Subgroups — #10618843

Order 640.

930 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#66067	C₂	1	1	yes	maximal, characteristic, complemented
3	#66055	C₂	1	1	yes	maximal, characteristic, complemented
4	#66031	C₂	1	1	yes	maximal, characteristic, complemented
5	#66025	C₂	1	1	yes	maximal, characteristic, complemented
6	#66024	C₂	1	1	yes	maximal, characteristic, complemented
7	#66019	C₂	1	1	yes	maximal, characteristic, complemented
8	#65980	C₂	1	2	yes	maximal, complemented
9	#65980	C₂	1	2	yes	maximal, complemented
10	#65977	C₂	1	2	yes	maximal, complemented
11	#65974	C₂	1	2	yes	maximal, complemented
12	#65973	C₂	1	2	yes	maximal, complemented
13	#65972	C₂	1	2	yes	maximal, complemented
14	#65918	C₂	1	1	yes	maximal, characteristic, complemented
15	#65912	C₂	1	1	yes	maximal, characteristic, complemented
16	#65896	C₂	1	1	yes	maximal, characteristic
17	#65895	C₂	1	1	yes	maximal, characteristic, complemented
18	#65893	C₂	1	1	yes	maximal, characteristic, complemented
19	#65893	C₂	1	1	yes	maximal, characteristic, complemented
20	#65891	C₂	1	1	yes	maximal, characteristic, complemented
21	#65876	C₂	1	1	yes	maximal, characteristic, complemented
22	#65849	C₂	1	2	yes	maximal, complemented
23	#65847	C₂	1	2	yes	maximal, complemented
24	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₅×#125	C₂²	1	1	yes	characteristic
26	C₅×#125	C₂²	1	1	yes	characteristic
27	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	#4093	C₂²	1	2	yes	—
36	#4092	C₂²	1	2	yes	—
37	#4092	C₂²	1	1	yes	characteristic
38	#4092	C₂²	1	2	yes	—
39	Q₈×Dic₅	C₂²	1	2	yes	—
40	#4090	C₂²	1	2	yes	—
41	#4090	C₂²	1	1	yes	characteristic
42	#4086	C₂²	1	1	yes	characteristic
43	#4084	C₂²	1	1	yes	characteristic
44	#4082	C₂²	1	1	yes	characteristic
45	#4082	C₂²	1	1	yes	characteristic
46	#4076	C₂²	1	2	yes	—
47	#4075	C₂²	1	2	yes	—
48	#4075	C₂²	1	2	yes	—
49	#4075	C₂²	1	2	yes	—
50	#4075	C₂²	1	2	yes	—
51	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
52	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₅	C₂²	1	2	yes	—
54	#4072	C₂²	1	2	yes	—
55	#4072	C₂²	1	2	yes	—
56	#4070	C₂²	1	2	yes	—
57	#4070	C₂²	1	2	yes	—
58	#4044	C₂²	1	2	yes	—
59	#4044	C₂²	1	2	yes	—
60	#4044	C₂²	1	2	yes	—
61	#4044	C₂²	1	2	yes	—
62	#4044	C₂²	1	2	yes	—
63	#4044	C₂²	1	2	yes	—
64	#4043	C₂²	1	1	yes	characteristic
65	#4043	C₂²	1	2	yes	—
66	#4043	C₂²	1	1	yes	characteristic
67	#4043	C₂²	1	1	yes	characteristic
68	#4042	C₂²	1	1	yes	characteristic
69	#4042	C₂²	1	2	yes	—
70	#4042	C₂²	1	1	yes	characteristic
71	#4042	C₂²	1	2	yes	—
72	#4041	C₂²	1	1	yes	characteristic
73	#4040	C₂²	1	2	yes	—
74	#4040	C₂²	1	2	yes	—
75	#4039	C₂²	1	1	yes	characteristic
76	#4039	C₂²	1	1	yes	characteristic
77	#4039	C₂²	1	2	yes	—
78	#4038	C₂²	1	2	yes	—
79	#4038	C₂²	1	2	yes	—
