Subgroups — #16798319

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131285	C₂	1	2	yes	maximal
2	#13130771	C₂	1	2	yes	maximal, complemented
3	#13130757	C₂	1	2	yes	maximal, complemented
4	#13130712	C₂	1	4	yes	maximal
5	C₄×#88101	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂×#88237	—	2	2	no	—
8	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	#11719136	—	2	2	no	—
11	#11719136	C₂²	1	4	yes	—
12	C₂×#88101	C₂²	1	8	yes	—
13	#11719060	—	2	2	no	—
14	#11719059	C₂²	1	4	yes	—
15	C₄×C₄⋊#261	—	2	2	no	—
16	C₄×C₄⋊#261	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
18	C₂×C₈×Dic₁₃	C₄	1	2	yes	complemented
19	C₂×C₄×#1055	C₄	1	1	yes	characteristic, complemented
20	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
21	C₄×C₈×D₁₃	C₄	1	2	yes	complemented
22	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
23	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
24	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₁₃	C₂²	1	2	yes	—
26	#11718265	C₂²	1	8	yes	—
27	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
30	C₂×C₂²⋊#261	—	2	4	no	—
31	#88237	—	4	8	no	—
32	C₂×C₄⋊#261	—	2	4	no	—
33	C₂×C₄⋊#261	—	2	4	no	—
34	C₂×C₄⋊#261	C₂³	1	8	yes	—
35	C₂×C₄×#261	—	2	4	no	—
36	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
40	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
41	C₂²×#1055	C₂×C₄	1	2	yes	—
42	C₂×C₈×D₁₃	—	2	8	no	—
43	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
44	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
45	C₂×C₈×D₁₃	C₂³	1	2	yes	—
46	C₂×C₈×D₁₃	C₂³	1	2	yes	—
47	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₁₃	D₄	1	1	yes	characteristic
50	C₄²×D₁₃	D₄	1	1	yes	characteristic
51	C₄²×D₁₃	Q₈	1	1	yes	characteristic
52	C₄²×D₁₃	Q₈	1	1	yes	characteristic
53	C₄²×D₁₃	C₂³	1	1	yes	characteristic
54	C₄²×D₁₃	C₂³	1	1	yes	characteristic
55	(C₂×#261)⋊C₄	—	2	4	no	—
56	(C₂×#261)⋊C₄	—	2	4	no	—
57	#88101	—	2	16	no	—
58	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
62	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
63	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
64	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
65	C₄×#1055	C₂×C₄	1	1	yes	characteristic
66	C₄×#1055	C₂×C₄	1	2	yes	—
67	C₄×#1055	C₂×C₄	1	1	yes	characteristic
68	#20816	—	13	1	no	maximal, Sylow
69	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×#261	—	2	8	no	—
71	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
77	C₂×C₄×D₁₃	—	2	4	no	—
78	C₂×C₄×D₁₃	—	2	4	no	—
79	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₃	SD₁₆	1	8	yes	—
84	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
92	C₂²⋊#261	—	4	8	no	—
93	C₄⋊#261	—	2	16	no	—
94	C₄⋊#261	—	4	8	no	—
95	C₄⋊#261	—	4	8	no	—
96	C₄×#261	—	4	8	no	—
