Subgroups — C₅×#19198 #11941918

Order 1280.

726 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3206	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3205	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2931	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1701	C₂	1	4	yes	maximal, complemented
6	C₅×#1681	C₂	1	4	yes	maximal, complemented
7	C₅×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#131	—	2	1	no	—
11	C₅×#532	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#127	C₂²	1	1	yes	characteristic
14	C₅×#493	—	2	1	no	—
15	C₅×#492	—	2	1	no	—
16	C₅×#487	—	2	1	no	—
17	C₅×#486	—	2	1	no	—
18	C₅×#486	—	2	1	no	—
19	C₅×#486	—	2	1	no	—
20	C₅×#486	C₂²	1	2	yes	—
21	C₅×#486	C₂²	1	2	yes	—
22	C₅×#461	C₂²	1	4	yes	complemented
23	C₅×#459	C₂²	1	4	yes	—
24	C₅×#448	—	2	2	no	—
25	C₅×#447	—	2	2	no	—
26	C₅×#436	—	2	1	no	—
27	C₅×#436	C₂²	1	2	yes	complemented
28	C₅×C₈×D₄	—	2	1	no	—
29	C₅×C₈×D₄	C₂²	1	2	yes	complemented
30	C₅×#431	C₂²	1	1	yes	characteristic
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#423	C₂²	1	1	yes	characteristic
33	C₂×C₅×#102	—	2	1	no	—
34	C₂×C₅×#102	—	2	1	no	—
35	C₅×#408	—	2	1	no	—
36	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₅×#335	C₂²	1	2	yes	complemented
38	C₅×#334	C₂²	1	2	yes	complemented
39	C₅×#332	C₂²	1	4	yes	complemented
40	C₅×#331	C₂²	1	4	yes	—
41	#19198	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	—	2	1	no	—
43	C₂²×C₅×Q₈	—	2	1	no	—
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂²×C₅×D₄	—	2	1	no	—
47	C₂×C₅×SD₁₆	—	2	4	no	—
48	C₂×C₅×D₈	—	2	4	no	—
49	C₅×#131	—	4	4	no	—
50	C₂×C₅×M₁₆	—	2	1	no	—
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
55	C₅×C₄⋊Q₈	—	2	1	no	—
56	C₅×C₄⋊Q₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	—	2	1	no	—
58	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₅×#127	—	2	1	no	—
61	C₅×#127	—	2	1	no	—
62	C₅×#127	—	2	1	no	—
63	C₅×#127	D₄	1	1	yes	characteristic
64	C₅×#127	C₂³	1	2	yes	—
65	C₅×#124	—	2	1	no	—
66	C₅×#121	—	2	1	no	—
67	C₅×#121	D₄	1	2	yes	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	C₂³	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	—	2	1	no	—
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₅×C₄⋊C₈	—	2	1	no	—
74	C₅×C₄⋊C₈	C₂³	1	2	yes	—
75	C₅×C₄⋊C₈	C₂³	1	2	yes	—
76	C₅×C₄⋊C₈	C₂³	1	2	yes	—
77	C₅×#103	—	2	4	no	—
78	C₅×#102	—	2	2	no	—
79	C₅×#102	—	2	2	no	—
80	C₅×#102	—	2	2	no	—
81	C₅×#102	—	2	2	no	—
82	C₅×#102	—	2	4	no	—
83	C₅×C₂²⋊C₈	—	2	1	no	—
84	C₅×C₂²⋊C₈	—	2	1	no	—
85	C₅×C₂²⋊C₈	—	2	2	no	—
86	C₅×C₂²⋊C₈	—	2	2	no	—
87	C₄×C₅×C₈	—	2	1	no	—
88	C₄×C₅×C₈	—	2	1	no	—
89	C₄×C₅×C₈	D₄	1	1	yes	characteristic
90	C₄×C₅×C₈	D₄	1	1	yes	characteristic
91	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
93	#3206	C₂×C₅	1	1	yes	characteristic, complemented
94	#3205	C₂×C₅	1	1	yes	characteristic
95	C₂×#486	C₂×C₅	1	1	yes	characteristic, complemented
96	#2931	C₂×C₅	1	1	yes	characteristic, complemented
97	#1701	C₂×C₅	1	4	yes	complemented
98	#1681	C₂×C₅	1	4	yes	complemented
99	#1564	C₂×C₅	1	1	yes	characteristic, complemented
100	#1549	C₂×C₅	1	1	yes	characteristic, complemented
101	#1545	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂⁴×C₅	—	4	1	no	—
103	C₅×#41	—	4	2	no	—
104	C₅×#41	—	4	2	no	—
105	C₂×C₅×Q₈	—	2	1	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	4	1	no	—
108	C₂×C₅×Q₈	—	8	2	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	1	no	—
111	C₂×C₅×D₄	—	2	1	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	2	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	2	no	—
119	C₂×C₅×D₄	—	4	2	no	—
120	C₂×C₅×D₄	—	8	2	no	—
121	C₂×C₅×D₄	—	8	2	no	—
122	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	4	1	no	—
125	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	#41	1	1	yes	characteristic