80	D₅×C₄⋊C₄	C₂²	1	2	yes	—
81	#4036	C₂²	1	1	yes	characteristic
82	#4036	C₂²	1	1	yes	characteristic
83	#4036	C₂²	1	2	yes	—
84	#4036	C₂²	1	2	yes	—
85	#4035	C₂²	1	2	yes	—
86	#4035	C₂²	1	2	yes	—
87	#4035	C₂²	1	1	yes	characteristic
88	#4035	C₂²	1	2	yes	—
89	#4035	C₂²	1	1	yes	characteristic
90	#4035	C₂²	1	2	yes	—
91	#4034	C₂²	1	1	yes	characteristic
92	#4034	C₂²	1	1	yes	characteristic
93	#4034	C₂²	1	2	yes	—
94	#4033	C₂²	1	1	yes	characteristic
95	#4033	C₂²	1	1	yes	characteristic
96	#4033	C₂²	1	1	yes	characteristic
97	#4033	C₂²	1	2	yes	—
98	#4033	C₂²	1	1	yes	characteristic
99	#4031	C₂²	1	2	yes	—
100	#4031	C₂²	1	2	yes	—
101	#4031	C₂²	1	2	yes	—
102	#4030	C₂²	1	2	yes	—
103	#4029	C₂²	1	2	yes	—
104	#4029	C₂²	1	2	yes	—
105	#4029	C₂²	1	2	yes	—
106	#4029	C₂²	1	2	yes	—
107	#4025	C₂²	1	2	yes	—
108	#4025	C₂²	1	2	yes	—
109	#4025	C₂²	1	2	yes	—
110	#4025	C₂²	1	2	yes	—
111	#4021	C₂²	1	1	yes	characteristic
112	#4021	C₂²	1	1	yes	characteristic
113	C₄×D₂₀	C₂²	1	1	yes	characteristic
114	#4018	C₂²	1	1	yes	characteristic
115	#4018	C₂²	1	1	yes	characteristic
116	C₄²×D₅	C₂²	1	1	yes	characteristic
117	#4015	C₂²	1	1	yes	characteristic
118	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
119	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
120	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
121	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
122	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
123	#3557	—	5	1	no	maximal, Sylow
124	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
125	C₂×C₅×Q₈	C₂³	1	2	yes	—
126	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂³	1	2	yes	—
128	C₂²×C₄×C₅	C₂³	1	2	yes	—
129	C₂²×C₄×C₅	C₂³	1	2	yes	—
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×D₂₀	C₂³	1	1	yes	characteristic
134	C₂×D₂₀	C₂³	1	2	yes	—
135	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₅	C₂³	1	2	yes	—
139	C₂×C₄×D₅	C₂³	1	2	yes	—
140	C₂×C₄×D₅	C₂³	1	2	yes	—
141	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
142	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
143	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
145	C₂×Dic₁₀	C₂³	1	1	yes	characteristic
146	C₂×Dic₁₀	C₂³	1	2	yes	—
147	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₂³	1	2	yes	—
149	C₅×C₄⋊C₄	C₂³	1	2	yes	—
150	C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₂³	1	2	yes	—
157	C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₄²×C₅	C₂³	1	1	yes	characteristic
162	C₄²×C₅	C₂³	1	1	yes	characteristic
163	C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₅	C₂³	1	2	yes	—
165	C₂²⋊Dic₅	C₂³	1	2	yes	—
166	C₂²⋊Dic₅	C₂³	1	2	yes	—
167	C₂²⋊Dic₅	C₂³	1	2	yes	—
168	C₂²⋊Dic₅	C₂³	1	2	yes	—
169	#685	C₂³	1	1	yes	characteristic
170	#685	C₂³	1	1	yes	characteristic
171	#685	C₂³	1	1	yes	characteristic
