Subgroups — #10618451

Order 640.

1142 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#66063	C₂	1	1	yes	maximal, characteristic, complemented
3	#66059	C₂	1	1	yes	maximal, characteristic, complemented
4	#66043	C₂	1	2	yes	maximal, complemented
5	#66039	C₂	1	2	yes	maximal, complemented
6	#66014	C₂	1	1	yes	maximal, characteristic, complemented
7	#66010	C₂	1	2	yes	maximal, complemented
8	#66008	C₂	1	1	yes	maximal, characteristic, complemented
9	#66004	C₂	1	2	yes	maximal, complemented
10	#65995	C₂	1	2	yes	maximal, complemented
11	#65988	C₂	1	2	yes	maximal, complemented
12	#65977	C₂	1	1	yes	maximal, characteristic, complemented
13	#65971	C₂	1	2	yes	maximal, complemented
14	#65965	C₂	1	2	yes	maximal, complemented
15	#65961	C₂	1	1	yes	maximal, characteristic, complemented
16	#65953	C₂	1	1	yes	maximal, characteristic, complemented
17	D₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
18	#65914	C₂	1	1	yes	maximal, characteristic, complemented
19	#65908	C₂	1	1	yes	maximal, characteristic, complemented
20	#65882	C₂	1	1	yes	maximal, characteristic, complemented
21	#65879	C₂	1	1	yes	maximal, characteristic, complemented
22	#65869	C₂	1	1	yes	maximal, characteristic, complemented
23	D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#713	C₂²	1	1	yes	characteristic
25	C₂×#713	C₂²	1	2	yes	complemented
26	C₂×D₄×D₅	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₅	C₂²	1	2	yes	—
28	C₂×#709	C₂²	1	2	yes	complemented
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	complemented
32	C₅×#124	C₂²	1	2	yes	complemented
33	C₅×#124	C₂²	1	1	yes	characteristic, complemented
34	C₅×#123	C₂²	1	2	yes	complemented
35	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₅×#121	C₂²	1	1	yes	characteristic
38	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₅×#117	C₂²	1	1	yes	characteristic, complemented
41	#4093	C₂²	1	2	yes	complemented
42	#4093	C₂²	1	1	yes	characteristic, complemented
43	#4092	C₂²	1	2	yes	—
44	#4092	C₂²	1	1	yes	characteristic, complemented
45	Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
46	#4090	C₂²	1	2	yes	complemented
47	#4086	C₂²	1	1	yes	characteristic, complemented
48	#4085	C₂²	1	2	yes	—
49	#4085	C₂²	1	2	yes	complemented
50	#4084	C₂²	1	1	yes	characteristic
51	#4084	C₂²	1	2	yes	complemented
52	D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
53	#4076	C₂²	1	1	yes	characteristic
54	#4076	C₂²	1	1	yes	characteristic, complemented
55	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
57	C₂×#685	C₂²	1	2	yes	—
58	#4072	C₂²	1	1	yes	characteristic, complemented
