Subgroups — C₄×#11718121 #15768099

Order 3328.

1182 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×#1055	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718121	C₂	1	4	yes	maximal
4	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	—	2	1	no	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₁₃	—	2	1	no	—
10	C₂³×#1055	C₂²	1	2	yes	—
11	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
12	C₄×C₁₃×C₄⋊C₄	C₄	1	4	yes	complemented
13	C₂×C₁₃×#95	—	2	1	no	—
14	C₂×#88071	—	2	1	no	—
15	C₄×C₄⋊Dic₁₃	—	2	2	no	—
16	C₄×C₄⋊Dic₁₃	C₄	1	4	yes	complemented
17	C₂×C₄×#1055	—	2	2	no	—
18	C₂×C₄×#1055	—	2	2	no	—
19	C₂×C₄×#1055	C₄	1	4	yes	complemented
20	#11718121	C₄	1	16	yes	direct product factor
21	C₂³×C₄×C₁₃	—	2	2	no	—
22	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂³×Dic₁₃	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
28	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
29	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
30	C₂×C₄²×C₁₃	—	2	4	no	—
31	C₂×C₄²×C₁₃	—	4	2	no	—
32	C₂×C₄²×C₁₃	—	4	2	no	—
33	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₃	D₄	1	2	yes	—
37	C₂×C₄²×C₁₃	D₄	1	2	yes	—
38	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
39	C₂×C₄⋊Dic₁₃	—	2	2	no	—
40	C₂×C₄⋊Dic₁₃	—	2	4	no	—
41	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
42	C₂×C₄⋊Dic₁₃	C₂×C₄	1	8	yes	—
43	C₂×C₄×Dic₁₃	—	2	4	no	—
44	C₂×C₄×Dic₁₃	—	4	2	no	—
45	C₂×C₄×Dic₁₃	—	4	2	no	—
46	C₂²×#1055	—	2	2	no	—
47	C₂²×#1055	—	2	2	no	—
48	C₂²×#1055	—	2	4	no	—
49	C₂²×#1055	C₂×C₄	1	4	yes	—
50	C₂²×#1055	C₂×C₄	1	8	yes	—
51	C₁₃×#95	—	2	4	no	—
52	#88071	—	2	4	no	—
53	C₄×#1055	—	2	8	no	—
54	C₄×#340	—	13	1	no	maximal, Sylow
55	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	—	2	4	no	—
57	C₂²×C₄×C₁₃	—	2	4	no	—
58	C₂²×C₄×C₁₃	—	2	8	no	—
59	C₂²×C₄×C₁₃	—	4	2	no	—
60	C₂²×C₄×C₁₃	—	4	2	no	—
61	C₂²×C₄×C₁₃	—	4	4	no	—
62	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₃	D₈	1	2	yes	—
69	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
70	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
71	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
72	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
75	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	#41	1	4	yes	—
80	C₂²×Dic₁₃	—	2	4	no	—
81	C₂²×Dic₁₃	—	2	8	no	—
82	C₂²×Dic₁₃	—	4	2	no	—
83	C₂²×Dic₁₃	—	4	2	no	—
84	C₂²×Dic₁₃	—	4	4	no	—
85	C₁₃×C₄⋊C₄	—	2	4	no	—
86	C₁₃×C₄⋊C₄	—	2	8	no	—
87	C₁₃×C₄⋊C₄	C₄²	1	8	yes	complemented
88	C₄²×C₁₃	—	4	8	no	—
89	C₄²×C₁₃	C₄²	1	4	yes	—
90	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
91	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
92	C₄²×C₁₃	C₄⋊C₄	1	4	yes	—
93	C₄⋊Dic₁₃	—	2	4	no	—
94	C₄⋊Dic₁₃	—	2	8	no	—
95	C₄⋊Dic₁₃	C₄²	1	8	yes	complemented
96	C₄×Dic₁₃	—	4	8	no	—
97	C₂×#1055	—	2	4	no	—
98	C₂×#1055	—	2	4	no	—
99	C₂×#1055	—	2	8	no	—
100	C₂×#1055	—	2	8	no	—
101	C₂×#1055	C₄²	1	8	yes	complemented
102	C₂²×C₄×C₈	—	13	1	no	—
103	C₂×C₄×C₄⋊C₄	—	13	1	no	—
