Subgroups — #13007918

Order 1280.

9494 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#4099	C₂	1	2	yes	maximal, complemented
3	#10619140	C₂	1	6	yes	maximal, complemented
4	#10617822	C₂	1	24	yes	maximal, complemented
5	#10617820	C₂	1	12	yes	maximal, complemented
6	#10617814	C₂	1	12	yes	maximal, complemented
7	#10617598	C₂	1	6	yes	maximal, complemented
8	C₂⁶×C₅	C₂²	1	1	yes	characteristic, complemented
9	C₂³×C₅×D₄	C₂²	1	3	yes	complemented
10	C₂³×C₂²⋊D₅	C₂²	1	6	yes	complemented
11	C₂×#4144	C₂²	1	6	yes	complemented
12	C₂×C₅×#120	C₂²	1	12	yes	complemented
13	C₂×C₅×#120	C₂²	1	12	yes	complemented
14	C₂²×C₅×C₂²⋊C₄	C₂²	1	3	yes	complemented
15	C₂×#4099	C₂²	1	12	yes	complemented
16	C₂×#4099	C₂²	1	12	yes	complemented
17	C₂×#4099	C₂²	1	24	yes	complemented
18	C₂×#4099	C₂²	1	4	yes	complemented
19	C₂²×C₂²⋊Dic₅	C₂²	1	6	yes	complemented
20	#66140	C₂²	1	48	yes	complemented
21	#66139	C₂²	1	12	yes	complemented
22	#66138	C₂²	1	12	yes	complemented
23	#66138	C₂²	1	12	yes	complemented
24	D₄×C₂²⋊D₅	C₂²	1	48	yes	complemented
25	#66132	C₂²	1	6	yes	complemented
26	#66125	C₂²	1	12	yes	complemented
27	#65929	C₂²	1	24	yes	complemented
28	#65928	C₂²	1	8	yes	complemented
29	#65927	C₂²	1	48	yes	complemented
30	#65926	C₂²	1	24	yes	complemented
31	#65925	C₂²	1	48	yes	complemented
32	#65924	C₂²	1	24	yes	complemented
33	#65923	C₂²	1	24	yes	complemented
34	D₅×#120	C₂²	1	8	yes	complemented
35	#65921	C₂²	1	24	yes	complemented
36	#65920	C₂²	1	24	yes	complemented
37	#65829	C₂²	1	48	yes	complemented
38	#65828	C₂²	1	24	yes	complemented
39	#65827	C₂²	1	6	yes	complemented
40	#65824	C₂²	1	48	yes	complemented
41	#65820	C₂²	1	12	yes	complemented
42	#65817	C₂²	1	6	yes	complemented
43	#62817	—	5	1	no	maximal, Sylow
44	C₂⁵×C₅	—	4	12	no	—
45	C₂⁵×C₅	C₂³	1	6	yes	—
46	C₂⁵×C₅	C₂³	1	3	yes	—
47	C₂⁵×C₅	C₂³	1	6	yes	—
48	C₂⁵×C₅	C₂³	1	1	yes	characteristic, complemented
49	C₂⁴×D₅	C₂³	1	2	yes	complemented
50	C₂²×C₅×D₄	—	4	12	no	—
51	C₂²×C₅×D₄	C₂³	1	6	yes	—
52	C₂²×C₅×D₄	C₂³	1	24	yes	complemented
53	C₂²×C₅×D₄	C₂³	1	6	yes	complemented
54	C₂³×C₄×C₅	C₂³	1	3	yes	complemented
55	C₂²×C₂²⋊D₅	—	4	24	no	—
56	C₂²×C₂²⋊D₅	C₂³	1	12	yes	—
57	C₂²×C₂²⋊D₅	C₂³	1	24	yes	complemented