59	#4044	C₂²	1	2	yes	complemented
60	#4044	C₂²	1	2	yes	complemented
61	#4043	C₂²	1	2	yes	complemented
62	#4042	C₂²	1	2	yes	—
63	#4041	C₂²	1	1	yes	characteristic
64	#4041	C₂²	1	1	yes	characteristic, complemented
65	#4041	C₂²	1	2	yes	complemented
66	#4040	C₂²	1	2	yes	—
67	#4040	C₂²	1	2	yes	complemented
68	#4040	C₂²	1	2	yes	complemented
69	#4040	C₂²	1	2	yes	complemented
70	#4039	C₂²	1	2	yes	—
71	#4039	C₂²	1	1	yes	characteristic, complemented
72	#4039	C₂²	1	1	yes	characteristic, complemented
73	#4039	C₂²	1	2	yes	complemented
74	#4039	C₂²	1	2	yes	complemented
75	#4038	C₂²	1	1	yes	characteristic
76	#4038	C₂²	1	1	yes	characteristic
77	#4038	C₂²	1	1	yes	characteristic
78	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
80	D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
81	D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
82	#4036	C₂²	1	1	yes	characteristic, complemented
83	#4035	C₂²	1	2	yes	complemented
84	#4034	C₂²	1	1	yes	characteristic, complemented
85	#4032	C₂²	1	2	yes	complemented
86	#4031	C₂²	1	2	yes	complemented
87	#4031	C₂²	1	2	yes	complemented
88	#4030	C₂²	1	2	yes	—
89	#4030	C₂²	1	2	yes	complemented
90	#4030	C₂²	1	2	yes	complemented
91	#4030	C₂²	1	2	yes	complemented
92	#4030	C₂²	1	2	yes	complemented
93	#4030	C₂²	1	2	yes	complemented
94	#4029	C₂²	1	2	yes	complemented
95	#4029	C₂²	1	2	yes	complemented
96	#4029	C₂²	1	2	yes	complemented
97	#4028	C₂²	1	2	yes	—
98	#4028	C₂²	1	2	yes	—
99	#4028	C₂²	1	2	yes	—
100	#4027	C₂²	1	2	yes	complemented
101	#4027	C₂²	1	2	yes	complemented
102	#4027	C₂²	1	2	yes	complemented
103	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
106	D₅×C₂²⋊C₄	C₂²	1	2	yes	—
107	#4025	C₂²	1	2	yes	complemented
108	#4023	C₂²	1	1	yes	characteristic, complemented
109	#4023	C₂²	1	1	yes	characteristic, complemented
110	#4023	C₂²	1	2	yes	complemented
111	#4020	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₂₀	C₂²	1	2	yes	—
113	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₂₀	C₂²	1	2	yes	complemented
116	#4018	C₂²	1	1	yes	characteristic
117	#4018	C₂²	1	1	yes	characteristic
118	#4018	C₂²	1	2	yes	complemented
119	#4018	C₂²	1	2	yes	complemented
120	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
121	C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
122	#4016	C₂²	1	1	yes	characteristic, complemented
123	#3494	—	5	1	no	maximal, Sylow
124	C₂³×D₅	C₂³	1	1	yes	characteristic
125	C₂³×D₅	C₂³	1	2	yes	—
126	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×Q₈	C₂³	1	2	yes	—
128	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₅×D₄	C₂³	1	2	yes	—