128	C₅×SD₁₆	—	8	4	no	—
129	C₅×D₈	—	8	4	no	—
130	C₅×M₁₆	—	4	4	no	—
131	C₅×M₁₆	—	4	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	4	4	no	—
138	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	4	1	no	—
146	C₅×C₄⋊C₄	—	4	1	no	—
147	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
148	C₅×C₂²⋊C₄	—	2	2	no	—
149	C₅×C₂²⋊C₄	—	2	2	no	—
150	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₅	#41	1	1	yes	characteristic
153	C₄²×C₅	C₂⁴	1	1	yes	characteristic
154	C₂×#131	—	2	1	no	—
155	#532	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×#127	C₂²×C₅	1	1	yes	characteristic
158	#493	—	2	1	no	—
159	#492	—	2	1	no	—
160	#487	—	2	1	no	—
161	#486	—	2	1	no	—
162	#486	—	2	1	no	—
163	#486	—	2	1	no	—
164	#486	C₂²×C₅	1	2	yes	—
165	#486	C₂²×C₅	1	2	yes	—
166	#461	C₂²×C₅	1	4	yes	complemented
167	#459	C₂²×C₅	1	4	yes	—
168	#448	—	2	2	no	—
169	#447	—	2	2	no	—
170	#436	—	2	1	no	—
171	#436	C₂²×C₅	1	2	yes	complemented
172	C₈×D₄	—	2	1	no	—
173	C₈×D₄	C₂²×C₅	1	2	yes	complemented
174	#431	C₂²×C₅	1	1	yes	characteristic
175	#431	C₂²×C₅	1	1	yes	characteristic
176	#423	C₂²×C₅	1	1	yes	characteristic
177	C₂×#102	—	2	1	no	—
178	C₂×#102	—	2	1	no	—
179	#408	—	2	1	no	—
180	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
181	#335	C₂²×C₅	1	2	yes	complemented
182	#334	C₂²×C₅	1	2	yes	complemented
183	#332	C₂²×C₅	1	4	yes	complemented
184	#331	C₂²×C₅	1	4	yes	—
185	C₂³×C₅	—	2	2	no	—
186	C₂³×C₅	—	4	2	no	—
187	C₂³×C₅	—	8	2	no	—
188	C₂³×C₅	—	8	2	no	—
189	C₂³×C₅	—	8	2	no	—
190	C₂³×C₅	#121	1	1	yes	characteristic
191	C₅×Q₈	—	4	2	no	—
192	C₅×Q₈	—	4	4	no	—
193	C₅×Q₈	—	8	2	no	—
194	C₅×D₄	—	2	4	no	—
195	C₅×D₄	—	4	4	no	—
196	C₅×D₄	—	4	2	no	—
197	C₅×D₄	—	4	2	no	—
198	C₅×D₄	—	4	4	no	—
199	C₅×D₄	—	4	2	no	—
200	C₅×D₄	—	4	2	no	—
201	C₅×D₄	—	8	2	no	—
202	C₅×D₄	—	8	2	no	—
203	C₅×D₄	—	8	2	no	—
204	C₅×D₄	—	8	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	—	8	2	no	—
212	C₂×C₄×C₅	#121	1	1	yes	characteristic
213	C₂×C₄×C₅	#121	1	1	yes	characteristic
214	C₂×C₄×C₅	#121	1	1	yes	characteristic
215	C₂×C₄×C₅	#135	1	2	yes	—
216	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
217	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
220	C₅×C₈	—	2	1	no	—
221	C₅×C₈	—	2	1	no	—
222	C₅×C₈	—	2	1	no	—
223	C₅×C₈	—	2	1	no	—
224	C₅×C₈	—	4	2	no	—
225	C₅×C₈	—	4	2	no	—
226	C₅×C₈	—	4	2	no	—
227	C₂×#41	—	2	1	no	—
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×D₄	—	2	1	no	—
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	—	2	1	no	—
232	C₂×SD₁₆	—	2	4	no	—
233	C₂×D₈	—	2	4	no	—
234	#131	—	4	4	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
239	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
244	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
245	#127	—	2	1	no	—
246	#127	—	2	1	no	—
247	#127	—	2	1	no	—
248	#127	C₅×D₄	1	1	yes	characteristic
249	#127	C₂³×C₅	1	2	yes	—
250	#124	—	2	1	no	—
251	#121	—	2	1	no	—
252	#121	C₅×D₄	1	2	yes	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	C₂³×C₅	1	2	yes	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	C₂³×C₅	1	2	yes	—
260	C₄⋊C₈	C₂³×C₅	1	2	yes	—
261	C₄⋊C₈	C₂³×C₅	1	2	yes	—
262	#103	—	2	4	no	—
263	#102	—	2	2	no	—
264	#102	—	2	2	no	—
265	#102	—	2	2	no	—
266	#102	—	2	2	no	—
267	#102	—	2	4	no	—
268	C₂²⋊C₈	—	2	1	no	—
269	C₂²⋊C₈	—	2	1	no	—
270	C₂²⋊C₈	—	2	2	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	2	1	no	—
274	C₄×C₈	C₅×D₄	1	1	yes	characteristic
275	C₄×C₈	C₅×D₄	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
278	C₂²×C₅	—	2	1	no	—
279	C₂²×C₅	—	2	1	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	—	4	2	no	—
283	C₂²×C₅	—	8	2	no	—
284	C₂²×C₅	—	8	2	no	—
285	C₂²×C₅	—	8	2	no	—
286	C₂²×C₅	—	16	4	no	—
287	C₂²×C₅	#463	1	2	yes	—