58	C₂²×C₂²⋊D₅	C₂³	1	12	yes	complemented
59	C₂²×C₂²⋊D₅	C₂³	1	24	yes	complemented
60	C₂²×C₂²⋊D₅	C₂³	1	12	yes	complemented
61	C₂³×Dic₅	C₂³	1	6	yes	complemented
62	#4144	—	4	24	no	—
63	C₂×#711	C₂³	1	24	yes	complemented
64	C₂×D₄×D₅	C₂³	1	24	yes	complemented
65	C₂×#709	C₂³	1	12	yes	complemented
66	C₅×#120	C₂³	1	24	yes	—
67	C₅×#120	C₂³	1	8	yes	complemented
68	C₅×#120	C₂³	1	24	yes	complemented
69	C₅×#120	C₂³	1	8	yes	complemented
70	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
71	C₂×C₅×C₂²⋊C₄	C₂³	1	24	yes	complemented
72	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	complemented
73	#4099	C₂³	1	48	yes	—
74	#4099	C₂³	1	24	yes	complemented
75	#4099	C₂³	1	8	yes	complemented
76	#4099	C₂³	1	8	yes	complemented
77	#4099	C₂³	1	24	yes	complemented
78	#4099	C₂³	1	16	yes	complemented
79	#4099	C₂³	1	24	yes	complemented
80	C₂×C₂²⋊Dic₅	C₂³	1	12	yes	—
81	C₂×C₂²⋊Dic₅	C₂³	1	24	yes	complemented
82	C₂×C₂²⋊Dic₅	C₂³	1	24	yes	complemented
83	C₂×C₂²⋊Dic₅	C₂³	1	12	yes	complemented
84	C₂×C₂²⋊Dic₅	C₂³	1	12	yes	complemented
85	#4086	C₂³	1	24	yes	complemented
86	#4085	C₂³	1	48	yes	complemented
87	#4085	C₂³	1	48	yes	complemented
88	#4084	C₂³	1	48	yes	complemented
89	#4083	C₂³	1	24	yes	complemented
90	#4083	C₂³	1	24	yes	complemented
91	#4082	C₂³	1	24	yes	complemented
92	#4081	C₂³	1	24	yes	complemented
93	#4081	C₂³	1	24	yes	complemented
94	D₄×Dic₅	C₂³	1	48	yes	complemented
95	#4076	C₂³	1	24	yes	complemented
96	#4075	C₂³	1	24	yes	complemented
97	C₄×C₂²⋊D₅	C₂³	1	48	yes	complemented
98	#4072	C₂³	1	12	yes	complemented
99	#4070	C₂³	1	24	yes	complemented
100	#4032	C₂³	1	24	yes	complemented
101	#4031	C₂³	1	48	yes	complemented
102	#4030	C₂³	1	48	yes	complemented
103	#4029	C₂³	1	48	yes	complemented
104	#4028	C₂³	1	24	yes	complemented
105	#4027	C₂³	1	48	yes	complemented
106	D₅×C₂²⋊C₄	C₂³	1	24	yes	complemented
107	#4025	C₂³	1	48	yes	complemented
108	#4024	C₂³	1	48	yes	complemented
109	#4023	C₂³	1	24	yes	complemented
110	#3532	—	5	24	no	—
111	#3490	—	5	12	no	—
112	#3490	—	5	6	no	—
113	#3484	—	5	6	no	—
114	#3484	—	5	12	no	—
115	C₂²×#120	—	5	2	no	—
116	C₂²×#120	D₅	1	1	yes	characteristic, complemented