130	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅	C₂³	1	2	yes	—
138	C₂²×Dic₅	C₂³	1	1	yes	characteristic
139	C₂²×Dic₅	C₂³	1	2	yes	—
140	#713	—	2	4	no	—
141	#713	—	4	4	no	—
142	D₄×D₅	—	2	4	no	—
143	D₄×D₅	—	4	4	no	—
144	#709	—	4	4	no	—
145	C₂×D₂₀	C₂³	1	2	yes	—
146	C₂×D₂₀	C₂³	1	2	yes	—
147	C₂×D₂₀	C₂³	1	1	yes	characteristic
148	C₂×D₂₀	C₂³	1	2	yes	—
149	C₂×D₂₀	C₂³	1	1	yes	characteristic
150	C₂×D₂₀	C₂³	1	2	yes	—
151	C₂×D₂₀	C₂³	1	2	yes	—
152	C₂×C₄×D₅	—	2	4	no	—
153	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₅	C₂³	1	2	yes	—
158	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₅	C₂³	1	2	yes	—
160	C₂×C₄×D₅	C₂³	1	2	yes	—
161	C₂×C₄×D₅	C₂³	1	2	yes	—
162	C₂×C₄×D₅	C₂³	1	2	yes	—
163	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₅	C₂³	1	2	yes	—
166	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
167	C₂×Dic₁₀	C₂³	1	2	yes	—
168	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
177	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
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	C₂²⋊Dic₅	C₂³	1	2	yes	—
186	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₅	C₂³	1	2	yes	—
189	#685	C₂³	1	1	yes	characteristic
190	#685	C₂³	1	1	yes	characteristic
191	#685	C₂³	1	1	yes	characteristic
192	#685	C₂³	1	1	yes	characteristic
193	#685	C₂³	1	2	yes	—
194	#685	C₂³	1	2	yes	—
195	#685	C₂³	1	2	yes	—
196	#685	C₂³	1	2	yes	—
197	#685	C₂³	1	2	yes	—
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	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₅	C₂³	1	2	yes	—
208	C₄⋊Dic₅	C₂³	1	2	yes	—
209	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₅	C₂³	1	1	yes	characteristic
211	#683	C₂³	1	2	yes	—
212	#683	C₂³	1	2	yes	—
213	#683	C₂³	1	1	yes	characteristic
214	#683	C₂³	1	1	yes	characteristic
215	#683	C₂³	1	1	yes	characteristic
216	#683	C₂³	1	1	yes	characteristic
217	#683	C₂³	1	2	yes	—
218	#683	C₂³	1	2	yes	—
219	#683	C₂³	1	2	yes	—
220	#683	C₂³	1	2	yes	—
221	C₄×Dic₅	C₂³	1	1	yes	characteristic
222	C₄×Dic₅	C₂³	1	1	yes	characteristic
223	C₄×Dic₅	C₂³	1	1	yes	characteristic
224	C₄×Dic₅	C₂³	1	1	yes	characteristic
225	C₄×Dic₅	C₂³	1	1	yes	characteristic
226	C₄×Dic₅	C₂³	1	1	yes	characteristic
227	C₄×Dic₅	C₂³	1	2	yes	—
228	C₄×Dic₅	C₂³	1	2	yes	—
229	#555	—	5	2	no	—
230	#553	—	5	2	no	—
231	#553	—	5	2	no	—
232	#551	—	5	2	no	—
233	#551	—	5	2	no	—
234	#547	—	5	2	no	—
235	#546	—	5	2	no	—
236	#546	—	5	2	no	—
237	#544	—	5	1	no	—
238	#542	—	5	1	no	—
239	#542	D₅	1	1	yes	characteristic, complemented
240	#540	—	5	1	no	—
241	#540	—	5	1	no	—
242	#535	—	5	1	no	—
243	#532	—	5	1	no	—
244	#532	—	5	1	no	—
245	#529	—	5	1	no	—
