Subgroups — C₄×#11718570 #16016252

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718570	C₂	1	1	yes	maximal, characteristic
2	C₄×#88158	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Dic₅₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116708	C₂	1	2	yes	maximal, complemented
5	#13116702	C₂	1	2	yes	maximal, complemented
6	C₄×Dic₁₀₄	C₂	1	2	yes	maximal, complemented
7	C₄×#88040	C₂	1	2	yes	maximal, complemented
8	#13116624	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116557	C₂	1	1	yes	maximal, characteristic, complemented
10	#13116549	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Dic₅₂	C₂²	1	1	yes	characteristic
13	C₂×#88158	C₂²	1	1	yes	characteristic
14	C₄×#6127	—	2	1	no	—
15	C₂×C₄×Dic₂₆	—	2	1	no	—
16	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	#11718774	—	2	1	no	—
20	#11718767	C₂²	1	1	yes	characteristic
21	C₂×#88058	C₂²	1	1	yes	characteristic
22	C₂×#88056	—	2	1	no	—
23	#11718570	C₄	1	8	yes	direct product factor
24	C₂×Dic₁₀₄	C₂²	1	2	yes	—
25	C₂×#88040	C₂²	1	2	yes	—
26	C₄×Dic₅₂	—	2	1	no	—
27	C₄×Dic₅₂	—	2	1	no	—
28	C₄×Dic₅₂	C₂²	1	2	yes	—
29	C₄×Dic₅₂	C₂²	1	2	yes	—
30	C₄×Dic₅₂	C₂²	1	1	yes	characteristic
31	C₄×Dic₅₂	C₂²	1	1	yes	characteristic
32	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
33	C₄×D₁₀₄	C₂²	1	1	yes	characteristic
34	C₄×#6095	—	2	1	no	—
35	C₄×#6095	—	2	1	no	—
36	C₁₃×#346	C₂²	1	2	yes	—
37	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
38	#11718101	C₂²	1	2	yes	—
39	#11718097	C₂²	1	2	yes	—
40	#11718096	C₂²	1	2	yes	—
41	#11718095	C₂²	1	2	yes	—
42	#11718095	C₂²	1	2	yes	—
43	#11718095	C₂²	1	2	yes	—
44	C₂×#6127	—	2	1	no	—
45	C₂²×Dic₂₆	—	2	1	no	—
46	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
49	C₄×C₂²⋊D₁₃	—	4	1	no	—
50	C₄×C₂²⋊D₁₃	—	4	1	no	—
51	#88180	—	2	1	no	—
52	C₂×C₄⋊Dic₁₃	—	2	1	no	—
53	C₂×#6101	—	4	1	no	—
54	C₂×C₄×Dic₁₃	—	4	1	no	—
55	C₂×Dic₅₂	—	2	1	no	—
56	C₂×Dic₅₂	—	2	2	no	—
57	C₂×Dic₅₂	C₂×C₄	1	4	yes	complemented
58	C₂×Dic₅₂	C₂³	1	1	yes	characteristic
59	C₂×Dic₅₂	C₂³	1	2	yes	—
60	#88158	—	2	2	no	—
61	#88158	C₂×C₄	1	4	yes	—
62	C₂×D₁₀₄	C₂³	1	1	yes	characteristic
63	C₂×#6095	—	2	1	no	—
64	C₄×D₅₂	—	2	1	no	—
65	C₄×D₅₂	—	2	1	no	—
66	#88126	—	4	1	no	—
67	C₄²×D₁₃	—	4	1	no	—
68	C₄×Dic₂₆	—	2	2	no	—
69	C₄×Dic₂₆	—	2	2	no	—
70	C₄×Dic₂₆	—	2	1	no	—
71	C₄×Dic₂₆	—	2	1	no	—
72	C₄×Dic₂₆	—	4	1	no	—
73	C₄×Dic₂₆	—	4	1	no	—
74	C₁₃×M₃₂	—	2	2	no	—
75	C₁₃×M₃₂	C₂×C₄	1	4	yes	complemented
76	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
77	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
78	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	#88061	—	2	1	no	—
83	#88061	—	2	1	no	—
84	#88058	—	2	1	no	—
85	#88058	C₂³	1	2	yes	—
86	#88058	C₂³	1	1	yes	characteristic
87	#88058	C₂³	1	1	yes	characteristic
88	#88057	—	2	1	no	—
89	#88056	—	2	2	no	—
90	#88056	—	2	2	no	—
91	#88056	—	2	1	no	—
92	#88056	—	2	1	no	—
93	Dic₁₀₄	C₂×C₄	1	8	yes	complemented
94	#88040	C₂×C₄	1	8	yes	complemented
95	C₄×#510	—	13	1	no	maximal, Sylow
96	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₁₃	—	4	1	no	—
100	C₂²×Dic₁₃	—	4	1	no	—
101	C₂²×Dic₁₃	—	4	1	no	—
102	#6127	—	2	4	no	—
