Subgroups — C₁₃×#32671 #15719010

Order 3328.

764 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2592	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2015	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2012	C₂	1	2	yes	maximal
6	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1968	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1926	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#124	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#106	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#103	C₂²	1	2	yes	—
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#397	—	2	2	no	—
23	C₁₃×#393	—	2	2	no	—
24	C₁₃×#391	C₂²	1	2	yes	—
25	C₁₃×#391	C₂²	1	2	yes	—
26	C₁₃×#390	C₂²	1	2	yes	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#388	—	2	2	no	—
29	C₁₃×#388	—	2	2	no	—
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₁₃×#340	C₂²	1	1	yes	characteristic
32	C₁₃×#340	C₂²	1	1	yes	characteristic
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂×C₁₃×Q₁₆	—	4	2	no	—
39	C₂×C₁₃×Q₁₆	—	4	1	no	—
40	C₂×C₁₃×SD₁₆	—	2	4	no	—
41	C₂×C₁₃×SD₁₆	—	4	2	no	—
42	C₂×C₁₃×SD₁₆	—	4	2	no	—
43	C₂×C₁₃×D₈	—	4	2	no	—
44	C₂×C₁₃×D₈	—	4	1	no	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₁₃×#124	—	4	2	no	—
49	C₁₃×#124	—	4	2	no	—
50	C₄×Q₈×C₁₃	—	4	1	no	—
51	C₄×Q₈×C₁₃	—	4	1	no	—
52	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₄²×C₁₃	—	2	2	no	—
63	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#106	—	4	2	no	—
66	C₁₃×C₄⋊C₈	—	4	1	no	—
67	C₁₃×#103	—	2	4	no	—
68	C₁₃×#103	—	4	2	no	—
69	C₁₃×#102	—	2	4	no	—
70	C₁₃×#102	—	4	2	no	—
71	C₄×C₈×C₁₃	—	4	1	no	—
72	C₁₃×#95	—	2	2	no	—
73	C₁₃×#95	—	2	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	#32671	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁴×C₁₃	—	2	2	no	—
79	C₂×Q₈×C₁₃	—	2	2	no	—
80	C₂×Q₈×C₁₃	—	2	2	no	—
81	C₂×Q₈×C₁₃	—	2	2	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	4	1	no	—
87	C₂×Q₈×C₁₃	—	4	1	no	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
102	C₁₃×Q₁₆	—	4	4	no	—
103	C₁₃×SD₁₆	—	4	8	no	—
104	C₁₃×D₈	—	4	4	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	#41	1	4	yes	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	4	1	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₂²⋊C₄	—	4	4	no	—
119	C₁₃×C₂²⋊C₄	—	4	4	no	—
120	C₁₃×C₂²⋊C₄	—	4	4	no	—
121	C₁₃×C₂²⋊C₄	—	4	4	no	—
122	C₁₃×C₂²⋊C₄	—	8	2	no	—
123	C₁₃×C₂²⋊C₄	—	8	2	no	—
124	C₄²×C₁₃	—	2	1	no	—
125	C₄²×C₁₃	—	2	1	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	8	2	no	—
129	#2592	C₂×C₁₃	1	2	yes	complemented
130	#2056	C₂×C₁₃	1	1	yes	characteristic, complemented
131	#2054	C₂×C₁₃	1	1	yes	characteristic
132	#2015	C₂×C₁₃	1	2	yes	complemented
133	#2012	C₂×C₁₃	1	2	yes	—
134	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#1968	C₂×C₁₃	1	2	yes	complemented
136	#1927	C₂×C₁₃	1	2	yes	complemented
137	#1926	C₂×C₁₃	1	2	yes	complemented
138	C₂³×C₁₃	—	4	2	no	—
139	C₂³×C₁₃	—	4	2	no	—
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	4	2	no	—
144	C₂³×C₁₃	—	4	2	no	—
145	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₁₃	—	4	4	no	—
147	Q₈×C₁₃	—	4	2	no	—
148	Q₈×C₁₃	—	4	2	no	—
149	Q₈×C₁₃	—	4	2	no	—
150	Q₈×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	4	2	no	—
152	D₄×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	4	2	no	—
154	D₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	#135	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
176	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
178	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
179	C₈×C₁₃	—	2	4	no	—
180	C₈×C₁₃	—	4	1	no	—
181	C₈×C₁₃	—	4	1	no	—
182	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
183	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
184	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×#124	C₂²×C₁₃	1	2	yes	—
186	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×#106	C₂²×C₁₃	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#103	C₂²×C₁₃	1	2	yes	—
190	C₂×#103	C₂²×C₁₃	1	2	yes	—
191	C₂×#102	C₂²×C₁₃	1	2	yes	—
192	C₂×#102	C₂²×C₁₃	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
194	#397	—	2	2	no	—
195	#393	—	2	2	no	—
196	#391	C₂²×C₁₃	1	2	yes	—
197	#391	C₂²×C₁₃	1	2	yes	—