246	#529	—	5	1	no	—
247	#525	—	5	1	no	—
248	C₂×#121	—	5	1	no	—
249	#520	—	5	1	no	—
250	#518	—	5	1	no	—
251	C₂×#117	—	5	1	no	—
252	C₂³×C₅	C₂⁴	1	1	yes	characteristic
253	C₂³×C₅	C₂⁴	1	2	yes	—
254	C₂²×D₅	—	2	2	no	—
255	C₂²×D₅	—	2	2	no	—
256	C₂²×D₅	—	2	4	no	—
257	C₂²×D₅	—	4	1	no	—
258	C₂²×D₅	—	4	2	no	—
259	C₂²×D₅	—	4	2	no	—
260	C₂²×D₅	C₂⁴	1	2	yes	—
261	C₂²×D₅	C₂⁴	1	2	yes	—
262	C₂²×D₅	C₂⁴	1	1	yes	characteristic
263	C₂²×D₅	C₂⁴	1	1	yes	characteristic
264	C₅×Q₈	—	2	2	no	—
265	C₅×Q₈	—	4	2	no	—
266	C₅×D₄	—	2	2	no	—
267	C₅×D₄	—	4	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	4	2	no	—
270	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂⁴	1	2	yes	—
276	C₂×C₄×C₅	C₂⁴	1	2	yes	—
277	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂²⋊D₅	—	2	4	no	—
280	C₂²⋊D₅	—	2	4	no	—
281	C₂²⋊D₅	—	4	2	no	—
282	C₂²⋊D₅	—	4	2	no	—
283	C₂²⋊D₅	—	4	2	no	—
284	C₂²⋊D₅	—	4	2	no	—
285	C₂×Dic₅	—	2	2	no	—
286	C₂×Dic₅	—	4	2	no	—
287	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₅	C₂⁴	1	2	yes	—
293	C₂×Dic₅	C₂⁴	1	2	yes	—
294	C₂×Dic₅	C₂⁴	1	1	yes	characteristic
295	D₂₀	—	2	4	no	—
296	D₂₀	—	2	4	no	—
297	D₂₀	—	2	4	no	—
298	D₂₀	—	2	2	no	—
299	D₂₀	—	2	2	no	—
300	D₂₀	—	4	2	no	—
301	D₂₀	—	4	2	no	—
302	C₄×D₅	—	2	2	no	—
303	C₄×D₅	—	2	2	no	—
304	C₄×D₅	—	2	2	no	—
305	C₄×D₅	—	2	2	no	—
306	C₄×D₅	—	2	2	no	—
307	C₄×D₅	—	2	4	no	—
308	C₄×D₅	—	4	1	no	—
309	C₄×D₅	—	4	2	no	—
310	C₄×D₅	—	4	1	no	—
311	C₄×D₅	—	4	2	no	—
312	C₄×D₅	—	4	2	no	—
313	C₄×D₅	—	4	2	no	—
314	C₄×D₅	—	4	2	no	—
315	C₄×D₅	#41	1	4	yes	complemented
316	Dic₁₀	—	4	2	no	—
317	C₂×#41	—	5	1	no	—
318	C₂×#41	—	5	2	no	—
319	C₂×#41	—	5	2	no	—
320	C₂²×D₄	—	5	1	no	—
321	C₂²×D₄	—	5	2	no	—
322	C₂³×C₄	—	5	1	no	—
323	C₄⋊Q₈	—	5	2	no	—
324	C₄⋊Q₈	—	5	1	no	—
325	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
326	#127	—	5	1	no	—
327	#127	—	5	1	no	—
328	#126	—	5	2	no	—
329	#126	—	5	2	no	—
330	#126	—	5	2	no	—
331	#126	C₂×D₅	1	2	yes	complemented
332	#125	—	5	1	no	—
333	#125	—	5	2	no	—
334	#125	—	5	1	no	—
335	#124	—	5	1	no	—
336	#124	—	5	2	no	—
337	#124	—	5	2	no	—
338	#124	—	5	2	no	—
339	#124	C₂×D₅	1	1	yes	characteristic, complemented
340	#124	C₂×D₅	1	2	yes	complemented
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	2	no	—
348	#123	—	5	2	no	—
349	#123	C₂×D₅	1	2	yes	complemented
350	C₂²⋊Q₈	—	5	1	no	—
351	C₂²⋊Q₈	—	5	2	no	—
352	C₂²⋊Q₈	—	5	2	no	—
353	C₂²⋊Q₈	—	5	2	no	—
354	C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
355	C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
356	#121	—	5	1	no	—
357	#121	—	5	2	no	—
358	#121	—	5	2	no	—
359	#121	—	5	2	no	—
360	#121	—	5	1	no	—
361	#121	—	5	1	no	—