103	#6127	—	4	2	no	—
104	C₂×D₅₂	—	2	1	no	—
105	C₂×C₄×D₁₃	—	4	1	no	—
106	C₂×C₄×D₁₃	—	4	1	no	—
107	C₂×C₄×D₁₃	—	4	1	no	—
108	C₂×Dic₂₆	—	2	4	no	—
109	C₂×Dic₂₆	—	2	1	no	—
110	C₂×Dic₂₆	—	2	2	no	—
111	C₂×Dic₂₆	—	4	1	no	—
112	C₂×Dic₂₆	—	4	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	#41	1	2	yes	—
119	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₄²×C₁₃	D₈	1	1	yes	characteristic
121	C₄²×C₁₃	D₈	1	1	yes	characteristic
122	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²⋊Dic₁₃	—	4	1	no	—
125	#6103	—	4	1	no	—
126	#6103	—	4	1	no	—
127	C₄⋊Dic₁₃	—	2	2	no	—
128	C₄⋊Dic₁₃	—	2	1	no	—
129	C₄⋊Dic₁₃	—	2	1	no	—
130	C₄⋊Dic₁₃	—	4	1	no	—
131	#6101	—	4	2	no	—
132	#6101	—	4	2	no	—
133	#6101	—	4	1	no	—
134	#6101	—	4	1	no	—
135	C₄×Dic₁₃	—	4	2	no	—
136	C₄×Dic₁₃	—	4	2	no	—
137	C₄×Dic₁₃	—	4	1	no	—
138	C₄×Dic₁₃	—	4	1	no	—
139	C₄×Dic₁₃	—	4	1	no	—
140	Dic₅₂	—	2	4	no	—
141	Dic₅₂	—	2	1	no	—
142	Dic₅₂	—	2	2	no	—
143	Dic₅₂	C₂²×C₄	1	2	yes	—
144	Dic₅₂	C₂²×C₄	1	4	yes	—
145	D₁₀₄	—	2	1	no	—
146	D₁₀₄	C₂²×C₄	1	2	yes	—
147	#6095	—	2	4	no	—
148	C₁₃×C₁₆	—	2	2	no	—
149	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
150	C₂×#510	—	13	1	no	—
151	C₄×#135	—	13	1	no	—
152	C₂×C₄×Q₁₆	—	13	1	no	—
153	#2176	—	13	2	no	—
154	#2175	—	13	2	no	—
155	C₄×Q₃₂	—	13	2	no	—
156	C₄×SD₃₂	—	13	2	no	—
157	#2159	—	13	1	no	—
158	#2141	—	13	1	no	—
159	#2139	—	13	1	no	—
160	C₄×M₃₂	D₁₃	1	1	yes	characteristic, complemented
161	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
162	C₂²×D₁₃	—	4	1	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	4	1	no	—
165	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃	#135	1	2	yes	—
172	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂²⋊D₁₃	—	4	4	no	—
174	C₂×Dic₁₃	—	4	2	no	—
175	C₂×Dic₁₃	—	4	1	no	—
176	C₂×Dic₁₃	—	4	4	no	—
177	C₂×Dic₁₃	—	4	2	no	—
178	C₂×Dic₁₃	—	4	1	no	—
179	C₂×Dic₁₃	—	4	1	no	—
180	C₂×Dic₁₃	—	8	2	no	—
181	D₅₂	—	2	2	no	—
182	D₅₂	—	4	1	no	—
183	C₄×D₁₃	—	4	4	no	—
184	C₄×D₁₃	—	8	2	no	—
185	C₄×D₁₃	—	8	2	no	—
186	Dic₂₆	—	2	2	no	—
187	Dic₂₆	—	2	4	no	—
188	Dic₂₆	—	4	2	no	—
189	Dic₂₆	—	4	1	no	—
190	Dic₂₆	—	4	4	no	—
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	—	2	1	no	—
193	C₈×C₁₃	C₄×D₄	1	2	yes	—
194	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×#135	—	13	1	no	—
197	C₂²×Q₁₆	—	13	1	no	—
198	C₄×#41	—	26	1	no	—
199	C₂×C₄×Q₈	—	26	1	no	—
200	#510	—	13	8	no	—
201	C₂×Q₃₂	—	13	2	no	—
202	C₂×SD₃₂	—	13	2	no	—
203	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
204	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
205	C₄×Q₁₆	—	13	2	no	—
206	C₄×Q₁₆	—	13	2	no	—
207	C₄×Q₁₆	—	13	1	no	—
208	C₄×Q₁₆	—	13	1	no	—
209	C₄×Q₁₆	—	26	1	no	—
210	C₄×Q₁₆	—	26	1	no	—
211	C₄×SD₁₆	—	26	1	no	—
212	C₄×SD₁₆	—	26	1	no	—
213	C₄×D₈	—	13	1	no	—
214	C₄×D₈	—	13	1	no	—
215	#427	—	13	1	no	—
216	C₂×#107	—	13	1	no	—
217	#416	—	26	1	no	—
218	C₂×#103	—	26	1	no	—
219	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
220	#367	—	13	2	no	—
221	#366	—	13	2	no	—
222	#358	—	13	2	no	—
223	#358	—	13	2	no	—
224	#358	—	13	2	no	—
225	#357	—	13	2	no	—
226	#346	C₂×D₁₃	1	2	yes	—
227	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	C₄×D₈	1	2	yes	—
