Subgroups — #12253567

Order 1280.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#65483	C₂	1	2	yes	maximal, complemented
3	#10610198	C₂	1	1	yes	maximal, characteristic, complemented
4	#10601709	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601708	C₂	1	2	yes	maximal, complemented
6	#10601707	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601685	C₂	1	1	yes	maximal, characteristic, complemented
8	#10601683	C₂	1	2	yes	maximal, complemented
9	#10601682	C₂	1	1	yes	maximal, characteristic, complemented
10	#10601444	C₂	1	2	yes	maximal, complemented
11	C₂×C₄⋊#672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₄×C₅×#41	—	2	1	no	—
14	C₂×#4050	—	2	1	no	—
15	C₂×#4050	C₂²	1	2	yes	—
16	#65811	—	2	1	no	—
17	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₄×C₅×SD₁₆	—	2	1	no	—
20	C₄×C₅×SD₁₆	—	2	1	no	—
21	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
23	C₅×#427	C₂²	1	1	yes	characteristic
24	C₅×#416	—	2	1	no	—
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	#65483	—	2	8	no	—
27	C₂×#3961	C₂²	1	2	yes	—
28	C₂×#3960	C₂²	1	2	yes	—
29	C₂×#3959	C₂²	1	2	yes	—
30	C₂×#3958	C₂²	1	2	yes	—
31	C₂²×#672	C₂²	1	2	yes	—
32	#64988	C₂²	1	1	yes	characteristic
33	#64985	—	2	1	no	—
34	#64985	C₂²	1	2	yes	—
35	#64984	C₂²	1	1	yes	characteristic
36	#64982	—	2	1	no	—
37	#64712	C₂²	1	2	yes	—
38	#64712	C₂²	1	2	yes	—
39	#64711	C₂²	1	2	yes	—
40	#64711	C₂²	1	2	yes	—
41	C₄⋊#672	C₂²	1	1	yes	characteristic
42	C₄⋊#672	C₂²	1	2	yes	—
43	C₄⋊#672	C₂²	1	1	yes	characteristic
44	#33579	—	5	1	no	maximal, Sylow
45	C₂×C₅×#41	—	2	1	no	—
46	C₂×#709	—	2	2	no	—
47	C₅×#135	—	2	2	no	—
48	C₅×#135	D₄	1	4	yes	complemented
49	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₅×SD₁₆	—	2	1	no	—
51	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
52	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₄×C₅×Q₈	—	2	1	no	—
55	C₄×C₅×Q₈	—	2	1	no	—
56	C₄×C₅×D₄	—	2	1	no	—
57	C₄×C₅×D₄	—	2	1	no	—
58	C₄×C₅×D₄	—	4	1	no	—
59	C₄×C₅×D₄	—	4	1	no	—
60	C₅×#117	—	2	1	no	—
61	C₅×#117	—	4	1	no	—
62	C₂×C₄²×C₅	—	4	1	no	—
63	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
64	#4076	—	4	1	no	—
65	#4076	—	4	1	no	—
66	C₂×Dic₂₀	—	2	1	no	—
67	C₂×Dic₂₀	C₂³	1	2	yes	—
68	#4050	—	2	4	no	—
69	#4050	—	2	4	no	—
70	#4050	—	4	4	no	—
71	C₂×D₄₀	—	2	1	no	—
72	C₂×D₄₀	C₂³	1	2	yes	—
73	C₂×#677	—	2	2	no	—
74	C₂×#677	—	2	2	no	—
75	#4021	—	2	2	no	—
76	#4020	—	2	1	no	—
77	C₄×D₂₀	—	4	1	no	—
78	C₄×D₂₀	—	4	1	no	—
79	#4015	—	2	1	no	—
80	C₅×#107	C₂³	1	1	yes	characteristic
81	C₅×#107	C₂³	1	1	yes	characteristic
82	C₅×#106	—	2	1	no	—
83	C₅×#103	—	2	1	no	—
84	C₅×#103	—	2	1	no	—
85	C₅×#102	—	2	1	no	—
86	C₅×#102	—	2	1	no	—
87	C₄×C₅×C₈	D₄	1	1	yes	characteristic
88	C₄×C₅×C₈	D₄	1	1	yes	characteristic
89	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
91	#3961	—	2	4	no	—
92	#3960	—	2	4	no	—
93	#3959	—	2	4	no	—
94	#3958	—	2	4	no	—
95	C₂×#672	—	2	4	no	—
96	C₂×#672	C₂³	1	2	yes	—
97	C₂×#672	C₂³	1	2	yes	—
98	C₂×#508	—	5	2	no	—
99	#3147	—	5	1	no	—
100	C₄×#135	D₅	1	1	yes	characteristic, complemented
101	#2211	—	5	2	no	—
102	#2210	—	5	2	no	—
103	#2209	—	5	1	no	—
