Subgroups — C₅×#3270 #10616865

Order 640.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#548	C₂	1	1	yes	maximal, characteristic
5	C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#448	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₅×#137	—	2	4	no	—
21	C₂×C₅×Q₁₆	—	2	4	no	—
22	C₂×C₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₅×Q₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₅×Q₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₅×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₅×Q₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₅×Q₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₅×SD₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₅×SD₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₅×SD₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₅×M₁₆	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×C₄⋊Q₈	—	2	1	no	—
34	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₅×#124	—	2	1	no	—
36	C₅×#124	C₂²	1	1	yes	characteristic
37	C₅×C₂²⋊Q₈	—	2	1	no	—
38	C₅×C₂²⋊Q₈	—	2	1	no	—
39	C₅×C₂²⋊Q₈	—	2	1	no	—
40	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₅×#121	—	2	1	no	—
44	C₅×#121	C₂²	1	1	yes	characteristic
45	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
46	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
47	C₄×C₅×D₄	—	2	1	no	—
48	C₄×C₅×D₄	—	2	1	no	—
49	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
50	C₅×#106	C₂²	1	1	yes	characteristic
51	C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×#103	C₂²	1	1	yes	characteristic
53	C₅×#103	C₂²	1	1	yes	characteristic
54	C₅×#103	C₂²	1	1	yes	characteristic
55	C₅×#103	C₂²	1	1	yes	characteristic
56	C₅×#103	C₂²	1	1	yes	characteristic
57	C₅×#102	C₂²	1	1	yes	characteristic
58	C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₅×#97	C₂²	1	1	yes	characteristic
61	#3270	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₅×#41	—	2	2	no	—
63	C₅×#41	—	4	1	no	—
64	C₂×C₅×Q₈	—	2	1	no	—
65	C₂×C₅×Q₈	—	2	1	no	—
66	C₂×C₅×Q₈	—	2	1	no	—
67	C₂×C₅×Q₈	—	2	2	no	—
68	C₂×C₅×Q₈	—	2	2	no	—
69	C₂×C₅×Q₈	—	2	2	no	—
70	C₂×C₅×Q₈	—	4	1	no	—
71	C₂×C₅×Q₈	—	4	1	no	—
72	C₂×C₅×Q₈	—	4	1	no	—
73	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
74	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
75	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
76	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₅×D₄	—	2	1	no	—
79	C₂×C₅×D₄	—	2	1	no	—
80	C₂×C₅×D₄	D₄	1	1	yes	characteristic
81	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₅	—	2	1	no	—
83	C₂²×C₄×C₅	—	2	1	no	—
84	C₂²×C₄×C₅	—	2	1	no	—
85	C₂²×C₄×C₅	—	2	1	no	—
86	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₅×Q₁₆	—	2	2	no	—
89	C₅×Q₁₆	—	2	2	no	—
90	C₅×Q₁₆	—	2	2	no	—
91	C₅×Q₁₆	—	2	2	no	—
92	C₅×Q₁₆	—	4	1	no	—
93	C₅×Q₁₆	D₄	1	4	yes	complemented
94	C₅×SD₁₆	—	2	2	no	—
95	C₅×SD₁₆	—	2	2	no	—
96	C₅×SD₁₆	—	4	1	no	—
97	C₅×M₁₆	—	2	2	no	—
98	C₂×C₅×C₈	—	2	2	no	—
99	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₅×C₄⋊C₄	—	2	1	no	—
