Subgroups — #10618552

Order 640.

1260 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	#66168	C₂	1	1	yes	maximal, characteristic, complemented
3	#66164	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#4086	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#66015	C₂	1	1	yes	maximal, characteristic, complemented
7	#66008	C₂	1	1	yes	maximal, characteristic, complemented
8	#66000	C₂	1	2	yes	maximal, complemented
9	#65997	C₂	1	2	yes	maximal, complemented
10	#65964	C₂	1	1	yes	maximal, characteristic, complemented
11	#65958	C₂	1	1	yes	maximal, characteristic, complemented
12	#65954	C₂	1	2	yes	maximal, complemented
13	#65953	C₂	1	1	yes	maximal, characteristic, complemented
14	#65943	C₂	1	1	yes	maximal, characteristic, complemented
15	#65941	C₂	1	2	yes	maximal, complemented
16	#65924	C₂	1	2	yes	maximal, complemented
17	#65923	C₂	1	2	yes	maximal, complemented
18	#65896	C₂	1	1	yes	maximal, characteristic, complemented
19	#65887	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
21	#65872	C₂	1	1	yes	maximal, characteristic, complemented
22	#65827	C₂	1	2	yes	maximal, complemented
23	#65824	C₂	1	2	yes	maximal, complemented
24	C₂×C₅×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
29	C₂×#713	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₄×D₅	C₂²	1	2	yes	complemented
32	C₂×D₄×D₅	C₂²	1	2	yes	complemented
33	C₂×#709	C₂²	1	2	yes	complemented
34	C₂²×D₂₀	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₂₀	C₂²	1	1	yes	characteristic, complemented
36	C₅×#124	C₂²	1	1	yes	characteristic, complemented
37	C₅×#123	C₂²	1	2	yes	complemented
38	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₅×#121	C₂²	1	2	yes	complemented
40	C₅×#121	C₂²	1	1	yes	characteristic, complemented
41	C₅×#120	C₂²	1	2	yes	complemented
42	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
45	#4099	C₂²	1	2	yes	complemented
46	#4093	C₂²	1	1	yes	characteristic, complemented
47	#4093	C₂²	1	1	yes	characteristic, complemented
48	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
49	#4086	C₂²	1	1	yes	characteristic
50	#4086	C₂²	1	1	yes	characteristic, complemented
51	#4086	C₂²	1	1	yes	characteristic, complemented
52	#4086	C₂²	1	1	yes	characteristic, complemented
53	#4086	C₂²	1	2	yes	complemented
54	#4086	C₂²	1	1	yes	characteristic, complemented
55	#4086	C₂²	1	2	yes	complemented
56	#4086	C₂²	1	2	yes	complemented
57	#4085	C₂²	1	1	yes	characteristic
58	#4085	C₂²	1	2	yes	complemented
59	#4085	C₂²	1	2	yes	complemented
60	#4084	C₂²	1	1	yes	characteristic, complemented
61	#4084	C₂²	1	2	yes	complemented
62	#4084	C₂²	1	2	yes	complemented
63	#4083	C₂²	1	2	yes	complemented
64	#4083	C₂²	1	2	yes	complemented
65	#4083	C₂²	1	2	yes	complemented
66	#4083	C₂²	1	2	yes	complemented
67	#4081	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
69	#4076	C₂²	1	1	yes	characteristic
70	#4076	C₂²	1	2	yes	complemented
71	#4076	C₂²	1	2	yes	complemented
72	#4076	C₂²	1	2	yes	complemented
73	#4076	C₂²	1	2	yes	complemented
74	#4076	C₂²	1	2	yes	complemented