104	#2208	—	5	1	no	—
105	#2207	—	5	1	no	—
106	#2206	—	5	1	no	—
107	C₂×C₄⋊C₁₆	—	5	1	no	—
108	#2138	—	5	2	no	—
109	C₅×#41	—	2	4	no	—
110	C₅×#41	—	4	2	no	—
111	C₂×C₅×Q₈	—	2	1	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	—	4	1	no	—
114	C₂²×C₄×C₅	—	4	1	no	—
115	C₂²×C₄×C₅	—	4	1	no	—
116	C₂²×C₄×C₅	—	4	1	no	—
117	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
118	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂×C₂²⋊D₅	—	4	2	no	—
121	#709	—	4	4	no	—
122	#709	—	4	4	no	—
123	C₂×D₂₀	—	2	2	no	—
124	C₂×D₂₀	—	4	1	no	—
125	C₂×D₂₀	—	4	1	no	—
126	C₂×C₄×D₅	—	4	2	no	—
127	C₂×Dic₁₀	—	2	2	no	—
128	C₅×Q₁₆	—	2	1	no	—
129	C₅×Q₁₆	C₂×D₄	1	2	yes	—
130	C₅×SD₁₆	—	2	4	no	—
131	C₅×D₈	—	2	1	no	—
132	C₅×D₈	C₂×D₄	1	2	yes	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
135	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×C₈	#41	1	2	yes	—
139	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	—	4	1	no	—
143	C₅×C₄⋊C₄	—	4	1	no	—
144	C₅×C₂²⋊C₄	—	4	1	no	—
145	C₅×C₂²⋊C₄	—	4	1	no	—
146	C₅×C₂²⋊C₄	—	4	1	no	—
147	C₄²×C₅	—	4	1	no	—
148	C₄²×C₅	—	4	1	no	—
149	C₄²×C₅	—	4	1	no	—
150	C₄²×C₅	D₈	1	1	yes	characteristic
151	C₄²×C₅	D₈	1	1	yes	characteristic
152	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
154	#685	—	4	2	no	—
155	#685	—	4	2	no	—
156	C₄⋊Dic₅	—	4	1	no	—
157	C₄⋊Dic₅	—	4	1	no	—
158	Dic₂₀	—	2	2	no	—
159	Dic₂₀	—	2	2	no	—
160	Dic₂₀	—	4	2	no	—
161	D₄₀	—	2	2	no	—
162	D₄₀	—	2	2	no	—
163	D₄₀	—	4	2	no	—
164	#677	—	4	4	no	—
165	#677	—	4	4	no	—
166	#672	—	2	2	no	—
167	#672	—	2	2	no	—
168	C₂×#135	—	5	2	no	—
169	C₂×#135	—	10	1	no	—
170	C₂×#135	C₂×D₅	1	1	yes	characteristic
171	#532	—	10	1	no	—
172	C₄×#41	—	2	1	no	—
173	#508	—	10	8	no	—
174	C₂×Q₃₂	—	5	2	no	—
175	C₂×SD₃₂	—	5	2	no	—
176	C₂×SD₃₂	—	5	2	no	—
177	C₂×D₁₆	—	5	2	no	—
178	C₂²×C₁₆	—	5	2	no	—
179	#495	—	5	2	no	—
180	#495	—	10	1	no	—
181	#494	—	5	1	no	—
182	#493	—	5	1	no	—
183	#492	—	10	1	no	—
184	C₄×Q₁₆	C₂×D₅	1	1	yes	characteristic
185	C₄×Q₁₆	C₂×D₅	1	1	yes	characteristic
186	C₄×SD₁₆	—	2	1	no	—
187	C₄×SD₁₆	—	2	1	no	—
188	C₄×D₈	C₂×D₅	1	1	yes	characteristic
189	C₄×D₈	C₂×D₅	1	1	yes	characteristic
190	#427	C₂×D₅	1	1	yes	characteristic
191	#416	—	2	1	no	—
192	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
193	C₄⋊C₁₆	—	5	1	no	—
194	C₄⋊C₁₆	—	5	1	no	—
195	C₄⋊C₁₆	—	5	2	no	—
196	#358	—	5	2	no	—
197	#358	—	5	2	no	—
198	#357	—	5	2	no	—
199	#357	—	5	2	no	—
200	C₂³×C₅	—	4	1	no	—
201	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
202	C₂²×D₅	—	4	2	no	—
203	C₅×Q₈	—	2	2	no	—
204	C₅×Q₈	—	4	1	no	—
205	C₅×D₄	—	2	2	no	—
206	C₅×D₄	—	4	4	no	—
207	C₅×D₄	—	4	1	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	4	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	8	2	no	—
215	C₂×C₄×C₅	—	8	2	no	—
216	C₂×C₄×C₅	#121	1	2	yes	—
217	C₂×C₄×C₅	C₂×D₈	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	C₂×D₈	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
222	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
223	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂²⋊D₅	—	8	4	no	—
225	C₂×Dic₅	—	4	2	no	—
226	D₂₀	—	4	2	no	—
227	D₂₀	—	4	2	no	—