117	C₂⁴×C₅	—	2	24	no	—
118	C₂⁴×C₅	—	2	12	no	—
119	C₂⁴×C₅	—	4	24	no	—
120	C₂⁴×C₅	—	4	12	no	—
121	C₂⁴×C₅	—	4	24	no	—
122	C₂⁴×C₅	—	4	12	no	—
123	C₂⁴×C₅	—	4	6	no	—
124	C₂⁴×C₅	—	4	64	no	—
125	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
126	C₂⁴×C₅	C₂⁴	1	2	yes	—
127	C₂⁴×C₅	C₂⁴	1	6	yes	—
128	C₂⁴×C₅	C₂⁴	1	12	yes	—
129	C₂⁴×C₅	C₂⁴	1	6	yes	—
130	C₂⁴×C₅	C₂⁴	1	6	yes	—
131	C₂⁴×C₅	C₂⁴	1	3	yes	—
132	C₂⁴×C₅	C₂⁴	1	2	yes	—
133	C₂⁴×C₅	C₂⁴	1	3	yes	—
134	C₂³×D₅	—	4	12	no	—
135	C₂³×D₅	C₂⁴	1	12	yes	—
136	C₂³×D₅	C₂⁴	1	4	yes	complemented
137	C₂×C₅×D₄	—	2	24	no	—
138	C₂×C₅×D₄	—	4	12	no	—
139	C₂×C₅×D₄	—	4	48	no	—
140	C₂×C₅×D₄	C₂⁴	1	24	yes	—
141	C₂×C₅×D₄	C₂⁴	1	24	yes	—
142	C₂²×C₄×C₅	—	4	6	no	—
143	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
144	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
145	C₂×C₂²⋊D₅	—	2	48	no	—
146	C₂×C₂²⋊D₅	—	4	24	no	—
147	C₂×C₂²⋊D₅	—	4	24	no	—
148	C₂×C₂²⋊D₅	—	4	48	no	—
149	C₂×C₂²⋊D₅	—	4	48	no	—
150	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
151	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	—
152	C₂×C₂²⋊D₅	C₂⁴	1	48	yes	—
153	C₂×C₂²⋊D₅	C₂⁴	1	24	yes	complemented
154	C₂²×Dic₅	—	4	12	no	—
155	C₂²×Dic₅	C₂⁴	1	12	yes	—
156	C₂²×Dic₅	C₂⁴	1	24	yes	—
157	C₂²×Dic₅	C₂⁴	1	12	yes	complemented
158	#711	—	4	48	no	—
159	D₄×D₅	—	4	48	no	—
160	#709	—	4	24	no	—
161	C₂×D₂₀	C₂⁴	1	12	yes	complemented
162	C₂×C₄×D₅	C₂⁴	1	24	yes	complemented
163	C₂×Dic₁₀	C₂⁴	1	12	yes	complemented
164	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
165	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
166	C₂²⋊Dic₅	C₂⁴	1	24	yes	—
167	C₂²⋊Dic₅	C₂⁴	1	24	yes	—
168	C₂²⋊Dic₅	C₂⁴	1	48	yes	—
169	C₂²⋊Dic₅	C₂⁴	1	24	yes	complemented
170	#685	C₂⁴	1	48	yes	complemented
171	C₄⋊Dic₅	C₂⁴	1	24	yes	complemented
172	#683	C₂⁴	1	48	yes	complemented
173	C₄×Dic₅	C₂⁴	1	24	yes	complemented
174	C₂⁶	C₂×D₅	1	1	yes	characteristic, complemented
175	C₂×H(5,𝔽₂)	—	5	6	no	—
176	C₂³×D₄	—	5	6	no	—
177	C₂³×D₄	C₂×D₅	1	3	yes	complemented
178	H(3,𝔽₄)	—	5	8	no	—
179	#560	—	5	24	no	—
180	#551	—	5	24	no	—
181	#551	—	5	48	no	—
182	#546	—	5	48	no	—
183	#546	—	5	48	no	—
184	#546	—	5	48	no	—
185	D₄²	—	5	48	no	—
186	D₄²	—	5	24	no	—
187	#543	—	5	6	no	—