104	C₂×C₄×C₄⋊C₄	D₁₃	1	1	yes	characteristic
105	C₂×#340	—	13	4	no	—
106	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₂³×C₁₃	C₄×D₄	1	4	yes	—
110	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
111	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
112	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
113	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
114	C₂³×C₁₃	#135	1	4	yes	—
115	C₂×C₄×C₁₃	—	2	4	no	—
116	C₂×C₄×C₁₃	—	2	4	no	—
117	C₂×C₄×C₁₃	—	2	4	no	—
118	C₂×C₄×C₁₃	—	2	8	no	—
119	C₂×C₄×C₁₃	—	4	4	no	—
120	C₂×C₄×C₁₃	—	4	4	no	—
121	C₂×C₄×C₁₃	—	4	8	no	—
122	C₂×C₄×C₁₃	—	4	8	no	—
123	C₂×C₄×C₁₃	#95	1	4	yes	—
124	C₂×C₄×C₁₃	#95	1	4	yes	—
125	C₂×C₄×C₁₃	#102	1	4	yes	—
126	C₂×C₄×C₁₃	#102	1	4	yes	—
127	C₂×C₄×C₁₃	#103	1	4	yes	—
128	C₂×C₄×C₁₃	#103	1	4	yes	—
129	C₂×C₄×C₁₃	#106	1	4	yes	—
130	C₂×C₄×C₁₃	#107	1	4	yes	—
131	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
132	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₃	#117	1	2	yes	—
139	C₂×C₄×C₁₃	#117	1	2	yes	—
140	C₂×C₄×C₁₃	#117	1	2	yes	—
141	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
142	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
143	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
144	C₂×Dic₁₃	—	2	8	no	—
145	C₂×Dic₁₃	—	4	4	no	—
146	C₂×Dic₁₃	—	4	4	no	—
147	C₂×Dic₁₃	—	4	8	no	—
148	C₂×Dic₁₃	—	4	8	no	—
149	#1055	—	2	8	no	—
150	C₂³×C₈	—	13	2	no	—
151	C₂²×C₄⋊C₄	—	13	2	no	—
152	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
153	C₂²×C₄²	—	2	1	no	—
154	C₂²×C₄²	—	26	1	no	—
155	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
156	C₂×C₄×C₈	—	13	4	no	—
157	C₂×C₄×C₈	—	26	2	no	—
158	C₂×C₄×C₈	—	26	2	no	—
159	C₄×C₄⋊C₄	—	2	2	no	—
160	C₄×C₄⋊C₄	—	13	4	no	—
161	C₄×C₄⋊C₄	—	26	2	no	—
162	C₄×C₄⋊C₄	Dic₁₃	1	4	yes	complemented
163	C₂×#95	—	2	1	no	—
164	C₂×#95	—	26	1	no	—
165	#340	—	13	16	no	—
166	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
167	C₂²×C₁₃	C₄×C₂²⋊C₄	1	2	yes	—
168	C₂²×C₁₃	C₄×C₂²⋊C₄	1	2	yes	—
169	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
170	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
171	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
172	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
173	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
174	C₂²×C₁₃	#416	1	2	yes	—
175	C₂²×C₁₃	#416	1	2	yes	—
176	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
177	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
178	C₂²×C₁₃	#427	1	2	yes	—
179	C₂²×C₁₃	C₄×D₈	1	4	yes	—
180	C₂²×C₁₃	C₄×SD₁₆	1	4	yes	—
181	C₂²×C₁₃	C₄×SD₁₆	1	4	yes	—
182	C₂²×C₁₃	C₄×Q₁₆	1	4	yes	—
183	C₄×C₁₃	—	2	4	no	—
184	C₄×C₁₃	—	4	8	no	—
185	C₄×C₁₃	#340	1	8	yes	complemented
186	C₄×C₁₃	C₄³	1	1	yes	characteristic
187	C₄×C₁₃	#376	1	1	yes	characteristic
188	C₄×C₁₃	C₄×C₂²⋊C₄	1	2	yes	—
189	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
190	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
191	Dic₁₃	—	4	8	no	—
192	C₂³×C₄	—	2	2	no	—
