Subgroups — #10618393

Order 640.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	#66052	C₂	1	1	yes	maximal, characteristic, complemented
3	#66051	C₂	1	1	yes	maximal, characteristic, complemented
4	#66029	C₂	1	1	yes	maximal, characteristic, complemented
5	#66028	C₂	1	1	yes	maximal, characteristic, complemented
6	#66001	C₂	1	2	yes	maximal, complemented
7	#66000	C₂	1	2	yes	maximal, complemented
8	#65992	C₂	1	2	yes	maximal, complemented
9	#65988	C₂	1	2	yes	maximal, complemented
10	#65953	C₂	1	2	yes	maximal, complemented
11	#65951	C₂	1	2	yes	maximal, complemented
12	#65942	C₂	1	1	yes	maximal, characteristic, complemented
13	#65941	C₂	1	1	yes	maximal, characteristic, complemented
14	#65941	C₂	1	2	yes	maximal, complemented
15	#65940	C₂	1	1	yes	maximal, characteristic, complemented
16	#65939	C₂	1	2	yes	maximal, complemented
17	D₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	#65897	C₂	1	1	yes	maximal, characteristic, complemented
19	#65888	C₂	1	1	yes	maximal, characteristic, complemented
20	#65888	C₂	1	1	yes	maximal, characteristic, complemented
21	#65885	C₂	1	1	yes	maximal, characteristic, complemented
22	#65868	C₂	1	1	yes	maximal, characteristic, complemented
23	#65858	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#711	C₂²	1	1	yes	characteristic, complemented
25	C₂×#711	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₅	C₂²	1	2	yes	—
28	C₂×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₅	C₂²	1	2	yes	complemented
30	C₂×#709	C₂²	1	1	yes	characteristic, complemented
31	C₂×#709	C₂²	1	2	yes	complemented
32	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
33	C₅×#127	C₂²	1	1	yes	characteristic, complemented
34	C₅×#125	C₂²	1	1	yes	characteristic, complemented
35	C₅×#123	C₂²	1	2	yes	complemented
36	C₅×#123	C₂²	1	2	yes	complemented
37	C₅×#121	C₂²	1	1	yes	characteristic, complemented
38	C₅×#121	C₂²	1	2	yes	complemented
39	C₅×#121	C₂²	1	1	yes	characteristic, complemented
40	C₅×#121	C₂²	1	2	yes	complemented
41	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₅×#117	C₂²	1	1	yes	characteristic, complemented
44	#4086	C₂²	1	2	yes	complemented
45	#4086	C₂²	1	2	yes	complemented
46	#4085	C₂²	1	2	yes	complemented
47	#4085	C₂²	1	2	yes	complemented
48	#4085	C₂²	1	2	yes	complemented
49	#4085	C₂²	1	2	yes	complemented
50	#4084	C₂²	1	1	yes	characteristic
51	#4084	C₂²	1	1	yes	characteristic, complemented
52	#4084	C₂²	1	2	yes	complemented
53	#4084	C₂²	1	1	yes	characteristic, complemented
54	#4084	C₂²	1	1	yes	characteristic, complemented
55	#4084	C₂²	1	2	yes	complemented
56	#4083	C₂²	1	2	yes	—
57	#4083	C₂²	1	2	yes	complemented
58	#4083	C₂²	1	2	yes	complemented
59	#4083	C₂²	1	2	yes	complemented
60	D₄×Dic₅	C₂²	1	2	yes	complemented
61	D₄×Dic₅	C₂²	1	2	yes	complemented
62	#4076	C₂²	1	1	yes	characteristic
63	#4076	C₂²	1	2	yes	complemented