172	#685	C₂³	1	1	yes	characteristic
173	#685	C₂³	1	2	yes	—
174	#685	C₂³	1	2	yes	—
175	#685	C₂³	1	2	yes	—
176	#685	C₂³	1	2	yes	—
177	#685	C₂³	1	2	yes	—
178	#685	C₂³	1	2	yes	—
179	#685	C₂³	1	2	yes	—
180	#685	C₂³	1	2	yes	—
181	#685	C₂³	1	2	yes	—
182	#685	C₂³	1	2	yes	—
183	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
184	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₅	C₂³	1	2	yes	—
188	C₄⋊Dic₅	C₂³	1	2	yes	—
189	C₄⋊Dic₅	C₂³	1	2	yes	—
190	C₄⋊Dic₅	C₂³	1	2	yes	—
191	C₄⋊Dic₅	C₂³	1	2	yes	—
192	C₄⋊Dic₅	C₂³	1	2	yes	—
193	#683	C₂³	1	1	yes	characteristic
194	#683	C₂³	1	1	yes	characteristic
195	#683	C₂³	1	2	yes	—
196	#683	C₂³	1	1	yes	characteristic
197	#683	C₂³	1	1	yes	characteristic
198	#683	C₂³	1	1	yes	characteristic
199	#683	C₂³	1	1	yes	characteristic
200	#683	C₂³	1	2	yes	—
201	#683	C₂³	1	1	yes	characteristic
202	#683	C₂³	1	1	yes	characteristic
203	#683	C₂³	1	1	yes	characteristic
204	#683	C₂³	1	1	yes	characteristic
205	#683	C₂³	1	2	yes	—
206	#683	C₂³	1	2	yes	—
207	#683	C₂³	1	2	yes	—
208	#683	C₂³	1	2	yes	—
209	#683	C₂³	1	2	yes	—
210	#683	C₂³	1	2	yes	—
211	#683	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	1	yes	characteristic
215	C₄×Dic₅	C₂³	1	2	yes	—
216	C₄×Dic₅	C₂³	1	2	yes	—
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	2	yes	—
222	C₄×Dic₅	C₂³	1	2	yes	—
223	#563	—	5	2	no	—
224	#563	—	5	2	no	—
225	#559	—	5	1	no	—
226	#559	—	5	1	no	—
227	#557	—	5	1	no	—
228	#557	—	5	1	no	—
229	#556	—	5	1	no	—
230	#556	—	5	1	no	—
231	#554	—	5	1	no	—
232	#554	D₅	1	1	yes	characteristic, complemented
233	#552	—	5	2	no	—
234	#552	—	5	2	no	—
235	#542	—	5	1	no	—
236	#542	—	5	2	no	—
237	#542	—	5	2	no	—
238	#542	—	5	1	no	—
239	#541	—	5	1	no	—
240	#540	—	5	1	no	—
241	#539	—	5	2	no	—
242	#539	—	5	2	no	—
243	#533	—	5	1	no	—
244	#529	—	5	1	no	—
245	#529	—	5	1	no	—
246	C₂³×C₅	C₂⁴	1	2	yes	—
247	C₂²×D₅	C₂⁴	1	1	yes	characteristic
248	C₂²×D₅	C₂⁴	1	2	yes	—
249	C₅×Q₈	—	4	1	no	—
250	C₅×Q₈	—	4	2	no	—
251	C₅×D₄	—	2	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	4	2	no	—
255	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂⁴	1	2	yes	—
257	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂⁴	1	2	yes	—
259	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂⁴	1	2	yes	—
261	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
265	C₂²⋊D₅	—	4	2	no	—
266	C₂²⋊D₅	—	4	2	no	—
267	C₂²⋊D₅	—	4	2	no	—
268	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₅	C₂⁴	1	2	yes	—
272	C₂×Dic₅	C₂⁴	1	2	yes	—
273	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₅	C₂⁴	1	2	yes	—
276	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
278	D₂₀	—	2	2	no	—
279	D₂₀	—	4	2	no	—
280	C₄×D₅	—	2	2	no	—
281	C₄×D₅	—	4	1	no	—
282	C₄×D₅	—	4	2	no	—
283	C₄×D₅	—	4	2	no	—
284	C₄×D₅	—	4	2	no	—
285	C₄×D₅	—	4	1	no	—
