Subgroups — C₅×#33618 #11956338

Order 1280.

656 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3407	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3067	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#472	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2223	C₂	1	4	yes	maximal, complemented
6	C₅×#2221	C₂	1	4	yes	maximal, complemented
7	C₅×#2161	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2148	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#361	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#575	—	2	1	no	—
11	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#131	C₂²	1	1	yes	characteristic
15	C₅×#509	—	2	2	no	—
16	C₅×#509	—	2	2	no	—
17	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₅×D₁₆	C₂²	1	2	yes	complemented
19	C₅×#504	—	2	2	no	—
20	C₅×#504	C₂²	1	4	yes	complemented
21	C₂×C₅×M₃₂	—	2	2	no	—
22	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
24	C₅×#473	C₂²	1	2	yes	complemented
25	C₅×#472	—	2	2	no	—
26	C₅×#472	C₂²	1	4	yes	—
27	C₅×#472	C₂²	1	2	yes	complemented
28	C₅×#471	—	2	2	no	—
29	C₂×C₅×#108	C₂²	1	1	yes	characteristic
30	C₂×C₅×#108	C₂²	1	1	yes	characteristic
31	C₅×#413	—	2	1	no	—
32	C₂×C₅×#100	—	2	1	no	—
33	C₅×#368	C₂²	1	4	yes	complemented
34	C₅×#362	C₂²	1	2	yes	complemented
35	C₅×#361	C₂²	1	4	yes	complemented
36	C₅×#361	C₂²	1	2	yes	complemented
37	#33618	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×C₅×#41	—	2	1	no	—
39	C₂×C₅×#41	D₄	1	1	yes	characteristic
40	C₂²×C₅×D₄	—	2	1	no	—
41	C₅×#137	—	2	2	no	—
42	C₅×#137	—	4	1	no	—
43	C₅×AGL(1,ℤ/8)	—	2	2	no	—
44	C₅×AGL(1,ℤ/8)	—	2	4	no	—
45	C₅×AGL(1,ℤ/8)	—	4	2	no	—
46	C₅×AGL(1,ℤ/8)	—	4	1	no	—
47	C₅×#135	—	2	1	no	—
48	C₅×#135	—	2	1	no	—
49	C₅×#135	—	2	1	no	—
50	C₅×#135	—	2	1	no	—
51	C₅×#135	—	4	2	no	—
52	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₅×SD₁₆	—	2	1	no	—
54	C₂×C₅×SD₁₆	—	4	1	no	—
55	C₂×C₅×D₈	—	2	1	no	—
56	C₂×C₅×D₈	—	2	1	no	—
57	C₂×C₅×D₈	—	2	1	no	—
58	C₂×C₅×D₈	—	2	1	no	—
59	C₂×C₅×D₈	—	2	1	no	—
60	C₂×C₅×D₈	—	4	1	no	—
61	C₂×C₅×D₈	C₂³	1	2	yes	—
62	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
63	C₅×#131	—	2	1	no	—
64	C₅×#131	—	2	1	no	—
65	C₅×#131	D₄	1	2	yes	—
66	C₅×#131	C₂³	1	2	yes	—
67	C₂×C₅×M₁₆	—	2	1	no	—
68	C₂×C₅×M₁₆	—	2	1	no	—
69	C₂×C₅×M₁₆	—	2	1	no	—
70	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
71	C₂²×C₅×C₈	—	2	1	no	—
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₅×SD₃₂	—	2	4	no	—
74	C₅×D₁₆	—	2	4	no	—
75	C₅×M₃₂	—	2	1	no	—
76	C₅×M₃₂	—	2	4	no	—
77	C₅×M₃₂	D₄	1	2	yes	—
78	C₅×M₃₂	D₄	1	2	yes	—
79	C₅×M₃₂	C₂³	1	2	yes	—