362	#121	—	5	1	no	—
363	#121	—	5	1	no	—
364	#121	—	5	2	no	—
365	#121	—	5	2	no	—
366	#121	—	5	2	no	—
367	#121	—	5	2	no	—
368	#121	—	5	2	no	—
369	#121	—	5	2	no	—
370	#121	—	5	2	no	—
371	#121	C₂×D₅	1	1	yes	characteristic
372	#120	—	5	2	no	—
373	#120	—	5	2	no	—
374	#120	—	5	2	no	—
375	C₄×Q₈	—	5	1	no	—
376	C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
377	C₄×D₄	—	5	1	no	—
378	C₄×D₄	—	5	2	no	—
379	C₄×D₄	—	5	2	no	—
380	C₄×D₄	—	5	1	no	—
381	C₄×D₄	—	5	1	no	—
382	C₄×D₄	—	5	2	no	—
383	C₄×D₄	—	5	2	no	—
384	C₄×D₄	—	5	2	no	—
385	C₄×D₄	—	5	2	no	—
386	C₄×D₄	—	5	2	no	—
387	C₄×D₄	—	5	2	no	—
388	C₄×D₄	—	5	1	no	—
389	C₄×D₄	—	5	1	no	—
390	C₄×D₄	—	5	2	no	—
391	C₄×D₄	—	5	2	no	—
392	C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
393	#117	—	5	1	no	—
394	#117	—	5	1	no	—
395	#117	—	5	1	no	—
396	#117	—	5	1	no	—
397	#117	—	5	1	no	—
398	#117	—	5	1	no	—
399	#117	—	5	2	no	—
400	#117	—	5	1	no	—
401	#117	—	5	1	no	—
402	#117	—	5	2	no	—
403	#117	—	5	2	no	—
404	#117	C₂×D₅	1	1	yes	characteristic, complemented
405	C₂×C₄⋊C₄	—	5	1	no	—
406	C₂×C₄⋊C₄	—	5	1	no	—
407	C₂×C₄⋊C₄	—	5	1	no	—
408	C₂×C₄⋊C₄	—	5	2	no	—
409	C₂×C₂²⋊C₄	—	5	2	no	—
410	C₂×C₂²⋊C₄	—	5	1	no	—
411	C₂×C₂²⋊C₄	—	5	1	no	—
412	C₂×C₂²⋊C₄	—	5	2	no	—
413	C₂×C₂²⋊C₄	—	5	2	no	—
414	C₂×C₄²	—	5	1	no	—
415	C₂×C₄²	—	5	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	2	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	C₂⁵	1	1	yes	characteristic
423	C₂×D₅	—	2	1	no	—
424	C₂×D₅	—	2	1	no	—
425	C₂×D₅	—	2	1	no	—
426	C₂×D₅	—	2	1	no	—
427	C₂×D₅	—	2	2	no	—
428	C₂×D₅	—	2	2	no	—
429	C₂×D₅	—	2	2	no	—
430	C₂×D₅	—	2	2	no	—
431	C₂×D₅	—	2	2	no	—
432	C₂×D₅	—	2	2	no	—
433	C₂×D₅	—	4	4	no	—
434	C₂×D₅	—	8	4	no	—
435	C₂×D₅	C₂×#41	1	2	yes	—
436	C₂×D₅	H(5,𝔽₂)	1	2	yes	—
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	2	2	no	—
439	C₄×C₅	—	2	2	no	—
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	2	1	no	—
442	C₄×C₅	—	2	2	no	—
443	C₄×C₅	—	2	1	no	—
444	C₄×C₅	—	2	1	no	—
445	C₄×C₅	C₂×#41	1	2	yes	—
446	Dic₅	—	2	1	no	—
447	Dic₅	—	2	1	no	—
448	Dic₅	—	2	2	no	—
449	Dic₅	—	2	1	no	—
450	Dic₅	—	2	1	no	—
451	Dic₅	—	2	2	no	—
452	Dic₅	—	2	1	no	—
453	Dic₅	C₂×#41	1	2	yes	—
454	C₂⁴	—	5	1	no	—
455	C₂⁴	—	5	2	no	—
456	#41	—	10	4	no	—
457	#41	—	20	4	no	—
458	#41	—	20	4	no	—
459	C₂×Q₈	—	5	2	no	—
460	C₂×Q₈	C₂²×D₅	1	1	yes	characteristic
461	C₂×Q₈	C₂²×D₅	1	2	yes	—
462	C₂×D₄	—	5	2	no	—
463	C₂×D₄	—	5	2	no	—
464	C₂×D₄	—	5	2	no	—
465	C₂×D₄	—	5	2	no	—
466	C₂×D₄	—	5	2	no	—
467	C₂×D₄	—	5	2	no	—
468	C₂×D₄	—	5	2	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	2	no	—
474	C₂×D₄	—	5	2	no	—
475	C₂×D₄	—	10	4	no	—