104	C₅×C₄⋊C₄	—	2	1	no	—
105	C₅×C₄⋊C₄	—	2	1	no	—
106	C₅×C₄⋊C₄	—	2	1	no	—
107	C₅×C₄⋊C₄	—	2	1	no	—
108	C₅×C₄⋊C₄	—	2	1	no	—
109	C₅×C₄⋊C₄	—	2	1	no	—
110	C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
111	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₅×C₂²⋊C₄	—	2	1	no	—
114	C₅×C₂²⋊C₄	—	2	1	no	—
115	C₅×C₂²⋊C₄	—	2	1	no	—
116	C₅×C₂²⋊C₄	—	2	1	no	—
117	C₅×C₂²⋊C₄	—	2	1	no	—
118	C₅×C₂²⋊C₄	—	2	1	no	—
119	C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
120	C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
121	C₄²×C₅	—	2	1	no	—
122	C₄²×C₅	—	2	1	no	—
123	C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₂×#137	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂²×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
126	D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
127	#548	C₂×C₅	1	1	yes	characteristic
128	#497	C₂×C₅	1	1	yes	characteristic, complemented
129	#470	C₂×C₅	1	1	yes	characteristic, complemented
130	#465	C₂×C₅	1	1	yes	characteristic, complemented
131	#464	C₂×C₅	1	1	yes	characteristic, complemented
132	#462	C₂×C₅	1	1	yes	characteristic, complemented
133	#452	C₂×C₅	1	1	yes	characteristic, complemented
134	#451	C₂×C₅	1	1	yes	characteristic, complemented
135	#451	C₂×C₅	1	1	yes	characteristic, complemented
136	#448	C₂×C₅	1	1	yes	characteristic, complemented
137	#441	C₂×C₅	1	1	yes	characteristic, complemented
138	#435	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂³×C₅	—	2	1	no	—
140	C₂³×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂³×C₅	C₂×D₄	1	1	yes	characteristic
142	C₅×Q₈	—	2	1	no	—
143	C₅×Q₈	—	2	1	no	—
144	C₅×Q₈	—	2	1	no	—
145	C₅×Q₈	—	2	1	no	—
146	C₅×Q₈	—	2	1	no	—
147	C₅×Q₈	—	2	1	no	—
148	C₅×Q₈	—	2	1	no	—
149	C₅×Q₈	—	2	1	no	—
150	C₅×Q₈	—	4	2	no	—
151	C₅×Q₈	—	4	2	no	—
152	C₅×Q₈	—	4	2	no	—
153	C₅×Q₈	C₂×D₄	1	2	yes	—
154	C₅×Q₈	C₂×D₄	1	2	yes	—
155	C₅×D₄	—	2	2	no	—
156	C₅×D₄	—	2	1	no	—
157	C₅×D₄	—	2	1	no	—
158	C₅×D₄	—	4	2	no	—
159	C₅×D₄	—	4	2	no	—
160	C₂×C₄×C₅	—	2	1	no	—
161	C₂×C₄×C₅	—	2	1	no	—
162	C₂×C₄×C₅	—	2	1	no	—
163	C₂×C₄×C₅	—	2	1	no	—
164	C₂×C₄×C₅	—	2	1	no	—
165	C₂×C₄×C₅	—	2	1	no	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	1	no	—
168	C₂×C₄×C₅	—	2	1	no	—
169	C₂×C₄×C₅	—	2	1	no	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	4	2	no	—
172	C₂×C₄×C₅	—	4	2	no	—
173	C₂×C₄×C₅	—	4	2	no	—
174	C₂×C₄×C₅	—	4	2	no	—
175	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
180	C₅×C₈	—	2	1	no	—
181	C₅×C₈	—	2	1	no	—
182	C₅×C₈	—	2	1	no	—
183	C₅×C₈	C₂×D₄	1	2	yes	—
184	C₂×#41	C₂²×C₅	1	1	yes	characteristic
185	C₂²×Q₈	C₂²×C₅	1	1	yes	characteristic
186	C₂²×Q₈	C₂²×C₅	1	1	yes	characteristic
187	C₂²×Q₈	C₂²×C₅	1	1	yes	characteristic
188	#137	—	2	4	no	—
189	C₂×Q₁₆	—	2	4	no	—
190	C₂×Q₁₆	C₂²×C₅	1	1	yes	characteristic
191	C₂×Q₁₆	C₂²×C₅	1	1	yes	characteristic
192	C₂×Q₁₆	C₂²×C₅	1	1	yes	characteristic
193	C₂×Q₁₆	C₂²×C₅	1	1	yes	characteristic
194	C₂×Q₁₆	C₂²×C₅	1	1	yes	characteristic
195	C₂×Q₁₆	C₂²×C₅	1	1	yes	characteristic
196	C₂×SD₁₆	C₂²×C₅	1	1	yes	characteristic
