Subgroups — #10618719

Order 640.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	#66045	C₂	1	2	yes	maximal, complemented
3	#66038	C₂	1	2	yes	maximal, complemented
4	#66017	C₂	1	1	yes	maximal, characteristic, complemented
5	#66008	C₂	1	1	yes	maximal, characteristic, complemented
6	#66000	C₂	1	1	yes	maximal, characteristic, complemented
7	#65988	C₂	1	2	yes	maximal, complemented
8	#65987	C₂	1	1	yes	maximal, characteristic, complemented
9	#65987	C₂	1	2	yes	maximal, complemented
10	#65978	C₂	1	2	yes	maximal, complemented
11	#65964	C₂	1	2	yes	maximal, complemented
12	#65924	C₂	1	1	yes	maximal, characteristic, complemented
13	D₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
14	#65894	C₂	1	2	yes	maximal, complemented
15	D₄×D₂₀	C₂	1	2	yes	maximal, complemented
16	#65861	C₂	1	2	yes	maximal, complemented
17	#65859	C₂	1	2	yes	maximal, complemented
18	#65824	C₂	1	2	yes	maximal, complemented
19	C₂×#4028	C₂	1	2	yes	maximal, complemented
20	C₂⁴×D₅	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₂²⋊D₅	C₂²	1	2	yes	complemented
22	C₂×#713	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₄×D₅	C₂²	1	2	yes	complemented
24	C₂×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₄×D₅	C₂²	1	2	yes	complemented
26	C₂×#709	C₂²	1	2	yes	complemented
27	C₂²×D₂₀	C₂²	1	2	yes	complemented
28	C₂²×D₂₀	C₂²	1	2	yes	complemented
29	C₂²×D₂₀	C₂²	1	1	yes	characteristic, complemented
30	C₅×#126	C₂²	1	2	yes	complemented
31	C₅×#124	C₂²	1	1	yes	characteristic, complemented
32	C₅×#123	C₂²	1	1	yes	characteristic, complemented
33	C₅×#123	C₂²	1	2	yes	complemented
34	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₅×#120	C₂²	1	1	yes	characteristic
36	C₄×C₅×D₄	C₂²	1	2	yes	complemented
37	C₅×#117	C₂²	1	2	yes	complemented
38	C₂×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
39	#4099	C₂²	1	1	yes	characteristic, complemented
40	#4093	C₂²	1	2	yes	complemented
41	#4093	C₂²	1	1	yes	characteristic, complemented
42	#4086	C₂²	1	1	yes	characteristic, complemented
43	#4085	C₂²	1	2	yes	complemented
44	#4083	C₂²	1	2	yes	complemented
45	#4083	C₂²	1	1	yes	characteristic, complemented
46	#4083	C₂²	1	1	yes	characteristic, complemented
47	#4076	C₂²	1	2	yes	complemented
48	#4076	C₂²	1	2	yes	complemented
49	#4075	C₂²	1	1	yes	characteristic, complemented
50	#4075	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
52	C₂×#685	C₂²	1	2	yes	complemented
53	C₂×#685	C₂²	1	2	yes	complemented
54	#4044	C₂²	1	2	yes	complemented
55	#4044	C₂²	1	2	yes	complemented
56	#4042	C₂²	1	2	yes	complemented
57	#4041	C₂²	1	2	yes	complemented
58	#4041	C₂²	1	2	yes	complemented
59	#4041	C₂²	1	2	yes	complemented
60	#4041	C₂²	1	2	yes	complemented
61	#4041	C₂²	1	2	yes	complemented
62	#4041	C₂²	1	2	yes	complemented
63	#4041	C₂²	1	2	yes	complemented
64	#4040	C₂²	1	2	yes	complemented
65	#4040	C₂²	1	2	yes	complemented