193	C₂³×C₄	—	26	2	no	—
194	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
195	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
196	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
197	C₂²×C₈	—	13	8	no	—
198	C₂²×C₈	—	13	4	no	—
199	C₂²×C₈	—	26	2	no	—
200	C₂²×C₈	—	26	4	no	—
201	C₂²×C₈	—	26	2	no	—
202	C₂×C₄⋊C₄	—	2	4	no	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	13	8	no	—
205	C₂×C₄⋊C₄	—	13	4	no	—
206	C₂×C₄⋊C₄	—	26	2	no	—
207	C₂×C₄⋊C₄	—	26	4	no	—
208	C₂×C₄⋊C₄	C₄×D₁₃	1	8	yes	—
209	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
210	C₂×C₄²	—	2	4	no	—
211	C₂×C₄²	—	4	2	no	—
212	C₂×C₄²	—	4	2	no	—
213	C₂×C₄²	—	26	4	no	—
214	C₂×C₄²	—	52	2	no	—
215	C₂×C₄²	—	52	2	no	—
216	C₂×C₄²	Dic₂₆	1	2	yes	—
217	C₂×C₄²	C₄×D₁₃	1	2	yes	—
218	C₂×C₄²	C₄×D₁₃	1	2	yes	—
219	C₂×C₄²	D₅₂	1	2	yes	—
220	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
221	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
222	C₄×C₈	—	26	8	no	—
223	#95	—	2	4	no	—
224	#95	—	26	4	no	—
225	C₂×C₁₃	C₄×#95	1	1	yes	characteristic
226	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
227	C₂×C₁₃	#1735	1	1	yes	characteristic
228	C₂×C₁₃	C₄×#102	1	2	yes	—
229	C₂×C₁₃	C₄×#102	1	2	yes	—
230	C₂×C₁₃	C₄×#103	1	2	yes	—
231	C₂×C₁₃	C₄×#103	1	2	yes	—
232	C₂×C₁₃	C₄×#106	1	2	yes	—
233	C₂×C₁₃	C₄×#107	1	2	yes	—
234	C₂⁴	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	8	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	4	2	no	—
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	4	no	—
241	C₂²×C₄	—	26	4	no	—
242	C₂²×C₄	—	26	8	no	—
243	C₂²×C₄	—	52	2	no	—
244	C₂²×C₄	—	52	2	no	—
245	C₂²×C₄	—	52	4	no	—
246	C₂²×C₄	#6101	1	2	yes	—
247	C₂²×C₄	#6101	1	2	yes	—
248	C₂²×C₄	#6103	1	2	yes	—
249	C₂²×C₄	#6103	1	2	yes	—
250	C₂²×C₄	#6104	1	2	yes	—
251	C₂²×C₄	#6105	1	2	yes	—
252	C₂²×C₄	#6106	1	2	yes	—
253	C₂²×C₄	#6107	1	2	yes	—
254	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
255	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
256	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
258	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
261	C₂²×C₄	#6127	1	4	yes	—
262	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
264	C₂×C₈	—	13	8	no	—
265	C₂×C₈	—	26	4	no	—
266	C₂×C₈	—	26	8	no	—
267	C₂×C₈	—	26	4	no	—
268	C₂×C₈	—	26	8	no	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	2	8	no	—
271	C₄⋊C₄	—	13	8	no	—
272	C₄⋊C₄	—	26	4	no	—
273	C₄⋊C₄	—	26	8	no	—
274	C₄⋊C₄	C₄×Dic₁₃	1	8	yes	complemented
275	C₄²	—	4	8	no	—
276	C₄²	—	52	8	no	—
277	C₄²	C₄×Dic₁₃	1	4	yes	—
278	C₄²	#6101	1	4	yes	—
279	C₄²	C₄⋊Dic₁₃	1	4	yes	—
280	C₄²	#6103	1	4	yes	—
281	C₁₃	C₄×#340	1	1	yes	characteristic, complemented, Sylow
282	C₂³	C₂×#6101	1	1	yes	characteristic
283	C₂³	C₂×#6103	1	1	yes	characteristic
284	C₂³	C₄×C₂²⋊D₁₃	1	4	yes	—
285	C₂³	C₂×#6104	1	1	yes	characteristic
286	C₂³	C₂×#6105	1	1	yes	characteristic
287	C₂³	C₂×#6106	1	1	yes	characteristic
288	C₂³	C₂×#6107	1	1	yes	characteristic