197	C₂×SD₁₆	C₂²×C₅	1	1	yes	characteristic
198	C₂×SD₁₆	C₂²×C₅	1	1	yes	characteristic
199	C₂×M₁₆	C₂²×C₅	1	1	yes	characteristic
200	C₂²×C₈	C₂²×C₅	1	1	yes	characteristic
201	C₄⋊Q₈	—	2	1	no	—
202	C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
203	#124	—	2	1	no	—
204	#124	C₂²×C₅	1	1	yes	characteristic
205	C₂²⋊Q₈	—	2	1	no	—
206	C₂²⋊Q₈	—	2	1	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
209	C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
210	C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
211	#121	—	2	1	no	—
212	#121	C₂²×C₅	1	1	yes	characteristic
213	C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
214	C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
215	C₄×D₄	—	2	1	no	—
216	C₄×D₄	—	2	1	no	—
217	C₄×D₄	C₂²×C₅	1	1	yes	characteristic
218	#106	C₂²×C₅	1	1	yes	characteristic
219	C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
220	#103	C₂²×C₅	1	1	yes	characteristic
221	#103	C₂²×C₅	1	1	yes	characteristic
222	#103	C₂²×C₅	1	1	yes	characteristic
223	#103	C₂²×C₅	1	1	yes	characteristic
224	#103	C₂²×C₅	1	1	yes	characteristic
225	#102	C₂²×C₅	1	1	yes	characteristic
226	C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
227	C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
228	#97	C₂²×C₅	1	1	yes	characteristic
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	2	1	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	2	1	no	—
234	C₂²×C₅	—	4	1	no	—
235	C₂²×C₅	—	4	1	no	—
236	C₂²×C₅	—	4	1	no	—
237	C₂²×C₅	#137	1	2	yes	complemented
238	C₂²×C₅	C₂²×D₄	1	1	yes	characteristic
239	C₄×C₅	—	2	1	no	—
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	2	no	—
242	C₄×C₅	—	2	2	no	—
243	C₄×C₅	—	2	1	no	—
244	C₄×C₅	—	2	1	no	—
245	C₄×C₅	—	4	1	no	—
246	C₄×C₅	—	4	1	no	—
247	C₄×C₅	—	4	1	no	—
248	C₄×C₅	—	4	1	no	—
249	C₄×C₅	—	4	1	no	—
250	C₄×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
252	#41	—	2	2	no	—
253	#41	—	4	1	no	—
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	—	2	1	no	—
256	C₂×Q₈	—	2	1	no	—
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	4	1	no	—
261	C₂×Q₈	—	4	1	no	—
262	C₂×Q₈	—	4	1	no	—
263	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
264	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
265	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
266	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
267	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	C₅×D₄	1	1	yes	characteristic
271	C₂×D₄	C₂³×C₅	1	1	yes	characteristic
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
278	Q₁₆	—	2	2	no	—
279	Q₁₆	—	2	2	no	—
280	Q₁₆	—	2	2	no	—
281	Q₁₆	—	2	2	no	—
282	Q₁₆	—	4	1	no	—
283	Q₁₆	C₅×D₄	1	4	yes	complemented
284	SD₁₆	—	2	2	no	—
285	SD₁₆	—	2	2	no	—
286	SD₁₆	—	4	1	no	—
287	M₁₆	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	C₂³×C₅	1	1	yes	characteristic
290	C₂×C₈	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₈	C₂³×C₅	1	1	yes	characteristic
292	C₂×C₈	C₂³×C₅	1	1	yes	characteristic
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
