Subgroups — #12068481

Order 1280.

662 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	#10611013	C₂	1	1	yes	maximal, characteristic
2	#10610769	C₂	1	1	yes	maximal, characteristic
3	C₂×#65126	C₂	1	1	yes	maximal, characteristic
4	C₅×#1571	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601542	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601287	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601214	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599368	C₂	1	4	yes	maximal, complemented
9	#10599364	C₂	1	4	yes	maximal, complemented
10	C₂²×#676	—	2	1	no	—
11	C₂×C₄²×D₅	C₂²	1	1	yes	characteristic
12	C₅×#431	C₂²	1	1	yes	characteristic
13	C₅×#423	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	#65415	—	2	1	no	—
16	M₁₆×Dic₅	—	2	1	no	—
17	C₂×#3946	—	2	1	no	—
18	#65214	C₂²	1	1	yes	characteristic
19	#65213	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
21	#65126	—	2	1	no	—
22	#65126	—	2	1	no	—
23	#65126	C₄	1	2	yes	—
24	#65126	C₂²	1	2	yes	—
25	#65126	C₂²	1	2	yes	—
26	#65124	—	2	1	no	—
27	#65124	C₄	1	2	yes	—
28	#65124	C₂²	1	2	yes	—
29	#65122	—	2	1	no	—
30	#65122	C₂²	1	2	yes	—
31	#65015	C₄	1	2	yes	—
32	#65008	C₄	1	2	yes	—
33	C₄×#676	C₂²	1	2	yes	—
34	#64974	C₂²	1	2	yes	—
35	C₅×#335	C₂²	1	4	yes	complemented
36	#64700	C₂²	1	4	yes	complemented
37	#64699	C₂²	1	4	yes	complemented
38	#64677	C₂²	1	4	yes	complemented
39	#17820	—	5	1	no	maximal, Sylow
40	C₂²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
42	C₂²×C₄×D₅	Q₈	1	1	yes	characteristic
43	C₂×C₅×M₁₆	—	2	1	no	—
44	C₂²×C₅×C₈	—	2	1	no	—
45	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₅	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₅	Q₈	1	1	yes	characteristic
49	C₂×#681	—	2	1	no	—
50	C₂²×#168	—	2	1	no	—
51	C₂×#676	—	2	2	no	—
52	C₂×#676	—	2	2	no	—
53	C₂×#676	—	4	4	no	—
54	C₂×#676	C₂×C₄	1	4	yes	—
55	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₅	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₅	D₄	1	1	yes	characteristic
58	C₄²×D₅	D₄	1	1	yes	characteristic
59	C₄²×D₅	Q₈	1	1	yes	characteristic
60	C₄²×D₅	Q₈	1	1	yes	characteristic
61	C₄²×D₅	C₂³	1	1	yes	characteristic
62	C₄²×D₅	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊C₈	—	2	1	no	—
64	C₅×C₄⋊C₈	—	2	1	no	—
65	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
66	C₅×C₄⋊C₈	C₂³	1	2	yes	—
67	C₅×C₄⋊C₈	C₂³	1	2	yes	—
68	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
69	C₄×C₅×C₈	C₂³	1	2	yes	—
70	C₂²⋊#168	C₂×C₄	1	2	yes	—
71	#3952	—	2	2	no	—
72	#3952	—	2	2	no	—
73	#3952	C₂×C₄	1	4	yes	—
74	#3947	—	2	2	no	—
75	#3947	C₂×C₄	1	4	yes	—
76	#3946	—	2	2	no	—
77	#3946	—	2	2	no	—
78	#3946	C₂×C₄	1	4	yes	—
79	C₈×Dic₅	—	2	2	no	—
80	C₄⋊#168	—	2	1	no	—
81	C₄⋊#168	—	2	1	no	—
82	C₄⋊#168	C₂×C₄	1	2	yes	—
83	C₄⋊#168	C₂³	1	2	yes	—
84	C₄⋊#168	C₂³	1	2	yes	—
85	C₄×#168	C₂³	1	2	yes	—
86	#2920	—	5	1	no	—
87	#2920	—	5	1	no	—
