Subgroups — #10618417

Order 640.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	#66061	C₂	1	1	yes	maximal, characteristic, complemented
3	#66060	C₂	1	1	yes	maximal, characteristic, complemented
4	#66044	C₂	1	2	yes	maximal, complemented
5	#66041	C₂	1	2	yes	maximal, complemented
6	#66038	C₂	1	2	yes	maximal, complemented
7	#66038	C₂	1	2	yes	maximal, complemented
8	#66034	C₂	1	2	yes	maximal, complemented
9	#66033	C₂	1	2	yes	maximal, complemented
10	#66029	C₂	1	1	yes	maximal, characteristic, complemented
11	#66029	C₂	1	2	yes	maximal, complemented
12	#66028	C₂	1	1	yes	maximal, characteristic, complemented
13	#66024	C₂	1	2	yes	maximal, complemented
14	#65963	C₂	1	1	yes	maximal, characteristic, complemented
15	#65962	C₂	1	1	yes	maximal, characteristic, complemented
16	#65961	C₂	1	1	yes	maximal, characteristic, complemented
17	D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	#65918	C₂	1	1	yes	maximal, characteristic, complemented
19	#65913	C₂	1	1	yes	maximal, characteristic, complemented
20	#65910	C₂	1	1	yes	maximal, characteristic, complemented
21	#65910	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×#713	C₂²	1	1	yes	characteristic
25	C₂×#713	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
28	C₂×#709	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₅	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₅×#126	C₂²	1	2	yes	—
32	C₅×#126	C₂²	1	2	yes	—
33	C₅×#125	C₂²	1	2	yes	complemented
34	C₅×#125	C₂²	1	1	yes	characteristic, complemented
35	C₅×#125	C₂²	1	2	yes	complemented
36	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₅×#117	C₂²	1	1	yes	characteristic
41	#4092	C₂²	1	1	yes	characteristic
42	#4092	C₂²	1	1	yes	characteristic
43	#4092	C₂²	1	1	yes	characteristic, complemented
44	#4092	C₂²	1	1	yes	characteristic, complemented
45	#4076	C₂²	1	1	yes	characteristic
46	#4070	C₂²	1	1	yes	characteristic
47	#4044	C₂²	1	2	yes	—
48	#4044	C₂²	1	2	yes	—
49	#4044	C₂²	1	2	yes	complemented
50	#4044	C₂²	1	2	yes	complemented
51	#4044	C₂²	1	2	yes	complemented
52	#4043	C₂²	1	1	yes	characteristic
53	#4043	C₂²	1	1	yes	characteristic
54	#4043	C₂²	1	1	yes	characteristic
55	#4043	C₂²	1	1	yes	characteristic, complemented
56	#4043	C₂²	1	2	yes	complemented
57	#4043	C₂²	1	2	yes	complemented
58	#4042	C₂²	1	2	yes	—
59	#4042	C₂²	1	2	yes	—
60	#4042	C₂²	1	2	yes	—
61	#4042	C₂²	1	2	yes	complemented
62	#4042	C₂²	1	2	yes	complemented
63	#4042	C₂²	1	2	yes	complemented