188	#538	—	5	48	no	—
189	#538	—	5	24	no	—
190	#535	—	5	12	no	—
191	#535	—	5	24	no	—
192	#534	—	5	12	no	—
193	#534	—	5	12	no	—
194	#534	—	5	24	no	—
195	#534	—	5	6	no	—
196	#525	—	5	12	no	—
197	#525	—	5	24	no	—
198	C₂×#120	—	5	12	no	—
199	C₂×#120	—	5	12	no	—
200	C₂×#120	—	5	24	no	—
201	C₂×#120	—	5	4	no	—
202	C₂×#120	—	5	8	no	—
203	C₂×#120	C₂×D₅	1	12	yes	complemented
204	C₂×#120	C₂×D₅	1	12	yes	complemented
205	#518	—	5	6	no	—
206	#518	—	5	12	no	—
207	C₂²×C₂²⋊C₄	—	5	6	no	—
208	C₂²×C₂²⋊C₄	C₂×D₅	1	3	yes	complemented
209	C₂³×C₅	—	2	12	no	—
210	C₂³×C₅	—	2	6	no	—
211	C₂³×C₅	—	2	24	no	—
212	C₂³×C₅	—	2	24	no	—
213	C₂³×C₅	—	2	12	no	—
214	C₂³×C₅	—	2	24	no	—
215	C₂³×C₅	—	2	6	no	—
216	C₂³×C₅	—	2	12	no	—
217	C₂³×C₅	—	4	6	no	—
218	C₂³×C₅	—	4	6	no	—
219	C₂³×C₅	—	4	12	no	—
220	C₂³×C₅	—	4	12	no	—
221	C₂³×C₅	—	4	6	no	—
222	C₂³×C₅	—	4	6	no	—
223	C₂³×C₅	—	4	12	no	—
224	C₂³×C₅	—	4	96	no	—
225	C₂³×C₅	—	4	48	no	—
226	C₂³×C₅	—	4	96	no	—
227	C₂³×C₅	—	8	8	no	—
228	C₂³×C₅	H(5,𝔽₂)	1	12	yes	complemented
229	C₂³×C₅	C₂⁵	1	6	yes	—
230	C₂³×C₅	C₂⁵	1	4	yes	—
231	C₂³×C₅	C₂⁵	1	3	yes	—
232	C₂³×C₅	C₂⁵	1	6	yes	—
233	C₂²×D₅	—	2	24	no	—
234	C₂²×D₅	—	4	24	no	—
235	C₂²×D₅	—	4	12	no	—
236	C₂²×D₅	—	8	16	no	—
237	C₂²×D₅	C₂⁵	1	8	yes	—
238	C₅×D₄	—	2	48	no	—
239	C₅×D₄	—	4	24	no	—
240	C₂×C₄×C₅	—	2	12	no	—
241	C₂×C₄×C₅	—	4	12	no	—
242	C₂×C₄×C₅	C₂⁵	1	12	yes	—
243	C₂²⋊D₅	—	2	48	no	—
244	C₂²⋊D₅	—	2	48	no	—
245	C₂²⋊D₅	—	4	24	no	—
246	C₂²⋊D₅	—	4	48	no	—
247	C₂×Dic₅	—	2	24	no	—
248	C₂×Dic₅	—	4	12	no	—
249	C₂×Dic₅	—	4	24	no	—
250	C₂×Dic₅	C₂⁵	1	24	yes	—
251	D₂₀	—	4	12	no	—
252	C₄×D₅	—	4	24	no	—
253	Dic₁₀	—	4	12	no	—
254	C₂⁵	—	4	12	no	—
255	C₂⁵	—	5	2	no	—
256	C₂⁵	C₂²×D₅	1	6	yes	—
257	C₂⁵	C₂²×D₅	1	3	yes	—
258	C₂⁵	C₂²×D₅	1	6	yes	—
259	C₂⁵	C₂²×D₅	1	1	yes	characteristic, complemented
260	H(5,𝔽₂)	—	20	24	no	—
261	C₂×#41	—	5	24	no	—
262	C₂×#41	—	5	12	no	—
263	C₂²×D₄	—	4	12	no	—
264	C₂²×D₄	—	5	12	no	—
265	C₂²×D₄	—	5	12	no	—
266	C₂²×D₄	—	5	24	no	—
267	C₂²×D₄	—	5	24	no	—
268	C₂²×D₄	—	5	12	no	—
269	C₂²×D₄	—	5	24	no	—
270	C₂²×D₄	—	20	24	no	—
271	C₂²×D₄	C₂²×D₅	1	6	yes	—
272	C₂²×D₄	C₂²×D₅	1	6	yes	complemented
273	C₂²×D₄	C₂²×D₅	1	24	yes	complemented