476	C₂×D₄	—	20	4	no	—
477	C₂×D₄	C₂²×D₅	1	1	yes	characteristic
478	C₂×D₄	C₂²×D₅	1	2	yes	—
479	C₂²×C₄	—	5	1	no	—
480	C₂²×C₄	—	5	1	no	—
481	C₂²×C₄	—	5	2	no	—
482	C₂²×C₄	—	5	1	no	—
483	C₂²×C₄	—	5	1	no	—
484	C₂²×C₄	—	5	1	no	—
485	C₂²×C₄	—	5	1	no	—
486	C₂²×C₄	—	5	1	no	—
487	C₂²×C₄	—	5	2	no	—
488	C₂²×C₄	—	5	1	no	—
489	C₂²×C₄	—	5	1	no	—
490	C₂²×C₄	—	5	2	no	—
491	C₂²×C₄	—	5	2	no	—
492	C₂²×C₄	—	5	2	no	—
493	C₂²×C₄	—	5	2	no	—
494	C₂²×C₄	—	5	2	no	—
495	C₂²×C₄	—	10	4	no	—
496	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₅	1	2	yes	—
498	C₄⋊C₄	—	5	1	no	—
499	C₄⋊C₄	—	5	2	no	—
500	C₄⋊C₄	—	5	1	no	—
501	C₄⋊C₄	—	5	1	no	—
502	C₄⋊C₄	—	5	1	no	—
503	C₄⋊C₄	—	5	1	no	—
504	C₄⋊C₄	—	5	1	no	—
505	C₄⋊C₄	—	5	1	no	—
506	C₄⋊C₄	—	5	2	no	—
507	C₄⋊C₄	—	5	2	no	—
508	C₄⋊C₄	—	5	1	no	—
509	C₄⋊C₄	—	5	2	no	—
510	C₄⋊C₄	—	5	2	no	—
511	C₄⋊C₄	—	5	2	no	—
512	C₄⋊C₄	—	5	2	no	—
513	C₄⋊C₄	—	5	2	no	—
514	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₅	1	2	yes	—
518	C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₅	1	2	yes	—
520	C₄⋊C₄	C₂²×D₅	1	2	yes	—
521	C₂²⋊C₄	—	5	1	no	—
522	C₂²⋊C₄	—	5	1	no	—
523	C₂²⋊C₄	—	5	2	no	—
524	C₂²⋊C₄	—	5	2	no	—
525	C₂²⋊C₄	—	5	1	no	—
526	C₂²⋊C₄	—	5	1	no	—
527	C₂²⋊C₄	—	5	2	no	—
528	C₂²⋊C₄	—	5	1	no	—
529	C₂²⋊C₄	—	5	1	no	—
530	C₂²⋊C₄	—	5	2	no	—
531	C₂²⋊C₄	—	5	2	no	—
532	C₂²⋊C₄	—	5	2	no	—
533	C₂²⋊C₄	—	5	2	no	—
534	C₂²⋊C₄	—	5	2	no	—
535	C₂²⋊C₄	—	5	2	no	—
536	C₂²⋊C₄	—	5	2	no	—
537	C₂²⋊C₄	—	5	2	no	—
538	C₂²⋊C₄	—	5	2	no	—
539	C₂²⋊C₄	—	5	2	no	—
540	C₂²⋊C₄	—	5	2	no	—
541	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
542	C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₅	1	2	yes	—
548	C₄²	—	5	1	no	—
549	C₄²	—	5	1	no	—
550	C₄²	—	5	1	no	—
551	C₄²	—	5	1	no	—
552	C₄²	—	5	1	no	—
553	C₄²	—	5	1	no	—
554	C₄²	—	5	2	no	—
555	C₄²	—	5	2	no	—
556	C₄²	C₂²×D₅	1	1	yes	characteristic
557	C₄²	C₂²×D₅	1	1	yes	characteristic
558	C₄²	C₂²×D₅	1	2	yes	—
559	C₂×C₅	—	4	1	no	—
560	C₂×C₅	—	4	2	no	—
561	C₂×C₅	C₂²×#41	1	1	yes	characteristic
562	C₂×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂×C₅	#585	1	1	yes	characteristic
564	D₅	—	2	2	no	—
565	D₅	—	2	2	no	—
566	D₅	—	4	2	no	—
567	D₅	—	4	2	no	—
568	C₂³	—	5	1	no	—
569	C₂³	—	5	1	no	—
570	C₂³	—	5	2	no	—
571	C₂³	—	5	2	no	—
572	C₂³	—	10	2	no	—
573	C₂³	—	10	2	no	—
574	C₂³	—	10	4	no	—
575	C₂³	—	20	1	no	—
576	C₂³	—	20	2	no	—
577	C₂³	—	20	2	no	—
578	C₂³	C₂³×D₅	1	1	yes	characteristic
579	C₂³	C₂³×D₅	1	2	yes	—
580	Q₈	—	2	2	no	—
581	Q₈	—	4	2	no	—
582	Q₈	—	20	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	10	4	no	—
586	D₄	—	10	4	no	—
587	D₄	—	10	4	no	—
588	D₄	—	10	4	no	—
