Subgroups — #14478477

Order 1920.

728 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91793	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3944	C₂	1	1	yes	maximal, characteristic, complemented
4	#11747563	C₂	1	2	yes	maximal, complemented
5	#11747562	C₂	1	2	yes	maximal, complemented
6	#11747548	C₂	1	2	yes	maximal, complemented
7	#11747547	C₂	1	2	yes	maximal, complemented
8	#11747546	C₂	1	4	yes	maximal, complemented
9	#10615625	—	3	1	no	maximal, Hall
10	C₂×#6817	—	2	1	no	—
11	C₂×C₅×#235	—	2	1	no	—
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×Dic₆₀	C₂²	1	1	yes	characteristic, complemented
14	#91793	—	2	1	no	—
15	#91793	—	2	1	no	—
16	#91793	C₂²	1	2	yes	—
17	#91793	C₂²	1	2	yes	complemented
18	C₂×D₁₂₀	C₂²	1	1	yes	characteristic, complemented
19	C₂×#6706	—	2	1	no	—
20	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
21	C₅×#904	—	2	1	no	—
22	C₅×#904	—	2	1	no	—
23	C₅×#904	C₂²	1	2	yes	—
24	C₅×#904	C₂²	1	2	yes	complemented
25	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#204	—	2	1	no	—
27	C₃×#3944	C₂²	1	2	yes	complemented
28	C₃×#3944	C₂²	1	2	yes	complemented
29	C₂×C₃×#672	C₂²	1	2	yes	complemented
30	#90948	C₂²	1	4	yes	complemented
31	#90945	C₂²	1	4	yes	complemented
32	#90944	C₂²	1	4	yes	complemented
33	#90939	C₂²	1	4	yes	complemented
34	#82009	—	5	1	no	maximal, Hall
35	C₂×C₅×#135	—	3	1	no	—
36	C₂×#4050	—	3	1	no	—
37	#65484	—	3	2	no	—
38	#65483	—	3	4	no	—
39	#65482	—	3	2	no	—
40	#65468	—	3	2	no	—
41	#65436	—	3	2	no	—
42	C₂×#3944	D₃	1	1	yes	characteristic, complemented
43	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂×#1220	—	4	1	no	—
45	#6817	—	2	2	no	—
46	#6817	—	2	2	no	—
47	#6817	—	4	1	no	—
48	#6817	—	4	1	no	—
49	C₂×D₆₀	—	2	1	no	—
50	C₂×C₄×D₁₅	—	4	1	no	—
51	C₂×Dic₃₀	—	2	1	no	—
52	C₂×C₅×#67	—	4	1	no	—
53	C₅×#235	—	2	2	no	—
54	C₅×#235	—	2	2	no	—
55	C₅×#235	—	4	1	no	—
56	C₅×#235	—	4	1	no	—
57	C₂×C₅×D₁₂	—	2	1	no	—
58	C₂×C₄×C₅×D₃	—	4	1	no	—
59	C₂×C₅×Dic₆	—	2	1	no	—
60	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
61	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	Dic₆₀	—	2	1	no	—
67	Dic₆₀	C₂³	1	2	yes	—
68	D₁₂₀	—	2	1	no	—
69	D₁₂₀	C₂³	1	2	yes	—
70	#6706	—	2	2	no	—
71	#6706	—	2	2	no	—
72	C₅×Dic₁₂	—	2	1	no	—
73	C₅×Dic₁₂	C₂³	1	2	yes	—
74	C₅×D₂₄	—	2	1	no	—
75	C₅×D₂₄	C₂³	1	2	yes	—
76	C₅×#204	—	2	2	no	—
77	C₅×#204	—	2	2	no	—
78	C₃×#672	C₂³	1	4	yes	—
79	C₂×#904	—	5	1	no	—
80	C₂×#904	D₅	1	1	yes	characteristic, complemented
81	C₂×C₃×M₃₂	—	5	1	no	—
82	#4909	—	5	2	no	—