274	C₂³×C₄	—	5	6	no	—
275	C₂³×C₄	C₂²×D₅	1	3	yes	complemented
276	#127	—	5	24	no	—
277	#126	—	5	48	no	—
278	#124	—	5	24	no	—
279	#124	—	5	48	no	—
280	#123	—	5	24	no	—
281	#123	—	5	24	no	—
282	#123	—	5	24	no	—
283	#123	—	5	24	no	—
284	#123	—	5	48	no	—
285	C₂²⋊Q₈	—	5	24	no	—
286	C₂²⋊Q₈	—	5	48	no	—
287	#121	—	5	48	no	—
288	#121	—	5	48	no	—
289	#121	—	5	48	no	—
290	#121	—	5	24	no	—
291	#121	—	5	48	no	—
292	#120	—	5	48	no	—
293	#120	—	5	8	no	—
294	#120	—	5	8	no	—
295	#120	—	5	24	no	—
296	#120	—	5	24	no	—
297	#120	—	5	16	no	—
298	#120	—	5	24	no	—
299	#120	—	5	24	no	—
300	#120	—	5	24	no	—
301	#120	—	5	24	no	—
302	#120	C₂²×D₅	1	24	yes	—
303	#120	C₂²×D₅	1	8	yes	complemented
304	#120	C₂²×D₅	1	24	yes	complemented
305	#120	C₂²×D₅	1	8	yes	complemented
306	C₄×D₄	—	5	48	no	—
307	C₄×D₄	—	5	48	no	—
308	C₄×D₄	—	5	48	no	—
309	#117	—	5	12	no	—
310	#117	—	5	24	no	—
311	C₂×C₂²⋊C₄	—	5	12	no	—
312	C₂×C₂²⋊C₄	—	5	12	no	—
313	C₂×C₂²⋊C₄	—	5	24	no	—
314	C₂×C₂²⋊C₄	—	5	24	no	—
315	C₂×C₂²⋊C₄	—	5	12	no	—
316	C₂×C₂²⋊C₄	—	5	24	no	—
317	C₂×C₂²⋊C₄	C₂²×D₅	1	6	yes	—
318	C₂×C₂²⋊C₄	C₂²×D₅	1	6	yes	complemented
319	C₂×C₂²⋊C₄	C₂²×D₅	1	24	yes	complemented
320	C₂²×C₅	—	2	16	no	—
321	C₂²×C₅	—	2	8	no	—
322	C₂²×C₅	—	2	12	no	—
323	C₂²×C₅	—	2	6	no	—
324	C₂²×C₅	—	2	12	no	—
325	C₂²×C₅	—	2	12	no	—
326	C₂²×C₅	—	2	6	no	—
327	C₂²×C₅	—	4	12	no	—
328	C₂²×C₅	—	4	24	no	—
329	C₂²×C₅	—	4	48	no	—
330	C₂²×C₅	—	4	24	no	—
331	C₂²×C₅	—	4	12	no	—
332	C₂²×C₅	—	4	8	no	—
333	C₂²×C₅	—	8	12	no	—
334	C₂²×C₅	C₂×H(5,𝔽₂)	1	12	yes	—
335	C₂²×C₅	C₂×H(5,𝔽₂)	1	6	yes	—
336	C₂²×C₅	C₂⁶	1	1	yes	characteristic
337	C₂×D₅	—	2	24	no	—
338	C₂×D₅	—	8	24	no	—
339	C₂×D₅	—	16	4	no	—
340	C₄×C₅	—	2	12	no	—
341	Dic₅	—	2	24	no	—
342	C₂⁴	—	2	12	no	—
343	C₂⁴	—	2	24	no	—
344	C₂⁴	—	4	12	no	—
345	C₂⁴	—	4	24	no	—
346	C₂⁴	—	4	24	no	—
347	C₂⁴	—	4	12	no	—
348	C₂⁴	—	4	6	no	—
349	C₂⁴	—	4	64	no	—
350	C₂⁴	—	5	12	no	—
351	C₂⁴	—	5	4	no	—
352	C₂⁴	—	20	12	no	—
353	C₂⁴	C₂³×D₅	1	1	yes	characteristic
354	C₂⁴	C₂³×D₅	1	2	yes	—
355	C₂⁴	C₂³×D₅	1	6	yes	—
356	C₂⁴	C₂³×D₅	1	12	yes	—
357	C₂⁴	C₂³×D₅	1	6	yes	—
358	C₂⁴	C₂³×D₅	1	6	yes	—
359	C₂⁴	C₂³×D₅	1	3	yes	—
360	C₂⁴	C₂³×D₅	1	2	yes	—
361	C₂⁴	C₂³×D₅	1	3	yes	—
362	#41	—	20	24	no	—