88	C₂×#423	—	5	1	no	—
89	#1574	—	5	4	no	—
90	#1571	—	5	1	no	—
91	#1571	D₅	1	1	yes	characteristic, complemented
92	#1570	—	5	1	no	—
93	#1570	—	5	1	no	—
94	#1569	—	5	4	no	—
95	C₂³×D₅	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
99	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₅	—	2	2	no	—
103	C₂×C₄×D₅	—	2	2	no	—
104	C₂×C₄×D₅	—	4	2	no	—
105	C₂×C₄×D₅	—	4	2	no	—
106	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
118	C₅×M₁₆	—	4	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	4	2	no	—
122	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
123	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
126	C₄²×C₅	C₂⁴	1	1	yes	characteristic
127	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₅	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
138	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
139	#681	—	4	2	no	—
140	C₂×#168	—	2	2	no	—
141	C₂×#168	—	2	2	no	—
142	C₂×#168	—	4	2	no	—
143	C₂×#168	C₂²×C₄	1	4	yes	—
144	#676	—	4	4	no	—
145	#676	—	4	4	no	—
146	#676	—	4	4	no	—
147	C₂²×M₁₆	—	10	1	no	—
148	C₂²×C₄²	—	5	1	no	—
149	#432	—	5	2	no	—
150	#432	—	5	2	no	—
151	#432	—	5	2	no	—
152	#432	—	10	1	no	—
153	#431	—	5	1	no	—
154	#431	—	5	2	no	—
155	#431	—	5	2	no	—
156	#431	—	10	1	no	—
157	#431	C₂×D₅	1	1	yes	characteristic
158	#423	—	5	2	no	—
159	#423	—	5	1	no	—
160	#423	—	5	2	no	—
161	#423	—	5	2	no	—
162	#423	—	10	1	no	—
163	#423	—	10	1	no	—
164	#423	C₂×D₅	1	1	yes	characteristic
165	C₂×C₄⋊C₈	—	5	1	no	—
166	C₂×C₄⋊C₈	—	10	1	no	—
167	C₂×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
168	#407	—	5	2	no	—
169	#407	—	10	1	no	—
170	C₄×M₁₆	—	5	2	no	—
171	C₄×M₁₆	—	10	1	no	—
172	#335	—	5	4	no	—
173	#335	C₂×D₅	1	4	yes	complemented
174	#334	—	5	4	no	—
175	#334	—	5	4	no	—
176	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×D₅	—	2	2	no	—
178	C₂²×D₅	—	4	1	no	—
179	C₂²×D₅	—	4	1	no	—
180	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	4	1	no	—
184	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
188	C₂×C₄×C₅	#137	1	2	yes	—
189	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
192	C₂×Dic₅	—	2	2	no	—
193	C₂×Dic₅	—	2	2	no	—
194	C₂×Dic₅	—	4	1	no	—
195	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₄×D₅	—	2	2	no	—
202	C₄×D₅	—	2	2	no	—
203	C₄×D₅	—	2	1	no	—
204	C₄×D₅	—	2	1	no	—
205	C₄×D₅	—	2	1	no	—
206	C₄×D₅	—	2	1	no	—
207	C₄×D₅	—	2	2	no	—
208	C₄×D₅	—	2	2	no	—
209	C₄×D₅	—	2	2	no	—
210	C₄×D₅	—	2	2	no	—
211	C₄×D₅	—	4	1	no	—
212	C₄×D₅	—	4	1	no	—
213	C₄×D₅	—	4	1	no	—
214	C₄×D₅	—	4	1	no	—
215	C₅×C₈	—	2	4	no	—
216	C₅×C₈	—	4	2	no	—
217	C₅×C₈	—	4	2	no	—
218	#168	—	2	4	no	—
219	#168	—	4	2	no	—
220	#168	—	4	2	no	—
221	C₂³×C₄	—	5	1	no	—
222	C₂³×C₄	—	5	1	no	—
223	C₂³×C₄	—	5	1	no	—
224	C₂×M₁₆	—	2	1	no	—
225	C₂×M₁₆	—	5	4	no	—
226	C₂×M₁₆	—	10	2	no	—
227	C₂×M₁₆	—	10	2	no	—
228	C₂×M₁₆	—	10	1	no	—
229	C₂×M₁₆	—	20	4	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	10	1	no	—