75	#4076	C₂²	1	1	yes	characteristic, complemented
76	#4075	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
80	#4072	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
82	#4044	C₂²	1	1	yes	characteristic, complemented
83	#4044	C₂²	1	2	yes	complemented
84	#4041	C₂²	1	2	yes	complemented
85	#4041	C₂²	1	1	yes	characteristic, complemented
86	#4041	C₂²	1	2	yes	complemented
87	#4040	C₂²	1	2	yes	complemented
88	#4039	C₂²	1	1	yes	characteristic, complemented
89	#4039	C₂²	1	1	yes	characteristic, complemented
90	#4038	C₂²	1	2	yes	complemented
91	#4036	C₂²	1	1	yes	characteristic, complemented
92	#4035	C₂²	1	1	yes	characteristic, complemented
93	#4032	C₂²	1	1	yes	characteristic, complemented
94	#4032	C₂²	1	2	yes	complemented
95	#4032	C₂²	1	2	yes	complemented
96	#4032	C₂²	1	2	yes	complemented
97	#4031	C₂²	1	2	yes	complemented
98	#4031	C₂²	1	1	yes	characteristic, complemented
99	#4030	C₂²	1	2	yes	complemented
100	#4030	C₂²	1	2	yes	complemented
101	#4030	C₂²	1	2	yes	complemented
102	#4030	C₂²	1	2	yes	complemented
103	#4030	C₂²	1	2	yes	complemented
104	#4030	C₂²	1	2	yes	complemented
105	#4029	C₂²	1	2	yes	complemented
106	#4029	C₂²	1	2	yes	complemented
107	#4029	C₂²	1	2	yes	complemented
108	#4028	C₂²	1	2	yes	complemented
109	#4028	C₂²	1	2	yes	complemented
110	#4028	C₂²	1	2	yes	complemented
111	#4028	C₂²	1	2	yes	complemented
112	#4028	C₂²	1	2	yes	complemented
113	#4028	C₂²	1	2	yes	complemented
114	#4027	C₂²	1	2	yes	complemented
115	#4027	C₂²	1	2	yes	complemented
116	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
117	#4025	C₂²	1	1	yes	characteristic, complemented
118	#4024	C₂²	1	1	yes	characteristic, complemented
119	#4020	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
121	#4018	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3543	—	5	1	no	maximal, Sylow
124	C₂⁴×C₅	C₂³	1	2	yes	—
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₂³×D₅	C₂³	1	2	yes	—
127	C₂³×D₅	C₂³	1	2	yes	—
128	C₅×#41	—	4	2	no	—
129	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
130	C₂×C₅×D₄	—	4	2	no	—
131	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
132	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
133	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
134	C₂×C₅×D₄	C₂³	1	2	yes	—
135	C₂×C₅×D₄	C₂³	1	2	yes	—
136	C₂×C₅×D₄	C₂³	1	2	yes	—
137	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂³	1	2	yes	—
140	C₂²×C₄×C₅	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₅	—	4	4	no	—
142	C₂×C₂²⋊D₅	—	4	4	no	—
143	C₂×C₂²⋊D₅	—	4	4	no	—
144	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
158	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
160	C₂²×Dic₅	C₂³	1	1	yes	characteristic
161	C₂²×Dic₅	C₂³	1	1	yes	characteristic
162	C₂²×Dic₅	C₂³	1	2	yes	—
163	#713	—	4	2	no	—
164	D₄×D₅	—	4	2	no	—
165	D₄×D₅	—	4	4	no	—
166	D₄×D₅	—	4	4	no	—
167	#709	—	4	4	no	—
168	C₂×D₂₀	—	4	2	no	—
169	C₂×D₂₀	—	4	2	no	—
170	C₂×D₂₀	C₂³	1	1	yes	characteristic
171	C₂×D₂₀	C₂³	1	1	yes	characteristic
172	C₂×D₂₀	C₂³	1	1	yes	characteristic
