Subgroups — C₁₃×#10808 #15697147

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#339	C₂	1	2	yes	maximal
3	C₂×C₁₃×#339	C₂	1	2	yes	maximal
4	C₁₃×#1728	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	complemented
12	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	complemented
13	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
14	C₁₃×#376	—	2	1	no	—
15	C₂×C₁₃×#95	—	2	2	no	—
16	C₄³×C₁₃	—	2	1	no	—
17	C₁₃×#339	—	2	4	no	—
18	C₁₃×#339	C₄	1	8	yes	complemented
19	C₁₃×#336	—	2	1	no	—
20	C₁₃×#336	—	2	1	no	—
21	C₂³×C₄×C₁₃	—	2	2	no	—
22	C₂³×C₄×C₁₃	D₄	1	2	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂×C₁₃×M₁₆	—	2	2	no	—
25	C₂×C₁₃×M₁₆	—	2	2	no	—
26	C₂×C₁₃×M₁₆	—	2	2	no	—
27	C₂×C₁₃×M₁₆	—	2	2	no	—
28	C₂×C₁₃×M₁₆	—	2	2	no	—
29	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
30	C₂²×C₈×C₁₃	—	2	2	no	—
31	C₁₃×#117	—	2	2	no	—
32	C₁₃×#117	—	2	1	no	—
33	C₁₃×#117	—	2	1	no	—
34	C₁₃×#117	C₂×C₄	1	4	yes	—
35	C₁₃×#117	D₄	1	2	yes	—
36	C₁₃×#117	Q₈	1	2	yes	—
37	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
40	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
41	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
42	C₂×C₄²×C₁₃	—	2	1	no	—
43	C₂×C₄²×C₁₃	—	2	1	no	—
44	C₂×C₄²×C₁₃	—	2	2	no	—
45	C₂×C₄²×C₁₃	—	2	2	no	—
46	C₂×C₄²×C₁₃	—	2	2	no	—
47	C₂×C₄²×C₁₃	—	2	2	no	—
48	C₂×C₄²×C₁₃	—	2	2	no	—
49	C₂×C₄²×C₁₃	—	2	2	no	—
50	C₂×C₄²×C₁₃	—	2	2	no	—
51	C₂×C₄²×C₁₃	—	2	2	no	—
52	C₂×C₄²×C₁₃	—	2	2	no	—
53	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
57	C₁₃×#95	—	2	8	no	—
58	C₁₃×#95	—	2	2	no	—
59	C₁₃×#95	—	2	2	no	—
60	#10808	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	—	2	8	no	—
63	C₂²×C₄×C₁₃	—	2	1	no	—
64	C₂²×C₄×C₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₃	—	2	2	no	—
66	C₂²×C₄×C₁₃	—	2	4	no	—
67	C₂²×C₄×C₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₃	—	2	4	no	—
69	C₂²×C₄×C₁₃	—	4	2	no	—
70	C₂²×C₄×C₁₃	—	4	4	no	—
71	C₂²×C₄×C₁₃	—	4	2	no	—
72	C₂²×C₄×C₁₃	—	4	2	no	—
73	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	#41	1	2	yes	—
83	C₂²×C₄×C₁₃	#41	1	2	yes	—
84	C₂²×C₄×C₁₃	#41	1	2	yes	—
85	C₁₃×M₁₆	—	2	4	no	—
86	C₁₃×M₁₆	—	2	4	no	—
87	C₁₃×M₁₆	—	4	2	no	—
88	C₁₃×M₁₆	—	4	2	no	—
89	C₂×C₈×C₁₃	—	2	4	no	—
90	C₂×C₈×C₁₃	—	4	2	no	—
91	C₂×C₈×C₁₃	—	4	2	no	—
92	C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₁₃×C₄⋊C₄	C₄²	1	2	yes	—
96	C₁₃×C₄⋊C₄	C₄²	1	2	yes	—
97	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
98	C₁₃×C₂²⋊C₄	—	2	4	no	—
99	C₁₃×C₂²⋊C₄	—	2	2	no	—
100	C₁₃×C₂²⋊C₄	—	2	2	no	—
101	C₄²×C₁₃	—	2	2	no	—
102	C₄²×C₁₃	—	2	2	no	—
103	C₄²×C₁₃	—	2	4	no	—
104	C₄²×C₁₃	—	2	2	no	—
105	C₄²×C₁₃	—	2	2	no	—
106	C₄²×C₁₃	—	2	2	no	—
107	C₄²×C₁₃	—	2	2	no	—
108	C₄²×C₁₃	—	2	4	no	—
109	C₄²×C₁₃	—	2	4	no	—
110	C₄²×C₁₃	—	4	4	no	—
111	C₄²×C₁₃	—	4	4	no	—
112	C₄²×C₁₃	—	4	2	no	—
113	C₄²×C₁₃	—	4	2	no	—
114	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
115	C₂×#339	C₂×C₁₃	1	2	yes	—
116	C₂×#339	C₂×C₁₃	1	2	yes	—
117	#1728	C₂×C₁₃	1	1	yes	characteristic
118	C₄×#95	C₂×C₁₃	1	1	yes	characteristic
119	C₂³×C₁₃	—	2	2	no	—
120	C₂³×C₁₃	—	2	2	no	—
121	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₃	C₄×D₄	1	2	yes	—
123	C₂³×C₁₃	#121	1	1	yes	characteristic
124	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
125	C₂³×C₁₃	#123	1	2	yes	—
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	2	8	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	4	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	4	8	no	—