363	#41	—	20	48	no	—
364	C₂×Q₈	—	5	12	no	—
365	C₂×D₄	—	2	24	no	—
366	C₂×D₄	—	4	12	no	—
367	C₂×D₄	—	4	48	no	—
368	C₂×D₄	—	5	24	no	—
369	C₂×D₄	—	5	24	no	—
370	C₂×D₄	—	5	48	no	—
371	C₂×D₄	—	5	24	no	—
372	C₂×D₄	—	5	12	no	—
373	C₂×D₄	—	10	48	no	—
374	C₂×D₄	—	20	24	no	—
375	C₂×D₄	—	20	48	no	—
376	C₂×D₄	—	20	48	no	—
377	C₂×D₄	—	20	48	no	—
378	C₂×D₄	—	20	24	no	—
379	C₂×D₄	C₂³×D₅	1	24	yes	—
380	C₂×D₄	C₂³×D₅	1	24	yes	—
381	C₂²×C₄	—	4	6	no	—
382	C₂²×C₄	—	5	12	no	—
383	C₂²×C₄	—	5	24	no	—
384	C₂²×C₄	—	5	12	no	—
385	C₂²×C₄	—	5	24	no	—
386	C₂²×C₄	—	20	12	no	—
387	C₂²×C₄	C₂³×D₅	1	6	yes	—
388	C₂²×C₄	C₂³×D₅	1	12	yes	—
389	C₄⋊C₄	—	5	48	no	—
390	C₄⋊C₄	—	5	24	no	—
391	C₂²⋊C₄	—	5	24	no	—
392	C₂²⋊C₄	—	5	24	no	—
393	C₂²⋊C₄	—	5	48	no	—
394	C₂²⋊C₄	—	5	24	no	—
395	C₂²⋊C₄	—	5	48	no	—
396	C₂²⋊C₄	C₂³×D₅	1	24	yes	—
397	C₂²⋊C₄	C₂³×D₅	1	24	yes	—
398	C₄²	—	5	24	no	—
399	C₂×C₅	—	2	12	no	—
400	C₂×C₅	—	2	6	no	—
401	C₂×C₅	—	4	4	no	—
402	C₂×C₅	—	4	6	no	—
403	C₂×C₅	C₂²×H(5,𝔽₂)	1	3	yes	—
404	D₅	—	4	8	no	—
405	C₂³	—	2	6	no	—
406	C₂³	—	2	12	no	—
407	C₂³	—	2	24	no	—
408	C₂³	—	2	6	no	—
409	C₂³	—	2	24	no	—
410	C₂³	—	2	24	no	—
411	C₂³	—	2	12	no	—
412	C₂³	—	2	12	no	—
413	C₂³	—	4	6	no	—
414	C₂³	—	4	12	no	—
415	C₂³	—	4	6	no	—
416	C₂³	—	4	6	no	—
417	C₂³	—	4	12	no	—
418	C₂³	—	4	6	no	—
419	C₂³	—	4	12	no	—
420	C₂³	—	4	48	no	—
421	C₂³	—	4	96	no	—
422	C₂³	—	4	96	no	—
423	C₂³	—	5	8	no	—
424	C₂³	—	8	8	no	—
425	C₂³	—	10	24	no	—
426	C₂³	—	20	24	no	—
427	C₂³	—	20	12	no	—
428	C₂³	—	40	16	no	—
429	C₂³	#4144	1	12	yes	complemented
430	C₂³	C₂⁴×D₅	1	6	yes	—
431	C₂³	C₂⁴×D₅	1	4	yes	—
432	C₂³	C₂⁴×D₅	1	3	yes	—
433	C₂³	C₂⁴×D₅	1	6	yes	—
434	Q₈	—	20	12	no	—
435	D₄	—	2	48	no	—
436	D₄	—	4	24	no	—
437	D₄	—	10	48	no	—
438	D₄	—	10	48	no	—
439	D₄	—	20	12	no	—
440	D₄	—	20	48	no	—
441	D₄	—	20	24	no	—
442	C₂×C₄	—	2	12	no	—
443	C₂×C₄	—	4	12	no	—
444	C₂×C₄	—	5	24	no	—
445	C₂×C₄	—	10	24	no	—
446	C₂×C₄	—	20	24	no	—
447	C₂×C₄	—	20	24	no	—
448	C₂×C₄	—	20	12	no	—
449	C₂×C₄	C₂⁴×D₅	1	12	yes	—
450	C₅	#62817	1	1	yes	characteristic, complemented, Sylow
451	C₂²	—	2	8	no	—
452	C₂²	—	2	16	no	—
453	C₂²	—	2	6	no	—
454	C₂²	—	2	12	no	—
455	C₂²	—	2	12	no	—
456	C₂²	—	2	6	no	—
457	C₂²	—	2	12	no	—