97	C₂×C₈×C₁₃	—	2	4	no	—
98	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
100	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
108	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
109	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
110	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
113	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
114	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
115	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
116	C₂×#1055	—	2	4	no	—
117	C₂×#1055	C₂²×C₄	1	2	yes	—
118	C₂×#1055	C₂²×C₄	1	2	yes	—
119	C₈×D₁₃	—	2	4	no	—
120	C₈×D₁₃	—	2	4	no	—
121	C₈×D₁₃	—	2	4	no	—
122	C₈×D₁₃	#41	1	8	yes	—
123	C₂²×C₄×C₈	—	13	1	no	—
124	#2285	—	13	2	no	—
125	#1844	—	13	2	no	—
126	#1834	—	13	2	no	—
127	#1807	—	13	4	no	—
128	C₄×#106	—	13	4	no	—
129	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂²×D₁₃	—	2	2	no	—
131	C₂²×D₁₃	—	2	2	no	—
132	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂²×D₁₃	C₂×SD₁₆	1	4	yes	—
134	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
135	C₂×#261	—	4	8	no	—
136	C₂×#261	—	4	8	no	—
137	C₂×#261	—	4	8	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	#106	1	4	yes	complemented
141	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×Dic₁₃	—	2	2	no	—
148	C₂×Dic₁₃	—	2	2	no	—
149	C₂×Dic₁₃	#106	1	4	yes	complemented
150	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
156	C₄×D₁₃	—	2	2	no	—
157	C₄×D₁₃	—	2	2	no	—
158	C₄×D₁₃	—	2	2	no	—
159	C₄×D₁₃	—	2	2	no	—
160	C₄×D₁₃	—	2	2	no	—
161	C₄×D₁₃	—	2	2	no	—
162	C₄×D₁₃	#106	1	4	yes	complemented
163	C₄×D₁₃	#106	1	4	yes	complemented
164	C₄×D₁₃	C₂×SD₁₆	1	4	yes	—
165	C₄×D₁₃	C₂×SD₁₆	1	4	yes	—
166	C₄×D₁₃	#135	1	4	yes	—
167	C₄×D₁₃	C₂×#41	1	4	yes	—
168	C₈×C₁₃	—	2	2	no	—
169	C₈×C₁₃	#117	1	4	yes	complemented
170	#1055	—	2	2	no	—
171	#1055	#117	1	4	yes	complemented
172	C₂³×C₈	—	13	2	no	—
173	C₂×#117	—	26	2	no	—
174	C₂²×C₄²	—	13	1	no	—
175	C₂×#106	—	13	8	no	—
176	C₂×C₄×C₈	—	13	2	no	—
177	C₂×C₄×C₈	—	13	1	no	—
178	C₂×C₄×C₈	—	13	1	no	—
179	C₂×C₄×C₈	—	13	1	no	—
180	C₂×C₄×C₈	—	13	1	no	—
181	C₂×C₄×C₈	—	13	2	no	—
182	C₂×C₄×C₈	—	13	1	no	—
183	C₂×C₄×C₈	—	13	2	no	—
184	C₂×C₄×C₈	#261	1	1	yes	characteristic, complemented
185	#384	—	13	4	no	—
186	#382	—	26	2	no	—
187	#380	—	13	4	no	—
188	#380	—	26	2	no	—
189	C₄×C₄⋊C₄	—	13	4	no	—
190	C₄×C₄⋊C₄	—	26	2	no	—
191	#340	—	13	8	no	—
192	C₂²×C₁₃	—	2	1	no	—
193	C₂²×C₁₃	—	2	1	no	—
194	C₂²×C₁₃	C₂×#106	1	2	yes	—
195	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
196	C₂×D₁₃	—	2	1	no	—
197	C₂×D₁₃	—	2	1	no	—
198	C₂×D₁₃	—	2	8	no	—
199	C₂×D₁₃	C₂×#106	1	2	yes	—
200	C₂×D₁₃	#532	1	2	yes	—
201	C₂×D₁₃	C₂²×SD₁₆	1	2	yes	—
202	C₂×D₁₃	C₂×#135	1	2	yes	—
203	#261	—	8	8	no	—
