Subgroups — C₁₃×#23719 #15710058

Order 3328.

808 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2079	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2063	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2051	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2018	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#100	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#442	—	2	2	no	—
17	C₁₃×#442	—	2	2	no	—
18	C₁₃×#442	—	2	2	no	—
19	C₁₃×#440	—	2	2	no	—
20	C₄×C₁₃×SD₁₆	—	2	2	no	—
21	C₄×C₁₃×D₈	—	2	2	no	—
22	C₁₃×#433	—	2	2	no	—
23	C₁₃×#432	—	2	2	no	—
24	C₂×C₁₃×#108	C₂²	1	2	yes	—
25	C₁₃×#428	C₂²	1	2	yes	—
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₁₃×#424	C₂²	1	1	yes	characteristic
28	C₁₃×#424	C₂²	1	1	yes	characteristic
29	C₁₃×#418	C₂²	1	2	yes	—
30	C₁₃×#417	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#100	C₂²	1	2	yes	—
33	C₂×C₁₃×#100	C₂²	1	2	yes	—
34	C₁₃×#408	C₂²	1	1	yes	characteristic
35	C₁₃×#408	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
38	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
39	C₁₃×#343	C₂²	1	2	yes	—
40	C₁₃×#343	C₂²	1	2	yes	—
41	C₁₃×#341	C₂²	1	1	yes	characteristic
42	C₁₃×#341	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
47	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	4	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
55	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₄×Q₈×C₁₃	D₄	1	2	yes	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	D₄	1	2	yes	—
65	C₁₃×#117	—	2	1	no	—
66	C₁₃×#117	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₄²×C₁₃	—	2	1	no	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#108	—	2	4	no	—
72	C₁₃×#107	—	2	2	no	—
73	C₁₃×#106	—	2	2	no	—
74	C₁₃×#106	—	2	2	no	—
75	C₁₃×C₄⋊C₈	—	2	2	no	—
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×#103	—	2	2	no	—
78	C₁₃×#102	—	2	2	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	—	2	2	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×#100	—	2	4	no	—
83	C₁₃×#100	—	2	4	no	—
84	C₁₃×C₂²⋊C₈	—	2	2	no	—
85	C₁₃×C₂²⋊C₈	—	2	2	no	—
86	C₁₃×#97	—	2	1	no	—
87	C₁₃×#97	—	2	2	no	—
88	C₁₃×#97	D₄	1	2	yes	—
89	C₁₃×#97	D₄	1	2	yes	—
90	C₄×C₈×C₁₃	—	2	1	no	—
91	C₄×C₈×C₁₃	—	2	2	no	—
92	#23719	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	2	no	—
94	C₁₃×#41	—	2	2	no	—
95	C₁₃×#41	—	2	2	no	—
96	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×D₄×C₁₃	#41	1	4	yes	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	4	2	no	—
110	C₂²×C₄×C₁₃	—	8	4	no	—
111	C₂²×C₄×C₁₃	#41	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
113	C₁₃×SD₁₆	—	2	8	no	—
114	C₁₃×D₈	—	2	8	no	—
115	C₁₃×D₈	—	2	8	no	—
116	C₁₃×M₁₆	—	2	2	no	—
117	C₁₃×M₁₆	—	2	2	no	—
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	—	2	2	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	#41	1	4	yes	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
134	C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₁₃×C₂²⋊C₄	—	2	2	no	—
136	C₁₃×C₂²⋊C₄	—	4	2	no	—
137	C₁₃×C₂²⋊C₄	—	4	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	1	no	—
140	C₄²×C₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	2	yes	complemented
144	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2090	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2079	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2063	C₂×C₁₃	1	2	yes	complemented
149	#2051	C₂×C₁₃	1	2	yes	complemented
150	#2045	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2018	C₂×C₁₃	1	1	yes	characteristic
152	#1778	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₄×#100	C₂×C₁₃	1	2	yes	complemented
154	C₂³×C₁₃	—	2	1	no	—
155	C₂³×C₁₃	—	2	4	no	—
156	C₂³×C₁₃	—	4	2	no	—
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	—	8	2	no	—
159	C₂³×C₁₃	—	8	2	no	—
160	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
161	Q₈×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	2	4	no	—
163	D₄×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	2	4	no	—
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	8	2	no	—
175	C₂×C₄×C₁₃	—	8	4	no	—
176	C₂×C₄×C₁₃	—	8	4	no	—
177	C₂×C₄×C₁₃	—	8	2	no	—
178	C₂×C₄×C₁₃	#121	1	2	yes	—
179	C₂×C₄×C₁₃	#121	1	2	yes	—
180	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
184	C₈×C₁₃	—	2	2	no	—
185	C₈×C₁₃	—	2	4	no	—
186	C₈×C₁₃	—	2	2	no	—
187	C₈×C₁₃	—	4	1	no	—
188	C₈×C₁₃	—	4	2	no	—
189	C₈×C₁₃	—	4	1	no	—
190	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
191	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
194	#442	—	2	2	no	—
195	#442	—	2	2	no	—
196	#442	—	2	2	no	—
197	#440	—	2	2	no	—
198	C₄×SD₁₆	—	2	2	no	—
199	C₄×D₈	—	2	2	no	—
200	#433	—	2	2	no	—
201	#432	—	2	2	no	—
202	C₂×#108	C₂²×C₁₃	1	2	yes	—
203	#428	C₂²×C₁₃	1	2	yes	—
204	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
205	#424	C₂²×C₁₃	1	1	yes	characteristic
206	#424	C₂²×C₁₃	1	1	yes	characteristic
207	#418	C₂²×C₁₃	1	2	yes	—
208	#417	C₂²×C₁₃	1	2	yes	—
209	C₂×#102	C₂²×C₁₃	1	2	yes	—
210	C₂×#100	C₂²×C₁₃	1	2	yes	—