458	C₂²	—	4	12	no	—
459	C₂²	—	4	48	no	—
460	C₂²	—	4	24	no	—
461	C₂²	—	4	12	no	—
462	C₂²	—	4	24	no	—
463	C₂²	—	4	8	no	—
464	C₂²	—	8	12	no	—
465	C₂²	—	10	24	no	—
466	C₂²	—	40	24	no	—
467	C₂²	—	80	4	no	—
468	C₂²	C₂×#4144	1	6	yes	—
469	C₂²	C₂×#4144	1	12	yes	—
470	C₂²	C₂⁵×D₅	1	1	yes	characteristic
471	C₄	—	2	12	no	—
472	C₄	—	10	24	no	—
473	C₂	—	2	6	no	—
474	C₂	—	2	12	no	—
475	C₂	—	4	6	no	—
476	C₂	—	4	4	no	—
477	C₂	—	20	8	no	—
478	C₂	C₂²×#4144	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁶
Fitting	C₂²×C₅×#120	C₂
hypercenter	C₂²×#120	D₅
hypocenter	C₅	#62817
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#120	C₂	semidirect
2. C₂²×#4099	C₂	semidirect
3. #10619140	C₂	semidirect
4. #10617822	C₂	semidirect
5. #10617820	C₂	semidirect
6. #10617814	C₂	semidirect
7. #10617598	C₂	semidirect
8. C₂⁶×C₅	C₂²	semidirect
9. C₂³×C₅×D₄	C₂²	semidirect
10. C₂³×C₂²⋊D₅	C₂²	semidirect
11. C₂×#4144	C₂²	semidirect
12. C₂×C₅×#120	C₂²	semidirect
13. C₂×C₅×#120	C₂²	semidirect
14. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
15. C₂×#4099	C₂²	semidirect
16. C₂×#4099	C₂²	semidirect
17. C₂×#4099	C₂²	semidirect
18. C₂×#4099	C₂²	semidirect
19. C₂²×C₂²⋊Dic₅	C₂²	semidirect
20. #66140	C₂²	semidirect
21. #66139	C₂²	semidirect
22. #66138	C₂²	semidirect
23. #66138	C₂²	semidirect
24. D₄×C₂²⋊D₅	C₂²	semidirect
25. #66132	C₂²	semidirect
26. #66125	C₂²	semidirect
27. #65929	C₂²	semidirect
28. #65928	C₂²	semidirect
29. #65927	C₂²	semidirect
30. #65926	C₂²	semidirect
31. #65925	C₂²	semidirect
32. #65924	C₂²	semidirect
33. #65923	C₂²	semidirect
34. D₅×#120	C₂²	semidirect
35. #65921	C₂²	semidirect
36. #65920	C₂²	semidirect
37. #65829	C₂²	semidirect
38. #65828	C₂²	semidirect
39. #65827	C₂²	semidirect
40. #65824	C₂²	semidirect
41. #65820	C₂²	semidirect
42. #65817	C₂²	semidirect
48. C₂⁵×C₅	C₂³	semidirect
49. C₂⁴×D₅	C₂³	semidirect
52. C₂²×C₅×D₄	C₂³	semidirect
53. C₂²×C₅×D₄	C₂³	semidirect
54. C₂³×C₄×C₅	C₂³	semidirect
57. C₂²×C₂²⋊D₅	C₂³	semidirect
58. C₂²×C₂²⋊D₅	C₂³	semidirect
59. C₂²×C₂²⋊D₅	C₂³	semidirect
60. C₂²×C₂²⋊D₅	C₂³	semidirect
61. C₂³×Dic₅	C₂³	semidirect
63. C₂×#711	C₂³	semidirect
64. C₂×D₄×D₅	C₂³	semidirect