83	#4909	—	5	2	no	—
84	#4908	—	5	2	no	—
85	#4908	—	5	2	no	—
86	#4904	—	5	4	no	—
87	C₂×C₅×#41	—	6	1	no	—
88	C₂×#709	—	6	1	no	—
89	C₅×#135	—	3	2	no	—
90	C₅×#135	—	3	2	no	—
91	C₅×#135	—	6	1	no	—
92	C₅×#135	—	6	1	no	—
93	C₂×C₅×Q₁₆	—	3	1	no	—
94	C₂×C₅×SD₁₆	—	6	1	no	—
95	C₂×C₅×D₈	—	3	1	no	—
96	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
97	C₂×Dic₂₀	—	3	1	no	—
98	#4050	—	3	2	no	—
99	#4050	—	3	2	no	—
100	#4050	—	6	1	no	—
101	#4050	—	6	1	no	—
102	C₂×D₄₀	—	3	1	no	—
103	C₂×#677	—	6	1	no	—
104	#3961	—	3	4	no	—
105	#3960	—	3	4	no	—
106	#3959	—	3	4	no	—
107	#3958	—	3	4	no	—
108	#3944	C₂×D₃	1	2	yes	complemented
109	#3944	C₂×D₃	1	2	yes	complemented
110	C₂×#672	C₂×D₃	1	2	yes	complemented
111	#3414	—	15	1	no	Sylow
112	C₂³×C₃×C₅	D₈	1	1	yes	characteristic
113	C₂²×D₁₅	—	4	1	no	—
114	C₂²×C₅×D₃	—	4	1	no	—
115	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	#1220	—	4	2	no	—
122	#1220	—	4	2	no	—
123	C₂×Dic₁₅	—	4	1	no	—
124	D₆₀	—	2	2	no	—
125	D₆₀	—	4	1	no	—
126	C₄×D₁₅	—	4	2	no	—
127	C₄×D₁₅	—	4	2	no	—
128	Dic₃₀	—	2	2	no	—
129	Dic₃₀	—	4	1	no	—
130	C₅×#67	—	4	2	no	—
131	C₅×#67	—	4	2	no	—
132	C₂×C₅×Dic₃	—	4	1	no	—
133	C₅×D₁₂	—	2	2	no	—
134	C₅×D₁₂	—	4	1	no	—
135	C₄×C₅×D₃	—	4	2	no	—
136	C₄×C₅×D₃	—	4	2	no	—
137	C₅×Dic₆	—	2	2	no	—
138	C₅×Dic₆	—	4	1	no	—
139	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
140	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
141	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
142	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
143	C₂×#235	—	2	1	no	—
144	C₂×#235	—	10	1	no	—
145	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
146	C₂×Dic₁₂	—	5	1	no	—
147	C₂×Dic₁₂	C₂×D₅	1	1	yes	characteristic, complemented
148	#904	—	2	1	no	—
149	#904	—	2	1	no	—
150	#904	—	5	2	no	—
151	#904	—	5	2	no	—
152	#904	—	10	1	no	—
153	#904	—	10	1	no	—
154	#904	C₂×D₅	1	2	yes	—
155	#904	C₂×D₅	1	2	yes	complemented
156	C₂×D₂₄	—	5	1	no	—
157	C₂×D₂₄	C₂×D₅	1	1	yes	characteristic, complemented
158	C₂×#204	—	2	1	no	—
159	C₂×#204	—	10	1	no	—
160	C₃×M₃₂	—	5	2	no	—
161	C₃×M₃₂	—	5	2	no	—
162	C₂×C₃×C₁₆	—	5	2	no	—
163	Dic₂₄	—	5	4	no	—
164	#800	—	5	4	no	—
165	#800	—	5	4	no	—
166	D₄₈	—	5	4	no	—
167	C₅×#41	—	6	2	no	—
168	C₅×#41	—	6	2	no	—
169	C₅×#41	—	12	1	no	—
170	C₅×#41	—	12	1	no	—
171	C₂×C₅×Q₈	—	6	1	no	—
172	C₂×C₅×D₄	—	6	1	no	—
173	C₂×C₅×D₄	—	12	1	no	—
174	C₂²×C₄×C₅	—	12	1	no	—
175	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
176	C₂×C₂²⋊D₅	—	12	1	no	—
177	#709	—	6	2	no	—
178	#709	—	6	2	no	—