211	C₂×#100	C₂²×C₁₃	1	2	yes	—
212	#408	C₂²×C₁₃	1	1	yes	characteristic
213	#408	C₂²×C₁₃	1	1	yes	characteristic
214	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
215	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
216	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
217	#343	C₂²×C₁₃	1	2	yes	—
218	#343	C₂²×C₁₃	1	2	yes	—
219	#341	C₂²×C₁₃	1	1	yes	characteristic
220	#341	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×C₁₃	—	2	2	no	—
222	C₂²×C₁₃	—	4	1	no	—
223	C₂²×C₁₃	—	4	4	no	—
224	C₂²×C₁₃	—	4	2	no	—
225	C₂²×C₁₃	—	8	4	no	—
226	C₂²×C₁₃	—	8	4	no	—
227	C₂²×C₁₃	—	8	2	no	—
228	C₂²×C₁₃	—	8	2	no	—
229	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
230	C₂²×C₁₃	#529	1	2	yes	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	4	1	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	8	2	no	—
236	C₄×C₁₃	#525	1	1	yes	characteristic
237	C₄×C₁₃	#525	1	2	yes	—
238	C₄×C₁₃	#532	1	1	yes	characteristic
239	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
240	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
241	C₂³×C₄	—	2	2	no	—
242	AGL(1,ℤ/8)	—	2	4	no	—
243	AGL(1,ℤ/8)	—	2	4	no	—
244	C₂×SD₁₆	—	2	2	no	—
245	C₂×D₈	—	2	2	no	—
246	C₂×D₈	—	2	4	no	—
247	C₂×D₈	—	2	2	no	—
248	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
249	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
250	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
251	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
252	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₄×Q₈	D₄×C₁₃	1	2	yes	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	D₄×C₁₃	1	2	yes	—
261	#117	—	2	1	no	—
262	#117	C₂³×C₁₃	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
267	#108	—	2	4	no	—
268	#107	—	2	2	no	—
269	#106	—	2	2	no	—
270	#106	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	—	2	2	no	—
273	#103	—	2	2	no	—
274	#102	—	2	2	no	—
275	#102	—	2	4	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#100	—	2	4	no	—
279	#100	—	2	4	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	#97	—	2	1	no	—
283	#97	—	2	2	no	—
284	#97	D₄×C₁₃	1	2	yes	—
285	#97	D₄×C₁₃	1	2	yes	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	—	2	2	no	—
288	C₂×C₁₃	—	2	2	no	—
289	C₂×C₁₃	—	8	1	no	—
290	C₂×C₁₃	—	8	4	no	—
291	C₂×C₁₃	#2392	1	1	yes	characteristic
292	C₂×C₁₃	#3068	1	2	yes	—
293	C₂⁴	—	2	2	no	—
294	#41	—	2	2	no	—
295	#41	—	2	2	no	—
296	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
304	C₂×D₄	C₁₃×#41	1	4	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	8	4	no	—
311	C₂²×C₄	C₁₃×#41	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
313	SD₁₆	—	2	8	no	—
314	D₈	—	2	8	no	—
315	D₈	—	2	8	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	C₁₃×#41	1	4	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
329	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	C₂×D₄×C₁₃	1	2	yes	—
341	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₁₃	#23719	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³	—	2	1	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	—	8	2	no	—
350	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	D₄	—	2	4	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	4	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	C₁₃×#121	1	2	yes	—
369	C₂×C₄	C₁₃×#121	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
373	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
374	C₈	—	2	2	no	—
375	C₈	—	2	4	no	—
376	C₈	—	2	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	1	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	8	4	no	—
385	C₂²	—	8	4	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
389	C₂²	C₁₃×#529	1	2	yes	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	8	2	no	—
395	C₄	C₁₃×#525	1	1	yes	characteristic
396	C₄	C₁₃×#525	1	2	yes	—
397	C₄	C₁₃×#532	1	1	yes	characteristic
398	C₂	—	2	2	no	—
399	C₂	—	8	1	no	—
400	C₂	—	8	4	no	—
401	C₂	C₁₃×#2392	1	1	yes	characteristic
402	C₂	C₁₃×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2018	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₁₃×#442	C₂	semidirect
3. C₁₃×#2923	C₂	semidirect
4. C₁₃×#2090	C₂	semidirect
5. C₁₃×#2079	C₂	semidirect
6. C₁₃×#2063	C₂	semidirect
7. C₁₃×#2051	C₂	semidirect
8. C₁₃×#2045	C₂	semidirect
10. C₁₃×#1778	C₂	semidirect
11. C₄×C₁₃×#100	C₂	semidirect
92. #23719	C₁₃	direct (N × H)
143. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
144. C₂×#442	C₂×C₁₃	semidirect
145. #2923	C₂×C₁₃	semidirect
146. #2090	C₂×C₁₃	semidirect
147. #2079	C₂×C₁₃	semidirect
148. #2063	C₂×C₁₃	semidirect
149. #2051	C₂×C₁₃	semidirect
150. #2045	C₂×C₁₃	semidirect
152. #1778	C₂×C₁₃	semidirect
153. C₄×#100	C₂×C₁₃	semidirect
343. C₁₃	#23719	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×AGL(1,ℤ/8)	2
C₂×C₁₃×#442	2
C₁₃×#2923	2
C₁₃×#2090	2
C₁₃×#2079	2
C₁₃×#2063	2
C₁₃×#2051	2
C₁₃×#2045	2
C₁₃×#2018	2
C₁₃×#1778	2
C₄×C₁₃×#100	2
#23719	13

Subgroups — C13×#23719 #15710058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23719 #15710058