66	#4040	C₂²	1	2	yes	complemented
67	#4040	C₂²	1	2	yes	complemented
68	#4040	C₂²	1	2	yes	complemented
69	#4039	C₂²	1	2	yes	complemented
70	#4031	C₂²	1	2	yes	complemented
71	#4031	C₂²	1	2	yes	complemented
72	#4030	C₂²	1	2	yes	complemented
73	#4030	C₂²	1	2	yes	complemented
74	#4030	C₂²	1	2	yes	complemented
75	#4030	C₂²	1	2	yes	complemented
76	#4030	C₂²	1	2	yes	complemented
77	#4029	C₂²	1	2	yes	complemented
78	#4028	C₂²	1	2	yes	—
79	#4028	C₂²	1	2	yes	complemented
80	#4028	C₂²	1	2	yes	complemented
81	#4028	C₂²	1	2	yes	complemented
82	#4028	C₂²	1	2	yes	complemented
83	#4028	C₂²	1	2	yes	complemented
84	#4028	C₂²	1	2	yes	complemented
85	#4028	C₂²	1	2	yes	complemented
86	#4028	C₂²	1	2	yes	complemented
87	#4028	C₂²	1	1	yes	characteristic, complemented
88	#4028	C₂²	1	2	yes	complemented
89	#4028	C₂²	1	2	yes	complemented
90	#4028	C₂²	1	2	yes	complemented
91	#4028	C₂²	1	2	yes	complemented
92	#4028	C₂²	1	1	yes	characteristic, complemented
93	#4027	C₂²	1	2	yes	complemented
94	#4027	C₂²	1	2	yes	complemented
95	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
96	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
97	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	D₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
99	#4024	C₂²	1	2	yes	complemented
100	#4022	C₂²	1	2	yes	complemented
101	#4021	C₂²	1	2	yes	complemented
102	#4021	C₂²	1	2	yes	complemented
103	#4020	C₂²	1	1	yes	characteristic, complemented
104	#4020	C₂²	1	2	yes	complemented
105	C₄×D₂₀	C₂²	1	2	yes	complemented
106	#4018	C₂²	1	1	yes	characteristic, complemented
107	#3532	—	5	1	no	maximal, Sylow
108	C₂⁴×C₅	C₂³	1	1	yes	characteristic
109	C₂³×D₅	—	4	2	no	—
110	C₂³×D₅	—	4	4	no	—
111	C₂³×D₅	C₂³	1	2	yes	—
112	C₂³×D₅	C₂³	1	2	yes	—
113	C₂³×D₅	C₂³	1	1	yes	characteristic
114	C₂³×D₅	C₂³	1	2	yes	—
115	C₂³×D₅	C₂³	1	1	yes	characteristic
116	C₂³×D₅	C₂³	1	1	yes	characteristic
117	C₂³×D₅	C₂³	1	1	yes	characteristic, complemented
118	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
119	C₂×C₅×D₄	C₂³	1	2	yes	—
120	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂³	1	2	yes	—
122	C₂²×C₄×C₅	C₂³	1	2	yes	—
123	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic, complemented
124	C₂×C₂²⋊D₅	—	4	4	no	—
125	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₅	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₅	C₂³	1	2	yes	complemented
134	C₂²×Dic₅	C₂³	1	2	yes	—
135	#713	—	4	2	no	—
136	D₄×D₅	—	4	2	no	—
137	D₄×D₅	—	4	4	no	—
138	D₄×D₅	—	4	4	no	—
139	#709	—	4	4	no	—
140	C₂×D₂₀	—	4	2	no	—
141	C₂×D₂₀	—	4	4	no	—
142	C₂×D₂₀	—	4	4	no	—
143	C₂×D₂₀	C₂³	1	2	yes	—
144	C₂×D₂₀	C₂³	1	2	yes	—
145	C₂×D₂₀	C₂³	1	2	yes	—
146	C₂×D₂₀	C₂³	1	2	yes	—
147	C₂×D₂₀	C₂³	1	2	yes	—
148	C₂×D₂₀	C₂³	1	2	yes	—
149	C₂×D₂₀	C₂³	1	2	yes	—
150	C₂×D₂₀	C₂³	1	2	yes	—
151	C₂×D₂₀	C₂³	1	2	yes	—
152	C₂×D₂₀	C₂³	1	1	yes	characteristic
153	C₂×D₂₀	C₂³	1	2	yes	complemented