80	C₂×C₅×C₁₆	—	2	1	no	—
81	C₂×C₅×C₁₆	—	2	4	no	—
82	C₂×C₅×C₁₆	C₂³	1	2	yes	—
83	C₅×#108	—	2	1	no	—
84	C₅×#108	—	2	1	no	—
85	C₅×#108	C₂³	1	2	yes	—
86	C₅×#108	C₂³	1	2	yes	—
87	C₅×#101	—	2	2	no	—
88	C₅×#100	—	2	4	no	—
89	C₅×#100	—	2	2	no	—
90	C₂×#509	C₂×C₅	1	1	yes	characteristic, complemented
91	#3407	C₂×C₅	1	1	yes	characteristic, complemented
92	#3067	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×#472	C₂×C₅	1	1	yes	characteristic, complemented
94	#2223	C₂×C₅	1	4	yes	complemented
95	#2221	C₂×C₅	1	4	yes	complemented
96	#2161	C₂×C₅	1	1	yes	characteristic, complemented
97	#2148	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂×#361	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂⁴×C₅	—	4	1	no	—
100	C₅×#41	—	2	1	no	—
101	C₅×#41	—	2	1	no	—
102	C₅×#41	—	4	1	no	—
103	C₅×#41	—	4	1	no	—
104	C₅×#41	—	4	1	no	—
105	C₅×#41	—	4	1	no	—
106	C₅×#41	D₈	1	2	yes	—
107	C₅×#41	C₂×D₄	1	2	yes	—
108	C₂×C₅×Q₈	—	2	1	no	—
109	C₂×C₅×Q₈	D₈	1	1	yes	characteristic
110	C₂×C₅×D₄	—	2	1	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	—	4	1	no	—
114	C₂×C₅×D₄	—	4	1	no	—
115	C₂×C₅×D₄	—	4	1	no	—
116	C₂×C₅×D₄	—	4	1	no	—
117	C₂×C₅×D₄	—	4	1	no	—
118	C₂×C₅×D₄	—	4	1	no	—
119	C₂×C₅×D₄	D₈	1	1	yes	characteristic
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	4	1	no	—
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₅×Q₁₆	—	2	1	no	—
124	C₅×Q₁₆	—	2	1	no	—
125	C₅×Q₁₆	—	4	2	no	—
126	C₅×SD₁₆	—	4	4	no	—
127	C₅×SD₁₆	—	4	2	no	—
128	C₅×SD₁₆	—	4	2	no	—
129	C₅×SD₁₆	—	4	1	no	—
130	C₅×SD₁₆	—	4	1	no	—
131	C₅×D₈	—	2	2	no	—
132	C₅×D₈	—	2	1	no	—
133	C₅×D₈	—	2	2	no	—
134	C₅×D₈	—	2	1	no	—
135	C₅×D₈	—	4	4	no	—
136	C₅×D₈	—	4	2	no	—
137	C₅×D₈	—	4	1	no	—
138	C₅×D₈	—	4	1	no	—
139	C₅×M₁₆	—	2	1	no	—
140	C₅×M₁₆	—	2	2	no	—
141	C₅×M₁₆	—	2	2	no	—
142	C₅×M₁₆	—	2	2	no	—
143	C₅×M₁₆	—	2	2	no	—
144	C₅×M₁₆	—	4	1	no	—
145	C₅×M₁₆	—	4	1	no	—
146	C₅×M₁₆	C₂×D₄	1	2	yes	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	4	1	no	—
151	C₂×C₅×C₈	—	4	1	no	—
152	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	#41	1	1	yes	characteristic
156	C₂×C₅×C₈	#41	1	1	yes	characteristic
157	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
158	C₅×C₁₆	—	2	2	no	—
159	C₅×C₁₆	C₂×D₄	1	4	yes	—
160	#575	—	2	1	no	—
161	C₂×AGL(1,ℤ/8)	—	2	1	no	—
162	C₂×#135	C₂²×C₅	1	1	yes	characteristic
163	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×#131	C₂²×C₅	1	1	yes	characteristic
165	#509	—	2	2	no	—
166	#509	—	2	2	no	—
167	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
168	C₂×D₁₆	C₂²×C₅	1	2	yes	complemented
169	#504	—	2	2	no	—
170	#504	C₂²×C₅	1	4	yes	complemented