231	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
232	C₂×D₁₃	—	4	2	no	—
233	C₂×D₁₃	—	8	1	no	—
234	C₂×D₁₃	—	8	1	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	C₄×D₈	1	2	yes	—
239	C₄×C₁₃	#510	1	2	yes	complemented
240	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
242	Dic₁₃	—	4	4	no	—
243	Dic₁₃	—	4	2	no	—
244	Dic₁₃	—	8	1	no	—
245	Dic₁₃	—	8	1	no	—
246	Dic₁₃	—	8	2	no	—
247	C₂×#41	—	26	1	no	—
248	C₂²×Q₈	—	26	1	no	—
249	#135	—	13	4	no	—
250	#135	—	26	2	no	—
251	C₂×Q₁₆	—	13	4	no	—
252	C₂×Q₁₆	—	13	2	no	—
253	C₂×Q₁₆	—	13	1	no	—
254	C₂×Q₁₆	—	26	1	no	—
255	C₂×Q₁₆	—	26	2	no	—
256	C₂×SD₁₆	—	26	1	no	—
257	C₂×D₈	—	13	1	no	—
258	C₂²×C₈	D₅₂	1	1	yes	characteristic
259	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
260	C₄×Q₈	—	26	2	no	—
261	C₄×Q₈	—	26	2	no	—
262	C₄×Q₈	—	26	1	no	—
263	C₄×Q₈	—	26	1	no	—
264	C₄×Q₈	—	52	1	no	—
265	C₄×Q₈	—	52	1	no	—
266	C₄×D₄	—	26	1	no	—
267	C₄×D₄	—	26	1	no	—
268	C₄×D₄	—	52	1	no	—
269	C₄×D₄	—	52	1	no	—
270	#117	—	26	1	no	—
271	#117	—	52	1	no	—
272	C₂×C₄⋊C₄	—	26	1	no	—
273	C₂×C₄⋊C₄	—	52	1	no	—
274	C₂×C₄²	—	52	1	no	—
275	C₂×C₄²	—	52	1	no	—
276	C₂×C₄²	D₅₂	1	1	yes	characteristic
277	Q₃₂	—	13	8	no	—
278	SD₃₂	—	13	8	no	—
279	M₃₂	—	2	2	no	—
280	M₃₂	C₄×D₁₃	1	4	yes	complemented
281	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
282	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
283	#107	—	13	2	no	—
284	#107	—	13	1	no	—
285	#107	—	13	1	no	—
286	#107	—	26	1	no	—
287	#106	—	26	1	no	—
288	#103	—	26	2	no	—
289	#103	—	26	2	no	—
290	#103	—	26	1	no	—
291	#103	—	26	1	no	—
292	#102	—	26	1	no	—
293	#102	—	26	1	no	—
294	C₄×C₈	D₅₂	1	1	yes	characteristic
295	C₄×C₈	D₅₂	1	1	yes	characteristic
296	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
298	C₂×C₁₃	—	2	2	no	—
299	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
300	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
301	C₂×C₁₃	#3414	1	1	yes	characteristic
302	D₁₃	—	8	2	no	—
303	#41	—	26	4	no	—
304	#41	—	52	2	no	—
305	C₂×Q₈	—	26	4	no	—
306	C₂×Q₈	—	26	1	no	—
307	C₂×Q₈	—	26	2	no	—
308	C₂×Q₈	—	52	1	no	—
309	C₂×Q₈	—	52	2	no	—
310	C₂×D₄	—	26	1	no	—
311	C₂×D₄	—	52	1	no	—
312	C₂²×C₄	—	52	1	no	—
313	C₂²×C₄	—	52	1	no	—
314	C₂²×C₄	—	52	1	no	—
315	C₂²×C₄	—	52	1	no	—
316	C₂²×C₄	—	52	1	no	—
317	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
318	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
320	Q₁₆	—	13	4	no	—
321	Q₁₆	—	13	2	no	—
322	Q₁₆	—	26	4	no	—
323	Q₁₆	—	26	2	no	—
324	Q₁₆	—	26	1	no	—
325	SD₁₆	—	26	4	no	—
326	D₈	—	13	2	no	—
327	D₈	—	26	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
330	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
331	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
332	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
333	C₂×C₈	#6127	1	2	yes	—
334	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
335	C₄⋊C₄	—	26	1	no	—
336	C₄⋊C₄	—	26	1	no	—
337	C₄⋊C₄	—	26	2	no	—
338	C₄⋊C₄	—	52	1	no	—
339	C₄⋊C₄	—	52	2	no	—
340	C₄⋊C₄	—	52	2	no	—
341	C₄⋊C₄	—	52	1	no	—
342	C₄⋊C₄	—	52	1	no	—
343	C₂²⋊C₄	—	52	1	no	—
344	C₂²⋊C₄	—	52	1	no	—
345	C₂²⋊C₄	—	52	1	no	—