154	C₂×D₂₀	C₂³	1	2	yes	complemented
155	C₂×D₂₀	C₂³	1	2	yes	complemented
156	C₂×D₂₀	C₂³	1	1	yes	characteristic, complemented
157	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₅	C₂³	1	2	yes	—
159	C₂×C₄×D₅	C₂³	1	2	yes	complemented
160	C₂×C₄×D₅	C₂³	1	2	yes	complemented
161	C₂×C₄×D₅	C₂³	1	2	yes	complemented
162	C₂×C₄×D₅	C₂³	1	2	yes	complemented
163	C₂×Dic₁₀	C₂³	1	2	yes	complemented
164	C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
165	C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
166	C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
167	C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
168	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₅×C₂²⋊C₄	C₂³	1	2	yes	complemented
175	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
176	C₄²×C₅	C₂³	1	1	yes	characteristic, complemented
177	C₄²×C₅	C₂³	1	2	yes	complemented
178	C₂²⋊Dic₅	C₂³	1	2	yes	—
179	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic, complemented
181	#685	C₂³	1	2	yes	—
182	#685	C₂³	1	2	yes	—
183	#685	C₂³	1	2	yes	—
184	#685	C₂³	1	2	yes	—
185	#685	C₂³	1	2	yes	—
186	#685	C₂³	1	2	yes	—
187	#685	C₂³	1	2	yes	—
188	#685	C₂³	1	2	yes	—
189	#685	C₂³	1	2	yes	—
190	#685	C₂³	1	2	yes	—
191	#685	C₂³	1	2	yes	—
192	#685	C₂³	1	2	yes	complemented
193	#685	C₂³	1	2	yes	complemented
194	#685	C₂³	1	2	yes	complemented
195	#685	C₂³	1	2	yes	complemented
196	#685	C₂³	1	2	yes	complemented
197	#685	C₂³	1	2	yes	complemented
198	#685	C₂³	1	2	yes	complemented
199	C₄⋊Dic₅	C₂³	1	2	yes	complemented
200	#683	C₂³	1	2	yes	complemented
201	#683	C₂³	1	2	yes	complemented
202	#683	C₂³	1	2	yes	complemented
203	#683	C₂³	1	2	yes	complemented
204	C₄×Dic₅	C₂³	1	1	yes	characteristic, complemented
205	C₄×Dic₅	C₂³	1	2	yes	complemented
206	H(3,𝔽₄)	—	5	1	no	—
207	#560	—	5	2	no	—
208	#560	—	5	1	no	—
209	#551	—	5	2	no	—
210	#551	D₅	1	1	yes	characteristic, complemented
211	#546	—	5	2	no	—
212	#546	—	5	2	no	—
213	#546	—	5	2	no	—
214	D₄²	—	5	1	no	—
215	D₄²	—	5	2	no	—
216	#538	—	5	2	no	—
217	#538	—	5	2	no	—
218	#538	—	5	2	no	—
219	#535	—	5	1	no	—
220	#535	—	5	2	no	—
221	#534	—	5	2	no	—
222	#534	—	5	1	no	—
223	C₂×#120	—	5	1	no	—
224	C₂×#120	—	5	2	no	—
225	C₂³×C₅	—	2	4	no	—
226	C₂³×C₅	—	4	1	no	—
227	C₂³×C₅	C₂⁴	1	1	yes	characteristic
228	C₂³×C₅	C₂⁴	1	1	yes	characteristic
229	C₂³×C₅	C₂⁴	1	2	yes	—
230	C₂²×D₅	—	2	4	no	—
231	C₂²×D₅	—	2	4	no	—
232	C₂²×D₅	—	2	4	no	—
233	C₂²×D₅	—	2	4	no	—
234	C₂²×D₅	—	2	2	no	—
235	C₂²×D₅	—	2	2	no	—
236	C₂²×D₅	—	4	2	no	—
237	C₂²×D₅	—	4	2	no	—
238	C₂²×D₅	—	4	1	no	—
239	C₂²×D₅	—	4	2	no	—
240	C₂²×D₅	—	4	2	no	—
241	C₂²×D₅	—	4	2	no	—
242	C₂²×D₅	—	4	2	no	—
243	C₂²×D₅	—	4	1	no	—
244	C₂²×D₅	—	4	2	no	—
245	C₂²×D₅	—	4	2	no	—
246	C₂²×D₅	—	4	2	no	—
247	C₂²×D₅	—	4	16	no	—
248	C₂²×D₅	C₂⁴	1	2	yes	—
249	C₂²×D₅	C₂⁴	1	1	yes	characteristic
250	C₂²×D₅	C₂⁴	1	2	yes	—
251	C₂²×D₅	C₂⁴	1	2	yes	—