64	#4076	C₂²	1	2	yes	complemented
65	#4076	C₂²	1	2	yes	complemented
66	C₂×#685	C₂²	1	2	yes	complemented
67	C₂×#685	C₂²	1	2	yes	complemented
68	#4072	C₂²	1	2	yes	complemented
69	#4070	C₂²	1	1	yes	characteristic, complemented
70	#4070	C₂²	1	2	yes	complemented
71	#4044	C₂²	1	2	yes	complemented
72	#4044	C₂²	1	2	yes	complemented
73	#4044	C₂²	1	2	yes	complemented
74	#4043	C₂²	1	1	yes	characteristic, complemented
75	#4043	C₂²	1	1	yes	characteristic, complemented
76	#4043	C₂²	1	1	yes	characteristic, complemented
77	#4043	C₂²	1	1	yes	characteristic, complemented
78	#4042	C₂²	1	2	yes	complemented
79	#4041	C₂²	1	1	yes	characteristic
80	#4041	C₂²	1	1	yes	characteristic
81	#4041	C₂²	1	1	yes	characteristic, complemented
82	#4041	C₂²	1	1	yes	characteristic, complemented
83	#4041	C₂²	1	2	yes	complemented
84	#4040	C₂²	1	2	yes	—
85	#4040	C₂²	1	2	yes	complemented
86	#4039	C₂²	1	2	yes	complemented
87	#4038	C₂²	1	1	yes	characteristic, complemented
88	#4038	C₂²	1	1	yes	characteristic, complemented
89	#4038	C₂²	1	2	yes	complemented
90	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
91	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
92	#4036	C₂²	1	2	yes	complemented
93	#4032	C₂²	1	1	yes	characteristic, complemented
94	#4032	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
99	#4031	C₂²	1	2	yes	complemented
100	#4031	C₂²	1	2	yes	complemented
101	#4030	C₂²	1	2	yes	complemented
102	#4030	C₂²	1	2	yes	complemented
103	#4029	C₂²	1	2	yes	complemented
104	#4029	C₂²	1	2	yes	complemented
105	#4029	C₂²	1	2	yes	complemented
106	#4029	C₂²	1	2	yes	complemented
107	#4028	C₂²	1	1	yes	characteristic
108	#4028	C₂²	1	1	yes	characteristic, complemented
109	#4028	C₂²	1	2	yes	complemented
110	#4028	C₂²	1	2	yes	complemented
111	#4028	C₂²	1	2	yes	complemented
112	#4027	C₂²	1	2	yes	complemented
113	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
114	#4024	C₂²	1	2	yes	complemented
115	#4021	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₂₀	C₂²	1	1	yes	characteristic
117	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
121	#4015	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	#3542	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	1	yes	characteristic
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₂³×D₅	C₂³	1	2	yes	—
127	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×D₄	C₂³	1	2	yes	—
130	C₂×C₅×D₄	C₂³	1	2	yes	—
131	C₂×C₅×D₄	C₂³	1	2	yes	—
132	C₂×C₅×D₄	C₂³	1	2	yes	—
133	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂³	1	2	yes	—
135	C₂²×C₄×C₅	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
147	C₂²×Dic₅	C₂³	1	1	yes	characteristic
148	C₂²×Dic₅	C₂³	1	2	yes	—
149	C₂²×Dic₅	C₂³	1	2	yes	—
150	#711	—	4	2	no	—
151	#711	—	4	2	no	—
152	D₄×D₅	—	4	2	no	—
153	D₄×D₅	—	4	2	no	—
154	D₄×D₅	—	4	4	no	—
155	D₄×D₅	—	4	4	no	—