65. C₂×#709	C₂³	semidirect
67. C₅×#120	C₂³	semidirect
68. C₅×#120	C₂³	semidirect
69. C₅×#120	C₂³	semidirect
71. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
72. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
74. #4099	C₂³	semidirect
75. #4099	C₂³	semidirect
76. #4099	C₂³	semidirect
77. #4099	C₂³	semidirect
78. #4099	C₂³	semidirect
79. #4099	C₂³	semidirect
81. C₂×C₂²⋊Dic₅	C₂³	semidirect
82. C₂×C₂²⋊Dic₅	C₂³	semidirect
83. C₂×C₂²⋊Dic₅	C₂³	semidirect
84. C₂×C₂²⋊Dic₅	C₂³	semidirect
85. #4086	C₂³	semidirect
86. #4085	C₂³	semidirect
87. #4085	C₂³	semidirect
88. #4084	C₂³	semidirect
89. #4083	C₂³	semidirect
90. #4083	C₂³	semidirect
91. #4082	C₂³	semidirect
92. #4081	C₂³	semidirect
93. #4081	C₂³	semidirect
94. D₄×Dic₅	C₂³	semidirect
95. #4076	C₂³	semidirect
96. #4075	C₂³	semidirect
97. C₄×C₂²⋊D₅	C₂³	semidirect
98. #4072	C₂³	semidirect
99. #4070	C₂³	semidirect
100. #4032	C₂³	semidirect
101. #4031	C₂³	semidirect
102. #4030	C₂³	semidirect
103. #4029	C₂³	semidirect
104. #4028	C₂³	semidirect
105. #4027	C₂³	semidirect
106. D₅×C₂²⋊C₄	C₂³	semidirect
107. #4025	C₂³	semidirect
108. #4024	C₂³	semidirect
109. #4023	C₂³	semidirect
116. C₂²×#120	D₅	semidirect
136. C₂³×D₅	C₂⁴	semidirect
153. C₂×C₂²⋊D₅	C₂⁴	semidirect
157. C₂²×Dic₅	C₂⁴	semidirect
161. C₂×D₂₀	C₂⁴	semidirect
162. C₂×C₄×D₅	C₂⁴	semidirect
163. C₂×Dic₁₀	C₂⁴	semidirect
169. C₂²⋊Dic₅	C₂⁴	semidirect
170. #685	C₂⁴	semidirect
171. C₄⋊Dic₅	C₂⁴	semidirect
172. #683	C₂⁴	semidirect
173. C₄×Dic₅	C₂⁴	semidirect
174. C₂⁶	C₂×D₅	semidirect
177. C₂³×D₄	C₂×D₅	semidirect
203. C₂×#120	C₂×D₅	semidirect
204. C₂×#120	C₂×D₅	semidirect
208. C₂²×C₂²⋊C₄	C₂×D₅	semidirect
228. C₂³×C₅	H(5,𝔽₂)	semidirect
259. C₂⁵	C₂²×D₅	semidirect
272. C₂²×D₄	C₂²×D₅	semidirect
273. C₂²×D₄	C₂²×D₅	semidirect
275. C₂³×C₄	C₂²×D₅	semidirect
303. #120	C₂²×D₅	semidirect
304. #120	C₂²×D₅	semidirect
305. #120	C₂²×D₅	semidirect
318. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
319. C₂×C₂²⋊C₄	C₂²×D₅	semidirect
429. C₂³	#4144	semidirect
450. C₅	#62817	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#120	2
C₂²×#4099	2
#10619140	2
#10617822	2
#10617820	2
#10617814	2
#10617598	2
#62817	5