Subgroups — C₁₃×#9254 #15695593

Order 3328.

534 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1965	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1545	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1292	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	C₄	1	2	yes	—
9	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#460	—	2	1	no	—
12	C₁₃×#460	—	2	1	no	—
13	C₁₃×#460	—	2	1	no	—
14	C₁₃×#460	—	2	1	no	—
15	C₁₃×#446	—	2	1	no	—
16	C₁₃×#446	—	2	2	no	—
17	C₈×Q₈×C₁₃	—	2	1	no	—
18	C₁₃×#431	C₂²	1	1	yes	characteristic
19	C₁₃×#423	—	2	1	no	—
20	C₁₃×#423	C₂²	1	1	yes	characteristic
21	C₁₃×#423	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₄	1	2	yes	—
24	C₂×C₁₃×#100	—	2	1	no	—
25	C₂×C₁₃×#100	—	2	1	no	—
26	C₄×C₁₃×M₁₆	—	2	1	no	—
27	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
28	C₁₃×#331	—	2	2	no	—
29	C₁₃×Q₈⋊C₈	—	2	1	no	—
30	C₁₃×Q₈⋊C₈	—	2	1	no	—
31	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	—	2	1	no	—
34	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₁₃×SD₁₆	—	2	2	no	—
36	C₂×C₁₃×SD₁₆	—	2	2	no	—
37	C₂×C₁₃×SD₁₆	—	4	4	no	—
38	C₂×C₁₃×M₁₆	—	2	1	no	—
39	C₂×C₁₃×M₁₆	—	2	1	no	—
40	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
41	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
43	C₁₃×#127	—	2	1	no	—
44	C₁₃×#127	—	2	1	no	—
45	C₁₃×#127	—	2	1	no	—
46	C₁₃×#127	—	2	1	no	—
47	C₄×Q₈×C₁₃	—	2	1	no	—
48	C₄×Q₈×C₁₃	—	2	1	no	—
49	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
50	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	—	2	1	no	—
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×C₄⋊C₈	—	2	2	no	—
58	C₁₃×C₄⋊C₈	—	2	2	no	—
59	C₁₃×C₄⋊C₈	—	2	1	no	—
60	C₁₃×C₄⋊C₈	—	2	1	no	—
61	C₁₃×C₄⋊C₈	—	2	1	no	—
62	C₁₃×C₄⋊C₈	—	2	1	no	—
63	C₁₃×C₄⋊C₈	—	2	1	no	—
64	C₁₃×C₄⋊C₈	—	2	1	no	—
65	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
66	C₁₃×#102	—	2	2	no	—
67	C₁₃×#102	—	2	2	no	—
68	C₁₃×#100	—	4	2	no	—
69	C₁₃×#100	—	4	2	no	—
70	C₁₃×C₂²⋊C₈	—	2	1	no	—
71	C₁₃×#97	—	2	2	no	—
72	C₁₃×#97	—	2	1	no	—
73	C₄×C₈×C₁₃	—	2	2	no	—
74	C₄×C₈×C₁₃	—	2	1	no	—
75	C₄×C₈×C₁₃	—	2	1	no	—
76	#9254	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	2	1	no	—
79	C₂×Q₈×C₁₃	—	2	2	no	—
80	C₂×Q₈×C₁₃	—	4	1	no	—
81	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×D₄×C₁₃	—	2	2	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	4	2	no	—
86	C₂×D₄×C₁₃	—	4	2	no	—
87	C₂×D₄×C₁₃	—	4	1	no	—
88	C₂×D₄×C₁₃	—	4	1	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	4	1	no	—
91	C₂×D₄×C₁₃	—	4	1	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	4	1	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	8	2	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
101	C₁₃×SD₁₆	—	4	4	no	—
102	C₁₃×SD₁₆	—	4	4	no	—
103	C₁₃×M₁₆	—	2	1	no	—
104	C₁₃×M₁₆	—	2	1	no	—
105	C₁₃×M₁₆	—	2	1	no	—
106	C₁₃×M₁₆	—	4	1	no	—
107	C₁₃×M₁₆	—	4	1	no	—
108	C₁₃×M₁₆	—	4	1	no	—
109	C₁₃×M₁₆	—	4	1	no	—
110	C₁₃×M₁₆	SD₁₆	1	2	yes	complemented
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	4	2	no	—
116	C₂×C₈×C₁₃	—	4	1	no	—
117	C₂×C₈×C₁₃	—	4	1	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
124	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
125	C₄²×C₁₃	—	2	1	no	—
126	C₄²×C₁₃	—	2	1	no	—
127	C₄²×C₁₃	—	2	1	no	—
128	C₄²×C₁₃	—	2	1	no	—
129	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₃	#41	1	1	yes	characteristic