156	#709	—	4	2	no	—
157	#709	—	4	4	no	—
158	C₂×D₂₀	C₂³	1	1	yes	characteristic
159	C₂×D₂₀	C₂³	1	1	yes	characteristic
160	C₂×D₂₀	C₂³	1	1	yes	characteristic
161	C₂×D₂₀	C₂³	1	1	yes	characteristic
162	C₂×D₂₀	C₂³	1	2	yes	—
163	C₂×D₂₀	C₂³	1	1	yes	characteristic
164	C₂×D₂₀	C₂³	1	1	yes	characteristic
165	C₂×D₂₀	C₂³	1	2	yes	—
166	C₂×C₄×D₅	—	4	2	no	—
167	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂³	1	2	yes	—
171	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
172	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
174	C₂×C₄×D₅	C₂³	1	2	yes	—
175	C₂×C₄×D₅	C₂³	1	2	yes	—
176	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
177	C₂×Dic₁₀	C₂³	1	2	yes	—
178	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
179	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₅×C₄⋊C₄	C₂³	1	2	yes	—
184	C₅×C₄⋊C₄	C₂³	1	2	yes	—
185	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₄²×C₅	C₂³	1	1	yes	characteristic
192	C₄²×C₅	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₅	C₂³	1	2	yes	—
194	C₂²⋊Dic₅	C₂³	1	2	yes	—
195	C₂²⋊Dic₅	C₂³	1	2	yes	—
196	C₂²⋊Dic₅	C₂³	1	2	yes	—
197	C₂²⋊Dic₅	C₂³	1	2	yes	—
198	#685	C₂³	1	1	yes	characteristic
199	#685	C₂³	1	1	yes	characteristic
200	#685	C₂³	1	1	yes	characteristic
201	#685	C₂³	1	1	yes	characteristic
202	#685	C₂³	1	1	yes	characteristic
203	#685	C₂³	1	1	yes	characteristic
204	#685	C₂³	1	1	yes	characteristic
205	#685	C₂³	1	2	yes	—
206	#685	C₂³	1	1	yes	characteristic
207	#685	C₂³	1	2	yes	—
208	#685	C₂³	1	2	yes	—
209	#685	C₂³	1	2	yes	—
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	2	yes	—
216	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₅	C₂³	1	2	yes	—
219	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
220	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
221	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
222	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
223	C₄⋊Dic₅	C₂³	1	2	yes	—
224	C₄⋊Dic₅	C₂³	1	2	yes	—
225	#683	C₂³	1	2	yes	—
226	#683	C₂³	1	2	yes	—
227	#683	C₂³	1	2	yes	—
228	#683	C₂³	1	2	yes	—
229	C₄×Dic₅	C₂³	1	2	yes	—
230	C₄×Dic₅	C₂³	1	2	yes	—
231	C₄×Dic₅	C₂³	1	2	yes	—
232	#562	—	5	2	no	—
233	#560	—	5	2	no	—
234	#555	—	5	1	no	—
235	#553	—	5	1	no	—
236	#552	—	5	1	no	—
237	#551	—	5	2	no	—
238	#550	—	5	1	no	—
239	#547	—	5	1	no	—
240	#546	—	5	2	no	—
241	#546	—	5	1	no	—
242	#546	—	5	1	no	—
243	D₄²	—	5	1	no	—
244	#542	—	5	1	no	—
245	#540	—	5	2	no	—
246	#540	D₅	1	1	yes	characteristic, complemented
247	#538	—	5	2	no	—
248	#537	—	5	1	no	—
249	#535	—	5	2	no	—
250	#535	—	5	1	no	—
251	#534	—	5	2	no	—
252	#525	—	5	1	no	—
253	#525	—	5	1	no	—
254	C₂×#121	—	5	1	no	—
255	C₂³×C₅	C₂⁴	1	1	yes	characteristic
256	C₂³×C₅	C₂⁴	1	2	yes	—
257	C₂³×C₅	C₂⁴	1	2	yes	—
258	C₂²×D₅	—	2	2	no	—
259	C₂²×D₅	—	2	4	no	—
260	C₂²×D₅	—	4	1	no	—
261	C₂²×D₅	—	4	1	no	—
262	C₂²×D₅	—	4	2	no	—