64	#4042	C₂²	1	2	yes	complemented
65	#4041	C₂²	1	2	yes	—
66	#4041	C₂²	1	1	yes	characteristic
67	#4041	C₂²	1	1	yes	characteristic
68	#4041	C₂²	1	1	yes	characteristic
69	#4041	C₂²	1	2	yes	—
70	#4041	C₂²	1	2	yes	—
71	#4041	C₂²	1	2	yes	—
72	#4041	C₂²	1	1	yes	characteristic, complemented
73	#4041	C₂²	1	2	yes	complemented
74	#4040	C₂²	1	2	yes	—
75	#4040	C₂²	1	2	yes	—
76	#4040	C₂²	1	2	yes	—
77	#4040	C₂²	1	2	yes	complemented
78	#4040	C₂²	1	2	yes	complemented
79	#4040	C₂²	1	2	yes	complemented
80	#4039	C₂²	1	2	yes	—
81	#4039	C₂²	1	2	yes	—
82	#4039	C₂²	1	2	yes	—
83	#4038	C₂²	1	1	yes	characteristic
84	#4038	C₂²	1	1	yes	characteristic, complemented
85	#4038	C₂²	1	2	yes	complemented
86	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
87	D₅×C₄⋊C₄	C₂²	1	2	yes	—
88	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
89	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
90	#4036	C₂²	1	2	yes	complemented
91	#4034	C₂²	1	2	yes	complemented
92	#4034	C₂²	1	2	yes	complemented
93	#4032	C₂²	1	1	yes	characteristic
94	#4032	C₂²	1	1	yes	characteristic
95	#4031	C₂²	1	2	yes	—
96	#4031	C₂²	1	2	yes	—
97	#4030	C₂²	1	2	yes	—
98	#4030	C₂²	1	2	yes	—
99	#4029	C₂²	1	2	yes	—
100	#4029	C₂²	1	2	yes	—
101	#4028	C₂²	1	1	yes	characteristic
102	#4028	C₂²	1	1	yes	characteristic
103	#4028	C₂²	1	2	yes	—
104	#4027	C₂²	1	2	yes	—
105	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
106	#4024	C₂²	1	2	yes	—
107	#4021	C₂²	1	2	yes	—
108	#4021	C₂²	1	2	yes	—
109	#4021	C₂²	1	1	yes	characteristic, complemented
110	#4021	C₂²	1	2	yes	complemented
111	C₄×D₂₀	C₂²	1	1	yes	characteristic
112	C₄×D₂₀	C₂²	1	1	yes	characteristic
113	C₄×D₂₀	C₂²	1	1	yes	characteristic
114	C₄×D₂₀	C₂²	1	1	yes	characteristic
115	C₄×D₂₀	C₂²	1	2	yes	—
116	C₄×D₂₀	C₂²	1	2	yes	—
117	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₂₀	C₂²	1	2	yes	complemented
119	#4016	C₂²	1	2	yes	complemented
120	#4015	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₀	C₂²	1	2	yes	complemented
123	#3541	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	1	yes	characteristic
125	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₂²×Dic₅	C₂³	1	1	yes	characteristic
132	#713	—	4	2	no	—
133	#713	—	4	2	no	—
134	Q₈×D₅	—	4	2	no	—
135	Q₈×D₅	—	4	2	no	—
136	#709	—	4	2	no	—
137	C₂×D₂₀	C₂³	1	1	yes	characteristic
138	C₂×D₂₀	C₂³	1	1	yes	characteristic
139	C₂×D₂₀	C₂³	1	1	yes	characteristic
140	C₂×D₂₀	C₂³	1	2	yes	—
141	C₂×D₂₀	C₂³	1	1	yes	characteristic