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	2	1	no	—
206	C₄×C₁₃	C₂×#106	1	2	yes	—
207	C₄×C₁₃	C₂×#106	1	2	yes	—
208	C₄×C₁₃	#427	1	2	yes	—
209	C₄×C₁₃	C₂×#117	1	2	yes	—
210	Dic₁₃	—	2	1	no	—
211	Dic₁₃	—	2	1	no	—
212	Dic₁₃	C₂×#106	1	2	yes	—
213	Dic₁₃	C₂×#106	1	2	yes	—
214	Dic₁₃	#427	1	2	yes	—
215	Dic₁₃	#533	1	2	yes	—
216	C₂³×C₄	—	13	1	no	—
217	C₂³×C₄	—	13	1	no	—
218	C₂³×C₄	—	13	1	no	—
219	C₂²×C₈	—	13	2	no	—
220	C₂²×C₈	—	13	2	no	—
221	C₂²×C₈	—	13	2	no	—
222	C₂²×C₈	—	13	2	no	—
223	C₂²×C₈	—	13	2	no	—
224	C₂²×C₈	—	26	8	no	—
225	C₂²×C₈	C₂×#261	1	2	yes	—
226	#117	—	52	8	no	—
227	C₂×C₄⋊C₄	—	13	8	no	—
228	C₂×C₄⋊C₄	—	26	4	no	—
229	C₂×C₄⋊C₄	—	26	4	no	—
230	C₂×C₂²⋊C₄	—	26	4	no	—
231	C₂×C₄²	—	13	1	no	—
232	C₂×C₄²	—	13	1	no	—
233	C₂×C₄²	—	13	1	no	—
234	C₂×C₄²	—	13	1	no	—
235	C₂×C₄²	—	13	1	no	—
236	C₂×C₄²	—	13	1	no	—
237	C₂×C₄²	—	13	1	no	—
238	C₂×C₄²	—	13	1	no	—
239	C₂×C₄²	—	13	1	no	—
240	C₂×C₄²	—	13	1	no	—
241	C₂×C₄²	—	13	1	no	—
242	C₂×C₄²	—	26	4	no	—
243	C₂×C₄²	C₂×#261	1	1	yes	characteristic
244	#106	—	26	16	no	—
245	C₄×C₈	—	13	2	no	—
246	C₄×C₈	—	13	2	no	—
247	C₄×C₈	—	13	2	no	—
248	C₄×C₈	—	13	2	no	—
249	C₄×C₈	—	13	1	no	—
250	C₄×C₈	—	13	1	no	—
251	C₄×C₈	—	13	2	no	—
252	C₄×C₈	C₂×#261	1	1	yes	characteristic
253	C₄×C₈	C₂×#261	1	1	yes	characteristic
254	C₄×C₈	C₂×#261	1	2	yes	—
255	#95	—	26	4	no	—
256	#95	—	26	4	no	—
257	C₂×C₁₃	—	2	2	no	—
258	C₂×C₁₃	#2285	1	1	yes	characteristic
259	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
260	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
261	D₁₃	—	2	2	no	—
262	D₁₃	#3167	1	4	yes	—
263	C₂⁴	—	13	1	no	—
264	C₂²×C₄	—	13	1	no	—
265	C₂²×C₄	—	13	8	no	—
266	C₂²×C₄	—	13	1	no	—
267	C₂²×C₄	—	13	1	no	—
268	C₂²×C₄	—	13	1	no	—
269	C₂²×C₄	—	13	1	no	—
270	C₂²×C₄	—	13	1	no	—
271	C₂²×C₄	—	13	1	no	—
272	C₂²×C₄	—	13	1	no	—
273	C₂²×C₄	—	13	1	no	—
274	C₂²×C₄	—	13	1	no	—
275	C₂²×C₄	—	13	1	no	—
276	C₂²×C₄	—	13	1	no	—
277	C₂²×C₄	—	13	1	no	—
278	C₂²×C₄	—	13	1	no	—
279	C₂²×C₄	—	13	1	no	—
280	C₂²×C₄	—	26	4	no	—
281	C₂²×C₄	—	26	4	no	—
282	C₂²×C₄	—	26	8	no	—
283	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
284	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
285	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	13	2	no	—
288	C₂×C₈	—	13	8	no	—
289	C₂×C₈	—	13	2	no	—
290	C₂×C₈	—	26	4	no	—
291	C₂×C₈	—	26	4	no	—
292	C₂×C₈	—	26	4	no	—
293	C₂×C₈	—	26	4	no	—
294	C₂×C₈	C₂²×#261	1	2	yes	—
295	C₂×C₈	C₂²×#261	1	2	yes	—
296	C₄⋊C₄	—	26	16	no	—
297	C₄⋊C₄	—	52	8	no	—
298	C₄⋊C₄	—	52	8	no	—
299	C₂²⋊C₄	—	52	8	no	—
300	C₄²	—	13	1	no	—
301	C₄²	—	13	1	no	—
302	C₄²	—	13	1	no	—
303	C₄²	—	13	1	no	—
304	C₄²	—	13	1	no	—
305	C₄²	—	13	1	no	—
306	C₄²	—	13	1	no	—
307	C₄²	—	13	1	no	—
308	C₄²	—	13	1	no	—
309	C₄²	—	13	1	no	—