263	C₂²×D₅	—	4	2	no	—
264	C₂²×D₅	—	4	2	no	—
265	C₂²×D₅	—	4	2	no	—
266	C₂²×D₅	—	4	2	no	—
267	C₂²×D₅	C₂⁴	1	1	yes	characteristic
268	C₂²×D₅	C₂⁴	1	2	yes	—
269	C₂²×D₅	C₂⁴	1	1	yes	characteristic
270	C₂²×D₅	C₂⁴	1	1	yes	characteristic
271	C₂²×D₅	C₂⁴	1	1	yes	characteristic
272	C₅×D₄	—	2	2	no	—
273	C₅×D₄	—	2	2	no	—
274	C₅×D₄	—	4	2	no	—
275	C₅×D₄	—	4	2	no	—
276	C₅×D₄	—	4	2	no	—
277	C₅×D₄	—	4	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	4	2	no	—
280	C₂×C₄×C₅	—	4	2	no	—
281	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂⁴	1	2	yes	—
283	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂⁴	1	2	yes	—
285	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
289	C₂²⋊D₅	—	2	4	no	—
290	C₂²⋊D₅	—	4	1	no	—
291	C₂²⋊D₅	—	4	1	no	—
292	C₂²⋊D₅	—	4	2	no	—
293	C₂²⋊D₅	—	4	2	no	—
294	C₂²⋊D₅	—	4	2	no	—
295	C₂²⋊D₅	—	4	2	no	—
296	C₂²⋊D₅	—	4	2	no	—
297	C₂²⋊D₅	—	4	2	no	—
298	C₂²⋊D₅	—	4	2	no	—
299	C₂²⋊D₅	—	4	2	no	—
300	C₂×Dic₅	—	4	1	no	—
301	C₂×Dic₅	—	4	2	no	—
302	C₂×Dic₅	—	4	2	no	—
303	C₂×Dic₅	C₂⁴	1	2	yes	—
304	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
305	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
306	C₂×Dic₅	C₂⁴	1	2	yes	—
307	C₂×Dic₅	C₂⁴	1	2	yes	—
308	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
309	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
310	D₂₀	—	2	2	no	—
311	D₂₀	—	2	2	no	—
312	D₂₀	—	2	2	no	—
313	D₂₀	—	4	1	no	—
314	D₂₀	—	4	2	no	—
315	D₂₀	—	4	1	no	—
316	D₂₀	—	4	1	no	—
317	D₂₀	—	4	2	no	—
318	C₄×D₅	—	2	4	no	—
319	C₄×D₅	—	2	2	no	—
320	C₄×D₅	—	2	2	no	—
321	C₄×D₅	—	2	2	no	—
322	C₄×D₅	—	2	2	no	—
323	C₄×D₅	—	4	1	no	—
324	C₄×D₅	—	4	1	no	—
325	C₄×D₅	—	4	2	no	—
326	C₄×D₅	—	4	2	no	—
327	Dic₁₀	—	2	2	no	—
328	Dic₁₀	—	4	1	no	—
329	Dic₁₀	—	4	2	no	—
330	C₂×#41	—	5	1	no	—
331	C₂×#41	—	5	1	no	—
332	C₂×#41	—	5	1	no	—
333	C₂×#41	—	5	2	no	—
334	C₂²×D₄	—	5	2	no	—
335	C₂²×D₄	—	5	1	no	—
336	C₂²×D₄	—	5	2	no	—
337	C₂²×D₄	—	5	1	no	—
338	C₂³×C₄	—	5	1	no	—
339	C₄⋊Q₈	—	5	1	no	—
340	#127	—	5	2	no	—
341	#127	—	5	2	no	—
342	#127	C₂×D₅	1	1	yes	characteristic, complemented
343	#126	—	5	2	no	—
344	#126	—	5	2	no	—
345	#126	—	5	2	no	—
346	#125	—	5	2	no	—
347	#125	C₂×D₅	1	1	yes	characteristic, complemented
348	#124	—	5	2	no	—
349	#124	—	5	2	no	—
350	#124	—	5	2	no	—
351	#124	—	5	2	no	—
352	#124	—	5	1	no	—
353	#123	—	5	2	no	—
354	#123	—	5	2	no	—
355	#123	—	5	1	no	—
356	#123	—	5	1	no	—
357	#123	—	5	2	no	—
358	#123	—	5	2	no	—
359	#123	—	5	2	no	—
360	#123	—	5	2	no	—
361	#123	—	5	2	no	—
362	#123	—	5	2	no	—
363	#123	C₂×D₅	1	2	yes	complemented
364	#123	C₂×D₅	1	2	yes	complemented
365	C₂²⋊Q₈	—	5	1	no	—
366	C₂²⋊Q₈	—	5	2	no	—
367	C₂²⋊Q₈	—	5	1	no	—
368	C₂²⋊Q₈	—	5	1	no	—
369	C₂²⋊Q₈	—	5	1	no	—
370	C₂²⋊Q₈	—	5	1	no	—
371	C₂²⋊Q₈	—	5	2	no	—
372	C₂²⋊Q₈	—	5	2	no	—
373	#121	—	5	2	no	—
374	#121	—	5	1	no	—
375	#121	—	5	1	no	—
376	#121	—	5	2	no	—
377	#121	—	5	2	no	—