133	C₂×#460	C₂×C₁₃	1	1	yes	characteristic
134	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#1965	C₂×C₁₃	1	1	yes	characteristic
136	#1545	C₂×C₁₃	1	1	yes	characteristic
137	#1487	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#1292	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#1283	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	4	2	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	8	2	no	—
144	C₂³×C₁₃	—	8	2	no	—
145	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
146	Q₈×C₁₃	—	2	1	no	—
147	Q₈×C₁₃	—	2	1	no	—
148	Q₈×C₁₃	—	2	1	no	—
149	Q₈×C₁₃	—	4	2	no	—
150	Q₈×C₁₃	#100	1	2	yes	complemented
151	D₄×C₁₃	—	4	2	no	—
152	D₄×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	8	2	no	—
154	D₄×C₁₃	—	8	2	no	—
155	D₄×C₁₃	—	8	2	no	—
156	D₄×C₁₃	—	8	1	no	—
157	D₄×C₁₃	—	8	1	no	—
158	D₄×C₁₃	—	8	1	no	—
159	D₄×C₁₃	—	8	1	no	—
160	C₂×C₄×C₁₃	—	2	1	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	8	1	no	—
169	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
172	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
176	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
177	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
179	C₈×C₁₃	—	2	2	no	—
180	C₈×C₁₃	—	4	2	no	—
181	C₈×C₁₃	—	4	1	no	—
182	C₈×C₁₃	—	4	2	no	—
183	C₈×C₁₃	—	8	1	no	—
184	C₈×C₁₃	—	8	1	no	—
185	C₂²×SD₁₆	C₄×C₁₃	1	2	yes	—
186	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
188	#460	—	2	1	no	—
189	#460	—	2	1	no	—
190	#460	—	2	1	no	—
191	#460	—	2	1	no	—
192	#446	—	2	1	no	—
193	#446	—	2	2	no	—
194	C₈×Q₈	—	2	1	no	—
195	#431	C₂²×C₁₃	1	1	yes	characteristic
196	#423	—	2	1	no	—
197	#423	C₂²×C₁₃	1	1	yes	characteristic
198	#423	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#102	C₄×C₁₃	1	2	yes	—
201	C₂×#100	—	2	1	no	—
202	C₂×#100	—	2	1	no	—
203	C₄×M₁₆	—	2	1	no	—
204	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
205	#331	—	2	2	no	—
206	Q₈⋊C₈	—	2	1	no	—
207	Q₈⋊C₈	—	2	1	no	—
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	8	2	no	—
211	C₂²×C₁₃	—	8	2	no	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	—	16	2	no	—
214	C₂²×C₁₃	—	16	2	no	—
215	C₂²×C₁₃	#386	1	1	yes	characteristic
216	C₂²×C₁₃	C₄×SD₁₆	1	1	yes	characteristic
217	C₂²×C₁₃	#440	1	1	yes	characteristic
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	4	1	no	—
223	C₄×C₁₃	—	4	1	no	—
224	C₄×C₁₃	—	4	1	no	—
225	C₄×C₁₃	C₂×#100	1	1	yes	characteristic
226	C₄×C₁₃	#413	1	1	yes	characteristic
227	C₄×C₁₃	#448	1	1	yes	characteristic
228	C₄×C₁₃	#449	1	1	yes	characteristic
229	C₄×C₁₃	#460	1	1	yes	characteristic
230	C₄×C₁₃	#464	1	1	yes	characteristic
231	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	—	4	4	no	—
238	C₂×M₁₆	—	2	1	no	—
239	C₂×M₁₆	—	2	1	no	—
240	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
241	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
242	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
243	#127	—	2	1	no	—
244	#127	—	2	1	no	—
245	#127	—	2	1	no	—
246	#127	—	2	1	no	—
247	C₄×Q₈	—	2	1	no	—
248	C₄×Q₈	—	2	1	no	—
249	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
250	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
251	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
252	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
266	#102	—	2	2	no	—
