes	—
65	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
66	C₂×C₃⋊#168	C₂³	1	2	yes	—
67	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
70	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
71	C₃×#685	C₂×C₄	1	2	yes	—
72	C₃×#685	C₂×C₄	1	2	yes	—
73	C₃×#685	C₂×C₄	1	2	yes	—
74	C₃×#685	C₂×C₄	1	2	yes	—
75	C₃×#685	C₂×C₄	1	2	yes	—
76	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
78	C₃×#683	C₂×C₄	1	2	yes	—
79	C₃×#683	C₂×C₄	1	2	yes	—
80	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	#6649	—	2	4	no	—
84	D₅×C₃⋊C₈	—	2	2	no	—
85	D₅×C₃⋊C₈	—	2	4	no	—
86	D₅×C₃⋊C₈	—	2	2	no	—
87	C₃×#529	—	5	1	no	—
88	#5024	D₅	1	1	yes	characteristic, complemented
89	Q₈×C₃⋊C₈	—	5	1	no	—
90	#5012	—	5	1	no	—
91	#5011	—	5	2	no	—
92	D₄×C₃⋊C₈	—	5	1	no	—
93	D₄×C₃⋊C₈	—	5	2	no	—
94	#5000	—	5	2	no	—
95	#4997	—	5	2	no	—
96	#4926	—	5	1	no	—
97	C₂×C₄×C₃⋊C₈	—	5	1	no	—
98	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
99	#4093	Dic₃	1	1	yes	characteristic
100	#4092	Dic₃	1	1	yes	characteristic
101	C₂×#676	—	3	2	no	—
102	C₂×C₈×D₅	—	3	1	no	—
103	C₂×C₈×D₅	—	3	2	no	—
104	C₂×C₈×D₅	—	3	1	no	—
105	#4044	Dic₃	1	2	yes	—
106	#4041	Dic₃	1	1	yes	characteristic
107	#4040	Dic₃	1	2	yes	—
108	#4036	Dic₃	1	1	yes	characteristic
109	C₄×D₂₀	C₂×D₃	1	1	yes	characteristic
110	C₄×D₂₀	C₂×D₃	1	2	yes	—
111	#4018	C₂×D₃	1	2	yes	—
112	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
113	C₅×C₄⋊C₈	—	3	1	no	—
114	C₅×C₄⋊C₈	—	3	2	no	—
115	C₅×#97	—	3	2	no	—
116	C₄×C₅×C₈	—	3	1	no	—
117	#3952	—	3	2	no	—
118	#3952	—	3	2	no	—
119	#3952	—	3	2	no	—
120	#3947	—	3	2	no	—
121	C₈×Dic₅	—	3	1	no	—
122	C₈×Dic₅	—	3	1	no	—
123	C₄⋊#168	—	3	1	no	—
124	C₄⋊#168	—	3	2	no	—
125	C₄×#168	—	3	1	no	—
126	C₄×#168	—	3	2	no	—
127	#2966	—	15	1	no	Sylow
128	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
129	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
130	C₃×C₅×Q₈	—	2	2	no	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
140	C₃×D₂₀	—	2	4	no	—
141	C₃×D₂₀	—	2	2	no	—
142	C₃×C₄×D₅	—	2	2	no	—
143	C₃×C₄×D₅	—	2	2	no	—
144	C₃×C₄×D₅	—	2	1	no	—
145	C₃×C₄×D₅	—	2	1	no	—
146	C₃×C₄×D₅	—	2	2	no	—
147	C₃×C₄×D₅	—	2	2	no	—
148	C₃⋊#168	—	2	1	no	—
149	C₃⋊#168	—	2	2	no	—
150	C₃⋊#168	#41	1	2	yes	—
151	C₅×C₃⋊C₈	—	2	1	no	—
152	C₅×C₃⋊C₈	—	2	2	no	—
153	C₅×C₃⋊C₈	#41	1	2	yes	—
154	C₃×#126	—	5	2	no	—
155	C₃×#125	—	5	1	no	—
156	C₃×#124	—	5	1	no	—
157	C₃×#123	—	5	2	no	—
158	C₃×C₂²⋊Q₈	—	5	1	no	—
159	C₃×#121	—	5	1	no	—
160	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
