Subgroups — C₁₃×#33531 #15719870

Order 3328.

1122 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#509	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2190	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2145	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2115	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#585	—	2	1	no	—
8	C₁₃×#578	—	2	2	no	—
9	C₁₃×#577	—	2	4	no	—
10	C₁₃×#576	—	2	2	no	—
11	C₁₃×#575	—	2	1	no	—
12	C₁₃×#575	C₂²	1	4	yes	complemented
13	C₂×C₁₃×#135	—	2	2	no	—
14	C₂×C₁₃×#135	C₂²	1	2	yes	—
15	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
17	C₁₃×#535	—	2	1	no	—
18	C₁₃×#509	—	2	4	no	—
19	C₁₃×#509	C₂²	1	8	yes	complemented
20	C₂×C₁₃×SD₃₂	—	2	2	no	—
21	C₂×C₁₃×D₁₆	—	2	2	no	—
22	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
23	C₁₃×#469	C₂²	1	4	yes	complemented
24	C₁₃×#466	—	2	2	no	—
25	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#418	—	2	1	no	—
27	C₁₃×#360	C₂²	1	8	yes	complemented
28	C₁₃×#349	C₂²	1	4	yes	complemented
29	C₁₃×2₋¹⁺⁴	—	2	4	no	—
30	C₁₃×2₋¹⁺⁴	—	4	1	no	—
31	C₁₃×H(5,𝔽₂)	—	2	4	no	—
32	C₁₃×H(5,𝔽₂)	—	4	2	no	—
33	C₁₃×H(5,𝔽₂)	—	4	1	no	—
34	C₂×C₁₃×#41	—	2	4	no	—
35	C₂×C₁₃×#41	—	2	2	no	—
36	C₂×C₁₃×#41	—	4	4	no	—
37	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₃	—	2	1	no	—
39	C₁₃×#137	—	2	4	no	—
40	C₁₃×#137	—	2	8	no	—
41	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
42	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
43	C₁₃×#135	—	2	4	no	—
44	C₁₃×#135	—	2	4	no	—
45	C₁₃×#135	—	2	2	no	—
46	C₁₃×#135	—	2	4	no	—
47	C₁₃×#135	—	2	2	no	—
48	C₁₃×#135	D₄	1	4	yes	complemented
49	C₁₃×#135	C₂³	1	4	yes	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	D₄	1	2	yes	complemented
52	C₂×C₁₃×SD₁₆	—	2	4	no	—
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×D₈	—	2	2	no	—
55	C₂×C₁₃×D₈	—	2	2	no	—
56	C₂×C₁₃×D₈	—	2	2	no	—
57	C₂×C₁₃×D₈	—	2	1	no	—
58	C₂×C₁₃×D₈	D₄	1	2	yes	complemented
59	C₂×C₁₃×D₈	C₂³	1	2	yes	—
60	C₁₃×#131	—	2	2	no	—
61	C₁₃×#131	—	2	2	no	—
62	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
63	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃	D₄	1	2	yes	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×#127	—	4	1	no	—
67	C₁₃×#124	—	4	1	no	—
68	C₁₃×#121	—	2	4	no	—
69	C₁₃×#120	—	4	2	no	—
70	C₁₃×#117	—	2	1	no	—
71	C₁₃×SD₃₂	—	2	8	no	—
72	C₁₃×D₁₆	—	2	8	no	—
73	C₁₃×M₃₂	—	2	2	no	—
74	C₁₃×M₃₂	C₂³	1	4	yes	—
75	C₂×C₁₃×C₁₆	—	2	2	no	—
76	C₁₃×#107	—	2	1	no	—
77	C₁₃×#106	C₂³	1	2	yes	—
78	C₁₃×#102	—	2	4	no	—
79	#33531	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂⁴×C₁₃	—	4	1	no	—
81	C₁₃×#41	—	2	2	no	—
82	C₁₃×#41	—	2	2	no	—
83	C₁₃×#41	—	2	8	no	—
84	C₁₃×#41	—	2	4	no	—
85	C₁₃×#41	—	2	4	no	—
86	C₁₃×#41	—	4	4	no	—
87	C₁₃×#41	—	4	8	no	—
88	C₁₃×#41	—	4	4	no	—