173	C₂×D₂₀	C₂³	1	2	yes	—
174	C₂×D₂₀	C₂³	1	2	yes	—
175	C₂×D₂₀	C₂³	1	2	yes	—
176	C₂×D₂₀	C₂³	1	2	yes	—
177	C₂×D₂₀	C₂³	1	2	yes	—
178	C₂×D₂₀	C₂³	1	2	yes	—
179	C₂×C₄×D₅	C₂³	1	2	yes	—
180	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₅	C₂³	1	2	yes	—
182	C₂×C₄×D₅	C₂³	1	2	yes	—
183	C₂×C₄×D₅	C₂³	1	2	yes	—
184	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
185	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₅×C₄⋊C₄	C₂³	1	2	yes	—
188	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₄²×C₅	C₂³	1	1	yes	characteristic
196	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
197	C₂²⋊Dic₅	C₂³	1	2	yes	—
198	C₂²⋊Dic₅	C₂³	1	2	yes	—
199	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
200	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
201	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
202	#685	C₂³	1	1	yes	characteristic
203	#685	C₂³	1	1	yes	characteristic
204	#685	C₂³	1	2	yes	—
205	#685	C₂³	1	2	yes	—
206	#685	C₂³	1	2	yes	—
207	#685	C₂³	1	2	yes	—
208	#685	C₂³	1	2	yes	—
209	#685	C₂³	1	1	yes	characteristic
210	#685	C₂³	1	2	yes	—
211	#685	C₂³	1	2	yes	—
212	#685	C₂³	1	2	yes	—
213	#685	C₂³	1	2	yes	—
214	#685	C₂³	1	2	yes	—
215	#685	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
219	C₄⋊Dic₅	C₂³	1	2	yes	—
220	C₄⋊Dic₅	C₂³	1	2	yes	—
221	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
222	#683	C₂³	1	1	yes	characteristic
223	#683	C₂³	1	1	yes	characteristic
224	#683	C₂³	1	1	yes	characteristic
225	#683	C₂³	1	1	yes	characteristic
226	#683	C₂³	1	1	yes	characteristic
227	#683	C₂³	1	1	yes	characteristic
228	#683	C₂³	1	2	yes	—
229	C₄×Dic₅	C₂³	1	1	yes	characteristic
230	C₄×Dic₅	C₂³	1	1	yes	characteristic
231	C₄×Dic₅	C₂³	1	1	yes	characteristic
232	C₄×Dic₅	C₂³	1	1	yes	characteristic
233	C₄×Dic₅	C₂³	1	2	yes	—
234	C₄×Dic₅	C₂³	1	1	yes	characteristic
235	#560	—	5	2	no	—
236	#560	—	5	2	no	—
237	#559	—	5	1	no	—
238	#550	—	5	1	no	—
239	#550	—	5	1	no	—
240	#546	—	5	1	no	—
241	#546	—	5	2	no	—
242	#546	D₅	1	1	yes	characteristic, complemented
243	D₄²	—	5	1	no	—
244	D₄²	—	5	1	no	—
245	D₄²	—	5	2	no	—
246	D₄²	—	5	1	no	—
247	#540	—	5	2	no	—
248	#540	—	5	1	no	—
249	#540	—	5	1	no	—
250	#535	—	5	1	no	—
251	#535	—	5	1	no	—
252	#535	—	5	2	no	—
253	#534	—	5	2	no	—
254	#534	—	5	2	no	—
255	C₂×#127	—	5	1	no	—
256	#529	—	5	1	no	—
257	#529	—	5	1	no	—
258	C₂³×C₅	—	2	4	no	—
259	C₂³×C₅	—	4	2	no	—
260	C₂³×C₅	—	4	2	no	—
261	C₂³×C₅	C₂⁴	1	1	yes	characteristic
262	C₂³×C₅	C₂⁴	1	2	yes	—
263	C₂³×C₅	C₂⁴	1	2	yes	—
264	C₂³×C₅	C₂⁴	1	1	yes	characteristic
265	C₂²×D₅	—	2	4	no	—
266	C₂²×D₅	—	4	2	no	—
267	C₂²×D₅	—	4	2	no	—
268	C₂²×D₅	—	4	2	no	—
269	C₂²×D₅	—	4	2	no	—
270	C₂²×D₅	—	4	2	no	—
271	C₂²×D₅	—	4	2	no	—
272	C₂²×D₅	—	4	2	no	—
273	C₂²×D₅	—	4	2	no	—
274	C₂²×D₅	C₂⁴	1	1	yes	characteristic
275	C₂²×D₅	C₂⁴	1	2	yes	—
276	C₂²×D₅	C₂⁴	1	2	yes	—
277	C₂²×D₅	C₂⁴	1	2	yes	—
278	C₅×Q₈	—	2	2	no	—
279	C₅×D₄	—	2	2	no	—
280	C₅×D₄	—	2	2	no	—
281	C₅×D₄	—	2	2	no	—
282	C₅×D₄	—	4	2	no	—
283	C₅×D₄	—	4	2	no	—