252	C₂²×D₅	C₂⁴	1	1	yes	characteristic
253	C₂²×D₅	C₂⁴	1	1	yes	characteristic
254	C₅×Q₈	—	4	1	no	—
255	C₅×D₄	—	2	4	no	—
256	C₅×D₄	—	4	1	no	—
257	C₂×C₄×C₅	—	2	4	no	—
258	C₂×C₄×C₅	—	4	2	no	—
259	C₂×C₄×C₅	—	4	1	no	—
260	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂⁴	1	2	yes	—
262	C₂×C₄×C₅	C₂⁴	1	2	yes	—
263	C₂×C₄×C₅	C₂⁴	1	2	yes	—
264	C₂×C₄×C₅	C₂⁴	1	2	yes	—
265	C₂×C₄×C₅	C₂⁴	1	2	yes	—
266	C₂²⋊D₅	—	2	4	no	—
267	C₂²⋊D₅	—	2	4	no	—
268	C₂²⋊D₅	—	2	4	no	—
269	C₂²⋊D₅	—	4	2	no	—
270	C₂²⋊D₅	—	4	1	no	—
271	C₂²⋊D₅	—	4	1	no	—
272	C₂²⋊D₅	—	4	2	no	—
273	C₂²⋊D₅	—	4	2	no	—
274	C₂²⋊D₅	—	4	2	no	—
275	C₂×Dic₅	—	4	2	no	—
276	C₂×Dic₅	C₂⁴	1	2	yes	—
277	C₂×Dic₅	C₂⁴	1	2	yes	—
278	C₂×Dic₅	C₂⁴	1	2	yes	—
279	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
280	D₂₀	—	2	4	no	—
281	D₂₀	—	2	4	no	—
282	D₂₀	—	4	2	no	—
283	D₂₀	—	4	2	no	—
284	D₂₀	—	4	2	no	—
285	D₂₀	—	4	2	no	—
286	D₂₀	—	4	2	no	—
287	D₂₀	—	4	2	no	—
288	D₂₀	—	4	2	no	—
289	D₂₀	—	4	1	no	—
290	D₂₀	—	4	2	no	—
291	D₂₀	—	4	2	no	—
292	D₂₀	—	4	2	no	—
293	D₂₀	—	4	1	no	—
294	C₄×D₅	—	2	2	no	—
295	C₄×D₅	—	4	2	no	—
296	C₄×D₅	—	4	2	no	—
297	C₄×D₅	—	4	2	no	—
298	C₄×D₅	—	4	2	no	—
299	C₄×D₅	—	4	2	no	—
300	Dic₁₀	—	4	2	no	—
301	C₂⁵	—	5	1	no	—
302	C₂×#41	—	5	1	no	—
303	C₂×#41	—	5	2	no	—
304	C₂²×D₄	—	5	2	no	—
305	C₂²×D₄	—	5	1	no	—
306	C₂²×D₄	—	5	2	no	—
307	C₂²×D₄	—	5	2	no	—
308	C₂²×D₄	—	5	2	no	—
309	C₂²×D₄	—	5	2	no	—
310	C₂²×D₄	—	5	1	no	—
311	#127	—	5	1	no	—
312	#127	—	5	1	no	—
313	#127	—	5	2	no	—
314	#126	—	5	2	no	—
315	#126	—	5	2	no	—
316	#126	—	5	2	no	—
317	#126	C₂×D₅	1	2	yes	complemented
318	#124	—	5	1	no	—
319	#124	—	5	2	no	—
320	#124	—	5	2	no	—
321	#124	—	5	2	no	—
322	#124	—	5	2	no	—
323	#124	—	5	2	no	—
324	#124	C₂×D₅	1	1	yes	characteristic, complemented
325	#123	—	5	2	no	—
326	#123	—	5	1	no	—
327	#123	—	5	2	no	—
328	#123	—	5	2	no	—
329	#123	—	5	2	no	—
330	#123	—	5	2	no	—
331	#123	—	5	2	no	—
332	#123	—	5	2	no	—
333	#123	C₂×D₅	1	1	yes	characteristic, complemented
334	#123	C₂×D₅	1	2	yes	complemented
335	C₂²⋊Q₈	—	5	2	no	—
336	C₂²⋊Q₈	—	5	2	no	—
337	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
338	#121	—	5	2	no	—
339	#121	—	5	2	no	—
340	#121	—	5	2	no	—
341	#121	—	5	2	no	—
342	#121	—	5	2	no	—
343	#121	—	5	2	no	—
344	#121	—	5	2	no	—
345	#121	—	5	2	no	—
346	#121	—	5	2	no	—
347	#121	—	5	2	no	—
348	#121	—	5	2	no	—
349	#121	—	5	2	no	—
350	#121	—	5	2	no	—
351	#121	—	5	2	no	—
352	#121	—	5	2	no	—
353	#120	—	5	1	no	—
354	#120	—	5	2	no	—
355	#120	—	5	1	no	—
356	#120	—	5	1	no	—
357	#120	—	5	2	no	—
358	#120	—	5	2	no	—
359	#120	—	5	2	no	—
360	#120	—	5	2	no	—
361	#120	—	5	2	no	—
362	#120	—	5	2	no	—
363	#120	—	5	2	no	—
364	#120	—	5	2	no	—
365	#120	—	5	1	no	—
366	#120	—	5	2	no	—
367	#120	—	5	2	no	—
368	#120	—	5	2	no	—
369	#120	—	5	1	no	—
370	#120	—	5	2	no	—
371	#120	—	5	2	no	—
372	#120	C₂×D₅	1	1	yes	characteristic
373	C₄×D₄	—	5	2	no	—
374	C₄×D₄	—	5	2	no	—