378	#121	—	5	2	no	—
379	#121	—	5	1	no	—
380	#121	—	5	1	no	—
381	#121	—	5	2	no	—
382	#121	—	5	2	no	—
383	#121	—	5	1	no	—
384	#121	—	5	2	no	—
385	#121	—	5	2	no	—
386	#121	—	5	2	no	—
387	#121	—	5	1	no	—
388	#121	—	5	1	no	—
389	#121	—	5	1	no	—
390	#121	—	5	1	no	—
391	#121	—	5	2	no	—
392	#121	—	5	2	no	—
393	#121	—	5	2	no	—
394	#121	C₂×D₅	1	1	yes	characteristic, complemented
395	#121	C₂×D₅	1	1	yes	characteristic, complemented
396	#121	C₂×D₅	1	2	yes	complemented
397	#121	C₂×D₅	1	2	yes	complemented
398	#120	—	5	2	no	—
399	#120	—	5	2	no	—
400	#120	—	5	2	no	—
401	#120	—	5	2	no	—
402	#120	—	5	1	no	—
403	#120	—	5	1	no	—
404	#120	—	5	2	no	—
405	#120	—	5	2	no	—
406	#120	—	5	2	no	—
407	C₄×Q₈	—	5	1	no	—
408	C₄×D₄	—	5	2	no	—
409	C₄×D₄	—	5	2	no	—
410	C₄×D₄	—	5	2	no	—
411	C₄×D₄	—	5	2	no	—
412	C₄×D₄	—	5	1	no	—
413	C₄×D₄	—	5	1	no	—
414	C₄×D₄	—	5	1	no	—
415	C₄×D₄	—	5	1	no	—
416	C₄×D₄	—	5	1	no	—
417	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
418	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
419	#117	—	5	2	no	—
420	#117	—	5	1	no	—
421	#117	—	5	2	no	—
422	#117	—	5	1	no	—
423	#117	C₂×D₅	1	1	yes	characteristic, complemented
424	C₂×C₄⋊C₄	—	5	1	no	—
425	C₂×C₄⋊C₄	—	5	1	no	—
426	C₂×C₂²⋊C₄	—	5	2	no	—
427	C₂×C₂²⋊C₄	—	5	2	no	—
428	C₂×C₂²⋊C₄	—	5	2	no	—
429	C₂²×C₅	—	2	1	no	—
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	2	2	no	—
432	C₂²×C₅	—	2	2	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	2	2	no	—
435	C₂²×C₅	—	2	2	no	—
436	C₂²×C₅	—	2	1	no	—
437	C₂²×C₅	—	2	2	no	—
438	C₂²×C₅	C₂⁵	1	1	yes	characteristic
439	C₂×D₅	—	2	1	no	—
440	C₂×D₅	—	2	1	no	—
441	C₂×D₅	—	2	1	no	—
442	C₂×D₅	—	2	1	no	—
443	C₂×D₅	—	2	1	no	—
444	C₂×D₅	—	2	1	no	—
445	C₂×D₅	—	2	2	no	—
446	C₂×D₅	—	2	2	no	—
447	C₂×D₅	—	2	1	no	—
448	C₂×D₅	—	2	1	no	—
449	C₂×D₅	—	2	1	no	—
450	C₂×D₅	—	2	1	no	—
451	C₂×D₅	—	2	1	no	—
452	C₂×D₅	—	2	2	no	—
453	C₂×D₅	—	4	4	no	—
454	C₂×D₅	—	8	4	no	—
455	C₂×D₅	—	8	4	no	—
456	C₂×D₅	H(5,𝔽₂)	1	2	yes	—
457	C₄×C₅	—	2	1	no	—
458	C₄×C₅	—	2	1	no	—
459	C₄×C₅	—	2	2	no	—
460	C₄×C₅	—	2	1	no	—
461	C₄×C₅	—	2	1	no	—
462	C₄×C₅	—	2	2	no	—
463	C₄×C₅	—	2	1	no	—
464	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
465	Dic₅	—	2	2	no	—
466	Dic₅	—	2	1	no	—
467	Dic₅	—	2	1	no	—
468	Dic₅	—	2	2	no	—
469	Dic₅	—	2	2	no	—
470	Dic₅	—	2	1	no	—
471	Dic₅	—	2	1	no	—
472	C₂⁴	—	5	2	no	—
473	C₂⁴	—	5	1	no	—
474	C₂⁴	—	5	2	no	—
475	#41	—	20	2	no	—
476	#41	—	20	4	no	—
477	#41	—	20	2	no	—
478	#41	—	20	2	no	—
479	C₂×Q₈	—	5	1	no	—
480	C₂×Q₈	—	5	1	no	—
481	C₂×Q₈	—	5	2	no	—
482	C₂×D₄	—	5	2	no	—
483	C₂×D₄	—	5	1	no	—
484	C₂×D₄	—	5	2	no	—
485	C₂×D₄	—	5	2	no	—
486	C₂×D₄	—	5	2	no	—
487	C₂×D₄	—	5	2	no	—
488	C₂×D₄	—	5	2	no	—
489	C₂×D₄	—	5	2	no	—
490	C₂×D₄	—	5	1	no	—
491	C₂×D₄	—	5	2	no	—
492	C₂×D₄	—	5	2	no	—
493	C₂×D₄	—	5	1	no	—
494	C₂×D₄	—	5	1	no	—
495	C₂×D₄	—	5	1	no	—
496	C₂×D₄	—	5	1	no	—