301	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
302	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
303	C₂²⋊C₄	—	2	1	no	—
304	C₂²⋊C₄	—	2	1	no	—
305	C₂²⋊C₄	—	2	1	no	—
306	C₂²⋊C₄	—	2	1	no	—
307	C₂²⋊C₄	—	2	1	no	—
308	C₂²⋊C₄	—	2	1	no	—
309	C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
310	C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	C₂³×C₅	1	1	yes	characteristic
314	C₂×C₅	—	2	2	no	—
315	C₂×C₅	—	4	1	no	—
316	C₂×C₅	—	8	1	no	—
317	C₂×C₅	D₄²	1	1	yes	characteristic
318	C₂×C₅	C₂×#137	1	1	yes	characteristic
319	C₂×C₅	#578	1	1	yes	characteristic
320	C₂³	—	2	1	no	—
321	C₂³	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂³	C₂×C₅×D₄	1	1	yes	characteristic
323	Q₈	—	2	1	no	—
324	Q₈	—	2	1	no	—
325	Q₈	—	2	1	no	—
326	Q₈	—	2	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	2	1	no	—
330	Q₈	—	2	1	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	4	2	no	—
333	Q₈	—	4	2	no	—
334	Q₈	C₂×C₅×D₄	1	2	yes	—
335	Q₈	C₂×C₅×D₄	1	2	yes	—
336	D₄	—	2	2	no	—
337	D₄	—	2	1	no	—
338	D₄	—	2	1	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂×C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂×C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	C₂×C₅×D₄	1	2	yes	—
365	C₅	#3270	1	1	yes	characteristic, direct product factor, Sylow
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	C₅×#137	1	2	yes	complemented
375	C₂²	C₂²×C₅×D₄	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	1	no	—
387	C₄	C₂²×C₅×D₄	1	1	yes	characteristic
388	C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	4	1	no	—
391	C₂	—	8	1	no	—
392	C₂	C₅×D₄²	1	1	yes	characteristic
393	C₂	C₂×C₅×#137	1	1	yes	characteristic
394	C₂	C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₅
prime radical	C₅×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#137	C₂	semidirect
2. C₂²×C₅×Q₁₆	C₂	semidirect
3. C₅×D₄×Q₈	C₂	semidirect
5. C₅×#497	C₂	semidirect
6. C₅×#470	C₂	semidirect
7. C₅×#465	C₂	semidirect
8. C₅×#464	C₂	semidirect
9. C₅×#462	C₂	semidirect
10. C₅×#452	C₂	semidirect
11. C₅×#451	C₂	semidirect
12. C₅×#451	C₂	semidirect
13. C₅×#448	C₂	semidirect
14. C₅×#441	C₂	semidirect
15. C₅×#435	C₂	semidirect
61. #3270	C₅	direct (N × H)
93. C₅×Q₁₆	D₄	semidirect
124. C₂×#137	C₂×C₅	semidirect
125. C₂²×Q₁₆	C₂×C₅	semidirect
126. D₄×Q₈	C₂×C₅	semidirect
128. #497	C₂×C₅	semidirect
129. #470	C₂×C₅	semidirect
130. #465	C₂×C₅	semidirect
131. #464	C₂×C₅	semidirect
132. #462	C₂×C₅	semidirect
133. #452	C₂×C₅	semidirect
134. #451	C₂×C₅	semidirect
135. #451	C₂×C₅	semidirect
136. #448	C₂×C₅	semidirect
137. #441	C₂×C₅	semidirect
138. #435	C₂×C₅	semidirect
237. C₂²×C₅	#137	semidirect
283. Q₁₆	C₅×D₄	semidirect
365. C₅	#3270	direct (N × H)
374. C₂²	C₅×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#137	2
C₂²×C₅×Q₁₆	2
C₅×D₄×Q₈	2
C₅×#548	2
C₅×#497	2
C₅×#470	2
C₅×#465	2
C₅×#464	2
C₅×#462	2
C₅×#452	2
C₅×#451	2
C₅×#448	2
C₅×#441	2
C₅×#435	2
#3270	5

Subgroups — C5×#3270 #10616865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#3270 #10616865