142	C₂×D₂₀	C₂³	1	2	yes	—
143	C₂×D₂₀	C₂³	1	2	yes	—
144	C₂×D₂₀	C₂³	1	1	yes	characteristic
145	C₂×D₂₀	C₂³	1	1	yes	characteristic
146	C₂×D₂₀	C₂³	1	2	yes	—
147	C₂×C₄×D₅	—	4	2	no	—
148	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂³	1	2	yes	—
155	C₂×C₄×D₅	C₂³	1	2	yes	—
156	C₂×C₄×D₅	C₂³	1	2	yes	—
157	C₂×C₄×D₅	C₂³	1	2	yes	—
158	C₂×C₄×D₅	C₂³	1	2	yes	—
159	C₂×C₄×D₅	C₂³	1	2	yes	—
160	C₂×C₄×D₅	C₂³	1	2	yes	—
161	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
162	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
163	C₂×Dic₁₀	C₂³	1	2	yes	—
164	C₂×Dic₁₀	C₂³	1	2	yes	—
165	C₂×Dic₁₀	C₂³	1	2	yes	—
166	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₄⋊C₄	C₂³	1	2	yes	—
171	C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₅×C₄⋊C₄	C₂³	1	2	yes	—
174	C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₅×C₄⋊C₄	C₂³	1	2	yes	—
176	C₅×C₄⋊C₄	C₂³	1	2	yes	—
177	C₅×C₄⋊C₄	C₂³	1	2	yes	—
178	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
180	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₄²×C₅	C₂³	1	1	yes	characteristic
183	C₄²×C₅	C₂³	1	1	yes	characteristic
184	C₄²×C₅	C₂³	1	2	yes	—
185	C₄²×C₅	C₂³	1	2	yes	—
186	C₂²⋊Dic₅	C₂³	1	2	yes	—
187	#685	C₂³	1	1	yes	characteristic
188	#685	C₂³	1	1	yes	characteristic
189	#685	C₂³	1	1	yes	characteristic
190	#685	C₂³	1	2	yes	—
191	#685	C₂³	1	1	yes	characteristic
192	#685	C₂³	1	1	yes	characteristic
193	#685	C₂³	1	2	yes	—
194	#685	C₂³	1	1	yes	characteristic
195	#685	C₂³	1	2	yes	—
196	#685	C₂³	1	1	yes	characteristic
197	#685	C₂³	1	1	yes	characteristic
198	#685	C₂³	1	2	yes	—
199	#685	C₂³	1	2	yes	—
200	#685	C₂³	1	2	yes	—
201	#685	C₂³	1	2	yes	—
202	#685	C₂³	1	2	yes	—
203	#685	C₂³	1	2	yes	—
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	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₅	C₂³	1	2	yes	—
212	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₅	C₂³	1	2	yes	—
215	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₅	C₂³	1	2	yes	—
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	2	yes	—
220	#683	C₂³	1	2	yes	—
221	#683	C₂³	1	2	yes	—
222	#683	C₂³	1	2	yes	—
223	#683	C₂³	1	2	yes	—
224	#683	C₂³	1	2	yes	—
225	#683	C₂³	1	2	yes	—
226	C₄×Dic₅	C₂³	1	2	yes	—
227	C₄×Dic₅	C₂³	1	2	yes	—
228	C₄×Dic₅	C₂³	1	2	yes	—
229	#563	—	5	2	no	—
230	#562	—	5	2	no	—
231	#556	—	5	1	no	—
232	#554	—	5	2	no	—
233	#554	—	5	1	no	—
234	#553	—	5	1	no	—
235	#553	—	5	2	no	—
236	#552	—	5	1	no	—
237	D₄×Q₈	—	5	1	no	—