161	C₃×C₄×D₄	—	5	2	no	—
162	C₃×C₄×D₄	—	5	1	no	—
163	C₃×#117	—	5	2	no	—
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₂×#208	—	5	2	no	—
166	C₂²×C₃⋊C₈	—	5	1	no	—
167	C₂²×C₃⋊C₈	—	5	1	no	—
168	C₂²×C₃⋊C₈	—	5	2	no	—
169	#830	—	5	2	no	—
170	#830	—	5	2	no	—
171	#830	—	5	2	no	—
172	C₄⋊(C₃⋊C₈)	—	5	1	no	—
173	C₄⋊(C₃⋊C₈)	—	5	2	no	—
174	C₄⋊(C₃⋊C₈)	C₂×D₅	1	1	yes	characteristic
175	C₄⋊(C₃⋊C₈)	C₂×D₅	1	2	yes	—
176	#803	—	5	2	no	—
177	#803	C₂×D₅	1	2	yes	—
178	C₄×C₃⋊C₈	—	5	1	no	—
179	C₄×C₃⋊C₈	—	5	2	no	—
180	C₄×C₃⋊C₈	—	5	1	no	—
181	C₄×C₃⋊C₈	—	5	1	no	—
182	C₄×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
183	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
184	C₂×D₂₀	C₂×Dic₃	1	2	yes	—
185	C₂×D₂₀	C₂×Dic₃	1	1	yes	characteristic
186	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
187	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
188	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
189	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
190	C₂×C₅×C₈	—	3	1	no	—
191	C₂×C₅×C₈	—	3	1	no	—
192	C₂×C₅×C₈	—	3	2	no	—
193	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
194	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
195	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₄²×C₅	C₂²×D₃	1	2	yes	—
197	#685	C₂×Dic₃	1	2	yes	—
198	#685	C₂×Dic₃	1	2	yes	—
199	#685	C₂×Dic₃	1	2	yes	—
200	#685	C₂×Dic₃	1	2	yes	—
201	#685	C₂×Dic₃	1	2	yes	—
202	C₄⋊Dic₅	C₂×Dic₃	1	2	yes	—
203	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
204	#683	C₂×Dic₃	1	2	yes	—
205	#683	C₂×Dic₃	1	2	yes	—
206	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
207	C₄×Dic₅	C₂×Dic₃	1	1	yes	characteristic
208	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
209	C₂×#168	—	3	1	no	—
210	C₂×#168	—	3	1	no	—
211	C₂×#168	—	3	2	no	—
212	#676	—	6	4	no	—
213	C₈×D₅	—	6	2	no	—
214	C₈×D₅	—	6	4	no	—
215	C₈×D₅	—	6	2	no	—
216	#529	—	5	1	no	—
217	#446	—	3	1	no	—
218	C₈×Q₈	—	15	1	no	—
219	#436	—	15	1	no	—
220	#435	—	15	2	no	—
221	C₈×D₄	—	15	1	no	—
222	C₈×D₄	—	15	2	no	—
223	#433	—	15	2	no	—
224	#432	—	15	1	no	—
225	#405	—	15	2	no	—
226	C₂×C₄×C₈	—	15	1	no	—
227	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₃×D₅	—	2	1	no	—
229	C₂×C₃×D₅	—	2	1	no	—
230	C₂×C₃×D₅	—	2	2	no	—
231	C₂×C₃×D₅	—	2	2	no	—
232	C₂×C₃×D₅	—	2	2	no	—
233	C₂×C₃×D₅	#131	1	2	yes	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	2	no	—
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	#131	1	2	yes	—
238	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₃×Dic₅	—	2	1	no	—