284	C₅×D₄	—	4	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	4	2	no	—
288	C₂×C₄×C₅	—	4	2	no	—
289	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂⁴	1	2	yes	—
291	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂⁴	1	2	yes	—
295	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
296	C₂²⋊D₅	—	2	4	no	—
297	C₂²⋊D₅	—	2	2	no	—
298	C₂²⋊D₅	—	2	4	no	—
299	C₂²⋊D₅	—	2	2	no	—
300	C₂²⋊D₅	—	2	4	no	—
301	C₂²⋊D₅	—	4	2	no	—
302	C₂²⋊D₅	—	4	2	no	—
303	C₂²⋊D₅	—	4	2	no	—
304	C₂²⋊D₅	—	4	2	no	—
305	C₂²⋊D₅	—	4	2	no	—
306	C₂²⋊D₅	—	4	2	no	—
307	C₂²⋊D₅	—	4	2	no	—
308	C₂²⋊D₅	—	4	2	no	—
309	C₂²⋊D₅	—	4	2	no	—
310	C₂²⋊D₅	—	4	2	no	—
311	C₂²⋊D₅	—	4	2	no	—
312	C₂×Dic₅	—	2	2	no	—
313	C₂×Dic₅	—	2	2	no	—
314	C₂×Dic₅	—	4	2	no	—
315	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
316	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
317	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
318	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
319	C₂×Dic₅	C₂⁴	1	2	yes	—
320	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
321	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
322	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
323	D₂₀	—	2	2	no	—
324	D₂₀	—	2	2	no	—
325	D₂₀	—	2	2	no	—
326	D₂₀	—	4	2	no	—
327	D₂₀	—	4	2	no	—
328	D₂₀	—	4	2	no	—
329	D₂₀	—	4	2	no	—
330	D₂₀	—	4	2	no	—
331	D₂₀	—	4	2	no	—
332	C₄×D₅	—	2	2	no	—
333	C₄×D₅	—	2	4	no	—
334	C₄×D₅	—	4	2	no	—
335	C₄×D₅	—	4	2	no	—
336	C₄×D₅	—	4	2	no	—
337	Dic₁₀	—	2	2	no	—
338	C₂×#41	—	5	1	no	—
339	C₂×#41	—	5	2	no	—
340	C₂×#41	C₂×D₅	1	1	yes	characteristic, complemented
341	C₂²×D₄	—	5	2	no	—
342	C₂²×D₄	—	5	2	no	—
343	C₂²×D₄	—	5	2	no	—
344	C₂²×D₄	—	5	2	no	—
345	C₂²×D₄	—	5	2	no	—
346	C₂²×D₄	—	5	1	no	—
347	C₂²×D₄	—	5	1	no	—
348	C₂²×D₄	—	5	1	no	—
349	C₂²×D₄	C₂×D₅	1	1	yes	characteristic, complemented
350	#127	—	5	2	no	—
351	#127	—	5	1	no	—
352	#127	—	5	1	no	—
353	#127	—	5	1	no	—
354	#127	—	5	1	no	—
355	#127	—	5	2	no	—
356	#127	—	5	2	no	—
357	#127	—	5	1	no	—
358	#127	—	5	1	no	—
359	#126	—	5	1	no	—
360	#126	—	5	2	no	—
361	#126	—	5	1	no	—
362	#125	—	5	1	no	—
363	#125	—	5	1	no	—
364	#124	—	5	1	no	—
365	#124	—	5	1	no	—
366	#124	—	5	1	no	—
367	#124	—	5	2	no	—
368	#124	C₂×D₅	1	1	yes	characteristic, complemented
369	#123	—	5	1	no	—
370	#123	—	5	2	no	—
371	#123	—	5	2	no	—
372	#123	—	5	2	no	—
373	#123	—	5	1	no	—
374	#123	—	5	2	no	—
375	#123	—	5	2	no	—
376	#123	—	5	2	no	—
377	#123	—	5	2	no	—
378	#123	—	5	2	no	—
379	#123	C₂×D₅	1	2	yes	complemented
380	C₂²⋊Q₈	—	5	1	no	—
381	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
382	#121	—	5	1	no	—
383	#121	—	5	2	no	—
384	#121	—	5	2	no	—
385	#121	—	5	1	no	—
386	#121	—	5	2	no	—
387	#121	—	5	2	no	—
388	#121	—	5	1	no	—
389	#121	—	5	2	no	—
390	#121	—	5	2	no	—
391	#121	—	5	2	no	—
392	#121	—	5	2	no	—
393	#121	—	5	2	no	—
394	#121	—	5	1	no	—
395	#121	—	5	2	no	—
396	#121	—	5	1	no	—
397	#121	—	5	2	no	—
398	#121	—	5	2	no	—
399	#121	—	5	2	no	—
400	#121	—	5	2	no	—
401	#121	—	5	2	no	—
402	#121	—	5	2	no	—
403	#121	—	5	2	no	—
404	#121	C₂×D₅	1	2	yes	complemented