238	#548	—	5	1	no	—
239	#548	—	5	1	no	—
240	#547	—	5	1	no	—
241	#542	—	5	2	no	—
242	#542	—	5	1	no	—
243	#541	D₅	1	1	yes	characteristic, complemented
244	#539	—	5	2	no	—
245	#538	—	5	2	no	—
246	#538	—	5	2	no	—
247	#537	—	5	1	no	—
248	#536	—	5	1	no	—
249	#525	—	5	1	no	—
250	#525	—	5	1	no	—
251	C₂×C₂²⋊Q₈	—	5	1	no	—
252	C₂³×C₅	C₂⁴	1	1	yes	characteristic
253	C₂²×D₅	—	2	2	no	—
254	C₂²×D₅	—	4	1	no	—
255	C₂²×D₅	—	4	1	no	—
256	C₂²×D₅	C₂⁴	1	1	yes	characteristic
257	C₂²×D₅	C₂⁴	1	1	yes	characteristic
258	C₂²×D₅	C₂⁴	1	1	yes	characteristic
259	C₂²×D₅	C₂⁴	1	2	yes	—
260	C₂²×D₅	C₂⁴	1	1	yes	characteristic
261	C₅×Q₈	—	2	2	no	—
262	C₅×Q₈	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	C₂⁴	1	2	yes	—
265	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂⁴	1	2	yes	—
268	C₂×C₄×C₅	C₂⁴	1	2	yes	—
269	C₂×C₄×C₅	C₂⁴	1	2	yes	—
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂²⋊D₅	—	4	1	no	—
275	C₂²⋊D₅	—	4	1	no	—
276	C₂²⋊D₅	—	4	2	no	—
277	C₂×Dic₅	—	4	1	no	—
278	C₂×Dic₅	C₂⁴	1	2	yes	—
279	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₅	C₂⁴	1	2	yes	—
282	C₂×Dic₅	C₂⁴	1	2	yes	—
283	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
285	D₂₀	—	2	2	no	—
286	D₂₀	—	2	2	no	—
287	D₂₀	—	2	4	no	—
288	D₂₀	—	2	2	no	—
289	D₂₀	—	4	1	no	—
290	D₂₀	—	4	1	no	—
291	D₂₀	—	4	2	no	—
292	D₂₀	—	4	1	no	—
293	D₂₀	—	4	2	no	—
294	D₂₀	—	4	2	no	—
295	C₄×D₅	—	2	2	no	—
296	C₄×D₅	—	2	2	no	—
297	C₄×D₅	—	2	2	no	—
298	C₄×D₅	—	2	2	no	—
299	C₄×D₅	—	4	1	no	—
300	C₄×D₅	—	4	1	no	—
301	C₄×D₅	—	4	2	no	—
302	C₄×D₅	—	4	2	no	—
303	C₄×D₅	—	4	2	no	—
304	C₄×D₅	—	4	2	no	—
305	C₄×D₅	—	4	2	no	—
306	C₄×D₅	—	4	2	no	—
307	C₄×D₅	—	4	2	no	—
308	Dic₁₀	—	2	2	no	—
309	Dic₁₀	—	4	2	no	—
310	Dic₁₀	—	4	1	no	—
311	Dic₁₀	—	4	2	no	—
312	Dic₁₀	—	4	2	no	—
313	C₂×#41	—	5	1	no	—
314	C₂×#41	—	5	1	no	—
315	C₂×#41	—	5	1	no	—
316	C₂²×Q₈	—	5	1	no	—
317	C₂²×Q₈	—	5	1	no	—
318	C₂³×C₄	—	5	1	no	—
319	C₄⋊Q₈	—	5	2	no	—
320	C₄⋊Q₈	—	5	2	no	—
321	C₄⋊Q₈	—	5	1	no	—
322	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
323	#126	—	5	2	no	—
324	#126	—	5	2	no	—
325	#126	—	5	2	no	—
326	#126	—	5	2	no	—
327	#126	—	5	2	no	—
328	#126	C₂×D₅	1	2	yes	—
329	#126	C₂×D₅	1	2	yes	—
330	#125	—	5	2	no	—
331	#125	—	5	2	no	—
332	#125	C₂×D₅	1	1	yes	characteristic, complemented
333	#125	C₂×D₅	1	2	yes	complemented
334	#125	C₂×D₅	1	2	yes	complemented
335	#124	—	5	2	no	—
336	#124	—	5	2	no	—
337	#124	—	5	2	no	—
338	#124	—	5	2	no	—
339	#124	—	5	1	no	—
340	#124	—	5	2	no	—