289	C₂³	#88204	1	4	yes	—
290	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	4	8	no	—
296	C₂×C₄	—	4	8	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	26	8	no	—
300	C₂×C₄	—	52	4	no	—
301	C₂×C₄	—	52	8	no	—
302	C₂×C₄	—	52	8	no	—
303	C₂×C₄	—	52	4	no	—
304	C₂×C₄	#88047	1	4	yes	—
305	C₂×C₄	#88048	1	4	yes	—
306	C₂×C₄	#88049	1	4	yes	—
307	C₂×C₄	#88050	1	4	yes	—
308	C₂×C₄	#88071	1	4	yes	—
309	C₂×C₄	#88071	1	4	yes	—
310	C₂×C₄	#88072	1	4	yes	—
311	C₂×C₄	#88075	1	4	yes	—
312	C₂×C₄	C₄×Dic₂₆	1	4	yes	—
313	C₂×C₄	C₄²×D₁₃	1	2	yes	—
314	C₂×C₄	C₄²×D₁₃	1	2	yes	—
315	C₂×C₄	#88126	1	2	yes	—
316	C₂×C₄	#88126	1	2	yes	—
317	C₂×C₄	C₄×D₅₂	1	4	yes	—
318	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
320	C₂×C₄	C₂×#6101	1	1	yes	characteristic
321	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
322	C₂×C₄	#88180	1	2	yes	—
323	C₂×C₄	C₂×#6103	1	1	yes	characteristic
324	C₂×C₄	C₄×C₂²⋊D₁₃	1	4	yes	—
325	C₈	—	26	8	no	—
326	C₂²	C₄×#6101	1	2	yes	—
327	C₂²	C₄×#6103	1	2	yes	—
328	C₂²	C₂×#88047	1	1	yes	characteristic
329	C₂²	C₂×#88048	1	1	yes	characteristic
330	C₂²	C₂×#88049	1	1	yes	characteristic
331	C₂²	C₂×#88050	1	1	yes	characteristic
332	C₂²	#11718659	1	2	yes	—
333	C₂²	#11718663	1	2	yes	—
334	C₂²	C₄×#6104	1	4	yes	—
335	C₂²	C₄×#6105	1	4	yes	—
336	C₂²	C₄×#6106	1	4	yes	—
337	C₂²	C₄×#6107	1	4	yes	—
338	C₂²	C₂×#88071	1	1	yes	characteristic
339	C₂²	C₄×C₂²⋊Dic₁₃	1	2	yes	—
340	C₂²	C₂×#88072	1	1	yes	characteristic
341	C₂²	C₂×#88075	1	1	yes	characteristic
342	C₂²	#11718894	1	2	yes	—
343	C₄	—	2	4	no	—
344	C₄	—	4	8	no	—
345	C₄	—	52	8	no	—
346	C₄	#11718121	1	8	yes	direct product factor
347	C₄	C₄²×Dic₁₃	1	1	yes	characteristic
348	C₄	C₄×#6101	1	2	yes	—
349	C₄	#11718593	1	1	yes	characteristic
350	C₄	C₄×C₄⋊Dic₁₃	1	2	yes	—
351	C₄	C₄×#6103	1	2	yes	—
352	C₂	C₄×#88071	1	1	yes	characteristic
353	C₂	C₂×#11718121	1	1	yes	characteristic
354	C₂	#13114552	1	1	yes	characteristic
355	C₂	C₄×#88072	1	2	yes	—
356	C₂	C₄×#88049	1	2	yes	—
357	C₂	C₄×#88075	1	2	yes	—
358	C₂	C₄×#88050	1	2	yes	—
359	C₂	C₄×#88048	1	2	yes	—
360	C₂	C₄×#88047	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²⋊D₁₃
commutator	C₄×C₁₃	C₄³
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₄⋊C₄	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₁₃
hypocenter	C₁₃	C₄×#340
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
12. C₄×C₁₃×C₄⋊C₄	C₄	semidirect
16. C₄×C₄⋊Dic₁₃	C₄	semidirect
19. C₂×C₄×#1055	C₄	semidirect
20. #11718121	C₄	direct (N × H)
87. C₁₃×C₄⋊C₄	C₄²	semidirect
95. C₄⋊Dic₁₃	C₄²	semidirect
101. C₂×#1055	C₄²	semidirect
162. C₄×C₄⋊C₄	Dic₁₃	semidirect
185. C₄×C₁₃	#340	semidirect
274. C₄⋊C₄	C₄×Dic₁₃	semidirect
281. C₁₃	C₄×#340	semidirect
346. C₄	#11718121	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×#1055	2
C₂×C₄×C₄⋊Dic₁₃	2
C₂×#11718121	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₄×#340	13

Subgroups — C4×#11718121 #15768099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718121 #15768099