497	C₂×D₄	—	5	2	no	—
498	C₂×D₄	—	5	1	no	—
499	C₂×D₄	—	5	1	no	—
500	C₂×D₄	—	5	2	no	—
501	C₂×D₄	—	20	2	no	—
502	C₂×D₄	—	20	2	no	—
503	C₂×D₄	—	20	4	no	—
504	C₂×D₄	—	20	4	no	—
505	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
506	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
507	C₂×D₄	C₂²×D₅	1	2	yes	—
508	C₂×D₄	C₂²×D₅	1	2	yes	—
509	C₂×D₄	C₂²×D₅	1	2	yes	—
510	C₂×D₄	C₂²×D₅	1	2	yes	—
511	C₂²×C₄	—	5	2	no	—
512	C₂²×C₄	—	5	2	no	—
513	C₂²×C₄	—	5	1	no	—
514	C₂²×C₄	—	5	2	no	—
515	C₂²×C₄	—	5	1	no	—
516	C₂²×C₄	—	5	1	no	—
517	C₂²×C₄	—	5	1	no	—
518	C₂²×C₄	—	5	1	no	—
519	C₂²×C₄	—	5	1	no	—
520	C₂²×C₄	—	5	2	no	—
521	C₂²×C₄	—	5	2	no	—
522	C₂²×C₄	—	5	1	no	—
523	C₂²×C₄	—	20	2	no	—
524	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₅	1	2	yes	—
526	C₂²×C₄	C₂²×D₅	1	2	yes	—
527	C₄⋊C₄	—	5	1	no	—
528	C₄⋊C₄	—	5	1	no	—
529	C₄⋊C₄	—	5	2	no	—
530	C₄⋊C₄	—	5	2	no	—
531	C₄⋊C₄	—	5	1	no	—
532	C₄⋊C₄	—	5	2	no	—
533	C₄⋊C₄	—	5	2	no	—
534	C₄⋊C₄	—	5	1	no	—
535	C₄⋊C₄	—	5	1	no	—
536	C₄⋊C₄	—	5	2	no	—
537	C₄⋊C₄	—	5	2	no	—
538	C₄⋊C₄	—	5	1	no	—
539	C₄⋊C₄	—	5	2	no	—
540	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
541	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₅	1	2	yes	—
543	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₅	1	2	yes	—
546	C₂²⋊C₄	—	5	2	no	—
547	C₂²⋊C₄	—	5	2	no	—
548	C₂²⋊C₄	—	5	2	no	—
549	C₂²⋊C₄	—	5	2	no	—
550	C₂²⋊C₄	—	5	2	no	—
551	C₂²⋊C₄	—	5	1	no	—
552	C₂²⋊C₄	—	5	2	no	—
553	C₂²⋊C₄	—	5	1	no	—
554	C₂²⋊C₄	—	5	2	no	—
555	C₂²⋊C₄	—	5	2	no	—
556	C₂²⋊C₄	—	5	2	no	—
557	C₂²⋊C₄	—	5	2	no	—
558	C₂²⋊C₄	—	5	2	no	—
559	C₂²⋊C₄	—	5	2	no	—
560	C₂²⋊C₄	—	5	1	no	—
561	C₂²⋊C₄	—	5	2	no	—
562	C₂²⋊C₄	—	5	2	no	—
563	C₂²⋊C₄	—	5	1	no	—
564	C₂²⋊C₄	—	5	1	no	—
565	C₂²⋊C₄	—	5	2	no	—
566	C₂²⋊C₄	—	5	1	no	—
567	C₂²⋊C₄	—	5	1	no	—
568	C₂²⋊C₄	—	5	1	no	—
569	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
572	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
575	C₄²	—	5	2	no	—
576	C₄²	—	5	2	no	—
577	C₄²	—	5	2	no	—
578	C₄²	C₂²×D₅	1	1	yes	characteristic
579	C₄²	C₂²×D₅	1	1	yes	characteristic
580	C₂×C₅	—	4	1	no	—
581	C₂×C₅	—	4	2	no	—
582	C₂×C₅	—	4	2	no	—
583	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
584	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
585	C₂×C₅	#585	1	1	yes	characteristic
586	D₅	—	2	2	no	—
587	D₅	—	4	1	no	—
588	D₅	—	4	1	no	—
589	D₅	—	4	1	no	—
590	D₅	—	4	2	no	—
591	C₂³	—	5	1	no	—
592	C₂³	—	5	1	no	—
593	C₂³	—	5	2	no	—
594	C₂³	—	5	1	no	—
595	C₂³	—	5	1	no	—
596	C₂³	—	10	2	no	—
597	C₂³	—	10	4	no	—
598	C₂³	—	20	1	no	—
599	C₂³	—	20	1	no	—
600	C₂³	—	20	2	no	—
601	C₂³	—	20	2	no	—
602	C₂³	—	20	2	no	—
603	C₂³	—	20	2	no	—
604	C₂³	—	20	2	no	—
605	C₂³	C₂³×D₅	1	1	yes	characteristic
606	C₂³	C₂³×D₅	1	2	yes	—
607	C₂³	C₂³×D₅	1	2	yes	—
608	Q₈	—	10	2	no	—
609	Q₈	—	20	1	no	—
610	Q₈	—	20	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	4	2	no	—