405	#121	C₂×D₅	1	1	yes	characteristic, complemented
406	#120	—	5	2	no	—
407	#120	—	5	2	no	—
408	#120	—	5	2	no	—
409	#120	—	5	2	no	—
410	#120	—	5	2	no	—
411	#120	—	5	2	no	—
412	#120	—	5	2	no	—
413	#120	—	5	2	no	—
414	#120	—	5	2	no	—
415	#120	—	5	2	no	—
416	#120	—	5	2	no	—
417	#120	C₂×D₅	1	2	yes	complemented
418	C₄×Q₈	—	5	1	no	—
419	C₄×Q₈	—	5	1	no	—
420	C₄×D₄	—	5	1	no	—
421	C₄×D₄	—	5	1	no	—
422	C₄×D₄	—	5	1	no	—
423	C₄×D₄	—	5	2	no	—
424	C₄×D₄	—	5	1	no	—
425	C₄×D₄	—	5	1	no	—
426	C₄×D₄	—	5	2	no	—
427	C₄×D₄	—	5	2	no	—
428	C₄×D₄	—	5	1	no	—
429	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
430	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
431	#117	—	5	1	no	—
432	#117	—	5	2	no	—
433	#117	—	5	1	no	—
434	C₂×C₂²⋊C₄	—	5	2	no	—
435	C₂×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
436	C₂×C₄²	—	5	1	no	—
437	C₂²×C₅	—	2	1	no	—
438	C₂²×C₅	—	2	1	no	—
439	C₂²×C₅	—	2	2	no	—
440	C₂²×C₅	—	2	2	no	—
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	2	1	no	—
443	C₂²×C₅	—	2	2	no	—
444	C₂²×C₅	—	2	1	no	—
445	C₂²×C₅	—	2	2	no	—
446	C₂²×C₅	—	2	1	no	—
447	C₂²×C₅	—	2	2	no	—
448	C₂²×C₅	—	8	4	no	—
449	C₂²×C₅	H(5,𝔽₂)	1	2	yes	—
450	C₂²×C₅	C₂⁵	1	1	yes	characteristic
451	C₂×D₅	—	2	1	no	—
452	C₂×D₅	—	2	2	no	—
453	C₂×D₅	—	2	2	no	—
454	C₂×D₅	—	2	2	no	—
455	C₂×D₅	—	2	2	no	—
456	C₂×D₅	—	2	2	no	—
457	C₂×D₅	—	2	2	no	—
458	C₂×D₅	—	2	1	no	—
459	C₂×D₅	—	2	2	no	—
460	C₂×D₅	—	2	2	no	—
461	C₂×D₅	—	2	2	no	—
462	C₂×D₅	—	2	1	no	—
463	C₂×D₅	—	8	4	no	—
464	C₂×D₅	—	8	4	no	—
465	C₂×D₅	—	8	4	no	—
466	C₄×C₅	—	2	1	no	—
467	C₄×C₅	—	2	2	no	—
468	C₄×C₅	—	2	1	no	—
469	C₄×C₅	—	2	2	no	—
470	C₄×C₅	—	2	1	no	—
471	C₄×C₅	—	2	1	no	—
472	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
473	Dic₅	—	2	1	no	—
474	Dic₅	—	2	1	no	—
475	Dic₅	—	2	2	no	—
476	Dic₅	—	2	1	no	—
477	Dic₅	—	2	1	no	—
478	Dic₅	—	2	1	no	—
479	Dic₅	—	2	1	no	—
480	Dic₅	H(5,𝔽₂)	1	2	yes	—
481	C₂⁴	—	5	2	no	—
482	C₂⁴	—	5	2	no	—
483	C₂⁴	—	5	2	no	—
484	C₂⁴	C₂²×D₅	1	2	yes	—
485	#41	—	4	2	no	—
486	#41	—	20	4	no	—
487	#41	—	20	2	no	—
488	C₂×Q₈	—	5	1	no	—
489	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
490	C₂×D₄	—	4	2	no	—
491	C₂×D₄	—	5	1	no	—
492	C₂×D₄	—	5	2	no	—
493	C₂×D₄	—	5	1	no	—
494	C₂×D₄	—	5	2	no	—
495	C₂×D₄	—	5	2	no	—
496	C₂×D₄	—	5	2	no	—
497	C₂×D₄	—	5	2	no	—
498	C₂×D₄	—	5	2	no	—
499	C₂×D₄	—	5	2	no	—
500	C₂×D₄	—	5	2	no	—
501	C₂×D₄	—	5	2	no	—
502	C₂×D₄	—	5	2	no	—
503	C₂×D₄	—	5	2	no	—
504	C₂×D₄	—	5	2	no	—
505	C₂×D₄	—	5	2	no	—
506	C₂×D₄	—	5	2	no	—
507	C₂×D₄	—	5	1	no	—
508	C₂×D₄	—	5	1	no	—
509	C₂×D₄	—	5	1	no	—
510	C₂×D₄	—	5	2	no	—
511	C₂×D₄	—	5	2	no	—
512	C₂×D₄	—	5	2	no	—
513	C₂×D₄	—	5	2	no	—
514	C₂×D₄	—	5	2	no	—
515	C₂×D₄	—	5	2	no	—
516	C₂×D₄	—	20	2	no	—
517	C₂×D₄	—	20	2	no	—
518	C₂×D₄	—	20	2	no	—
519	C₂×D₄	—	20	4	no	—
520	C₂×D₄	—	20	4	no	—
521	C₂×D₄	—	20	4	no	—
522	C₂×D₄	—	20	4	no	—
523	C₂×D₄	—	20	4	no	—
524	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
525	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
526	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