589	D₄	—	10	4	no	—
590	D₄	—	10	2	no	—
591	D₄	—	10	2	no	—
592	D₄	—	20	2	no	—
593	D₄	—	20	2	no	—
594	D₄	—	20	2	no	—
595	D₄	—	20	2	no	—
596	D₄	—	20	2	no	—
597	D₄	—	20	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	5	1	no	—
601	C₂×C₄	—	5	4	no	—
602	C₂×C₄	—	5	1	no	—
603	C₂×C₄	—	5	1	no	—
604	C₂×C₄	—	5	1	no	—
605	C₂×C₄	—	5	1	no	—
606	C₂×C₄	—	5	1	no	—
607	C₂×C₄	—	5	2	no	—
608	C₂×C₄	—	5	2	no	—
609	C₂×C₄	—	10	2	no	—
610	C₂×C₄	—	10	4	no	—
611	C₂×C₄	—	10	2	no	—
612	C₂×C₄	—	10	2	no	—
613	C₂×C₄	—	10	2	no	—
614	C₂×C₄	—	10	2	no	—
615	C₂×C₄	—	10	2	no	—
616	C₂×C₄	—	20	2	no	—
617	C₂×C₄	—	20	2	no	—
618	C₂×C₄	—	20	2	no	—
619	C₂×C₄	—	20	2	no	—
620	C₂×C₄	—	20	2	no	—
621	C₂×C₄	—	20	1	no	—
622	C₂×C₄	—	20	1	no	—
623	C₂×C₄	—	20	2	no	—
624	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₅	1	2	yes	—
626	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₅	1	2	yes	—
630	C₂×C₄	C₂³×D₅	1	2	yes	—
631	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₅	1	1	yes	characteristic
633	C₅	#3494	1	1	yes	characteristic, complemented, Sylow
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	5	2	no	—
641	C₂²	—	5	2	no	—
642	C₂²	—	10	1	no	—
643	C₂²	—	10	1	no	—
644	C₂²	—	10	1	no	—
645	C₂²	—	10	1	no	—
646	C₂²	—	10	2	no	—
647	C₂²	—	10	2	no	—
648	C₂²	—	10	2	no	—
649	C₂²	—	10	2	no	—
650	C₂²	—	10	2	no	—
651	C₂²	—	10	2	no	—
652	C₂²	—	20	4	no	—
653	C₂²	—	40	4	no	—
654	C₂²	C₂⁴×D₅	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	5	2	no	—
664	C₄	—	10	1	no	—
665	C₄	—	10	1	no	—
666	C₄	—	10	1	no	—
667	C₄	—	10	2	no	—
668	C₄	—	10	1	no	—
669	C₄	—	10	2	no	—
670	C₄	—	10	1	no	—
671	C₄	D₅×#41	1	2	yes	—
672	C₂	—	4	1	no	—
673	C₂	—	4	2	no	—
674	C₂	—	10	2	no	—
675	C₂	—	10	2	no	—
676	C₂	—	20	2	no	—
677	C₂	—	20	2	no	—
678	C₂	C₂×D₅×#41	1	1	yes	characteristic
679	C₂	D₅×H(5,𝔽₂)	1	1	yes	characteristic
680	C₂	#66287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅
commutator, socle, cosocle	C₂²×C₅	C₂⁵
Fitting	C₅×#542	C₂
hypercenter	#542	D₅
hypocenter	C₅	#3494
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₅×#542	C₂	semidirect
2. #66063	C₂	semidirect
3. #66059	C₂	semidirect
4. #66043	C₂	semidirect
5. #66039	C₂	semidirect
6. #66014	C₂	semidirect
7. #66010	C₂	semidirect
8. #66008	C₂	semidirect
9. #66004	C₂	semidirect
10. #65995	C₂	semidirect
11. #65988	C₂	semidirect
12. #65977	C₂	semidirect
13. #65971	C₂	semidirect
14. #65965	C₂	semidirect
15. #65961	C₂	semidirect
16. #65953	C₂	semidirect
17. D₅×#121	C₂	semidirect
18. #65914	C₂	semidirect
19. #65908	C₂	semidirect
20. #65882	C₂	semidirect
21. #65879	C₂	semidirect
22. #65869	C₂	semidirect