617	D₄	—	10	2	no	—
618	D₄	—	10	2	no	—
619	D₄	—	10	4	no	—
620	D₄	—	10	2	no	—
621	D₄	—	20	2	no	—
622	D₄	—	20	1	no	—
623	D₄	—	20	1	no	—
624	D₄	—	20	2	no	—
625	D₄	—	20	1	no	—
626	D₄	—	20	2	no	—
627	D₄	—	20	2	no	—
628	D₄	—	20	2	no	—
629	D₄	—	20	2	no	—
630	D₄	—	20	2	no	—
631	D₄	—	20	1	no	—
632	D₄	—	20	1	no	—
633	D₄	—	20	2	no	—
634	D₄	—	20	2	no	—
635	D₄	—	20	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	5	1	no	—
640	C₂×C₄	—	5	1	no	—
641	C₂×C₄	—	5	2	no	—
642	C₂×C₄	—	5	2	no	—
643	C₂×C₄	—	5	2	no	—
644	C₂×C₄	—	5	1	no	—
645	C₂×C₄	—	5	1	no	—
646	C₂×C₄	—	10	4	no	—
647	C₂×C₄	—	10	2	no	—
648	C₂×C₄	—	10	2	no	—
649	C₂×C₄	—	10	2	no	—
650	C₂×C₄	—	10	2	no	—
651	C₂×C₄	—	20	1	no	—
652	C₂×C₄	—	20	1	no	—
653	C₂×C₄	—	20	2	no	—
654	C₂×C₄	—	20	2	no	—
655	C₂×C₄	—	20	1	no	—
656	C₂×C₄	—	20	2	no	—
657	C₂×C₄	—	20	2	no	—
658	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
659	C₂×C₄	C₂³×D₅	1	2	yes	—
660	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₅	1	2	yes	—
665	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
666	C₅	#3542	1	1	yes	characteristic, complemented, Sylow
667	C₂²	—	2	1	no	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	5	2	no	—
677	C₂²	—	10	1	no	—
678	C₂²	—	10	1	no	—
679	C₂²	—	10	1	no	—
680	C₂²	—	10	1	no	—
681	C₂²	—	10	1	no	—
682	C₂²	—	10	2	no	—
683	C₂²	—	10	1	no	—
684	C₂²	—	10	2	no	—
685	C₂²	—	10	1	no	—
686	C₂²	—	10	1	no	—
687	C₂²	—	10	1	no	—
688	C₂²	—	10	1	no	—
689	C₂²	—	10	1	no	—
690	C₂²	—	10	2	no	—
691	C₂²	—	20	4	no	—
692	C₂²	—	40	4	no	—
693	C₂²	—	40	4	no	—
694	C₂²	C₂⁴×D₅	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	1	no	—
702	C₄	—	10	1	no	—
703	C₄	—	10	1	no	—
704	C₄	—	10	1	no	—
705	C₄	—	10	1	no	—
706	C₄	—	10	2	no	—
707	C₄	—	10	2	no	—
708	C₄	—	10	2	no	—
709	C₄	#4149	1	2	yes	—
710	C₂	—	4	1	no	—
711	C₂	—	4	2	no	—
712	C₂	—	4	2	no	—
713	C₂	—	10	2	no	—
714	C₂	—	20	1	no	—
715	C₂	—	20	1	no	—
716	C₂	—	20	2	no	—
717	C₂	—	20	1	no	—
718	C₂	C₂×#4149	1	1	yes	characteristic
719	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic
720	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#540	C₂
hypercenter	#540	D₅
hypocenter	C₅	#3542
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. C₅×#540	C₂	semidirect
2. #66052	C₂	semidirect
3. #66051	C₂	semidirect
4. #66029	C₂	semidirect
5. #66028	C₂	semidirect
6. #66001	C₂	semidirect
7. #66000	C₂	semidirect
8. #65992	C₂	semidirect
9. #65988	C₂	semidirect
10. #65953	C₂	semidirect
11. #65951	C₂	semidirect
12. #65942	C₂	semidirect
13. #65941	C₂	semidirect
14. #65941	C₂	semidirect
15. #65940	C₂	semidirect
16. #65939	C₂	semidirect
17. D₅×#121	C₂	semidirect
18. #65897	C₂	semidirect
19. #65888	C₂	semidirect
20. #65888	C₂	semidirect
21. #65885	C₂	semidirect
22. #65868	C₂	semidirect
23. #65858	C₂	semidirect
24. C₂×#711	C₂²	semidirect
25. C₂×#711	C₂²	semidirect
28. C₂×D₄×D₅	C₂²	semidirect