527	C₂×D₄	C₂²×D₅	1	2	yes	—
528	C₂×D₄	C₂²×D₅	1	2	yes	—
529	C₂×D₄	C₂²×D₅	1	2	yes	—
530	C₂²×C₄	—	5	1	no	—
531	C₂²×C₄	—	5	1	no	—
532	C₂²×C₄	—	5	2	no	—
533	C₂²×C₄	—	5	2	no	—
534	C₂²×C₄	—	5	1	no	—
535	C₂²×C₄	—	5	2	no	—
536	C₂²×C₄	—	5	2	no	—
537	C₂²×C₄	—	5	2	no	—
538	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
539	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
540	C₂²×C₄	C₂²×D₅	1	2	yes	—
541	C₂²×C₄	C₂²×D₅	1	2	yes	—
542	C₄⋊C₄	—	5	1	no	—
543	C₄⋊C₄	—	5	1	no	—
544	C₄⋊C₄	—	5	1	no	—
545	C₄⋊C₄	—	5	1	no	—
546	C₄⋊C₄	—	5	2	no	—
547	C₄⋊C₄	—	5	1	no	—
548	C₄⋊C₄	—	5	1	no	—
549	C₄⋊C₄	—	5	1	no	—
550	C₄⋊C₄	—	5	2	no	—
551	C₄⋊C₄	—	5	1	no	—
552	C₄⋊C₄	—	5	1	no	—
553	C₄⋊C₄	—	5	2	no	—
554	C₄⋊C₄	—	5	1	no	—
555	C₄⋊C₄	C₂²×D₅	1	2	yes	—
556	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
557	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
558	C₂²⋊C₄	—	5	1	no	—
559	C₂²⋊C₄	—	5	1	no	—
560	C₂²⋊C₄	—	5	1	no	—
561	C₂²⋊C₄	—	5	1	no	—
562	C₂²⋊C₄	—	5	2	no	—
563	C₂²⋊C₄	—	5	2	no	—
564	C₂²⋊C₄	—	5	2	no	—
565	C₂²⋊C₄	—	5	2	no	—
566	C₂²⋊C₄	—	5	1	no	—
567	C₂²⋊C₄	—	5	2	no	—
568	C₂²⋊C₄	—	5	2	no	—
569	C₂²⋊C₄	—	5	1	no	—
570	C₂²⋊C₄	—	5	1	no	—
571	C₂²⋊C₄	—	5	2	no	—
572	C₂²⋊C₄	—	5	2	no	—
573	C₂²⋊C₄	—	5	1	no	—
574	C₂²⋊C₄	—	5	2	no	—
575	C₂²⋊C₄	—	5	2	no	—
576	C₂²⋊C₄	—	5	2	no	—
577	C₂²⋊C₄	—	5	2	no	—
578	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
579	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
580	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
581	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
582	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
583	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
584	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
585	C₄²	—	5	1	no	—
586	C₄²	—	5	1	no	—
587	C₄²	—	5	1	no	—
588	C₄²	—	5	1	no	—
589	C₄²	—	5	2	no	—
590	C₄²	—	5	1	no	—
591	C₄²	C₂²×D₅	1	1	yes	characteristic
592	C₂×C₅	—	2	2	no	—
593	C₂×C₅	—	4	1	no	—
594	C₂×C₅	—	4	2	no	—
595	C₂×C₅	—	4	2	no	—
596	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
598	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
599	D₅	—	4	2	no	—
600	D₅	—	4	1	no	—
601	D₅	—	4	2	no	—
602	D₅	—	4	2	no	—
603	C₂³	—	2	4	no	—
604	C₂³	—	4	2	no	—
605	C₂³	—	4	2	no	—
606	C₂³	—	5	1	no	—
607	C₂³	—	5	2	no	—
608	C₂³	—	5	2	no	—
609	C₂³	—	5	2	no	—
610	C₂³	—	10	4	no	—
611	C₂³	—	20	2	no	—
612	C₂³	—	20	2	no	—
613	C₂³	—	20	2	no	—
614	C₂³	—	20	2	no	—
615	C₂³	—	20	2	no	—
616	C₂³	—	20	2	no	—
617	C₂³	—	20	2	no	—
618	C₂³	—	20	2	no	—
619	C₂³	C₂³×D₅	1	1	yes	characteristic
620	C₂³	C₂³×D₅	1	2	yes	—
621	C₂³	C₂³×D₅	1	2	yes	—
622	C₂³	C₂³×D₅	1	1	yes	characteristic
623	Q₈	—	2	2	no	—
624	Q₈	—	10	2	no	—
625	D₄	—	2	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	2	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	4	2	no	—
631	D₄	—	10	2	no	—
632	D₄	—	10	4	no	—
633	D₄	—	10	4	no	—
634	D₄	—	10	4	no	—
635	D₄	—	10	2	no	—
636	D₄	—	10	2	no	—
637	D₄	—	10	2	no	—
638	D₄	—	10	2	no	—
639	D₄	—	20	2	no	—
640	D₄	—	20	2	no	—
641	D₄	—	20	2	no	—
642	D₄	—	20	2	no	—