341	#123	—	5	2	no	—
342	#123	—	5	2	no	—
343	#123	—	5	2	no	—
344	#123	—	5	2	no	—
345	#123	—	5	2	no	—
346	#123	—	5	2	no	—
347	#123	—	5	1	no	—
348	#123	—	5	1	no	—
349	#123	—	5	2	no	—
350	#123	—	5	2	no	—
351	C₂²⋊Q₈	—	5	1	no	—
352	C₂²⋊Q₈	—	5	1	no	—
353	C₂²⋊Q₈	—	5	1	no	—
354	C₂²⋊Q₈	—	5	1	no	—
355	C₂²⋊Q₈	—	5	1	no	—
356	C₂²⋊Q₈	—	5	1	no	—
357	C₂²⋊Q₈	—	5	2	no	—
358	C₂²⋊Q₈	—	5	1	no	—
359	C₂²⋊Q₈	—	5	1	no	—
360	C₂²⋊Q₈	—	5	1	no	—
361	C₂²⋊Q₈	—	5	2	no	—
362	C₂²⋊Q₈	—	5	2	no	—
363	C₂²⋊Q₈	—	5	2	no	—
364	C₂²⋊Q₈	—	5	2	no	—
365	C₂²⋊Q₈	—	5	2	no	—
366	C₂²⋊Q₈	—	5	2	no	—
367	C₂²⋊Q₈	—	5	2	no	—
368	C₂²⋊Q₈	—	5	2	no	—
369	C₂²⋊Q₈	—	5	2	no	—
370	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
371	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
372	#121	—	5	1	no	—
373	#121	—	5	1	no	—
374	#121	—	5	1	no	—
375	#121	—	5	1	no	—
376	#121	—	5	1	no	—
377	#121	—	5	2	no	—
378	#121	—	5	2	no	—
379	#121	—	5	2	no	—
380	#121	—	5	2	no	—
381	#121	—	5	2	no	—
382	#121	—	5	2	no	—
383	#121	—	5	2	no	—
384	#120	—	5	2	no	—
385	#120	—	5	1	no	—
386	#120	—	5	1	no	—
387	C₄×Q₈	—	5	1	no	—
388	C₄×Q₈	—	5	2	no	—
389	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
390	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
391	C₄×D₄	—	5	2	no	—
392	C₄×D₄	—	5	2	no	—
393	C₄×D₄	—	5	2	no	—
394	C₄×D₄	—	5	2	no	—
395	C₄×D₄	—	5	1	no	—
396	C₄×D₄	—	5	1	no	—
397	C₄×D₄	—	5	1	no	—
398	C₄×D₄	—	5	1	no	—
399	C₄×D₄	—	5	2	no	—
400	C₄×D₄	—	5	2	no	—
401	C₄×D₄	—	5	2	no	—
402	C₄×D₄	—	5	1	no	—
403	#117	—	5	1	no	—
404	#117	—	5	1	no	—
405	#117	—	5	2	no	—
406	#117	C₂×D₅	1	1	yes	characteristic
407	C₂×C₄⋊C₄	—	5	2	no	—
408	C₂×C₄⋊C₄	—	5	1	no	—
409	C₂×C₄⋊C₄	—	5	1	no	—
410	C₂×C₄⋊C₄	—	5	2	no	—
411	C₂×C₂²⋊C₄	—	5	2	no	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	C₂⁵	1	1	yes	characteristic
416	C₂×D₅	—	2	1	no	—
417	C₂×D₅	—	2	1	no	—
418	C₂×D₅	—	2	1	no	—
419	C₂×D₅	—	2	1	no	—
420	C₂×D₅	—	2	1	no	—
421	C₂×D₅	—	2	2	no	—
422	C₂×D₅	—	2	1	no	—
423	C₂×D₅	—	2	1	no	—
424	C₂×D₅	—	2	2	no	—
425	C₂×D₅	—	2	1	no	—
426	C₂×D₅	—	2	1	no	—
427	C₂×D₅	—	2	2	no	—
428	C₂×D₅	—	2	1	no	—
429	C₂×D₅	—	2	1	no	—
430	C₂×D₅	—	4	4	no	—
431	C₂×D₅	2₋¹⁺⁴	1	2	yes	—
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	2	2	no	—
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	2	1	no	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	2	1	no	—
439	C₄×C₅	—	2	2	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	H(5,𝔽₂)	1	2	yes	—
442	Dic₅	—	2	2	no	—
443	Dic₅	—	2	1	no	—