267	#102	—	2	2	no	—
268	#100	—	4	2	no	—
269	#100	—	4	2	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	#97	—	2	2	no	—
272	#97	—	2	1	no	—
273	C₄×C₈	—	2	2	no	—
274	C₄×C₈	—	2	1	no	—
275	C₄×C₈	—	2	1	no	—
276	C₂×C₁₃	—	2	1	no	—
277	C₂×C₁₃	—	2	1	no	—
278	C₂×C₁₃	—	16	2	no	—
279	C₂×C₁₃	#1880	1	1	yes	characteristic
280	C₂×C₁₃	#1900	1	1	yes	characteristic
281	C₂×C₁₃	#1903	1	1	yes	characteristic
282	C₂⁴	—	2	2	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	8	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
306	SD₁₆	—	4	4	no	—
307	SD₁₆	—	4	4	no	—
308	M₁₆	—	2	1	no	—
309	M₁₆	—	2	1	no	—
310	M₁₆	—	2	1	no	—
311	M₁₆	—	4	1	no	—
312	M₁₆	—	4	1	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	—	4	1	no	—
315	M₁₆	C₁₃×SD₁₆	1	2	yes	complemented
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
329	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₄²	C₁₃×#41	1	1	yes	characteristic
338	C₁₃	#9254	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	8	2	no	—
343	C₂³	—	8	2	no	—
344	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
345	Q₈	—	2	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	2	1	no	—
348	Q₈	—	4	2	no	—
349	Q₈	C₁₃×#100	1	2	yes	complemented
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	1	no	—
357	D₄	—	8	1	no	—
358	D₄	—	8	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	1	no	—
368	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
369	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
370	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
371	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
372	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
373	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
374	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
375	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
376	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	1	no	—
381	C₈	—	4	2	no	—
382	C₈	—	8	1	no	—
383	C₈	—	8	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	2	no	—
390	C₂²	—	16	2	no	—
391	C₂²	C₁₃×#386	1	1	yes	characteristic
392	C₂²	C₄×C₁₃×SD₁₆	1	1	yes	characteristic
393	C₂²	C₁₃×#440	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	C₂×C₁₃×#100	1	1	yes	characteristic
402	C₄	C₁₃×#413	1	1	yes	characteristic
403	C₄	C₁₃×#448	1	1	yes	characteristic
404	C₄	C₁₃×#449	1	1	yes	characteristic
405	C₄	C₁₃×#460	1	1	yes	characteristic
406	C₄	C₁₃×#464	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	16	2	no	—
410	C₂	C₁₃×#1880	1	1	yes	characteristic
411	C₂	C₁₃×#1900	1	1	yes	characteristic
412	C₂	C₁₃×#1903	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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
2. Q₈×C₁₃×M₁₆	C₂	semidirect
5. C₁₃×#1487	C₂	semidirect
6. C₁₃×#1292	C₂	semidirect
7. C₁₃×#1283	C₂	semidirect
76. #9254	C₁₃	direct (N × H)
110. C₁₃×M₁₆	SD₁₆	semidirect
134. Q₈×M₁₆	C₂×C₁₃	semidirect
137. #1487	C₂×C₁₃	semidirect
138. #1292	C₂×C₁₃	semidirect
139. #1283	C₂×C₁₃	semidirect
150. Q₈×C₁₃	#100	semidirect
315. M₁₆	C₁₃×SD₁₆	semidirect
338. C₁₃	#9254	direct (N × H)
349. Q₈	C₁₃×#100	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#460	2
Q₈×C₁₃×M₁₆	2
C₁₃×#1965	2
C₁₃×#1545	2
C₁₃×#1487	2
C₁₃×#1292	2
C₁₃×#1283	2
#9254	13

Subgroups — C13×#9254 #15695593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9254 #15695593