310	C₄²	—	13	1	no	—
311	C₄²	—	13	1	no	—
312	C₄²	—	52	8	no	—
313	C₄²	C₄⋊#261	1	1	yes	characteristic
314	C₄²	C₄⋊#261	1	1	yes	characteristic
315	C₄²	C₂²×#261	1	1	yes	characteristic
316	C₄²	C₂²×#261	1	1	yes	characteristic
317	C₁₃	#20816	1	1	yes	characteristic, complemented, Sylow
318	C₂³	—	13	1	no	—
319	C₂³	—	13	4	no	—
320	C₂³	—	13	1	no	—
321	C₂³	—	26	2	no	—
322	C₂³	—	26	2	no	—
323	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	13	4	no	—
327	C₂×C₄	—	13	1	no	—
328	C₂×C₄	—	13	1	no	—
329	C₂×C₄	—	13	1	no	—
330	C₂×C₄	—	13	1	no	—
331	C₂×C₄	—	13	4	no	—
332	C₂×C₄	—	13	4	no	—
333	C₂×C₄	—	13	4	no	—
334	C₂×C₄	—	13	4	no	—
335	C₂×C₄	—	13	4	no	—
336	C₂×C₄	—	13	4	no	—
337	C₂×C₄	—	13	1	no	—
338	C₂×C₄	—	13	1	no	—
339	C₂×C₄	—	26	2	no	—
340	C₂×C₄	—	26	2	no	—
341	C₂×C₄	—	26	2	no	—
342	C₂×C₄	—	26	2	no	—
343	C₂×C₄	—	26	2	no	—
344	C₂×C₄	—	26	2	no	—
345	C₂×C₄	—	26	2	no	—
346	C₂×C₄	—	26	2	no	—
347	C₂×C₄	—	52	8	no	—
348	C₂×C₄	—	52	8	no	—
349	C₂×C₄	—	52	8	no	—
350	C₂×C₄	#88101	1	4	yes	complemented
351	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
356	C₂×C₄	C₂³×#261	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	13	4	no	—
359	C₈	—	26	2	no	—
360	C₈	#88237	1	4	yes	complemented
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	13	2	no	—
364	C₂²	—	13	2	no	—
365	C₂²	—	13	2	no	—
366	C₂²	—	13	2	no	—
367	C₂²	—	26	8	no	—
368	C₂²	—	26	1	no	—
369	C₂²	—	26	1	no	—
370	C₂²	C₂×#88101	1	2	yes	—
371	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	13	2	no	—
375	C₄	—	13	2	no	—
376	C₄	—	13	2	no	—
377	C₄	—	13	2	no	—
378	C₄	—	26	1	no	—
379	C₄	—	26	1	no	—
380	C₄	—	104	8	no	—
381	C₄	C₂×#88101	1	2	yes	—
382	C₄	C₂×#88101	1	2	yes	—
383	C₄	#11719092	1	2	yes	—
384	C₄	C₂×#88237	1	2	yes	—
385	C₂	—	2	2	no	—
386	C₂	—	13	4	no	—
387	C₂	—	26	2	no	—
388	C₂	#13131285	1	1	yes	characteristic
389	C₂	C₂²×#88101	1	1	yes	characteristic
390	C₂	C₂×#11719092	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#20816
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13130771	C₂	semidirect
3. #13130757	C₂	semidirect
5. C₄×#88101	C₂	semidirect
17. C₂×C₄×C₈×C₁₃	C₄	semidirect
18. C₂×C₈×Dic₁₃	C₄	semidirect
19. C₂×C₄×#1055	C₄	semidirect
20. C₄×C₈×D₁₃	C₄	semidirect
21. C₄×C₈×D₁₃	C₄	semidirect
22. C₄×C₈×D₁₃	C₄	semidirect
140. C₂×C₄×C₁₃	#106	semidirect
149. C₂×Dic₁₃	#106	semidirect
162. C₄×D₁₃	#106	semidirect
163. C₄×D₁₃	#106	semidirect
169. C₈×C₁₃	#117	semidirect
171. #1055	#117	semidirect
184. C₂×C₄×C₈	#261	semidirect
317. C₁₃	#20816	semidirect
350. C₂×C₄	#88101	semidirect
360. C₈	#88237	semidirect

Maximal subgroups

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

subgroup	index
#13131285	2
#13130771	2
#13130757	2
#13130712	2
C₄×#88101	2
C₂×C₄×C₈×D₁₃	2
#20816	13