444	Dic₅	—	2	1	no	—
445	Dic₅	—	2	1	no	—
446	Dic₅	—	2	1	no	—
447	Dic₅	—	2	2	no	—
448	Dic₅	—	2	2	no	—
449	C₂⁴	—	5	1	no	—
450	#41	—	20	2	no	—
451	#41	—	20	2	no	—
452	#41	—	20	2	no	—
453	C₂×Q₈	—	5	1	no	—
454	C₂×Q₈	—	5	2	no	—
455	C₂×Q₈	—	5	2	no	—
456	C₂×Q₈	—	5	1	no	—
457	C₂×Q₈	—	5	2	no	—
458	C₂×Q₈	—	20	2	no	—
459	C₂×Q₈	—	20	2	no	—
460	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
461	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
462	C₂×D₄	—	5	2	no	—
463	C₂×D₄	—	5	1	no	—
464	C₂×D₄	—	5	1	no	—
465	C₂×D₄	—	5	2	no	—
466	C₂×D₄	—	5	1	no	—
467	C₂×D₄	—	5	1	no	—
468	C₂×D₄	—	5	1	no	—
469	C₂×D₄	—	5	1	no	—
470	C₂×D₄	—	5	1	no	—
471	C₂×D₄	—	5	2	no	—
472	C₂×D₄	—	5	2	no	—
473	C₂×D₄	—	5	1	no	—
474	C₂×D₄	—	5	2	no	—
475	C₂²×C₄	—	5	1	no	—
476	C₂²×C₄	—	5	1	no	—
477	C₂²×C₄	—	5	1	no	—
478	C₂²×C₄	—	5	1	no	—
479	C₂²×C₄	—	5	1	no	—
480	C₂²×C₄	—	5	2	no	—
481	C₂²×C₄	—	5	2	no	—
482	C₂²×C₄	—	5	1	no	—
483	C₂²×C₄	—	5	2	no	—
484	C₂²×C₄	—	5	2	no	—
485	C₂²×C₄	—	5	2	no	—
486	C₂²×C₄	—	5	2	no	—
487	C₂²×C₄	—	5	2	no	—
488	C₂²×C₄	—	5	1	no	—
489	C₂²×C₄	—	20	2	no	—
490	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
491	C₄⋊C₄	—	5	1	no	—
492	C₄⋊C₄	—	5	2	no	—
493	C₄⋊C₄	—	5	2	no	—
494	C₄⋊C₄	—	5	1	no	—
495	C₄⋊C₄	—	5	1	no	—
496	C₄⋊C₄	—	5	2	no	—
497	C₄⋊C₄	—	5	2	no	—
498	C₄⋊C₄	—	5	2	no	—
499	C₄⋊C₄	—	5	2	no	—
500	C₄⋊C₄	—	5	1	no	—
501	C₄⋊C₄	—	5	1	no	—
502	C₄⋊C₄	—	5	2	no	—
503	C₄⋊C₄	—	5	2	no	—
504	C₄⋊C₄	—	5	1	no	—
505	C₄⋊C₄	—	5	2	no	—
506	C₄⋊C₄	—	5	2	no	—
507	C₄⋊C₄	—	5	2	no	—
508	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₅	1	2	yes	—
510	C₄⋊C₄	C₂²×D₅	1	2	yes	—
511	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₅	1	2	yes	—
513	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₅	1	2	yes	—
516	C₄⋊C₄	C₂²×D₅	1	2	yes	—
517	C₄⋊C₄	C₂²×D₅	1	2	yes	—
518	C₄⋊C₄	C₂²×D₅	1	2	yes	—
519	C₄⋊C₄	C₂²×D₅	1	2	yes	—
520	C₂²⋊C₄	—	5	2	no	—
521	C₂²⋊C₄	—	5	2	no	—
522	C₂²⋊C₄	—	5	2	no	—
523	C₂²⋊C₄	—	5	1	no	—
524	C₂²⋊C₄	—	5	2	no	—
525	C₂²⋊C₄	—	5	2	no	—
526	C₂²⋊C₄	—	5	2	no	—
527	C₂²⋊C₄	—	5	2	no	—
528	C₂²⋊C₄	—	5	1	no	—
529	C₂²⋊C₄	—	5	1	no	—
530	C₂²⋊C₄	—	5	1	no	—
531	C₂²⋊C₄	—	5	1	no	—
532	C₂²⋊C₄	—	5	1	no	—
533	C₂²⋊C₄	—	5	2	no	—
534	C₂²⋊C₄	—	5	2	no	—
535	C₂²⋊C₄	—	5	2	no	—
536	C₂²⋊C₄	—	5	1	no	—
537	C₂²⋊C₄	—	5	2	no	—
538	C₂²⋊C₄	—	5	1	no	—
539	C₂²⋊C₄	—	5	2	no	—
540	C₂²⋊C₄	—	5	2	no	—
541	C₂²⋊C₄	—	5	2	no	—
542	C₂²⋊C₄	—	5	2	no	—
543	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
547	C₄²	—	5	2	no	—