375	C₄×D₄	—	5	2	no	—
376	C₄×D₄	—	5	2	no	—
377	C₄×D₄	—	5	2	no	—
378	C₄×D₄	C₂×D₅	1	2	yes	complemented
379	#117	—	5	1	no	—
380	#117	C₂×D₅	1	2	yes	complemented
381	C₂×C₂²⋊C₄	—	5	2	no	—
382	C₂×C₂²⋊C₄	—	5	2	no	—
383	C₂×C₂²⋊C₄	—	5	1	no	—
384	C₂×C₂²⋊C₄	—	5	2	no	—
385	C₂×C₂²⋊C₄	—	5	2	no	—
386	C₂×C₂²⋊C₄	—	5	1	no	—
387	C₂×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	2	2	no	—
390	C₂²×C₅	—	2	2	no	—
391	C₂²×C₅	—	2	2	no	—
392	C₂²×C₅	—	2	1	no	—
393	C₂²×C₅	—	2	1	no	—
394	C₂²×C₅	—	4	4	no	—
395	C₂²×C₅	H(5,𝔽₂)	1	4	yes	—
396	C₂²×C₅	C₂⁵	1	1	yes	characteristic
397	C₂×D₅	—	2	2	no	—
398	C₂×D₅	—	2	2	no	—
399	C₂×D₅	—	2	2	no	—
400	C₂×D₅	—	2	2	no	—
401	C₂×D₅	—	2	2	no	—
402	C₂×D₅	—	2	2	no	—
403	C₂×D₅	—	2	2	no	—
404	C₂×D₅	—	2	1	no	—
405	C₂×D₅	—	2	2	no	—
406	C₂×D₅	—	2	2	no	—
407	C₂×D₅	—	2	2	no	—
408	C₂×D₅	—	2	2	no	—
409	C₂×D₅	—	2	2	no	—
410	C₂×D₅	—	2	1	no	—
411	C₂×D₅	—	4	8	no	—
412	C₂×D₅	—	4	4	no	—
413	C₂×D₅	—	4	8	no	—
414	C₂×D₅	—	4	4	no	—
415	C₂×D₅	—	8	2	no	—
416	C₂×D₅	—	8	4	no	—
417	C₂×D₅	—	8	2	no	—
418	C₂×D₅	H(5,𝔽₂)	1	2	yes	—
419	C₄×C₅	—	2	2	no	—
420	C₄×C₅	—	2	1	no	—
421	C₄×C₅	—	2	2	no	—
422	C₄×C₅	—	2	2	no	—
423	C₄×C₅	—	2	2	no	—
424	C₄×C₅	—	2	2	no	—
425	Dic₅	—	2	2	no	—
426	Dic₅	—	2	2	no	—
427	Dic₅	—	2	1	no	—
428	Dic₅	—	2	2	no	—
429	C₂⁴	—	5	2	no	—
430	C₂⁴	—	5	1	no	—
431	C₂⁴	—	5	2	no	—
432	C₂⁴	—	5	1	no	—
433	C₂⁴	—	5	2	no	—
434	C₂⁴	—	5	1	no	—
435	C₂⁴	—	5	1	no	—
436	C₂⁴	—	20	4	no	—
437	C₂⁴	—	20	2	no	—
438	C₂⁴	C₂²×D₅	1	1	yes	characteristic
439	#41	—	20	4	no	—
440	#41	—	20	2	no	—
441	C₂×Q₈	—	5	2	no	—
442	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
443	C₂×D₄	—	5	2	no	—
444	C₂×D₄	—	5	2	no	—
445	C₂×D₄	—	5	2	no	—
446	C₂×D₄	—	5	1	no	—
447	C₂×D₄	—	5	2	no	—
448	C₂×D₄	—	5	2	no	—
449	C₂×D₄	—	5	1	no	—
450	C₂×D₄	—	5	2	no	—
451	C₂×D₄	—	5	2	no	—
452	C₂×D₄	—	5	2	no	—
453	C₂×D₄	—	5	2	no	—
454	C₂×D₄	—	5	2	no	—
455	C₂×D₄	—	5	2	no	—
456	C₂×D₄	—	5	2	no	—
457	C₂×D₄	—	5	2	no	—
458	C₂×D₄	—	5	2	no	—
459	C₂×D₄	—	5	2	no	—
460	C₂×D₄	—	5	1	no	—
461	C₂×D₄	—	5	2	no	—
462	C₂×D₄	—	5	1	no	—
463	C₂×D₄	—	5	2	no	—
464	C₂×D₄	—	5	2	no	—
465	C₂×D₄	—	5	2	no	—
466	C₂×D₄	—	20	4	no	—
467	C₂×D₄	—	20	4	no	—
468	C₂×D₄	—	20	2	no	—
469	C₂×D₄	—	20	2	no	—
470	C₂×D₄	—	20	4	no	—
471	C₂×D₄	—	20	4	no	—
472	C₂×D₄	—	20	4	no	—
473	C₂×D₄	C₂²×D₅	1	2	yes	—
474	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
475	C₂²×C₄	—	5	2	no	—
476	C₂²×C₄	—	5	1	no	—
477	C₂²×C₄	—	5	2	no	—
478	C₂²×C₄	—	5	2	no	—
479	C₂²×C₄	—	5	2	no	—
480	C₂²×C₄	—	5	2	no	—
481	C₂²×C₄	—	5	2	no	—
482	C₂²×C₄	C₂²×D₅	1	2	yes	—
483	C₂²×C₄	C₂²×D₅	1	2	yes	—
484	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic, complemented
485	C₄⋊C₄	—	5	2	no	—
486	C₄⋊C₄	—	5	2	no	—
487	C₄⋊C₄	—	5	2	no	—
488	C₄⋊C₄	—	5	2	no	—
489	C₄⋊C₄	—	5	2	no	—
490	C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
491	C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