171	C₂×M₃₂	—	2	2	no	—
172	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
173	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
174	#473	C₂²×C₅	1	2	yes	complemented
175	#472	—	2	2	no	—
176	#472	C₂²×C₅	1	4	yes	—
177	#472	C₂²×C₅	1	2	yes	complemented
178	#471	—	2	2	no	—
179	C₂×#108	C₂²×C₅	1	1	yes	characteristic
180	C₂×#108	C₂²×C₅	1	1	yes	characteristic
181	#413	—	2	1	no	—
182	C₂×#100	—	2	1	no	—
183	#368	C₂²×C₅	1	4	yes	complemented
184	#362	C₂²×C₅	1	2	yes	complemented
185	#361	C₂²×C₅	1	4	yes	complemented
186	#361	C₂²×C₅	1	2	yes	complemented
187	C₂³×C₅	—	2	1	no	—
188	C₂³×C₅	—	4	1	no	—
189	C₂³×C₅	—	4	2	no	—
190	C₂³×C₅	—	8	1	no	—
191	C₂³×C₅	—	8	1	no	—
192	C₂³×C₅	—	16	2	no	—
193	C₂³×C₅	#135	1	1	yes	characteristic
194	C₅×Q₈	—	2	1	no	—
195	C₅×Q₈	—	4	1	no	—
196	C₅×Q₈	—	4	1	no	—
197	C₅×Q₈	C₂×D₈	1	2	yes	—
198	C₅×D₄	—	2	2	no	—
199	C₅×D₄	—	2	2	no	—
200	C₅×D₄	—	2	1	no	—
201	C₅×D₄	—	4	2	no	—
202	C₅×D₄	—	4	1	no	—
203	C₅×D₄	—	4	2	no	—
204	C₅×D₄	—	4	1	no	—
205	C₅×D₄	—	8	1	no	—
206	C₅×D₄	—	8	1	no	—
207	C₅×D₄	—	8	1	no	—
208	C₅×D₄	—	8	1	no	—
209	C₅×D₄	C₂×D₈	1	2	yes	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	8	1	no	—
215	C₂×C₄×C₅	—	8	1	no	—
216	C₂×C₄×C₅	#121	1	1	yes	characteristic
217	C₂×C₄×C₅	#121	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
220	C₂×C₄×C₅	#135	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
222	C₅×C₈	—	2	2	no	—
223	C₅×C₈	—	4	2	no	—
224	C₅×C₈	—	4	2	no	—
225	C₅×C₈	#121	1	1	yes	characteristic
226	C₅×C₈	#121	1	1	yes	characteristic
227	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
228	C₅×C₈	C₂×#41	1	1	yes	characteristic
229	C₂×#41	—	2	1	no	—
230	C₂×#41	C₅×D₄	1	1	yes	characteristic
231	C₂²×D₄	—	2	1	no	—
232	#137	—	2	2	no	—
233	#137	—	4	1	no	—
234	AGL(1,ℤ/8)	—	2	4	no	—
235	AGL(1,ℤ/8)	—	2	2	no	—
236	AGL(1,ℤ/8)	—	4	2	no	—
237	AGL(1,ℤ/8)	—	4	1	no	—
238	#135	—	2	1	no	—
239	#135	—	2	1	no	—
240	#135	—	2	1	no	—
241	#135	—	2	1	no	—
242	#135	—	4	2	no	—
243	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
244	C₂×SD₁₆	—	2	1	no	—
245	C₂×SD₁₆	—	4	1	no	—
246	C₂×D₈	—	2	1	no	—
247	C₂×D₈	—	2	1	no	—
248	C₂×D₈	—	2	1	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	—	4	1	no	—
252	C₂×D₈	C₂³×C₅	1	2	yes	—
253	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
254	#131	—	2	1	no	—
255	#131	—	2	1	no	—
256	#131	C₅×D₄	1	2	yes	—
257	#131	C₂³×C₅	1	2	yes	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
264	SD₃₂	—	2	4	no	—
265	D₁₆	—	2	4	no	—
266	M₃₂	—	2	1	no	—
267	M₃₂	—	2	4	no	—
268	M₃₂	C₅×D₄	1	2	yes	—
269	M₃₂	C₅×D₄	1	2	yes	—
270	M₃₂	C₂³×C₅	1	2	yes	—