232	C₂×C₄²	—	5	1	no	—
233	C₂×C₄²	—	5	1	no	—
234	C₂×C₄²	—	5	1	no	—
235	C₂×C₄²	—	5	1	no	—
236	C₂×C₄²	—	5	1	no	—
237	C₂×C₄²	—	5	1	no	—
238	C₂×C₄²	—	5	1	no	—
239	C₂×C₄²	—	5	1	no	—
240	C₂×C₄²	—	5	1	no	—
241	C₂×C₄²	—	5	1	no	—
242	C₂×C₄²	—	5	1	no	—
243	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	5	4	no	—
247	C₄⋊C₈	—	5	2	no	—
248	C₄⋊C₈	—	5	2	no	—
249	C₄⋊C₈	—	5	2	no	—
250	C₄⋊C₈	—	10	2	no	—
251	C₄⋊C₈	—	10	2	no	—
252	C₄⋊C₈	—	10	1	no	—
253	C₄⋊C₈	—	10	1	no	—
254	C₄⋊C₈	C₄×D₅	1	2	yes	—
255	C₄⋊C₈	C₂²×D₅	1	2	yes	—
256	C₄⋊C₈	C₂²×D₅	1	2	yes	—
257	C₂²⋊C₈	—	5	2	no	—
258	C₂²⋊C₈	—	5	4	no	—
259	C₂²⋊C₈	—	10	2	no	—
260	C₂²⋊C₈	—	10	2	no	—
261	C₂²⋊C₈	C₄×D₅	1	2	yes	—
262	#97	—	5	4	no	—
263	#97	—	10	2	no	—
264	C₄×C₈	—	5	2	no	—
265	C₄×C₈	—	10	2	no	—
266	C₄×C₈	C₂²×D₅	1	2	yes	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	—	2	1	no	—
269	C₂²×C₅	#428	1	2	yes	—
270	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
271	C₂×D₅	—	2	1	no	—
272	C₂×D₅	—	2	1	no	—
273	C₂×D₅	—	2	1	no	—
274	C₂×D₅	—	2	1	no	—
275	C₂×D₅	—	2	1	no	—
276	C₂×D₅	—	2	1	no	—
277	C₂×D₅	—	4	4	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	#428	1	2	yes	—
282	C₄×C₅	#568	1	2	yes	—
283	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₄×C₅	C₂×#137	1	1	yes	characteristic
285	Dic₅	—	2	1	no	—
286	Dic₅	—	2	1	no	—
287	Dic₅	—	2	1	no	—
288	Dic₅	—	2	1	no	—
289	Dic₅	—	2	1	no	—
290	Dic₅	#430	1	2	yes	—
291	C₂⁴	—	5	1	no	—
292	C₂²×C₄	—	5	1	no	—
293	C₂²×C₄	—	5	1	no	—
294	C₂²×C₄	—	5	1	no	—
295	C₂²×C₄	—	5	1	no	—
296	C₂²×C₄	—	5	1	no	—
297	C₂²×C₄	—	5	1	no	—
298	C₂²×C₄	—	5	1	no	—
299	C₂²×C₄	—	5	1	no	—
300	C₂²×C₄	—	5	1	no	—
301	C₂²×C₄	—	5	1	no	—
302	C₂²×C₄	—	5	1	no	—
303	C₂²×C₄	—	5	1	no	—
304	C₂²×C₄	—	5	1	no	—
305	C₂²×C₄	—	5	1	no	—
306	C₂²×C₄	—	5	1	no	—
307	C₂²×C₄	—	10	2	no	—
308	C₂²×C₄	—	10	2	no	—
309	C₂²×C₄	—	20	2	no	—
310	C₂²×C₄	—	20	2	no	—
311	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
312	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
313	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
314	M₁₆	—	4	2	no	—
315	M₁₆	—	20	4	no	—
316	M₁₆	—	20	4	no	—
317	M₁₆	—	20	4	no	—
318	M₁₆	—	20	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	5	4	no	—
323	C₂×C₈	—	10	2	no	—
324	C₂×C₈	—	10	2	no	—
325	C₂×C₈	—	20	2	no	—
326	C₂×C₈	C₂×C₄×D₅	1	4	yes	—
327	C₄²	—	5	1	no	—
328	C₄²	—	5	1	no	—
329	C₄²	—	5	1	no	—
330	C₄²	—	5	1	no	—
331	C₄²	—	5	1	no	—
332	C₄²	—	5	1	no	—
333	C₄²	—	5	1	no	—
334	C₄²	—	5	1	no	—
335	C₄²	—	5	1	no	—
336	C₄²	—	5	1	no	—
337	C₄²	—	5	1	no	—
338	C₄²	—	5	1	no	—
339	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
340	C₄²	D₄×D₅	1	1	yes	characteristic
341	C₄²	Q₈×D₅	1	1	yes	characteristic
342	C₄²	C₂³×D₅	1	1	yes	characteristic
343	C₂×C₅	—	2	2	no	—
344	C₂×C₅	#2905	1	1	yes	characteristic
345	C₂×C₅	C₂×#428	1	1	yes	characteristic
346	C₂×C₅	C₂×#430	1	1	yes	characteristic