179	#709	—	12	1	no	—
180	#709	—	12	1	no	—
181	C₂×D₂₀	—	6	1	no	—
182	C₂×C₄×D₅	—	12	1	no	—
183	C₂×Dic₁₀	—	6	1	no	—
184	C₅×Q₁₆	—	3	2	no	—
185	C₅×Q₁₆	—	6	1	no	—
186	C₅×SD₁₆	—	6	2	no	—
187	C₅×SD₁₆	—	6	2	no	—
188	C₅×D₈	—	3	2	no	—
189	C₅×D₈	—	6	1	no	—
190	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
191	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
192	C₂×C₅×C₈	D₁₂	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
196	Dic₂₀	—	3	2	no	—
197	Dic₂₀	—	6	1	no	—
198	D₄₀	—	3	2	no	—
199	D₄₀	—	6	1	no	—
200	#677	—	6	2	no	—
201	#677	—	6	2	no	—
202	#672	C₂²×D₃	1	4	yes	—
203	C₂×#135	—	3	1	no	—
204	C₂×#135	—	15	1	no	—
205	#510	—	15	2	no	—
206	#510	—	15	2	no	—
207	#509	—	15	2	no	—
208	#509	—	15	2	no	—
209	#508	—	15	4	no	—
210	C₂×M₃₂	—	5	1	no	—
211	C₂²×C₃×C₅	—	4	1	no	—
212	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
213	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
214	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
215	C₂×D₁₅	—	4	2	no	—
216	C₂×D₁₅	—	8	2	no	—
217	C₂×C₅×D₃	—	4	2	no	—
218	C₂×C₅×D₃	—	8	2	no	—
219	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
220	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
221	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
222	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	Dic₁₅	—	4	2	no	—
224	C₅×Dic₃	—	4	2	no	—
225	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
226	C₂×#67	—	4	1	no	—
227	C₂×#67	—	20	1	no	—
228	#235	—	2	2	no	—
229	#235	—	2	2	no	—
230	#235	—	4	1	no	—
231	#235	—	4	1	no	—
232	#235	—	10	2	no	—
233	#235	—	10	2	no	—
234	#235	—	20	1	no	—
235	#235	—	20	1	no	—
236	C₂×D₁₂	—	2	1	no	—
237	C₂×D₁₂	—	10	1	no	—
238	C₂×C₄×D₃	—	4	1	no	—
239	C₂×C₄×D₃	—	20	1	no	—
240	C₂×Dic₆	—	2	1	no	—
241	C₂×Dic₆	—	10	1	no	—
242	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
243	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
244	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
245	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
246	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
247	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
248	Dic₁₂	—	2	1	no	—
249	Dic₁₂	—	5	2	no	—
250	Dic₁₂	—	10	1	no	—
251	Dic₁₂	C₂²×D₅	1	2	yes	—
252	D₂₄	—	2	1	no	—
253	D₂₄	—	5	2	no	—
254	D₂₄	—	10	1	no	—
255	D₂₄	C₂²×D₅	1	2	yes	—
256	#204	—	2	2	no	—
257	#204	—	2	2	no	—
258	#204	—	10	2	no	—
259	#204	—	10	2	no	—
260	C₃×C₁₆	—	5	4	no	—
261	C₂³×C₅	—	12	1	no	—
262	C₂³×C₅	D₂₄	1	1	yes	characteristic
263	C₂²×D₅	—	12	1	no	—
264	C₅×Q₈	—	6	2	no	—