271	C₂×C₁₆	—	2	1	no	—
272	C₂×C₁₆	—	2	4	no	—
273	C₂×C₁₆	C₂³×C₅	1	2	yes	—
274	#108	—	2	1	no	—
275	#108	—	2	1	no	—
276	#108	C₂³×C₅	1	2	yes	—
277	#108	C₂³×C₅	1	2	yes	—
278	#101	—	2	2	no	—
279	#100	—	2	4	no	—
280	#100	—	2	2	no	—
281	C₂²×C₅	—	2	2	no	—
282	C₂²×C₅	—	4	1	no	—
283	C₂²×C₅	—	8	1	no	—
284	C₂²×C₅	—	8	1	no	—
285	C₂²×C₅	—	8	2	no	—
286	C₂²×C₅	—	16	1	no	—
287	C₂²×C₅	—	16	2	no	—
288	C₂²×C₅	—	16	2	no	—
289	C₂²×C₅	—	16	2	no	—
290	C₂²×C₅	#466	1	1	yes	characteristic
291	C₂²×C₅	#466	1	1	yes	characteristic
292	C₂²×C₅	C₂×#135	1	1	yes	characteristic
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	8	1	no	—
295	C₄×C₅	#466	1	1	yes	characteristic
296	C₄×C₅	#466	1	1	yes	characteristic
297	C₄×C₅	C₂×#121	1	1	yes	characteristic
298	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
299	C₂⁴	—	4	1	no	—
300	#41	—	2	1	no	—
301	#41	—	2	1	no	—
302	#41	—	4	1	no	—
303	#41	—	4	1	no	—
304	#41	—	4	1	no	—
305	#41	—	4	1	no	—
306	#41	C₅×D₈	1	2	yes	—
307	#41	C₂×C₅×D₄	1	2	yes	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	C₅×D₈	1	1	yes	characteristic
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	C₅×D₈	1	1	yes	characteristic
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
323	Q₁₆	—	2	1	no	—
324	Q₁₆	—	2	1	no	—
325	Q₁₆	—	4	2	no	—
326	SD₁₆	—	4	4	no	—
327	SD₁₆	—	4	2	no	—
328	SD₁₆	—	4	2	no	—
329	SD₁₆	—	4	1	no	—
330	SD₁₆	—	4	1	no	—
331	D₈	—	2	1	no	—
332	D₈	—	2	2	no	—
333	D₈	—	2	2	no	—
334	D₈	—	2	1	no	—
335	D₈	—	4	4	no	—
336	D₈	—	4	2	no	—
337	D₈	—	4	1	no	—
338	D₈	—	4	1	no	—
339	M₁₆	—	2	1	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	—	4	1	no	—
346	M₁₆	C₂×C₅×D₄	1	2	yes	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂×C₈	C₅×#41	1	1	yes	characteristic
356	C₂×C₈	C₅×#41	1	1	yes	characteristic
357	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
358	C₁₆	—	2	2	no	—
359	C₁₆	C₂×C₅×D₄	1	4	yes	—
360	C₂×C₅	—	2	1	no	—
361	C₂×C₅	—	2	1	no	—
362	C₂×C₅	—	2	1	no	—
363	C₂×C₅	—	4	2	no	—
364	C₂×C₅	—	16	1	no	—
365	C₂×C₅	—	16	2	no	—
366	C₂×C₅	C₂×#466	1	1	yes	characteristic
367	C₂³	—	2	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	8	1	no	—
371	C₂³	—	8	1	no	—
372	C₂³	—	16	2	no	—
373	C₂³	C₅×#135	1	1	yes	characteristic
374	Q₈	—	2	1	no	—
375	Q₈	—	4	1	no	—
376	Q₈	—	4	1	no	—
377	Q₈	C₂×C₅×D₈	1	2	yes	—
378	D₄	—	2	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	2	1	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	1	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	1	no	—
385	D₄	—	8	1	no	—
386	D₄	—	8	1	no	—
387	D₄	—	8	1	no	—
388	D₄	—	8	1	no	—