346	C₄²	—	52	1	no	—
347	C₄²	—	52	1	no	—
348	C₄²	—	52	2	no	—
349	C₄²	—	52	1	no	—
350	C₄²	—	52	2	no	—
351	C₄²	D₁₀₄	1	1	yes	characteristic
352	C₄²	D₁₀₄	1	1	yes	characteristic
353	C₄²	C₂×D₅₂	1	1	yes	characteristic
354	C₄²	C₂×D₅₂	1	1	yes	characteristic
355	C₁₆	—	2	2	no	—
356	C₁₆	C₂×C₄×D₁₃	1	4	yes	—
357	C₁₃	C₄×#510	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	52	1	no	—
359	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
360	Q₈	—	26	2	no	—
361	Q₈	—	26	4	no	—
362	Q₈	—	52	2	no	—
363	Q₈	—	52	1	no	—
364	Q₈	—	52	4	no	—
365	D₄	—	26	2	no	—
366	D₄	—	52	4	no	—
367	D₄	—	52	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	52	1	no	—
371	C₂×C₄	—	52	2	no	—
372	C₂×C₄	—	52	4	no	—
373	C₂×C₄	—	52	4	no	—
374	C₂×C₄	—	52	1	no	—
375	C₂×C₄	—	52	1	no	—
376	C₂×C₄	—	52	2	no	—
377	C₂×C₄	—	104	2	no	—
378	C₂×C₄	—	104	2	no	—
379	C₂×C₄	—	104	2	no	—
380	C₂×C₄	C₄×D₅₂	1	2	yes	—
381	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
382	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
383	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
384	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
385	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
386	C₂×C₄	#88158	1	2	yes	—
387	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	C₄×D₅₂	1	2	yes	—
391	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
392	C₈	C₂×#6127	1	1	yes	characteristic
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	52	2	no	—
396	C₂²	—	104	1	no	—
397	C₂²	—	104	1	no	—
398	C₂²	C₄×D₁₀₄	1	2	yes	—
399	C₂²	C₂²×D₁₀₄	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	52	2	no	—
404	C₄	—	52	4	no	—
405	C₄	—	104	1	no	—
406	C₄	—	104	1	no	—
407	C₄	—	104	2	no	—
408	C₄	C₄×D₁₀₄	1	2	yes	—
409	C₄	#11718570	1	2	yes	direct product factor
410	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
411	C₄	C₂×#88158	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	104	2	no	—
414	C₂	C₂×C₄×D₁₀₄	1	1	yes	characteristic
415	C₂	C₂×#11718570	1	1	yes	characteristic
416	C₂	#13127972	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₁₀₄
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₄×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂×#88158	C₂²
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₄×M₃₂	D₁₃
hypocenter	C₁₃	C₄×#510
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Dic₅₂	C₂	semidirect
4. #13116708	C₂	semidirect
5. #13116702	C₂	semidirect
6. C₄×Dic₁₀₄	C₂	semidirect
7. C₄×#88040	C₂	semidirect
8. #13116624	C₂	semidirect
9. #13116557	C₂	semidirect
11. C₄×C₁₃×M₃₂	C₂	semidirect
23. #11718570	C₄	direct (N × H)
57. C₂×Dic₅₂	C₂×C₄	semidirect
75. C₁₃×M₃₂	C₂×C₄	semidirect
93. Dic₁₀₄	C₂×C₄	semidirect
94. #88040	C₂×C₄	semidirect
160. C₄×M₃₂	D₁₃	semidirect
239. C₄×C₁₃	#510	semidirect
280. M₃₂	C₄×D₁₃	semidirect
357. C₁₃	C₄×#510	semidirect
409. C₄	#11718570	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×#11718570	2
C₄×#88158	2
C₂×C₄×Dic₅₂	2
#13116708	2
#13116702	2
C₄×Dic₁₀₄	2
C₄×#88040	2
#13116624	2
#13116557	2
#13116549	2
C₄×C₁₃×M₃₂	2
C₄×#510	13

Subgroups — C4×#11718570 #16016252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718570 #16016252