286	Dic₁₀	—	2	2	no	—
287	Dic₁₀	—	2	2	no	—
288	Dic₁₀	—	4	2	no	—
289	Dic₁₀	—	4	1	no	—
290	Dic₁₀	—	4	1	no	—
291	Dic₁₀	—	4	1	no	—
292	C₄⋊Q₈	—	5	1	no	—
293	C₄⋊Q₈	—	5	2	no	—
294	C₄⋊Q₈	—	5	1	no	—
295	C₄⋊Q₈	—	5	1	no	—
296	C₄⋊Q₈	—	5	2	no	—
297	C₄⋊Q₈	—	5	1	no	—
298	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
299	#127	—	5	1	no	—
300	#126	—	5	2	no	—
301	#126	—	5	2	no	—
302	#126	—	5	2	no	—
303	#126	—	5	2	no	—
304	#126	—	5	2	no	—
305	#126	—	5	2	no	—
306	#126	—	5	2	no	—
307	#126	—	5	2	no	—
308	#126	—	5	2	no	—
309	#126	—	5	2	no	—
310	#125	—	5	1	no	—
311	#125	—	5	1	no	—
312	#125	—	5	1	no	—
313	#125	—	5	2	no	—
314	#125	—	5	2	no	—
315	#125	—	5	2	no	—
316	#125	—	5	2	no	—
317	#125	—	5	1	no	—
318	#125	—	5	2	no	—
319	#125	—	5	2	no	—
320	#125	C₂×D₅	1	1	yes	characteristic
321	#125	C₂×D₅	1	1	yes	characteristic
322	#124	—	5	2	no	—
323	#124	—	5	1	no	—
324	#124	—	5	1	no	—
325	#124	—	5	2	no	—
326	#124	—	5	2	no	—
327	#124	—	5	2	no	—
328	#124	—	5	1	no	—
329	#124	—	5	1	no	—
330	#123	—	5	2	no	—
331	#123	—	5	2	no	—
332	#123	—	5	2	no	—
333	#123	—	5	2	no	—
334	#123	—	5	2	no	—
335	#123	—	5	2	no	—
336	#123	—	5	2	no	—
337	#123	—	5	2	no	—
338	#123	—	5	2	no	—
339	#123	—	5	2	no	—
340	C₂²⋊Q₈	—	5	1	no	—
341	C₂²⋊Q₈	—	5	2	no	—
342	C₂²⋊Q₈	—	5	2	no	—
343	C₂²⋊Q₈	—	5	2	no	—
344	C₂²⋊Q₈	—	5	2	no	—
345	C₂²⋊Q₈	—	5	1	no	—
346	C₂²⋊Q₈	—	5	1	no	—
347	C₂²⋊Q₈	—	5	1	no	—
348	C₂²⋊Q₈	—	5	1	no	—
349	C₂²⋊Q₈	—	5	1	no	—
350	C₂²⋊Q₈	—	5	2	no	—
351	C₂²⋊Q₈	—	5	2	no	—
352	C₂²⋊Q₈	—	5	2	no	—
353	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
354	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
355	C₂²⋊Q₈	C₂×D₅	1	2	yes	—
356	#121	—	5	1	no	—
357	#121	—	5	2	no	—
358	#121	—	5	1	no	—
359	#121	—	5	2	no	—
360	C₄×Q₈	—	5	2	no	—
361	C₄×Q₈	—	5	1	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×Q₈	—	5	1	no	—
364	C₄×Q₈	—	5	2	no	—
365	C₄×Q₈	—	5	1	no	—
366	C₄×Q₈	—	5	1	no	—
367	C₄×Q₈	—	5	1	no	—
368	C₄×Q₈	—	5	1	no	—
369	C₄×Q₈	—	5	1	no	—
370	C₄×Q₈	—	5	1	no	—
371	C₄×Q₈	C₂×D₅	1	1	yes	characteristic
372	C₄×D₄	—	5	2	no	—
373	C₄×D₄	—	5	2	no	—
374	C₄×D₄	—	5	2	no	—
375	C₄×D₄	—	5	2	no	—
376	C₄×D₄	—	5	1	no	—
377	C₄×D₄	—	5	1	no	—
378	C₄×D₄	—	5	1	no	—
379	C₄×D₄	C₂×D₅	1	1	yes	characteristic
380	C₄×D₄	C₂×D₅	1	1	yes	characteristic
381	C₄×D₄	C₂×D₅	1	1	yes	characteristic
382	#117	—	5	2	no	—
383	#117	—	5	2	no	—
384	#117	—	5	2	no	—
385	#117	—	5	2	no	—
386	#117	—	5	1	no	—
387	#117	—	5	1	no	—
388	C₂×C₄⋊C₄	—	5	2	no	—
389	C₂×C₄⋊C₄	C₂×D₅	1	2	yes	—
390	C₂×C₄²	—	5	1	no	—
391	C₂²×C₅	—	2	2	no	—
392	C₂²×C₅	—	2	2	no	—
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	C₂⁵	1	1	yes	characteristic
395	C₂×D₅	—	2	1	no	—
396	C₂×D₅	—	2	2	no	—
397	C₂×D₅	—	2	2	no	—
398	C₂×D₅	—	2	1	no	—
399	C₂×D₅	—	2	2	no	—
400	C₂×D₅	—	2	1	no	—
401	C₄×C₅	—	2	2	no	—
402	C₄×C₅	—	2	1	no	—