389	D₄	C₂×C₅×D₈	1	2	yes	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	—	8	1	no	—
396	C₂×C₄	C₅×#121	1	1	yes	characteristic
397	C₂×C₄	C₅×#121	1	1	yes	characteristic
398	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
399	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
400	C₂×C₄	C₅×#135	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₈	C₅×#121	1	1	yes	characteristic
406	C₈	C₅×#121	1	1	yes	characteristic
407	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
408	C₈	C₂×C₅×#41	1	1	yes	characteristic
409	C₅	#33618	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	16	2	no	—
416	C₂²	—	16	1	no	—
417	C₂²	—	16	2	no	—
418	C₂²	—	16	2	no	—
419	C₂²	C₅×#466	1	1	yes	characteristic
420	C₂²	C₅×#466	1	1	yes	characteristic
421	C₂²	C₂×C₅×#135	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	8	1	no	—
424	C₄	C₅×#466	1	1	yes	characteristic
425	C₄	C₅×#466	1	1	yes	characteristic
426	C₄	C₂×C₅×#121	1	1	yes	characteristic
427	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
428	C₂	—	2	1	no	—
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	4	2	no	—
432	C₂	—	16	2	no	—
433	C₂	—	16	1	no	—
434	C₂	C₂×C₅×#466	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	C₂×#466
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#509	C₂	semidirect
2. C₅×#3407	C₂	semidirect
3. C₅×#3067	C₂	semidirect
4. C₂×C₅×#472	C₂	semidirect
5. C₅×#2223	C₂	semidirect
6. C₅×#2221	C₂	semidirect
7. C₅×#2161	C₂	semidirect
8. C₅×#2148	C₂	semidirect
9. C₂×C₅×#361	C₂	semidirect
17. C₂×C₅×SD₃₂	C₂²	semidirect
18. C₂×C₅×D₁₆	C₂²	semidirect
20. C₅×#504	C₂²	semidirect
24. C₅×#473	C₂²	semidirect
27. C₅×#472	C₂²	semidirect
33. C₅×#368	C₂²	semidirect
34. C₅×#362	C₂²	semidirect
35. C₅×#361	C₂²	semidirect
36. C₅×#361	C₂²	semidirect
37. #33618	C₅	direct (N × H)
90. C₂×#509	C₂×C₅	semidirect
91. #3407	C₂×C₅	semidirect
92. #3067	C₂×C₅	semidirect
93. C₂×#472	C₂×C₅	semidirect
94. #2223	C₂×C₅	semidirect
95. #2221	C₂×C₅	semidirect
96. #2161	C₂×C₅	semidirect
97. #2148	C₂×C₅	semidirect
98. C₂×#361	C₂×C₅	semidirect
167. C₂×SD₃₂	C₂²×C₅	semidirect
168. C₂×D₁₆	C₂²×C₅	semidirect
170. #504	C₂²×C₅	semidirect
174. #473	C₂²×C₅	semidirect
177. #472	C₂²×C₅	semidirect
183. #368	C₂²×C₅	semidirect
184. #362	C₂²×C₅	semidirect
185. #361	C₂²×C₅	semidirect
186. #361	C₂²×C₅	semidirect
409. C₅	#33618	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#509	2
C₅×#3407	2
C₅×#3067	2
C₂×C₅×#472	2
C₅×#2223	2
C₅×#2221	2
C₅×#2161	2
C₅×#2148	2
C₂×C₅×#361	2
#33618	5

Subgroups — C5×#33618 #11956338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33618 #11956338