29. C₂×D₄×D₅	C₂²	semidirect
30. C₂×#709	C₂²	semidirect
31. C₂×#709	C₂²	semidirect
32. C₂²×C₄×D₅	C₂²	semidirect
33. C₅×#127	C₂²	semidirect
34. C₅×#125	C₂²	semidirect
35. C₅×#123	C₂²	semidirect
36. C₅×#123	C₂²	semidirect
37. C₅×#121	C₂²	semidirect
38. C₅×#121	C₂²	semidirect
39. C₅×#121	C₂²	semidirect
40. C₅×#121	C₂²	semidirect
41. C₄×C₅×D₄	C₂²	semidirect
42. C₄×C₅×D₄	C₂²	semidirect
43. C₅×#117	C₂²	semidirect
44. #4086	C₂²	semidirect
45. #4086	C₂²	semidirect
46. #4085	C₂²	semidirect
47. #4085	C₂²	semidirect
48. #4085	C₂²	semidirect
49. #4085	C₂²	semidirect
51. #4084	C₂²	semidirect
52. #4084	C₂²	semidirect
53. #4084	C₂²	semidirect
54. #4084	C₂²	semidirect
55. #4084	C₂²	semidirect
57. #4083	C₂²	semidirect
58. #4083	C₂²	semidirect
59. #4083	C₂²	semidirect
60. D₄×Dic₅	C₂²	semidirect
61. D₄×Dic₅	C₂²	semidirect
63. #4076	C₂²	semidirect
64. #4076	C₂²	semidirect
65. #4076	C₂²	semidirect
66. C₂×#685	C₂²	semidirect
67. C₂×#685	C₂²	semidirect
68. #4072	C₂²	semidirect
69. #4070	C₂²	semidirect
70. #4070	C₂²	semidirect
71. #4044	C₂²	semidirect
72. #4044	C₂²	semidirect
73. #4044	C₂²	semidirect
74. #4043	C₂²	semidirect
75. #4043	C₂²	semidirect
76. #4043	C₂²	semidirect
77. #4043	C₂²	semidirect
78. #4042	C₂²	semidirect
81. #4041	C₂²	semidirect
82. #4041	C₂²	semidirect
83. #4041	C₂²	semidirect
85. #4040	C₂²	semidirect
86. #4039	C₂²	semidirect
87. #4038	C₂²	semidirect
88. #4038	C₂²	semidirect
89. #4038	C₂²	semidirect
90. D₅×C₄⋊C₄	C₂²	semidirect
91. D₅×C₄⋊C₄	C₂²	semidirect
92. #4036	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. #4031	C₂²	semidirect
100. #4031	C₂²	semidirect
101. #4030	C₂²	semidirect
102. #4030	C₂²	semidirect
103. #4029	C₂²	semidirect
104. #4029	C₂²	semidirect
105. #4029	C₂²	semidirect
106. #4029	C₂²	semidirect
108. #4028	C₂²	semidirect
109. #4028	C₂²	semidirect
110. #4028	C₂²	semidirect
111. #4028	C₂²	semidirect
112. #4027	C₂²	semidirect
113. D₅×C₂²⋊C₄	C₂²	semidirect
114. #4024	C₂²	semidirect
115. #4021	C₂²	semidirect
117. C₄×D₂₀	C₂²	semidirect
118. C₄×D₂₀	C₂²	semidirect
119. C₄×D₂₀	C₂²	semidirect
120. C₄×D₂₀	C₂²	semidirect
121. #4015	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
246. #540	D₅	semidirect
342. #127	C₂×D₅	semidirect
347. #125	C₂×D₅	semidirect
363. #123	C₂×D₅	semidirect
364. #123	C₂×D₅	semidirect
394. #121	C₂×D₅	semidirect
395. #121	C₂×D₅	semidirect
396. #121	C₂×D₅	semidirect
397. #121	C₂×D₅	semidirect
417. C₄×D₄	C₂×D₅	semidirect
418. C₄×D₄	C₂×D₅	semidirect
423. #117	C₂×D₅	semidirect
666. C₅	#3542	semidirect

Maximal subgroups

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

subgroup	index
C₅×#540	2
#66052	2
#66051	2
#66029	2
#66028	2
#66001	2
#66000	2
#65992	2
#65988	2
#65953	2
#65951	2
#65942	2
#65941	2
#65940	2
#65939	2
D₅×#121	2
#65897	2
#65888	2
#65885	2
#65868	2
#65858	2
#3542	5