403	C₄×C₅	—	2	1	no	—
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	2	2	no	—
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	2₋¹⁺⁴	1	2	yes	—
411	Dic₅	—	2	2	no	—
412	Dic₅	—	2	2	no	—
413	Dic₅	—	2	1	no	—
414	Dic₅	—	2	1	no	—
415	Dic₅	—	2	1	no	—
416	Dic₅	—	2	1	no	—
417	Dic₅	—	2	2	no	—
418	Dic₅	—	2	1	no	—
419	Dic₅	—	2	1	no	—
420	Dic₅	—	2	1	no	—
421	C₂×Q₈	—	5	1	no	—
422	C₂×Q₈	—	5	1	no	—
423	C₂×Q₈	—	5	1	no	—
424	C₂×Q₈	—	5	2	no	—
425	C₂×Q₈	—	5	1	no	—
426	C₂×Q₈	—	5	1	no	—
427	C₂×Q₈	C₂²×D₅	1	2	yes	—
428	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
429	C₂×D₄	—	5	2	no	—
430	C₂×D₄	—	5	2	no	—
431	C₂×D₄	—	5	2	no	—
432	C₂×D₄	—	5	1	no	—
433	C₂×D₄	—	5	2	no	—
434	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
435	C₂²×C₄	—	5	1	no	—
436	C₂²×C₄	—	5	1	no	—
437	C₂²×C₄	—	5	1	no	—
438	C₂²×C₄	—	5	2	no	—
439	C₂²×C₄	—	5	2	no	—
440	C₂²×C₄	—	5	2	no	—
441	C₂²×C₄	C₂²×D₅	1	2	yes	—
442	C₂²×C₄	C₂²×D₅	1	2	yes	—
443	C₂²×C₄	C₂²×D₅	1	2	yes	—
444	C₄⋊C₄	—	5	1	no	—
445	C₄⋊C₄	—	5	2	no	—
446	C₄⋊C₄	—	5	2	no	—
447	C₄⋊C₄	—	5	1	no	—
448	C₄⋊C₄	—	5	2	no	—
449	C₄⋊C₄	—	5	2	no	—
450	C₄⋊C₄	—	5	1	no	—
451	C₄⋊C₄	—	5	1	no	—
452	C₄⋊C₄	—	5	2	no	—
453	C₄⋊C₄	—	5	2	no	—
454	C₄⋊C₄	—	5	1	no	—
455	C₄⋊C₄	—	5	1	no	—
456	C₄⋊C₄	—	5	1	no	—
457	C₄⋊C₄	—	5	1	no	—
458	C₄⋊C₄	—	5	1	no	—
459	C₄⋊C₄	—	5	2	no	—
460	C₄⋊C₄	—	5	1	no	—
461	C₄⋊C₄	—	5	1	no	—
462	C₄⋊C₄	—	5	2	no	—
463	C₄⋊C₄	—	5	2	no	—
464	C₄⋊C₄	—	5	1	no	—
465	C₄⋊C₄	—	5	2	no	—
466	C₄⋊C₄	—	5	2	no	—
467	C₄⋊C₄	—	5	1	no	—
468	C₄⋊C₄	—	5	1	no	—
469	C₄⋊C₄	—	5	2	no	—
470	C₄⋊C₄	—	5	2	no	—
471	C₄⋊C₄	—	5	2	no	—
472	C₄⋊C₄	—	5	2	no	—
473	C₄⋊C₄	C₂²×D₅	1	2	yes	—
474	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×D₅	1	2	yes	—
476	C₄⋊C₄	C₂²×D₅	1	2	yes	—
477	C₄⋊C₄	C₂²×D₅	1	2	yes	—
478	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₅	1	2	yes	—
482	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	2	no	—
489	C₂²⋊C₄	—	5	2	no	—
490	C₂²⋊C₄	—	5	1	no	—
491	C₂²⋊C₄	—	5	1	no	—
492	C₂²⋊C₄	—	5	2	no	—
493	C₂²⋊C₄	—	5	1	no	—
494	C₂²⋊C₄	—	5	1	no	—
495	C₂²⋊C₄	—	5	2	no	—
496	C₂²⋊C₄	—	5	2	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	C₂²×D₅	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
505	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
506	C₄²	—	5	1	no	—
507	C₄²	—	5	1	no	—
508	C₄²	—	5	1	no	—
509	C₄²	—	5	2	no	—
510	C₄²	—	5	2	no	—
511	C₄²	—	5	1	no	—
512	C₄²	—	5	1	no	—
513	C₄²	—	5	2	no	—
514	C₄²	—	5	2	no	—
515	C₄²	—	5	2	no	—
516	C₄²	—	5	2	no	—
517	C₄²	C₂²×D₅	1	1	yes	characteristic
518	C₄²	C₂²×D₅	1	1	yes	characteristic
519	C₄²	C₂²×D₅	1	1	yes	characteristic
520	C₂×C₅	—	4	2	no	—
521	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
522	C₂×C₅	#585	1	1	yes	characteristic
523	C₂×C₅	#585	1	1	yes	characteristic
524	D₅	—	4	1	no	—
525	D₅	—	4	2	no	—