241	C₃×Dic₅	—	2	2	no	—
242	C₃×Dic₅	—	2	1	no	—
243	C₃×Dic₅	—	2	1	no	—
244	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
245	C₂×C₃×D₄	—	5	2	no	—
246	C₂×C₃×D₄	—	5	1	no	—
247	C₂²×C₃×C₄	—	5	1	no	—
248	C₂²×C₃×C₄	—	5	1	no	—
249	C₂²×C₃×C₄	—	5	1	no	—
250	C₂²×C₃×C₄	—	5	2	no	—
251	C₃×C₄⋊C₄	—	5	2	no	—
252	C₃×C₄⋊C₄	—	5	2	no	—
253	C₃×C₄⋊C₄	—	5	1	no	—
254	C₃×C₄⋊C₄	—	5	2	no	—
255	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
256	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
257	C₃×C₂²⋊C₄	—	5	2	no	—
258	C₃×C₂²⋊C₄	—	5	2	no	—
259	C₃×C₂²⋊C₄	—	5	2	no	—
260	C₃×C₂²⋊C₄	—	5	2	no	—
261	C₃×C₂²⋊C₄	—	5	2	no	—
262	C₃×C₄²	—	5	1	no	—
263	C₃×C₄²	—	5	1	no	—
264	C₃×C₄²	—	5	1	no	—
265	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
266	C₃×C₄²	C₂²×D₅	1	2	yes	—
267	#208	—	10	4	no	—
268	C₂×C₃⋊C₈	—	5	1	no	—
269	C₂×C₃⋊C₈	—	5	1	no	—
270	C₂×C₃⋊C₈	—	5	2	no	—
271	C₂×C₃⋊C₈	—	10	2	no	—
272	C₂×C₃⋊C₈	—	10	4	no	—
273	C₂×C₃⋊C₈	—	10	2	no	—
274	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
275	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
276	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
277	C₂²×D₅	C₂²×Dic₃	1	2	yes	—
278	C₂²×D₅	C₂²×Dic₃	1	1	yes	characteristic
279	C₅×Q₈	—	2	2	no	—
280	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
282	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
283	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
285	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
286	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
287	C₂×Dic₅	C₂²×Dic₃	1	1	yes	characteristic
288	C₂×Dic₅	C₂²×Dic₃	1	2	yes	—
289	D₂₀	—	2	4	no	—
290	D₂₀	—	2	2	no	—
291	C₄×D₅	—	2	2	no	—
292	C₄×D₅	—	2	2	no	—
293	C₄×D₅	—	2	1	no	—
294	C₄×D₅	—	2	1	no	—
295	C₄×D₅	—	2	2	no	—
296	C₄×D₅	—	2	2	no	—
297	C₅×C₈	—	3	2	no	—
298	C₅×C₈	—	6	1	no	—
299	C₅×C₈	—	6	2	no	—
300	#168	—	3	2	no	—
301	#168	—	6	1	no	—
302	#168	—	6	2	no	—
303	C₂×M₁₆	—	15	2	no	—
304	C₂²×C₈	—	15	1	no	—
305	C₂²×C₈	—	15	1	no	—
306	C₂²×C₈	—	15	2	no	—
307	#126	—	5	2	no	—
308	#125	—	5	1	no	—
309	#124	—	5	1	no	—
310	#123	—	5	2	no	—
311	C₂²⋊Q₈	—	5	1	no	—
312	#121	—	5	1	no	—
313	C₄×Q₈	D₃×D₅	1	1	yes	characteristic
314	C₄×D₄	—	5	2	no	—
315	C₄×D₄	—	5	1	no	—
316	#117	—	5	2	no	—
317	C₂×C₄²	—	5	1	no	—
318	C₄⋊C₈	—	3	1	no	—
319	C₄⋊C₈	—	3	2	no	—
320	C₄⋊C₈	—	15	1	no	—
321	C₄⋊C₈	—	15	2	no	—
322	C₂²⋊C₈	—	15	2	no	—
323	C₂²⋊C₈	—	15	2	no	—
324	C₂²⋊C₈	—	15	2	no	—
325	#97	—	3	2	no	—
326	#97	—	15	2	no	—
327	C₄×C₈	—	3	1	no	—
328	C₄×C₈	—	15	1	no	—