198	#390	C₂²×C₁₃	1	2	yes	—
199	#390	C₂²×C₁₃	1	2	yes	—
200	#388	—	2	2	no	—
201	#388	—	2	2	no	—
202	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
203	#340	C₂²×C₁₃	1	1	yes	characteristic
204	#340	C₂²×C₁₃	1	1	yes	characteristic
205	#336	C₂²×C₁₃	1	2	yes	—
206	#336	C₂²×C₁₃	1	2	yes	—
207	C₂²×C₁₃	—	8	2	no	—
208	C₂²×C₁₃	—	8	2	no	—
209	C₂²×C₁₃	—	8	2	no	—
210	C₂²×C₁₃	—	8	2	no	—
211	C₂²×C₁₃	—	8	2	no	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	—	8	2	no	—
214	C₂²×C₁₃	#534	1	1	yes	characteristic
215	C₂²×C₁₃	#550	1	2	yes	—
216	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
217	C₂²×C₁₃	#575	1	1	yes	characteristic
218	C₂²×C₁₃	#577	1	2	yes	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	4	2	no	—
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	4	1	no	—
223	C₄×C₁₃	—	8	2	no	—
224	C₄×C₁₃	—	8	2	no	—
225	C₄×C₁₃	—	8	2	no	—
226	C₄×C₁₃	#538	1	2	yes	—
227	C₄×C₁₃	#555	1	1	yes	characteristic
228	C₄×C₁₃	H(3,𝔽₄)	1	1	yes	characteristic
229	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
230	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
231	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
232	C₂×Q₁₆	—	4	2	no	—
233	C₂×Q₁₆	—	4	1	no	—
234	C₂×SD₁₆	—	2	4	no	—
235	C₂×SD₁₆	—	4	2	no	—
236	C₂×SD₁₆	—	4	2	no	—
237	C₂×D₈	—	4	2	no	—
238	C₂×D₈	—	4	1	no	—
239	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
242	#124	—	4	2	no	—
243	#124	—	4	2	no	—
244	C₄×Q₈	—	4	1	no	—
245	C₄×Q₈	—	4	1	no	—
246	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
247	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
258	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
259	#106	—	4	2	no	—
260	C₄⋊C₈	—	4	1	no	—
261	#103	—	2	4	no	—
262	#103	—	4	2	no	—
263	#102	—	2	4	no	—
264	#102	—	4	2	no	—
265	C₄×C₈	—	4	1	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	C₂×C₁₃	—	16	2	no	—
272	C₂×C₁₃	#2733	1	1	yes	characteristic
273	C₂×C₁₃	#3191	1	1	yes	characteristic
274	C₂×C₁₃	#3204	1	1	yes	characteristic
275	C₂×C₁₃	#3394	1	2	yes	—
276	C₂×C₁₃	#3401	1	2	yes	—
277	C₂⁴	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
301	Q₁₆	—	4	4	no	—
302	SD₁₆	—	4	8	no	—
303	D₈	—	4	4	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	C₁₃×#41	1	4	yes	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	4	4	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	8	2	no	—
322	C₂²⋊C₄	—	8	2	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	8	2	no	—
328	C₁₃	#32671	1	1	yes	characteristic, direct product factor, Sylow
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
337	Q₈	—	4	4	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	C₁₃×#135	1	2	yes	—
366	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
367	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
369	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	C₁₃×#534	1	1	yes	characteristic
381	C₂²	C₁₃×#550	1	2	yes	—
382	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
383	C₂²	C₁₃×#575	1	1	yes	characteristic
384	C₂²	C₁₃×#577	1	2	yes	—
385	C₄	—	2	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	1	no	—
389	C₄	—	8	2	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	2	no	—
392	C₄	C₁₃×#538	1	2	yes	—
393	C₄	C₁₃×#555	1	1	yes	characteristic
394	C₄	C₁₃×H(3,𝔽₄)	1	1	yes	characteristic
395	C₂	—	16	2	no	—
396	C₂	C₁₃×#2733	1	1	yes	characteristic
397	C₂	C₁₃×#3191	1	1	yes	characteristic
398	C₂	C₁₃×#3204	1	1	yes	characteristic
399	C₂	C₁₃×#3394	1	2	yes	—
400	C₂	C₁₃×#3401	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2592	C₂	semidirect
2. C₁₃×#2056	C₂	semidirect
4. C₁₃×#2015	C₂	semidirect
6. C₁₃×#1984	C₂	semidirect
7. C₁₃×#1968	C₂	semidirect
8. C₁₃×#1927	C₂	semidirect
9. C₁₃×#1926	C₂	semidirect
77. #32671	C₁₃	direct (N × H)
129. #2592	C₂×C₁₃	semidirect
130. #2056	C₂×C₁₃	semidirect
132. #2015	C₂×C₁₃	semidirect
134. #1984	C₂×C₁₃	semidirect
135. #1968	C₂×C₁₃	semidirect
136. #1927	C₂×C₁₃	semidirect
137. #1926	C₂×C₁₃	semidirect
328. C₁₃	#32671	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2592	2
C₁₃×#2056	2
C₁₃×#2054	2
C₁₃×#2015	2
C₁₃×#2012	2
C₁₃×#1984	2
C₁₃×#1968	2
C₁₃×#1927	2
C₁₃×#1926	2
#32671	13

Subgroups — C13×#32671 #15719010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32671 #15719010