548	C₄²	—	5	2	no	—
549	C₄²	—	5	2	no	—
550	C₄²	C₂²×D₅	1	1	yes	characteristic
551	C₄²	C₂²×D₅	1	1	yes	characteristic
552	C₄²	C₂²×D₅	1	2	yes	—
553	C₄²	C₂²×D₅	1	2	yes	—
554	C₂×C₅	—	4	1	no	—
555	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
556	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
557	C₂×C₅	#585	1	1	yes	characteristic
558	D₅	—	2	2	no	—
559	D₅	—	4	1	no	—
560	D₅	—	4	1	no	—
561	D₅	—	4	2	no	—
562	D₅	—	4	1	no	—
563	C₂³	—	5	1	no	—
564	C₂³	—	5	1	no	—
565	C₂³	—	5	1	no	—
566	C₂³	—	5	1	no	—
567	C₂³	—	5	2	no	—
568	C₂³	—	10	2	no	—
569	C₂³	—	20	1	no	—
570	C₂³	—	20	1	no	—
571	C₂³	C₂³×D₅	1	1	yes	characteristic
572	Q₈	—	2	2	no	—
573	Q₈	—	2	2	no	—
574	Q₈	—	10	2	no	—
575	Q₈	—	20	2	no	—
576	Q₈	—	20	2	no	—
577	Q₈	—	20	1	no	—
578	Q₈	—	20	2	no	—
579	D₄	—	10	4	no	—
580	D₄	—	10	2	no	—
581	D₄	—	10	2	no	—
582	D₄	—	10	2	no	—
583	D₄	—	20	1	no	—
584	D₄	—	20	2	no	—
585	D₄	—	20	2	no	—
586	D₄	—	20	1	no	—
587	D₄	—	20	2	no	—
588	D₄	—	20	1	no	—
589	D₄	—	20	1	no	—
590	D₄	—	20	1	no	—
591	D₄	—	20	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	5	2	no	—
594	C₂×C₄	—	5	1	no	—
595	C₂×C₄	—	5	1	no	—
596	C₂×C₄	—	5	2	no	—
597	C₂×C₄	—	5	2	no	—
598	C₂×C₄	—	5	1	no	—
599	C₂×C₄	—	5	1	no	—
600	C₂×C₄	—	10	2	no	—
601	C₂×C₄	—	10	2	no	—
602	C₂×C₄	—	10	2	no	—
603	C₂×C₄	—	10	2	no	—
604	C₂×C₄	—	20	1	no	—
605	C₂×C₄	—	20	1	no	—
606	C₂×C₄	—	20	2	no	—
607	C₂×C₄	—	20	2	no	—
608	C₂×C₄	—	20	2	no	—
609	C₂×C₄	—	20	2	no	—
610	C₂×C₄	—	20	2	no	—
611	C₂×C₄	—	20	2	no	—
612	C₂×C₄	—	20	2	no	—
613	C₂×C₄	—	20	1	no	—
614	C₂×C₄	C₂³×D₅	1	2	yes	—
615	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₅	1	2	yes	—
620	C₂×C₄	C₂³×D₅	1	2	yes	—
621	C₂×C₄	C₂³×D₅	1	2	yes	—
622	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
624	C₅	#3541	1	1	yes	characteristic, complemented, Sylow
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	5	2	no	—
629	C₂²	—	10	1	no	—
630	C₂²	—	10	1	no	—
631	C₂²	—	10	1	no	—
632	C₂²	—	10	1	no	—
633	C₂²	—	10	1	no	—
634	C₂²	—	10	2	no	—
635	C₂²	—	10	1	no	—
636	C₂²	—	10	1	no	—
637	C₂²	—	10	2	no	—
638	C₂²	—	10	1	no	—
639	C₂²	—	10	1	no	—
640	C₂²	—	10	2	no	—
641	C₂²	—	10	1	no	—
642	C₂²	—	10	1	no	—
643	C₂²	—	20	4	no	—
644	C₂²	C₂⁴×D₅	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	10	1	no	—
655	C₄	—	10	1	no	—
656	C₄	—	10	1	no	—
657	C₄	—	10	1	no	—
658	C₄	—	10	2	no	—
659	C₄	—	10	2	no	—
660	C₄	—	10	2	no	—
661	C₄	#4149	1	2	yes	—
662	C₂	—	4	1	no	—
663	C₂	—	10	2	no	—
664	C₂	—	20	1	no	—