265	C₅×Q₈	—	12	1	no	—
266	C₅×D₄	—	6	2	no	—
267	C₅×D₄	—	12	2	no	—
268	C₅×D₄	—	12	2	no	—
269	C₅×D₄	—	12	1	no	—
270	C₂×C₄×C₅	—	12	1	no	—
271	C₂×C₄×C₅	—	12	2	no	—
272	C₂×C₄×C₅	—	12	2	no	—
273	C₂×C₄×C₅	D₂₄	1	1	yes	characteristic
274	C₂×C₄×C₅	D₂₄	1	1	yes	characteristic
275	C₂×C₄×C₅	D₂₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
279	C₂²⋊D₅	—	12	2	no	—
280	C₂²⋊D₅	—	12	2	no	—
281	C₂×Dic₅	—	12	1	no	—
282	D₂₀	—	6	2	no	—
283	D₂₀	—	12	1	no	—
284	C₄×D₅	—	12	2	no	—
285	C₄×D₅	—	12	2	no	—
286	Dic₁₀	—	6	2	no	—
287	Dic₁₀	—	12	1	no	—
288	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
289	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
290	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
291	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
292	C₂×#41	—	6	1	no	—
293	C₂×#41	—	30	1	no	—
294	#135	—	3	2	no	—
295	#135	—	3	2	no	—
296	#135	—	6	1	no	—
297	#135	—	6	1	no	—
298	#135	—	15	2	no	—
299	#135	—	15	2	no	—
300	#135	—	30	1	no	—
301	#135	—	30	1	no	—
302	C₂×Q₁₆	—	3	1	no	—
303	C₂×Q₁₆	—	15	1	no	—
304	C₂×SD₁₆	—	6	1	no	—
305	C₂×SD₁₆	—	30	1	no	—
306	C₂×D₈	—	3	1	no	—
307	C₂×D₈	—	15	1	no	—
308	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
309	Q₃₂	—	15	4	no	—
310	SD₃₂	—	15	4	no	—
311	SD₃₂	—	15	4	no	—
312	D₁₆	—	15	4	no	—
313	M₃₂	—	5	2	no	—
314	M₃₂	—	5	2	no	—
315	C₂×C₁₆	—	5	2	no	—
316	C₂×C₃×C₅	—	2	1	no	—
317	C₂×C₃×C₅	—	2	1	no	—
318	C₂×C₃×C₅	—	2	1	no	—
319	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
320	D₁₅	—	8	2	no	—
321	C₅×D₃	—	8	2	no	—
322	C₂³×C₃	#686	1	1	yes	characteristic
323	C₂²×D₃	—	4	1	no	—
324	C₂²×D₃	—	20	1	no	—
325	C₂×C₃×C₄	#686	1	1	yes	characteristic
326	C₂×C₃×C₄	#686	1	1	yes	characteristic
327	C₂×C₃×C₄	#686	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
331	#67	—	4	2	no	—
332	#67	—	4	2	no	—
333	#67	—	20	2	no	—
334	#67	—	20	2	no	—
335	C₂×Dic₃	—	4	1	no	—
336	C₂×Dic₃	—	20	1	no	—
337	D₁₂	—	2	2	no	—
338	D₁₂	—	4	1	no	—
339	D₁₂	—	10	2	no	—
340	D₁₂	—	20	1	no	—
341	C₄×D₃	—	4	2	no	—
342	C₄×D₃	—	4	2	no	—
343	C₄×D₃	—	20	2	no	—
344	C₄×D₃	—	20	2	no	—
345	Dic₆	—	2	2	no	—
346	Dic₆	—	4	1	no	—
347	Dic₆	—	10	2	no	—
348	Dic₆	—	20	1	no	—
349	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
350	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
351	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
352	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
353	C₂²×C₅	—	4	1	no	—
354	C₂²×C₅	—	12	2	no	—
355	C₂²×C₅	—	24	2	no	—
356	C₂²×C₅	C₂×D₂₄	1	1	yes	characteristic