492	C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
493	C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
494	C₂²⋊C₄	—	5	2	no	—
495	C₂²⋊C₄	—	5	1	no	—
496	C₂²⋊C₄	—	5	1	no	—
497	C₂²⋊C₄	—	5	2	no	—
498	C₂²⋊C₄	—	5	2	no	—
499	C₂²⋊C₄	—	5	2	no	—
500	C₂²⋊C₄	—	5	2	no	—
501	C₂²⋊C₄	—	5	2	no	—
502	C₂²⋊C₄	—	5	2	no	—
503	C₂²⋊C₄	—	5	2	no	—
504	C₂²⋊C₄	—	5	2	no	—
505	C₂²⋊C₄	—	5	2	no	—
506	C₂²⋊C₄	—	5	2	no	—
507	C₂²⋊C₄	—	5	2	no	—
508	C₂²⋊C₄	—	5	2	no	—
509	C₂²⋊C₄	—	5	2	no	—
510	C₂²⋊C₄	—	5	2	no	—
511	C₂²⋊C₄	—	5	2	no	—
512	C₂²⋊C₄	—	5	2	no	—
513	C₂²⋊C₄	—	5	2	no	—
514	C₂²⋊C₄	—	5	2	no	—
515	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
518	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
519	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
520	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic, complemented
522	C₂²⋊C₄	C₂²×D₅	1	2	yes	complemented
523	C₄²	—	5	1	no	—
524	C₄²	—	5	2	no	—
525	C₄²	C₂²×D₅	1	1	yes	characteristic, complemented
526	C₄²	C₂²×D₅	1	2	yes	complemented
527	C₂×C₅	—	2	4	no	—
528	C₂×C₅	—	4	1	no	—
529	C₂×C₅	—	4	1	no	—
530	C₂×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
531	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	D₅	—	2	2	no	—
533	D₅	—	4	2	no	—
534	D₅	—	4	1	no	—
535	D₅	—	4	2	no	—
536	D₅	—	4	1	no	—
537	D₅	—	4	2	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	5	1	no	—
541	C₂³	—	5	2	no	—
542	C₂³	—	5	1	no	—
543	C₂³	—	5	2	no	—
544	C₂³	—	5	1	no	—
545	C₂³	—	5	2	no	—
546	C₂³	—	10	4	no	—
547	C₂³	—	10	2	no	—
548	C₂³	—	10	2	no	—
549	C₂³	—	10	4	no	—
550	C₂³	—	10	4	no	—
551	C₂³	—	10	4	no	—
552	C₂³	—	20	2	no	—
553	C₂³	—	20	2	no	—
554	C₂³	—	20	2	no	—
555	C₂³	—	20	2	no	—
556	C₂³	—	20	2	no	—
557	C₂³	—	20	1	no	—
558	C₂³	—	20	2	no	—
559	C₂³	—	20	2	no	—
560	C₂³	—	20	2	no	—
561	C₂³	—	20	2	no	—
562	C₂³	—	20	1	no	—
563	C₂³	—	20	16	no	—
564	C₂³	C₂³×D₅	1	1	yes	characteristic
565	C₂³	C₂³×D₅	1	1	yes	characteristic
566	C₂³	C₂³×D₅	1	2	yes	—
567	Q₈	—	4	1	no	—
568	Q₈	—	20	2	no	—
569	D₄	—	2	4	no	—
570	D₄	—	4	1	no	—
571	D₄	—	10	4	no	—
572	D₄	—	10	4	no	—
573	D₄	—	10	4	no	—
574	D₄	—	10	4	no	—
575	D₄	—	10	4	no	—
576	D₄	—	20	2	no	—
577	D₄	—	20	2	no	—
578	D₄	—	20	2	no	—
579	D₄	—	20	2	no	—
580	D₄	—	20	2	no	—
581	D₄	—	20	2	no	—
582	D₄	—	20	2	no	—
583	D₄	—	20	2	no	—
584	D₄	—	20	2	no	—
585	D₄	—	20	1	no	—
586	D₄	—	20	2	no	—
587	D₄	—	20	1	no	—
588	D₄	—	20	2	no	—
589	D₄	—	20	2	no	—
590	D₄	—	20	2	no	—
591	D₄	—	20	2	no	—
592	D₄	—	20	1	no	—
593	D₄	—	20	1	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	5	2	no	—
598	C₂×C₄	—	5	2	no	—
599	C₂×C₄	—	5	2	no	—
600	C₂×C₄	—	5	1	no	—
601	C₂×C₄	—	10	2	no	—
602	C₂×C₄	—	20	2	no	—
603	C₂×C₄	—	20	2	no	—
604	C₂×C₄	—	20	2	no	—
605	C₂×C₄	—	20	2	no	—
606	C₂×C₄	—	20	2	no	—
607	C₂×C₄	—	20	2	no	—
608	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₅	1	2	yes	—
610	C₂×C₄	C₂³×D₅	1	2	yes	—
611	C₂×C₄	C₂³×D₅	1	2	yes	—
612	C₂×C₄	C₂³×D₅	1	2	yes	—