665	C₂	—	20	1	no	—
666	C₂	—	20	1	no	—
667	C₂	—	20	2	no	—
668	C₂	C₂×#4149	1	1	yes	characteristic
669	C₂	D₅×2₋¹⁺⁴	1	1	yes	characteristic
670	C₂	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#541	C₂
hypercenter	#541	D₅
hypocenter	C₅	#3541
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. C₅×#541	C₂	semidirect
2. #66061	C₂	semidirect
3. #66060	C₂	semidirect
4. #66044	C₂	semidirect
5. #66041	C₂	semidirect
6. #66038	C₂	semidirect
7. #66038	C₂	semidirect
8. #66034	C₂	semidirect
9. #66033	C₂	semidirect
10. #66029	C₂	semidirect
11. #66029	C₂	semidirect
12. #66028	C₂	semidirect
13. #66024	C₂	semidirect
14. #65963	C₂	semidirect
15. #65962	C₂	semidirect
16. #65961	C₂	semidirect
17. D₅×C₂²⋊Q₈	C₂	semidirect
18. #65918	C₂	semidirect
19. #65913	C₂	semidirect
20. #65910	C₂	semidirect
21. #65910	C₂	semidirect
22. #65868	C₂	semidirect
23. #65858	C₂	semidirect
25. C₂×#713	C₂²	semidirect
27. C₂×Q₈×D₅	C₂²	semidirect
30. C₅×C₄⋊Q₈	C₂²	semidirect
33. C₅×#125	C₂²	semidirect
34. C₅×#125	C₂²	semidirect
35. C₅×#125	C₂²	semidirect
38. C₄×C₅×Q₈	C₂²	semidirect
39. C₄×C₅×Q₈	C₂²	semidirect
43. #4092	C₂²	semidirect
44. #4092	C₂²	semidirect
49. #4044	C₂²	semidirect
50. #4044	C₂²	semidirect
51. #4044	C₂²	semidirect
55. #4043	C₂²	semidirect
56. #4043	C₂²	semidirect
57. #4043	C₂²	semidirect
61. #4042	C₂²	semidirect
62. #4042	C₂²	semidirect
63. #4042	C₂²	semidirect
64. #4042	C₂²	semidirect
72. #4041	C₂²	semidirect
73. #4041	C₂²	semidirect
77. #4040	C₂²	semidirect
78. #4040	C₂²	semidirect
79. #4040	C₂²	semidirect
84. #4038	C₂²	semidirect
85. #4038	C₂²	semidirect
88. D₅×C₄⋊C₄	C₂²	semidirect
89. D₅×C₄⋊C₄	C₂²	semidirect
90. #4036	C₂²	semidirect
91. #4034	C₂²	semidirect
92. #4034	C₂²	semidirect
109. #4021	C₂²	semidirect
110. #4021	C₂²	semidirect
117. C₄×D₂₀	C₂²	semidirect
118. C₄×D₂₀	C₂²	semidirect
119. #4016	C₂²	semidirect
120. #4015	C₂²	semidirect
121. C₄×Dic₁₀	C₂²	semidirect
122. C₄×Dic₁₀	C₂²	semidirect
243. #541	D₅	semidirect
322. C₄⋊Q₈	C₂×D₅	semidirect
332. #125	C₂×D₅	semidirect
333. #125	C₂×D₅	semidirect
334. #125	C₂×D₅	semidirect
389. C₄×Q₈	C₂×D₅	semidirect
390. C₄×Q₈	C₂×D₅	semidirect
624. C₅	#3541	semidirect

Maximal subgroups

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

subgroup	index
C₅×#541	2
#66061	2
#66060	2
#66044	2
#66041	2
#66038	2
#66034	2
#66033	2
#66029	2
#66028	2
#66024	2
#65963	2
#65962	2
#65961	2
D₅×C₂²⋊Q₈	2
#65918	2
#65913	2
#65910	2
#65868	2
#65858	2
#3541	5