357	C₂²×C₅	C₂×D₂₄	1	1	yes	characteristic
358	C₂²×C₅	C₂×D₂₄	1	1	yes	characteristic
359	C₂×D₅	—	12	2	no	—
360	C₂×D₅	—	24	2	no	—
361	C₄×C₅	—	12	2	no	—
362	C₄×C₅	C₂×D₂₄	1	1	yes	characteristic
363	C₄×C₅	C₂×D₂₄	1	1	yes	characteristic
364	C₄×C₅	C₂×D₂₄	1	1	yes	characteristic
365	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
366	Dic₅	—	12	2	no	—
367	#41	—	6	2	no	—
368	#41	—	6	2	no	—
369	#41	—	12	1	no	—
370	#41	—	12	1	no	—
371	#41	—	30	2	no	—
372	#41	—	30	2	no	—
373	#41	—	60	1	no	—
374	#41	—	60	1	no	—
375	C₂×Q₈	—	6	1	no	—
376	C₂×Q₈	—	30	1	no	—
377	C₂×D₄	—	6	1	no	—
378	C₂×D₄	—	12	1	no	—
379	C₂×D₄	—	30	1	no	—
380	C₂×D₄	—	60	1	no	—
381	C₂²×C₄	—	12	1	no	—
382	C₂²×C₄	—	60	1	no	—
383	C₂²×C₄	#1203	1	1	yes	characteristic
384	Q₁₆	—	3	2	no	—
385	Q₁₆	—	6	1	no	—
386	Q₁₆	—	15	2	no	—
387	Q₁₆	—	30	1	no	—
388	SD₁₆	—	6	2	no	—
389	SD₁₆	—	6	2	no	—
390	SD₁₆	—	30	2	no	—
391	SD₁₆	—	30	2	no	—
392	D₈	—	3	2	no	—
393	D₈	—	6	1	no	—
394	D₈	—	15	2	no	—
395	D₈	—	30	1	no	—
396	C₂×C₈	#1203	1	1	yes	characteristic
397	C₂×C₈	#1203	1	1	yes	characteristic
398	C₂×C₈	#1203	1	1	yes	characteristic
399	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
400	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
401	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
402	C₁₆	—	5	4	no	—
403	C₃×C₅	#3414	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	4	1	no	—
405	C₂²×C₃	C₂×#686	1	1	yes	characteristic
406	C₂²×C₃	C₂×#686	1	1	yes	characteristic
407	C₂²×C₃	C₂×#686	1	1	yes	characteristic
408	C₂×D₃	—	4	2	no	—
409	C₂×D₃	—	8	2	no	—
410	C₂×D₃	—	20	2	no	—
411	C₂×D₃	—	40	2	no	—
412	C₃×C₄	C₂×#686	1	1	yes	characteristic
413	C₃×C₄	C₂×#686	1	1	yes	characteristic
414	C₃×C₄	C₂×#686	1	1	yes	characteristic
415	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
416	Dic₃	—	4	2	no	—
417	Dic₃	—	20	2	no	—
418	C₂×C₅	—	2	1	no	—
419	C₂×C₅	—	2	1	no	—
420	C₂×C₅	—	2	1	no	—
421	C₂×C₅	—	24	2	no	—
422	C₂×C₅	C₂²×D₂₄	1	1	yes	characteristic
423	D₅	—	24	2	no	—
424	C₂³	—	12	1	no	—
425	C₂³	—	60	1	no	—
426	C₂³	#6654	1	1	yes	characteristic
427	Q₈	—	6	2	no	—
428	Q₈	—	12	1	no	—
429	Q₈	—	30	2	no	—
430	Q₈	—	60	1	no	—
431	D₄	—	6	2	no	—
432	D₄	—	12	2	no	—
433	D₄	—	12	2	no	—
434	D₄	—	12	1	no	—
435	D₄	—	30	2	no	—
436	D₄	—	60	2	no	—
437	D₄	—	60	2	no	—
438	D₄	—	60	1	no	—
439	C₂×C₄	—	12	1	no	—
440	C₂×C₄	—	12	2	no	—
441	C₂×C₄	—	12	2	no	—
442	C₂×C₄	—	60	1	no	—
443	C₂×C₄	—	60	2	no	—
444	C₂×C₄	—	60	2	no	—
445	C₂×C₄	#6654	1	1	yes	characteristic
446	C₂×C₄	#6654	1	1	yes	characteristic