136	C₂×C₄×C₁₃	—	4	8	no	—
137	C₂×C₄×C₁₃	—	4	8	no	—
138	C₂×C₄×C₁₃	—	4	4	no	—
139	C₂×C₄×C₁₃	—	4	4	no	—
140	C₂×C₄×C₁₃	—	4	2	no	—
141	C₂×C₄×C₁₃	—	4	2	no	—
142	C₂×C₄×C₁₃	—	4	2	no	—
143	C₂×C₄×C₁₃	—	4	2	no	—
144	C₂×C₄×C₁₃	#104	1	4	yes	—
145	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
148	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
149	C₂×C₄×C₁₃	#117	1	2	yes	—
150	C₂×C₄×C₁₃	#117	1	2	yes	—
151	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
156	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#123	1	2	yes	—
159	C₂×C₄×C₁₃	#124	1	2	yes	—
160	C₂×C₄×C₁₃	#125	1	2	yes	—
161	C₂×C₄×C₁₃	#126	1	2	yes	—
162	C₂×C₄×C₁₃	#126	1	2	yes	—
163	C₈×C₁₃	—	4	4	no	—
164	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
165	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
166	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
167	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
168	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
169	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	complemented
170	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	complemented
171	C₄×C₂²⋊C₄	—	2	2	no	—
172	#376	—	2	1	no	—
173	C₂×#95	—	2	2	no	—
174	C₄³	—	2	1	no	—
175	#339	—	2	4	no	—
176	#339	C₄×C₁₃	1	8	yes	complemented
177	#336	—	2	1	no	—
178	#336	—	2	1	no	—
179	C₂²×C₁₃	—	2	2	no	—
180	C₂²×C₁₃	—	2	2	no	—
181	C₂²×C₁₃	—	2	4	no	—
182	C₂²×C₁₃	—	2	2	no	—
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₁₃	#380	1	1	yes	characteristic
186	C₂²×C₁₃	#381	1	1	yes	characteristic
187	C₂²×C₁₃	#387	1	2	yes	—
188	C₂²×C₁₃	#388	1	2	yes	—
189	C₂²×C₁₃	C₂×#104	1	2	yes	—
190	C₂²×C₁₃	#421	1	2	yes	—
191	C₄×C₁₃	—	2	4	no	—
192	C₄×C₁₃	—	4	8	no	—
193	C₄×C₁₃	—	4	4	no	—
194	C₄×C₁₃	—	4	2	no	—
195	C₄×C₁₃	—	4	2	no	—
196	C₄×C₁₃	—	4	2	no	—
197	C₄×C₁₃	#376	1	1	yes	characteristic
198	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
199	C₄×C₁₃	#382	1	1	yes	characteristic
200	C₄×C₁₃	#383	1	1	yes	characteristic
201	C₄×C₁₃	#387	1	2	yes	—
202	C₄×C₁₃	#388	1	2	yes	—
203	C₂³×C₄	—	2	2	no	—
204	C₂³×C₄	D₄×C₁₃	1	2	yes	—
205	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
206	C₂×M₁₆	—	2	2	no	—
207	C₂×M₁₆	—	2	2	no	—
208	C₂×M₁₆	—	2	2	no	—
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
212	C₂²×C₈	—	2	2	no	—
213	#117	—	2	2	no	—
214	#117	—	2	1	no	—
215	#117	—	2	1	no	—
216	#117	C₂×C₄×C₁₃	1	4	yes	—
217	#117	D₄×C₁₃	1	2	yes	—
218	#117	Q₈×C₁₃	1	2	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
222	C₂×C₂²⋊C₄	—	2	1	no	—
223	C₂×C₂²⋊C₄	—	2	1	no	—
224	C₂×C₄²	—	2	1	no	—
225	C₂×C₄²	—	2	1	no	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	—	2	2	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
236	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
237	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
239	#95	—	2	8	no	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	C₂×C₁₃	—	2	2	no	—
243	C₂×C₁₃	—	2	2	no	—
244	C₂×C₁₃	#1434	1	1	yes	characteristic
245	C₂×C₁₃	C₄×#104	1	1	yes	characteristic
246	C₂×C₁₃	#1759	1	1	yes	characteristic
247	C₂×C₁₃	#1806	1	2	yes	—
248	C₂×C₁₃	#1826	1	2	yes	—
249	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	4	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
262	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
267	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
268	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