613	C₂×C₄	C₂³×D₅	1	2	yes	—
614	C₅	#3532	1	1	yes	characteristic, complemented, Sylow
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	5	2	no	—
623	C₂²	—	10	2	no	—
624	C₂²	—	10	2	no	—
625	C₂²	—	10	2	no	—
626	C₂²	—	10	2	no	—
627	C₂²	—	10	2	no	—
628	C₂²	—	10	2	no	—
629	C₂²	—	10	2	no	—
630	C₂²	—	10	2	no	—
631	C₂²	—	10	2	no	—
632	C₂²	—	10	2	no	—
633	C₂²	—	10	2	no	—
634	C₂²	—	10	1	no	—
635	C₂²	—	10	2	no	—
636	C₂²	—	10	1	no	—
637	C₂²	—	20	8	no	—
638	C₂²	—	20	8	no	—
639	C₂²	—	20	4	no	—
640	C₂²	—	20	4	no	—
641	C₂²	—	40	4	no	—
642	C₂²	—	40	2	no	—
643	C₂²	—	40	2	no	—
644	C₂²	#4149	1	4	yes	—
645	C₂²	C₂⁴×D₅	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	10	2	no	—
653	C₄	—	10	2	no	—
654	C₄	—	10	2	no	—
655	C₄	—	10	1	no	—
656	C₂	—	2	4	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	1	no	—
659	C₂	—	10	2	no	—
660	C₂	—	20	2	no	—
661	C₂	—	20	1	no	—
662	C₂	—	20	2	no	—
663	C₂	—	20	1	no	—
664	C₂	—	20	2	no	—
665	C₂	C₂×#4149	1	2	yes	—
666	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×#551	C₂
hypercenter	#551	D₅
hypocenter	C₅	#3532
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. C₅×#551	C₂	semidirect
2. #66045	C₂	semidirect
3. #66038	C₂	semidirect
4. #66017	C₂	semidirect
5. #66008	C₂	semidirect
6. #66000	C₂	semidirect
7. #65988	C₂	semidirect
8. #65987	C₂	semidirect
9. #65987	C₂	semidirect
10. #65978	C₂	semidirect
11. #65964	C₂	semidirect
12. #65924	C₂	semidirect
13. D₅×#120	C₂	semidirect
14. #65894	C₂	semidirect
15. D₄×D₂₀	C₂	semidirect
16. #65861	C₂	semidirect
17. #65859	C₂	semidirect
18. #65824	C₂	semidirect
19. C₂×#4028	C₂	semidirect
20. C₂⁴×D₅	C₂²	semidirect
21. C₂²×C₂²⋊D₅	C₂²	semidirect
22. C₂×#713	C₂²	semidirect
23. C₂×D₄×D₅	C₂²	semidirect
24. C₂×D₄×D₅	C₂²	semidirect
25. C₂×D₄×D₅	C₂²	semidirect
26. C₂×#709	C₂²	semidirect
27. C₂²×D₂₀	C₂²	semidirect
28. C₂²×D₂₀	C₂²	semidirect
29. C₂²×D₂₀	C₂²	semidirect
30. C₅×#126	C₂²	semidirect
31. C₅×#124	C₂²	semidirect
32. C₅×#123	C₂²	semidirect
33. C₅×#123	C₂²	semidirect
34. C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₄×C₅×D₄	C₂²	semidirect
37. C₅×#117	C₂²	semidirect
38. C₂×C₅×C₂²⋊C₄	C₂²	semidirect
39. #4099	C₂²	semidirect
40. #4093	C₂²	semidirect
41. #4093	C₂²	semidirect
42. #4086	C₂²	semidirect
43. #4085	C₂²	semidirect
44. #4083	C₂²	semidirect
45. #4083	C₂²	semidirect
46. #4083	C₂²	semidirect
47. #4076	C₂²	semidirect
48. #4076	C₂²	semidirect
49. #4075	C₂²	semidirect
50. #4075	C₂²	semidirect
51. C₄×C₂²⋊D₅	C₂²	semidirect
52. C₂×#685	C₂²	semidirect
53. C₂×#685	C₂²	semidirect
54. #4044	C₂²	semidirect
55. #4044	C₂²	semidirect
56. #4042	C₂²	semidirect
57. #4041	C₂²	semidirect
58. #4041	C₂²	semidirect
59. #4041	C₂²	semidirect
60. #4041	C₂²	semidirect
61. #4041	C₂²	semidirect
62. #4041	C₂²	semidirect
63. #4041	C₂²	semidirect
64. #4040	C₂²	semidirect
65. #4040	C₂²	semidirect
66. #4040	C₂²	semidirect