23. D₅×#117	C₂	semidirect
25. C₂×#713	C₂²	semidirect
28. C₂×#709	C₂²	semidirect
30. C₅×C₄⋊Q₈	C₂²	semidirect
31. C₅×#126	C₂²	semidirect
32. C₅×#124	C₂²	semidirect
33. C₅×#124	C₂²	semidirect
34. C₅×#123	C₂²	semidirect
35. C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₅×C₂²⋊Q₈	C₂²	semidirect
38. C₄×C₅×Q₈	C₂²	semidirect
39. C₄×C₅×D₄	C₂²	semidirect
40. C₅×#117	C₂²	semidirect
41. #4093	C₂²	semidirect
42. #4093	C₂²	semidirect
44. #4092	C₂²	semidirect
45. Q₈×Dic₅	C₂²	semidirect
46. #4090	C₂²	semidirect
47. #4086	C₂²	semidirect
49. #4085	C₂²	semidirect
51. #4084	C₂²	semidirect
52. D₄×Dic₅	C₂²	semidirect
54. #4076	C₂²	semidirect
55. C₄×C₂²⋊D₅	C₂²	semidirect
56. C₄×C₂²⋊D₅	C₂²	semidirect
58. #4072	C₂²	semidirect
59. #4044	C₂²	semidirect
60. #4044	C₂²	semidirect
61. #4043	C₂²	semidirect
64. #4041	C₂²	semidirect
65. #4041	C₂²	semidirect
67. #4040	C₂²	semidirect
68. #4040	C₂²	semidirect
69. #4040	C₂²	semidirect
71. #4039	C₂²	semidirect
72. #4039	C₂²	semidirect
73. #4039	C₂²	semidirect
74. #4039	C₂²	semidirect
79. D₅×C₄⋊C₄	C₂²	semidirect
80. D₅×C₄⋊C₄	C₂²	semidirect
81. D₅×C₄⋊C₄	C₂²	semidirect
82. #4036	C₂²	semidirect
83. #4035	C₂²	semidirect
84. #4034	C₂²	semidirect
85. #4032	C₂²	semidirect
86. #4031	C₂²	semidirect
87. #4031	C₂²	semidirect
89. #4030	C₂²	semidirect
90. #4030	C₂²	semidirect
91. #4030	C₂²	semidirect
92. #4030	C₂²	semidirect
93. #4030	C₂²	semidirect
94. #4029	C₂²	semidirect
95. #4029	C₂²	semidirect
96. #4029	C₂²	semidirect
100. #4027	C₂²	semidirect
101. #4027	C₂²	semidirect
102. #4027	C₂²	semidirect
107. #4025	C₂²	semidirect
108. #4023	C₂²	semidirect
109. #4023	C₂²	semidirect
110. #4023	C₂²	semidirect
111. #4020	C₂²	semidirect
113. C₄×D₂₀	C₂²	semidirect
114. C₄×D₂₀	C₂²	semidirect
115. C₄×D₂₀	C₂²	semidirect
118. #4018	C₂²	semidirect
119. #4018	C₂²	semidirect
120. C₄²×D₅	C₂²	semidirect
121. C₄²×D₅	C₂²	semidirect
122. #4016	C₂²	semidirect
239. #542	D₅	semidirect
315. C₄×D₅	#41	semidirect
325. C₄⋊Q₈	C₂×D₅	semidirect
331. #126	C₂×D₅	semidirect
339. #124	C₂×D₅	semidirect
340. #124	C₂×D₅	semidirect
349. #123	C₂×D₅	semidirect
354. C₂²⋊Q₈	C₂×D₅	semidirect
355. C₂²⋊Q₈	C₂×D₅	semidirect
376. C₄×Q₈	C₂×D₅	semidirect
392. C₄×D₄	C₂×D₅	semidirect
404. #117	C₂×D₅	semidirect
633. C₅	#3494	semidirect

Maximal subgroups

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

subgroup	index
C₅×#542	2
#66063	2
#66059	2
#66043	2
#66039	2
#66014	2
#66010	2
#66008	2
#66004	2
#65995	2
#65988	2
#65977	2
#65971	2
#65965	2
#65961	2
#65953	2
D₅×#121	2
#65914	2
#65908	2
#65882	2
#65879	2
#65869	2
D₅×#117	2
#3494	5