288	C₂²×C₅	C₂×#121	1	1	yes	characteristic
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	4	2	no	—
292	C₄×C₅	—	8	2	no	—
293	C₄×C₅	#463	1	2	yes	—
294	C₄×C₅	#471	1	2	yes	—
295	C₄×C₅	C₂×#135	1	1	yes	characteristic
296	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₄×C₅	#576	1	2	yes	—
298	C₂⁴	—	4	1	no	—
299	#41	—	4	2	no	—
300	#41	—	4	2	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	8	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	8	2	no	—
317	C₂×D₄	—	8	2	no	—
318	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂²×C₄	C₅×#41	1	1	yes	characteristic
324	SD₁₆	—	8	4	no	—
325	D₈	—	8	4	no	—
326	M₁₆	—	4	4	no	—
327	M₁₆	—	4	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	4	no	—
334	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
336	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
337	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
347	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
348	C₄²	C₅×#41	1	1	yes	characteristic
349	C₄²	C₂⁴×C₅	1	1	yes	characteristic
350	C₂×C₅	—	2	2	no	—
351	C₂×C₅	—	8	2	no	—
352	C₂×C₅	—	16	2	no	—
353	C₂×C₅	C₂×#463	1	1	yes	characteristic
354	C₂×C₅	#3058	1	1	yes	characteristic
355	C₂×C₅	C₂×#471	1	1	yes	characteristic
356	C₂³	—	2	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	C₅×#121	1	1	yes	characteristic
362	Q₈	—	4	2	no	—
363	Q₈	—	4	4	no	—
364	Q₈	—	8	2	no	—
365	D₄	—	2	4	no	—
366	D₄	—	4	4	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	4	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	C₅×#121	1	1	yes	characteristic
384	C₂×C₄	C₅×#121	1	1	yes	characteristic
385	C₂×C₄	C₅×#121	1	1	yes	characteristic
386	C₂×C₄	C₅×#135	1	2	yes	—
387	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
388	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
389	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
390	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
391	C₈	—	2	1	no	—
392	C₈	—	2	1	no	—
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₅	#19198	1	1	yes	characteristic, direct product factor, Sylow
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	16	4	no	—
408	C₂²	C₅×#463	1	2	yes	—
409	C₂²	C₂×C₅×#121	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₅×#463	1	2	yes	—
415	C₄	C₅×#471	1	2	yes	—
416	C₄	C₂×C₅×#135	1	1	yes	characteristic
417	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
418	C₄	C₅×#576	1	2	yes	—
419	C₂	—	2	2	no	—
420	C₂	—	8	2	no	—
421	C₂	—	16	2	no	—
422	C₂	C₂×C₅×#463	1	1	yes	characteristic
423	C₂	C₅×#3058	1	1	yes	characteristic
424	C₂	C₂×C₅×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3205	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3206	C₂	semidirect
3. C₂×C₅×#486	C₂	semidirect
4. C₅×#2931	C₂	semidirect
5. C₅×#1701	C₂	semidirect
6. C₅×#1681	C₂	semidirect
7. C₅×#1564	C₂	semidirect
8. C₅×#1549	C₂	semidirect
9. C₅×#1545	C₂	semidirect
22. C₅×#461	C₂²	semidirect
27. C₅×#436	C₂²	semidirect
29. C₅×C₈×D₄	C₂²	semidirect
37. C₅×#335	C₂²	semidirect
38. C₅×#334	C₂²	semidirect
39. C₅×#332	C₂²	semidirect
41. #19198	C₅	direct (N × H)
93. #3206	C₂×C₅	semidirect
95. C₂×#486	C₂×C₅	semidirect
96. #2931	C₂×C₅	semidirect
97. #1701	C₂×C₅	semidirect
98. #1681	C₂×C₅	semidirect
99. #1564	C₂×C₅	semidirect
100. #1549	C₂×C₅	semidirect
101. #1545	C₂×C₅	semidirect
166. #461	C₂²×C₅	semidirect
171. #436	C₂²×C₅	semidirect
173. C₈×D₄	C₂²×C₅	semidirect
181. #335	C₂²×C₅	semidirect
182. #334	C₂²×C₅	semidirect
183. #332	C₂²×C₅	semidirect
398. C₅	#19198	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3206	2
C₅×#3205	2
C₂×C₅×#486	2
C₅×#2931	2
C₅×#1701	2
C₅×#1681	2
C₅×#1564	2
C₅×#1549	2
C₅×#1545	2
#19198	5

Subgroups — C5×#19198 #11941918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19198 #11941918