329	C₄×C₈	—	15	1	no	—
330	C₄×C₈	—	15	1	no	—
331	C₄×C₈	—	15	2	no	—
332	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
333	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
335	C₃×D₅	—	2	2	no	—
336	C₃×D₅	—	4	2	no	—
337	C₂³×C₃	—	5	1	no	—
338	C₂³×C₃	—	5	2	no	—
339	C₃×Q₈	—	2	2	no	—
340	C₃×D₄	—	10	4	no	—
341	C₃×D₄	—	10	2	no	—
342	C₂×C₃×C₄	—	5	1	no	—
343	C₂×C₃×C₄	—	5	1	no	—
344	C₂×C₃×C₄	—	5	1	no	—
345	C₂×C₃×C₄	—	5	2	no	—
346	C₂×C₃×C₄	—	10	2	no	—
347	C₂×C₃×C₄	—	10	1	no	—
348	C₂×C₃×C₄	—	10	2	no	—
349	C₂×C₃×C₄	—	10	1	no	—
350	C₂×C₃×C₄	—	10	2	no	—
351	C₂×C₃×C₄	—	10	2	no	—
352	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
354	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
355	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
357	C₃⋊C₈	—	2	1	no	—
358	C₃⋊C₈	—	2	2	no	—
359	C₃⋊C₈	—	5	2	no	—
360	C₃⋊C₈	—	10	1	no	—
361	C₃⋊C₈	—	10	2	no	—
362	C₃⋊C₈	#713	1	2	yes	—
363	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
364	C₂×D₅	—	2	1	no	—
365	C₂×D₅	—	2	1	no	—
366	C₂×D₅	—	2	2	no	—
367	C₂×D₅	—	2	2	no	—
368	C₂×D₅	—	2	2	no	—
369	C₂×D₅	#948	1	2	yes	—
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	2	no	—
372	C₄×C₅	—	2	2	no	—
373	C₄×C₅	#948	1	2	yes	—
374	C₄×C₅	D₃×#41	1	1	yes	characteristic
375	C₄×C₅	D₃×#41	1	1	yes	characteristic
376	Dic₅	—	2	1	no	—
377	Dic₅	—	2	1	no	—
378	Dic₅	—	2	1	no	—
379	Dic₅	—	2	2	no	—
380	C₂×Q₈	D₅×Dic₃	1	1	yes	characteristic
381	C₂×D₄	—	5	2	no	—
382	C₂×D₄	—	5	1	no	—
383	C₂²×C₄	—	5	1	no	—
384	C₂²×C₄	—	5	1	no	—
385	C₂²×C₄	—	5	1	no	—
386	C₂²×C₄	—	5	2	no	—
387	M₁₆	—	30	4	no	—
388	C₂×C₈	—	3	1	no	—
389	C₂×C₈	—	3	1	no	—
390	C₂×C₈	—	3	2	no	—
391	C₂×C₈	—	15	1	no	—
392	C₂×C₈	—	15	1	no	—
393	C₂×C₈	—	15	2	no	—
394	C₂×C₈	—	30	2	no	—
395	C₂×C₈	—	30	2	no	—
396	C₂×C₈	—	30	4	no	—
397	C₄⋊C₄	—	5	2	no	—
398	C₄⋊C₄	—	5	2	no	—
399	C₄⋊C₄	—	5	1	no	—
400	C₄⋊C₄	—	5	2	no	—
401	C₄⋊C₄	D₅×Dic₃	1	1	yes	characteristic
402	C₄⋊C₄	D₅×Dic₃	1	2	yes	—
403	C₂²⋊C₄	—	5	2	no	—
404	C₂²⋊C₄	—	5	2	no	—
405	C₂²⋊C₄	—	5	2	no	—
406	C₂²⋊C₄	—	5	2	no	—
407	C₂²⋊C₄	—	5	2	no	—
408	C₄²	—	5	1	no	—
409	C₄²	—	5	1	no	—
410	C₄²	—	5	1	no	—
411	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
412	C₄²	C₂×D₃×D₅	1	2	yes	—
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	5	2	no	—
415	C₂²×C₃	—	10	1	no	—
416	C₂²×C₃	—	10	1	no	—
417	C₂²×C₃	—	10	2	no	—
418	C₂²×C₃	—	10	2	no	—
419	C₂²×C₃	—	10	2	no	—
420	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	2	no	—
424	C₃×C₄	—	10	1	no	—
425	C₃×C₄	—	10	1	no	—
426	C₃×C₄	—	10	1	no	—