67. #4040	C₂²	semidirect
68. #4040	C₂²	semidirect
69. #4039	C₂²	semidirect
70. #4031	C₂²	semidirect
71. #4031	C₂²	semidirect
72. #4030	C₂²	semidirect
73. #4030	C₂²	semidirect
74. #4030	C₂²	semidirect
75. #4030	C₂²	semidirect
76. #4030	C₂²	semidirect
77. #4029	C₂²	semidirect
79. #4028	C₂²	semidirect
80. #4028	C₂²	semidirect
81. #4028	C₂²	semidirect
82. #4028	C₂²	semidirect
83. #4028	C₂²	semidirect
84. #4028	C₂²	semidirect
85. #4028	C₂²	semidirect
86. #4028	C₂²	semidirect
87. #4028	C₂²	semidirect
88. #4028	C₂²	semidirect
89. #4028	C₂²	semidirect
90. #4028	C₂²	semidirect
91. #4028	C₂²	semidirect
92. #4028	C₂²	semidirect
93. #4027	C₂²	semidirect
94. #4027	C₂²	semidirect
95. D₅×C₂²⋊C₄	C₂²	semidirect
96. D₅×C₂²⋊C₄	C₂²	semidirect
97. D₅×C₂²⋊C₄	C₂²	semidirect
98. D₅×C₂²⋊C₄	C₂²	semidirect
99. #4024	C₂²	semidirect
100. #4022	C₂²	semidirect
101. #4021	C₂²	semidirect
102. #4021	C₂²	semidirect
103. #4020	C₂²	semidirect
104. #4020	C₂²	semidirect
105. C₄×D₂₀	C₂²	semidirect
106. #4018	C₂²	semidirect
117. C₂³×D₅	C₂³	semidirect
118. C₂×C₅×Q₈	C₂³	semidirect
123. C₂²×C₄×C₅	C₂³	semidirect
133. C₂×C₂²⋊D₅	C₂³	semidirect
153. C₂×D₂₀	C₂³	semidirect
154. C₂×D₂₀	C₂³	semidirect
155. C₂×D₂₀	C₂³	semidirect
156. C₂×D₂₀	C₂³	semidirect
159. C₂×C₄×D₅	C₂³	semidirect
160. C₂×C₄×D₅	C₂³	semidirect
161. C₂×C₄×D₅	C₂³	semidirect
162. C₂×C₄×D₅	C₂³	semidirect
163. C₂×Dic₁₀	C₂³	semidirect
164. C₅×C₄⋊C₄	C₂³	semidirect
165. C₅×C₄⋊C₄	C₂³	semidirect
166. C₅×C₄⋊C₄	C₂³	semidirect
167. C₅×C₄⋊C₄	C₂³	semidirect
174. C₅×C₂²⋊C₄	C₂³	semidirect
175. C₅×C₂²⋊C₄	C₂³	semidirect
176. C₄²×C₅	C₂³	semidirect
177. C₄²×C₅	C₂³	semidirect
180. C₂²⋊Dic₅	C₂³	semidirect
192. #685	C₂³	semidirect
193. #685	C₂³	semidirect
194. #685	C₂³	semidirect
195. #685	C₂³	semidirect
196. #685	C₂³	semidirect
197. #685	C₂³	semidirect
198. #685	C₂³	semidirect
199. C₄⋊Dic₅	C₂³	semidirect
200. #683	C₂³	semidirect
201. #683	C₂³	semidirect
202. #683	C₂³	semidirect
203. #683	C₂³	semidirect
204. C₄×Dic₅	C₂³	semidirect
205. C₄×Dic₅	C₂³	semidirect
210. #551	D₅	semidirect
317. #126	C₂×D₅	semidirect
324. #124	C₂×D₅	semidirect
333. #123	C₂×D₅	semidirect
334. #123	C₂×D₅	semidirect
337. C₂²⋊Q₈	C₂×D₅	semidirect
378. C₄×D₄	C₂×D₅	semidirect
380. #117	C₂×D₅	semidirect
387. C₂×C₂²⋊C₄	C₂×D₅	semidirect
442. C₂×Q₈	C₂²×D₅	semidirect
484. C₂²×C₄	C₂²×D₅	semidirect
490. C₄⋊C₄	C₂²×D₅	semidirect
491. C₄⋊C₄	C₂²×D₅	semidirect
492. C₄⋊C₄	C₂²×D₅	semidirect
493. C₄⋊C₄	C₂²×D₅	semidirect
521. C₂²⋊C₄	C₂²×D₅	semidirect
522. C₂²⋊C₄	C₂²×D₅	semidirect
525. C₄²	C₂²×D₅	semidirect
526. C₄²	C₂²×D₅	semidirect
614. C₅	#3532	semidirect

Maximal subgroups

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

subgroup	index
C₅×#551	2
#66045	2
#66038	2
#66017	2
#66008	2
#66000	2
#65988	2
#65987	2
#65978	2
#65964	2
#65924	2
D₅×#120	2
#65894	2
D₄×D₂₀	2
#65861	2
#65859	2
#65824	2
C₂×#4028	2
#3532	5