347	D₅	—	4	1	no	—
348	D₅	—	4	1	no	—
349	C₂³	—	5	1	no	—
350	C₂³	—	5	1	no	—
351	C₂³	—	10	2	no	—
352	C₂³	—	20	1	no	—
353	C₂³	—	20	1	no	—
354	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	5	1	no	—
358	C₂×C₄	—	5	1	no	—
359	C₂×C₄	—	5	1	no	—
360	C₂×C₄	—	5	1	no	—
361	C₂×C₄	—	5	1	no	—
362	C₂×C₄	—	5	1	no	—
363	C₂×C₄	—	10	2	no	—
364	C₂×C₄	—	10	2	no	—
365	C₂×C₄	—	10	2	no	—
366	C₂×C₄	—	10	2	no	—
367	C₂×C₄	—	10	2	no	—
368	C₂×C₄	—	10	2	no	—
369	C₂×C₄	—	10	1	no	—
370	C₂×C₄	—	10	1	no	—
371	C₂×C₄	—	10	1	no	—
372	C₂×C₄	—	10	1	no	—
373	C₂×C₄	—	10	2	no	—
374	C₂×C₄	—	10	2	no	—
375	C₂×C₄	—	20	1	no	—
376	C₂×C₄	—	20	1	no	—
377	C₂×C₄	—	20	1	no	—
378	C₂×C₄	—	20	1	no	—
379	C₂×C₄	—	20	1	no	—
380	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
381	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
382	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
383	C₂×C₄	#4057	1	2	yes	—
384	C₂×C₄	#4064	1	2	yes	—
385	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
386	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
387	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
388	C₈	—	2	4	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	10	4	no	—
392	C₈	—	20	2	no	—
393	C₈	—	20	2	no	—
394	C₅	#17820	1	1	yes	characteristic, complemented, Sylow
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	10	1	no	—
398	C₂²	—	10	1	no	—
399	C₂²	—	10	1	no	—
400	C₂²	—	10	1	no	—
401	C₂²	—	10	1	no	—
402	C₂²	—	10	1	no	—
403	C₂²	—	20	4	no	—
404	C₂²	#65170	1	2	yes	—
405	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	5	2	no	—
410	C₄	—	10	1	no	—
411	C₄	—	10	1	no	—
412	C₄	—	10	1	no	—
413	C₄	—	10	1	no	—
414	C₄	—	10	1	no	—
415	C₄	#65170	1	2	yes	—
416	C₄	#66084	1	2	yes	—
417	C₄	C₂×#4057	1	1	yes	characteristic
418	C₄	C₂×#4064	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	—	20	1	no	—
421	C₂	—	20	1	no	—
422	C₂	#10610811	1	1	yes	characteristic
423	C₂	C₂×#65170	1	1	yes	characteristic
424	C₂	D₅×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1571	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂³×D₅	C₄⋊C₄
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1571	D₅
hypocenter	C₅	#17820
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1571

Complements

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

N	H ≅ G/N	type
4. C₅×#1571	C₂	semidirect
5. #10601542	C₂	semidirect
6. #10601287	C₂	semidirect
7. #10601214	C₂	semidirect
8. #10599368	C₂	semidirect
9. #10599364	C₂	semidirect
35. C₅×#335	C₂²	semidirect
36. #64700	C₂²	semidirect
37. #64699	C₂²	semidirect
38. #64677	C₂²	semidirect
91. #1571	D₅	semidirect
173. #335	C₂×D₅	semidirect
394. C₅	#17820	semidirect

Maximal subgroups

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

subgroup	index
#10611013	2
#10610769	2
C₂×#65126	2
C₅×#1571	2
#10601542	2
#10601287	2
#10601214	2
#10599368	2
#10599364	2
#17820	5