427	C₃×C₄	—	10	2	no	—
428	C₃×C₄	#4053	1	2	yes	—
429	C₃×C₄	C₂×#713	1	1	yes	characteristic
430	C₃×C₄	D₅×#41	1	1	yes	characteristic
431	C₂×C₅	C₂×#948	1	1	yes	characteristic
432	C₂×C₅	C₂×#948	1	1	yes	characteristic
433	C₂×C₅	Dic₃×#41	1	1	yes	characteristic
434	D₅	—	2	2	no	—
435	D₅	—	4	2	no	—
436	C₂³	—	5	1	no	—
437	C₂³	—	5	2	no	—
438	Q₈	—	2	2	no	—
439	D₄	—	10	4	no	—
440	D₄	—	10	2	no	—
441	C₂×C₄	—	5	1	no	—
442	C₂×C₄	—	5	1	no	—
443	C₂×C₄	—	5	1	no	—
444	C₂×C₄	—	5	2	no	—
445	C₂×C₄	—	10	2	no	—
446	C₂×C₄	—	10	1	no	—
447	C₂×C₄	—	10	2	no	—
448	C₂×C₄	—	10	1	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
452	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
453	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
454	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
456	C₈	—	3	2	no	—
457	C₈	—	6	1	no	—
458	C₈	—	6	2	no	—
459	C₈	—	15	2	no	—
460	C₈	—	30	1	no	—
461	C₈	—	30	2	no	—
462	C₂×C₃	—	10	2	no	—
463	C₂×C₃	—	20	2	no	—
464	C₂×C₃	C₄×#713	1	1	yes	characteristic
465	C₂×C₃	C₂×#4053	1	1	yes	characteristic
466	C₂×C₃	D₅×#131	1	1	yes	characteristic
467	C₅	#83126	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	5	2	no	—
469	C₂²	—	10	1	no	—
470	C₂²	—	10	1	no	—
471	C₂²	—	10	2	no	—
472	C₂²	—	10	2	no	—
473	C₂²	—	10	2	no	—
474	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	10	1	no	—
479	C₄	—	10	1	no	—
480	C₄	—	10	1	no	—
481	C₄	—	10	2	no	—
482	C₄	#91284	1	2	yes	—
483	C₄	D₃×#713	1	1	yes	characteristic
484	C₄	#92034	1	1	yes	characteristic
485	C₃	#10611670	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	10	2	no	—
487	C₂	—	20	2	no	—
488	C₂	C₂×#91284	1	1	yes	characteristic
489	C₂	Dic₃×#713	1	1	yes	characteristic
490	C₂	D₅×#948	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	C₃×#4041	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	#2966
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. Q₈×C₃⋊#168	C₂	semidirect
3. C₅×#5024	C₂	semidirect
4. #11747010	C₂	semidirect
5. #11746996	C₂	semidirect
6. #11746996	C₂	semidirect
7. #11746991	C₂	semidirect
8. #11746975	C₂	semidirect
9. C₄×D₅×C₃⋊C₈	C₂	semidirect
10. #11746873	C₂	semidirect
11. #11746871	C₂	semidirect
88. #5024	D₅	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	#83126	semidirect
485. C₃	#10611670	semidirect

Maximal subgroups

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

subgroup	index
C₃×#65914	2
Q₈×C₃⋊#168	2
C₅×#5024	2
#11747010	2
#11746996	2
#11746991	2
#11746975	2
C₄×D₅×C₃⋊C₈	2
#11746873	2
#11746871	2
#10611670	3
#83126	5