269	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
270	C₂²×C₄	C₁₃×#41	1	2	yes	—
271	C₂²×C₄	C₁₃×#41	1	2	yes	—
272	C₂²×C₄	C₁₃×#41	1	2	yes	—
273	M₁₆	—	2	4	no	—
274	M₁₆	—	2	4	no	—
275	M₁₆	—	4	2	no	—
276	M₁₆	—	4	2	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	4	2	no	—
279	C₂×C₈	—	4	2	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	C₄²×C₁₃	1	2	yes	—
284	C₄⋊C₄	C₄²×C₁₃	1	2	yes	—
285	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
286	C₂²⋊C₄	—	2	4	no	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	4	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	4	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	4	4	no	—
299	C₄²	—	4	4	no	—
300	C₄²	—	4	2	no	—
301	C₄²	—	4	2	no	—
302	C₁₃	#10808	1	1	yes	characteristic, direct product factor, Sylow
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
306	C₂³	C₄×D₄×C₁₃	1	2	yes	—
307	C₂³	C₁₃×#121	1	1	yes	characteristic
308	C₂³	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
309	C₂³	C₁₃×#123	1	2	yes	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	8	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	—	4	8	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	C₁₃×#104	1	4	yes	—
329	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
330	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
332	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
333	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
334	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
335	C₂×C₄	C₁₃×#117	1	2	yes	—
336	C₂×C₄	C₁₃×#117	1	2	yes	—
337	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
338	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
339	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
340	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
341	C₂×C₄	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
342	C₂×C₄	C₁₃×#123	1	2	yes	—
343	C₂×C₄	C₁₃×#124	1	2	yes	—
344	C₂×C₄	C₁₃×#125	1	2	yes	—
345	C₂×C₄	C₁₃×#126	1	2	yes	—
346	C₂×C₄	C₁₃×#126	1	2	yes	—
347	C₈	—	4	4	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	C₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
354	C₂²	C₁₃×#380	1	1	yes	characteristic
355	C₂²	C₁₃×#381	1	1	yes	characteristic
356	C₂²	C₁₃×#387	1	2	yes	—
357	C₂²	C₁₃×#388	1	2	yes	—
358	C₂²	C₂×C₁₃×#104	1	2	yes	—
359	C₂²	C₁₃×#421	1	2	yes	—
360	C₄	—	2	4	no	—
361	C₄	—	4	8	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	4	no	—
365	C₄	—	4	2	no	—
366	C₄	C₁₃×#376	1	1	yes	characteristic
367	C₄	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
368	C₄	C₁₃×#382	1	1	yes	characteristic
369	C₄	C₁₃×#383	1	1	yes	characteristic
370	C₄	C₁₃×#387	1	2	yes	—
371	C₄	C₁₃×#388	1	2	yes	—
372	C₂	—	2	2	no	—
373	C₂	—	2	2	no	—
374	C₂	C₁₃×#1434	1	1	yes	characteristic
375	C₂	C₄×C₁₃×#104	1	1	yes	characteristic
376	C₂	C₁₃×#1759	1	1	yes	characteristic
377	C₂	C₁₃×#1806	1	2	yes	—
378	C₂	C₁₃×#1826	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₄×C₁₃×C₄⋊C₄	C₄	semidirect
12. C₄×C₁₃×C₄⋊C₄	C₄	semidirect
18. C₁₃×#339	C₄	semidirect
60. #10808	C₁₃	direct (N × H)
169. C₄×C₄⋊C₄	C₄×C₁₃	semidirect
170. C₄×C₄⋊C₄	C₄×C₁₃	semidirect
176. #339	C₄×C₁₃	semidirect
302. C₁₃	#10808	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#117	2
C₂×C₁₃×#339	2
C₁₃×#1728	2
C₄×C₁₃×#95	2
#10808	13

Subgroups — C13×#10808 #15697147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10808 #15697147