643	D₄	—	20	2	no	—
644	D₄	—	20	2	no	—
645	D₄	—	20	2	no	—
646	D₄	—	20	2	no	—
647	D₄	—	20	2	no	—
648	D₄	—	20	2	no	—
649	D₄	—	20	2	no	—
650	D₄	—	20	2	no	—
651	D₄	—	20	2	no	—
652	D₄	—	20	2	no	—
653	D₄	—	20	2	no	—
654	D₄	—	20	2	no	—
655	D₄	—	20	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	5	1	no	—
661	C₂×C₄	—	5	1	no	—
662	C₂×C₄	—	5	1	no	—
663	C₂×C₄	—	5	1	no	—
664	C₂×C₄	—	5	1	no	—
665	C₂×C₄	—	5	1	no	—
666	C₂×C₄	—	5	2	no	—
667	C₂×C₄	—	5	1	no	—
668	C₂×C₄	—	10	4	no	—
669	C₂×C₄	—	10	2	no	—
670	C₂×C₄	—	10	2	no	—
671	C₂×C₄	—	10	2	no	—
672	C₂×C₄	—	20	2	no	—
673	C₂×C₄	—	20	2	no	—
674	C₂×C₄	—	20	2	no	—
675	C₂×C₄	—	20	2	no	—
676	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
677	C₂×C₄	C₂³×D₅	1	2	yes	—
678	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
679	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
680	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
681	C₂×C₄	C₂³×D₅	1	2	yes	—
682	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
683	C₅	#3543	1	1	yes	characteristic, complemented, Sylow
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	2	no	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	8	4	no	—
696	C₂²	—	10	1	no	—
697	C₂²	—	10	2	no	—
698	C₂²	—	10	2	no	—
699	C₂²	—	10	2	no	—
700	C₂²	—	10	2	no	—
701	C₂²	—	10	2	no	—
702	C₂²	—	10	1	no	—
703	C₂²	—	10	2	no	—
704	C₂²	—	10	2	no	—
705	C₂²	—	10	2	no	—
706	C₂²	—	10	1	no	—
707	C₂²	—	10	2	no	—
708	C₂²	—	40	4	no	—
709	C₂²	—	40	4	no	—
710	C₂²	—	40	4	no	—
711	C₂²	#4149	1	2	yes	—
712	C₂²	C₂⁴×D₅	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	2	no	—
719	C₄	—	5	2	no	—
720	C₄	—	10	1	no	—
721	C₄	—	10	1	no	—
722	C₄	—	10	1	no	—
723	C₄	—	10	2	no	—
724	C₄	—	10	1	no	—
725	C₄	—	10	1	no	—
726	C₄	—	10	1	no	—
727	C₄	#4144	1	2	yes	—
728	C₂	—	2	2	no	—
729	C₂	—	4	2	no	—
730	C₂	—	4	2	no	—
731	C₂	—	4	1	no	—
732	C₂	—	20	1	no	—
733	C₂	—	20	2	no	—
734	C₂	—	20	2	no	—
735	C₂	—	20	2	no	—
736	C₂	C₂×#4144	1	1	yes	characteristic
737	C₂	C₂×#4149	1	1	yes	characteristic
738	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#546	C₂
hypercenter	#546	D₅
hypocenter	C₅	#3543
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₅×#546	C₂	semidirect
2. #66168	C₂	semidirect
3. #66164	C₂	semidirect
4. C₂×#4086	C₂	semidirect
5. D₄×C₂²⋊D₅	C₂	semidirect
6. #66015	C₂	semidirect
7. #66008	C₂	semidirect
8. #66000	C₂	semidirect
9. #65997	C₂	semidirect
10. #65964	C₂	semidirect
11. #65958	C₂	semidirect
12. #65954	C₂	semidirect
13. #65953	C₂	semidirect
14. #65943	C₂	semidirect
15. #65941	C₂	semidirect
16. #65924	C₂	semidirect
17. #65923	C₂	semidirect
18. #65896	C₂	semidirect
19. #65887	C₂	semidirect
20. D₄×D₂₀	C₂	semidirect
21. #65872	C₂	semidirect
22. #65827	C₂	semidirect
23. #65824	C₂	semidirect
24. C₂×C₅×#41	C₂²	semidirect
25. C₂²×C₅×D₄	C₂²	semidirect
26. C₂²×C₂²⋊D₅	C₂²	semidirect
27. C₂²×C₂²⋊D₅	C₂²	semidirect
28. C₂²×C₂²⋊D₅	C₂²	semidirect
29. C₂×#713	C₂²	semidirect
30. C₂×D₄×D₅	C₂²	semidirect
31. C₂×D₄×D₅	C₂²	semidirect
32. C₂×D₄×D₅	C₂²	semidirect