526	C₂³	—	5	1	no	—
527	C₂³	—	5	2	no	—
528	C₂³	C₂³×D₅	1	2	yes	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	2	no	—
531	Q₈	—	10	2	no	—
532	Q₈	—	10	2	no	—
533	Q₈	—	20	2	no	—
534	Q₈	—	20	1	no	—
535	Q₈	—	20	1	no	—
536	Q₈	—	20	1	no	—
537	D₄	—	2	2	no	—
538	D₄	—	10	2	no	—
539	D₄	—	20	2	no	—
540	D₄	—	20	2	no	—
541	D₄	—	20	2	no	—
542	D₄	—	20	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	5	1	no	—
547	C₂×C₄	—	5	2	no	—
548	C₂×C₄	—	5	2	no	—
549	C₂×C₄	—	5	1	no	—
550	C₂×C₄	—	5	1	no	—
551	C₂×C₄	—	5	1	no	—
552	C₂×C₄	—	5	1	no	—
553	C₂×C₄	—	5	1	no	—
554	C₂×C₄	—	5	2	no	—
555	C₂×C₄	—	5	1	no	—
556	C₂×C₄	—	10	2	no	—
557	C₂×C₄	—	20	2	no	—
558	C₂×C₄	—	20	2	no	—
559	C₂×C₄	—	20	1	no	—
560	C₂×C₄	—	20	1	no	—
561	C₂×C₄	—	20	2	no	—
562	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
563	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₅	1	2	yes	—
565	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₅	1	2	yes	—
567	C₂×C₄	C₂³×D₅	1	2	yes	—
568	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
572	C₅	#3557	1	1	yes	characteristic, complemented, Sylow
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	10	1	no	—
577	C₂²	—	10	2	no	—
578	C₂²	—	10	2	no	—
579	C₂²	—	10	1	no	—
580	C₂²	—	10	1	no	—
581	C₂²	—	10	2	no	—
582	C₂²	C₂⁴×D₅	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	1	no	—
592	C₄	—	10	1	no	—
593	C₄	—	10	2	no	—
594	C₄	—	10	2	no	—
595	C₄	—	10	1	no	—
596	C₄	—	10	2	no	—
597	C₄	—	10	1	no	—
598	C₄	—	10	1	no	—
599	C₄	—	10	1	no	—
600	C₄	—	10	1	no	—
601	C₄	—	10	1	no	—
602	C₄	#4147	1	2	yes	—
603	C₂	—	4	2	no	—
604	C₂	—	20	1	no	—
605	C₂	—	20	2	no	—
606	C₂	C₂×#4147	1	1	yes	characteristic
607	C₂	#66283	1	1	yes	characteristic
608	C₂	#66285	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#554	C₂
prime radical	#65896	C₂
hypercenter	#554	D₅
hypocenter	C₅	#3557
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₅×#554	C₂	semidirect
2. #66067	C₂	semidirect
3. #66055	C₂	semidirect
4. #66031	C₂	semidirect
5. #66025	C₂	semidirect
6. #66024	C₂	semidirect
7. #66019	C₂	semidirect
8. #65980	C₂	semidirect
9. #65980	C₂	semidirect
10. #65977	C₂	semidirect
11. #65974	C₂	semidirect
12. #65973	C₂	semidirect
13. #65972	C₂	semidirect
14. #65918	C₂	semidirect
15. #65912	C₂	semidirect
17. #65895	C₂	semidirect
18. #65893	C₂	semidirect
19. #65893	C₂	semidirect
20. #65891	C₂	semidirect
21. #65876	C₂	semidirect
22. #65849	C₂	semidirect
23. #65847	C₂	semidirect
232. #554	D₅	semidirect
572. C₅	#3557	semidirect

Maximal subgroups

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

subgroup	index
C₅×#554	2
#66067	2
#66055	2
#66031	2
#66025	2
#66024	2
#66019	2
#65980	2
#65977	2
#65974	2
#65973	2
#65972	2
#65918	2
#65912	2
#65896	2
#65895	2
#65893	2
#65891	2
#65876	2
#65849	2
#65847	2
#3557	5