228	D₂₀	—	8	2	no	—
229	D₂₀	—	8	2	no	—
230	C₄×D₅	—	8	4	no	—
231	Dic₁₀	—	4	2	no	—
232	Dic₁₀	—	4	2	no	—
233	C₅×C₈	—	2	1	no	—
234	C₅×C₈	—	2	1	no	—
235	C₅×C₈	#121	1	2	yes	—
236	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
237	C₅×C₈	C₂×#41	1	1	yes	characteristic
238	C₂×#41	—	2	1	no	—
239	C₂×#41	—	10	2	no	—
240	#135	—	2	2	no	—
241	#135	—	10	4	no	—
242	#135	—	10	4	no	—
243	#135	—	20	4	no	—
244	#135	D₂₀	1	4	yes	complemented
245	C₂×Q₁₆	—	5	2	no	—
246	C₂×Q₁₆	—	10	1	no	—
247	C₂×Q₁₆	C₂²×D₅	1	1	yes	characteristic
248	C₂×SD₁₆	—	2	1	no	—
249	C₂×SD₁₆	—	10	2	no	—
250	C₂×SD₁₆	—	10	2	no	—
251	C₂×D₈	—	5	2	no	—
252	C₂×D₈	—	10	1	no	—
253	C₂×D₈	C₂²×D₅	1	1	yes	characteristic
254	C₂²×C₈	C₂²⋊D₅	1	1	yes	characteristic
255	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
256	C₄⋊Q₈	—	10	1	no	—
257	#127	—	10	1	no	—
258	#124	—	10	2	no	—
259	#121	—	20	1	no	—
260	#121	—	20	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	4	1	no	—
266	C₄×D₄	—	4	1	no	—
267	C₄×D₄	—	20	1	no	—
268	C₄×D₄	—	20	1	no	—
269	#117	—	2	1	no	—
270	#117	—	4	1	no	—
271	C₂×C₄²	—	4	1	no	—
272	C₂×C₄²	C₂²⋊D₅	1	1	yes	characteristic
273	Q₃₂	—	10	4	no	—
274	SD₃₂	—	10	4	no	—
275	SD₃₂	—	10	4	no	—
276	D₁₆	—	10	4	no	—
277	C₂×C₁₆	—	5	2	no	—
278	C₂×C₁₆	—	5	2	no	—
279	C₂×C₁₆	—	10	4	no	—
280	#107	C₂²×D₅	1	1	yes	characteristic
281	#107	C₂²×D₅	1	1	yes	characteristic
282	#106	—	2	1	no	—
283	#103	—	2	1	no	—
284	#103	—	2	1	no	—
285	#102	—	2	1	no	—
286	#102	—	2	1	no	—
287	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
288	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
289	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	—	2	1	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	—	8	1	no	—
295	C₂²×C₅	—	8	1	no	—
296	C₂²×C₅	#459	1	2	yes	—
297	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
298	C₂×D₅	—	8	2	no	—
299	C₂×D₅	—	8	2	no	—
300	C₂×D₅	—	8	2	no	—
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	2	1	no	—
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	8	1	no	—
306	C₄×C₅	—	8	1	no	—
307	C₄×C₅	#459	1	2	yes	—
308	C₄×C₅	#508	1	2	yes	complemented
309	C₄×C₅	C₂×#121	1	1	yes	characteristic
310	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
311	Dic₅	—	8	2	no	—
312	#41	—	2	4	no	—
313	#41	—	4	2	no	—
314	#41	—	20	4	no	—
315	#41	—	20	4	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	10	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	10	2	no	—
321	C₂×D₄	—	20	2	no	—
322	C₂×D₄	—	20	1	no	—
323	C₂×D₄	—	20	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	20	2	no	—
328	C₂²×C₄	#686	1	1	yes	characteristic
329	C₂²×C₄	#686	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
331	Q₁₆	—	2	1	no	—
332	Q₁₆	—	10	2	no	—
333	Q₁₆	—	10	2	no	—
334	Q₁₆	—	20	2	no	—
335	Q₁₆	C₂×D₂₀	1	2	yes	—
336	SD₁₆	—	2	4	no	—
337	SD₁₆	—	20	4	no	—
338	SD₁₆	—	20	4	no	—
339	D₈	—	2	1	no	—
340	D₈	—	10	2	no	—
341	D₈	—	10	2	no	—
342	D₈	—	20	2	no	—
343	D₈	C₂×D₂₀	1	2	yes	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	C₂×D₂₀	1	2	yes	—
346	C₂×C₈	#709	1	2	yes	—
347	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