33. C₂×#709	C₂²	semidirect
34. C₂²×D₂₀	C₂²	semidirect
35. C₂²×D₂₀	C₂²	semidirect
36. C₅×#124	C₂²	semidirect
37. C₅×#123	C₂²	semidirect
38. C₅×C₂²⋊Q₈	C₂²	semidirect
39. C₅×#121	C₂²	semidirect
40. C₅×#121	C₂²	semidirect
41. C₅×#120	C₂²	semidirect
42. C₄×C₅×D₄	C₂²	semidirect
43. C₄×C₅×D₄	C₂²	semidirect
44. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
45. #4099	C₂²	semidirect
46. #4093	C₂²	semidirect
47. #4093	C₂²	semidirect
48. Q₈×Dic₅	C₂²	semidirect
50. #4086	C₂²	semidirect
51. #4086	C₂²	semidirect
52. #4086	C₂²	semidirect
53. #4086	C₂²	semidirect
54. #4086	C₂²	semidirect
55. #4086	C₂²	semidirect
56. #4086	C₂²	semidirect
58. #4085	C₂²	semidirect
59. #4085	C₂²	semidirect
60. #4084	C₂²	semidirect
61. #4084	C₂²	semidirect
62. #4084	C₂²	semidirect
63. #4083	C₂²	semidirect
64. #4083	C₂²	semidirect
65. #4083	C₂²	semidirect
66. #4083	C₂²	semidirect
67. #4081	C₂²	semidirect
68. D₄×Dic₅	C₂²	semidirect
70. #4076	C₂²	semidirect
71. #4076	C₂²	semidirect
72. #4076	C₂²	semidirect
73. #4076	C₂²	semidirect
74. #4076	C₂²	semidirect
75. #4076	C₂²	semidirect
76. #4075	C₂²	semidirect
77. C₄×C₂²⋊D₅	C₂²	semidirect
78. C₄×C₂²⋊D₅	C₂²	semidirect
79. C₄×C₂²⋊D₅	C₂²	semidirect
80. #4072	C₂²	semidirect
81. C₂×C₄×Dic₅	C₂²	semidirect
82. #4044	C₂²	semidirect
83. #4044	C₂²	semidirect
84. #4041	C₂²	semidirect
85. #4041	C₂²	semidirect
86. #4041	C₂²	semidirect
87. #4040	C₂²	semidirect
88. #4039	C₂²	semidirect
89. #4039	C₂²	semidirect
90. #4038	C₂²	semidirect
91. #4036	C₂²	semidirect
92. #4035	C₂²	semidirect
93. #4032	C₂²	semidirect
94. #4032	C₂²	semidirect
95. #4032	C₂²	semidirect
96. #4032	C₂²	semidirect
97. #4031	C₂²	semidirect
98. #4031	C₂²	semidirect
99. #4030	C₂²	semidirect
100. #4030	C₂²	semidirect
101. #4030	C₂²	semidirect
102. #4030	C₂²	semidirect
103. #4030	C₂²	semidirect
104. #4030	C₂²	semidirect
105. #4029	C₂²	semidirect
106. #4029	C₂²	semidirect
107. #4029	C₂²	semidirect
108. #4028	C₂²	semidirect
109. #4028	C₂²	semidirect
110. #4028	C₂²	semidirect
111. #4028	C₂²	semidirect
112. #4028	C₂²	semidirect
113. #4028	C₂²	semidirect
114. #4027	C₂²	semidirect
115. #4027	C₂²	semidirect
116. D₅×C₂²⋊C₄	C₂²	semidirect
117. #4025	C₂²	semidirect
118. #4024	C₂²	semidirect
119. #4020	C₂²	semidirect
120. C₄×D₂₀	C₂²	semidirect
121. #4018	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
242. #546	D₅	semidirect
340. C₂×#41	C₂×D₅	semidirect
349. C₂²×D₄	C₂×D₅	semidirect
368. #124	C₂×D₅	semidirect
379. #123	C₂×D₅	semidirect
381. C₂²⋊Q₈	C₂×D₅	semidirect
404. #121	C₂×D₅	semidirect
405. #121	C₂×D₅	semidirect
417. #120	C₂×D₅	semidirect
429. C₄×D₄	C₂×D₅	semidirect
430. C₄×D₄	C₂×D₅	semidirect
435. C₂×C₂²⋊C₄	C₂×D₅	semidirect
683. C₅	#3543	semidirect

Maximal subgroups

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

subgroup	index
C₅×#546	2
#66168	2
#66164	2
C₂×#4086	2
D₄×C₂²⋊D₅	2
#66015	2
#66008	2
#66000	2
#65997	2
#65964	2
#65958	2
#65954	2
#65953	2
#65943	2
#65941	2
#65924	2
#65923	2
#65896	2
#65887	2
D₄×D₂₀	2
#65872	2
#65827	2
#65824	2
#3543	5