447	C₂×C₄	#6654	1	1	yes	characteristic
448	C₂×C₄	C₂×#1203	1	1	yes	characteristic
449	C₂×C₄	C₂×#1203	1	1	yes	characteristic
450	C₂×C₄	C₂×#1203	1	1	yes	characteristic
451	C₈	C₂×#1203	1	1	yes	characteristic
452	C₈	C₂×#1203	1	1	yes	characteristic
453	C₈	C₂×#1203	1	1	yes	characteristic
454	C₈	C₂²×D₃×D₅	1	1	yes	characteristic
455	C₂×C₃	—	2	1	no	—
456	C₂×C₃	—	2	1	no	—
457	C₂×C₃	—	2	1	no	—
458	C₂×C₃	C₂²×#686	1	1	yes	characteristic
459	D₃	—	8	2	no	—
460	D₃	—	40	2	no	—
461	C₅	#82009	1	1	yes	characteristic, complemented, Sylow
462	C₂²	—	4	1	no	—
463	C₂²	—	12	2	no	—
464	C₂²	—	24	2	no	—
465	C₂²	—	60	2	no	—
466	C₂²	—	120	2	no	—
467	C₂²	C₂×#6654	1	1	yes	characteristic
468	C₂²	C₂×#6654	1	1	yes	characteristic
469	C₂²	C₂×#6654	1	1	yes	characteristic
470	C₄	—	12	2	no	—
471	C₄	—	60	2	no	—
472	C₄	C₂×#6654	1	1	yes	characteristic
473	C₄	C₂×#6654	1	1	yes	characteristic
474	C₄	C₂×#6654	1	1	yes	characteristic
475	C₄	C₂²×#1203	1	1	yes	characteristic
476	C₃	#10615625	1	1	yes	characteristic, complemented, Sylow
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	2	1	no	—
480	C₂	—	24	2	no	—
481	C₂	—	120	2	no	—
482	C₂	C₂²×#6654	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#6654
commutator, cosocle	C₃×C₅×C₈	C₂⁴
Frattini	C₈	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂×C₃×C₅	C₂²×D₈
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#3414
LCS	G ▷ C₃×C₅×C₈ ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#91793	C₂	semidirect
2. C₂×C₅×#904	C₂	semidirect
3. C₂×C₃×#3944	C₂	semidirect
4. #11747563	C₂	semidirect
5. #11747562	C₂	semidirect
6. #11747548	C₂	semidirect
7. #11747547	C₂	semidirect
8. #11747546	C₂	semidirect
13. C₂×Dic₆₀	C₂²	semidirect
17. #91793	C₂²	semidirect
18. C₂×D₁₂₀	C₂²	semidirect
20. C₂×C₅×Dic₁₂	C₂²	semidirect
24. C₅×#904	C₂²	semidirect
25. C₂×C₅×D₂₄	C₂²	semidirect
27. C₃×#3944	C₂²	semidirect
28. C₃×#3944	C₂²	semidirect
29. C₂×C₃×#672	C₂²	semidirect
30. #90948	C₂²	semidirect
31. #90945	C₂²	semidirect
32. #90944	C₂²	semidirect
33. #90939	C₂²	semidirect
42. C₂×#3944	D₃	semidirect
80. C₂×#904	D₅	semidirect
108. #3944	C₂×D₃	semidirect
109. #3944	C₂×D₃	semidirect
110. C₂×#672	C₂×D₃	semidirect
147. C₂×Dic₁₂	C₂×D₅	semidirect
155. #904	C₂×D₅	semidirect
157. C₂×D₂₄	C₂×D₅	semidirect
403. C₃×C₅	#3414	semidirect
461. C₅	#82009	semidirect
476. C₃	#10615625	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91793	2
C₂×C₅×#904	2
C₂×C₃×#3944	2
#11747563	2
#11747562	2
#11747548	2
#11747547	2
#11747546	2
#10615625	3
#82009	5