348	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
349	C₂×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
350	C₂×C₈	C₂³×D₅	1	1	yes	characteristic
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	20	1	no	—
356	C₄⋊C₄	—	20	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	20	2	no	—
361	C₂²⋊C₄	—	20	2	no	—
362	C₄²	—	4	1	no	—
363	C₄²	—	4	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	#686	1	1	yes	characteristic
366	C₄²	#686	1	1	yes	characteristic
367	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
368	C₄²	C₂×C₂²⋊D₅	1	1	yes	characteristic
369	C₁₆	—	10	2	no	—
370	C₁₆	—	10	2	no	—
371	C₂×C₅	—	2	2	no	—
372	C₂×C₅	—	8	2	no	—
373	C₂×C₅	C₂×#459	1	1	yes	characteristic
374	C₂×C₅	C₂×#508	1	1	yes	characteristic
375	C₂×C₅	#3414	1	1	yes	characteristic
376	D₅	—	16	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	20	2	no	—
379	C₂³	C₂×#686	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	20	2	no	—
383	Q₈	—	20	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	1	no	—
387	D₄	—	20	2	no	—
388	D₄	—	20	2	no	—
389	D₄	—	40	2	no	—
390	D₄	—	40	4	no	—
391	D₄	—	40	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	20	2	no	—
401	C₂×C₄	—	40	4	no	—
402	C₂×C₄	#4076	1	2	yes	—
403	C₂×C₄	C₂×#686	1	1	yes	characteristic
404	C₂×C₄	C₂×#686	1	1	yes	characteristic
405	C₂×C₄	C₂×#686	1	1	yes	characteristic
406	C₂×C₄	C₂×#686	1	1	yes	characteristic
407	C₂×C₄	C₂×#686	1	1	yes	characteristic
408	C₂×C₄	#4095	1	2	yes	—
409	C₂×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	#4076	1	2	yes	—
413	C₈	C₂²×D₂₀	1	1	yes	characteristic
414	C₈	C₂×#709	1	1	yes	characteristic
415	C₅	#33579	1	1	yes	characteristic, complemented, Sylow
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	40	2	no	—
422	C₂²	—	40	2	no	—
423	C₂²	—	40	2	no	—
424	C₂²	#65304	1	2	yes	—
425	C₂²	C₂²×#686	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	1	no	—
432	C₄	—	40	2	no	—
433	C₄	#65304	1	2	yes	—
434	C₄	#65483	1	2	yes	complemented
435	C₄	C₂×#4076	1	1	yes	characteristic
436	C₄	C₂×#4095	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	80	2	no	—
440	C₂	C₂×#65304	1	1	yes	characteristic
441	C₂	C₂×#65483	1	1	yes	characteristic
442	C₂	#10615625	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#686
commutator, cosocle	C₂×C₅×C₈	C₂⁴
Frattini	C₂×C₈	C₂³×D₅
Fitting	C₄×C₅×#135	C₂
socle	C₂²×C₅	C₂²×D₈
hypercenter	C₄×#135	D₅
hypocenter	C₅	#33579
LCS	G ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. C₄×C₅×#135	C₂	semidirect
2. C₂×#65483	C₂	semidirect
3. #10610198	C₂	semidirect
4. #10601709	C₂	semidirect
5. #10601708	C₂	semidirect
6. #10601707	C₂	semidirect
7. #10601685	C₂	semidirect
8. #10601683	C₂	semidirect
9. #10601682	C₂	semidirect
10. #10601444	C₂	semidirect
11. C₂×C₄⋊#672	C₂	semidirect
48. C₅×#135	D₄	semidirect
100. C₄×#135	D₅	semidirect
244. #135	D₂₀	semidirect
308. C₄×C₅	#508	semidirect
415. C₅	#33579	semidirect
434. C₄	#65483	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#135	2
C₂×#65483	2
#10610198	2
#10601709	2
#10601708	2
#10601707	2
#10601685	2
#10601683	2
#10601682	2
#10601444	2
C₂×C₄⋊#672	2
#33579	5