89	C₁₃×#41	—	4	4	no	—
90	C₁₃×#41	—	4	4	no	—
91	C₁₃×#41	—	4	2	no	—
92	C₁₃×#41	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	2	4	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	4	4	no	—
96	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
97	C₂×D₄×C₁₃	—	2	4	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	4	8	no	—
101	C₂×D₄×C₁₃	—	4	4	no	—
102	C₂×D₄×C₁₃	—	4	4	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	—	4	4	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	—	4	1	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	D₈	1	2	yes	—
109	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	—	4	4	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₁₃×Q₁₆	—	2	4	no	—
115	C₁₃×Q₁₆	—	2	2	no	—
116	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
117	C₁₃×SD₁₆	—	2	8	no	—
118	C₁₃×SD₁₆	—	2	4	no	—
119	C₁₃×SD₁₆	—	2	4	no	—
120	C₁₃×D₈	—	2	4	no	—
121	C₁₃×D₈	—	2	2	no	—
122	C₁₃×D₈	—	2	4	no	—
123	C₁₃×D₈	—	4	1	no	—
124	C₁₃×D₈	—	4	1	no	—
125	C₁₃×D₈	C₂×D₄	1	4	yes	—
126	C₁₃×M₁₆	—	2	2	no	—
127	C₁₃×M₁₆	—	2	4	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₂²⋊C₄	—	4	1	no	—
137	C₁₃×C₂²⋊C₄	—	4	4	no	—
138	C₄²×C₁₃	—	4	1	no	—
139	C₁₃×C₁₆	—	2	4	no	—
140	#3584	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂×#509	C₂×C₁₃	1	2	yes	complemented
142	#3058	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2190	C₂×C₁₃	1	8	yes	complemented
144	#2145	C₂×C₁₃	1	2	yes	complemented
145	#2115	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂³×C₁₃	—	4	4	no	—
147	C₂³×C₁₃	—	4	2	no	—
148	C₂³×C₁₃	—	4	2	no	—
149	C₂³×C₁₃	—	8	2	no	—
150	C₂³×C₁₃	—	16	2	no	—
151	C₂³×C₁₃	C₂×D₈	1	2	yes	—
152	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
153	Q₈×C₁₃	—	2	2	no	—
154	Q₈×C₁₃	—	2	4	no	—
155	Q₈×C₁₃	—	4	4	no	—
156	Q₈×C₁₃	—	4	2	no	—
157	D₄×C₁₃	—	2	4	no	—
158	D₄×C₁₃	—	2	4	no	—
159	D₄×C₁₃	—	2	2	no	—
160	D₄×C₁₃	—	4	4	no	—
161	D₄×C₁₃	—	4	8	no	—
162	D₄×C₁₃	—	4	4	no	—
163	D₄×C₁₃	—	4	4	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	8	2	no	—
168	D₄×C₁₃	—	16	4	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	4	8	no	—
172	C₂×C₄×C₁₃	—	4	4	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	4	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	#120	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
181	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₁₃	—	2	2	no	—
183	C₈×C₁₃	#120	1	1	yes	characteristic
184	C₈×C₁₃	#120	1	1	yes	characteristic
185	C₈×C₁₃	C₂²×D₄	1	2	yes	—
186	#585	—	2	1	no	—
187	#578	—	2	2	no	—
188	#577	—	2	4	no	—
189	#576	—	2	2	no	—
190	#575	—	2	1	no	—
191	#575	C₂²×C₁₃	1	4	yes	complemented
192	C₂×#135	—	2	2	no	—
193	C₂×#135	C₂²×C₁₃	1	2	yes	—
194	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
196	#535	—	2	1	no	—
197	#509	—	2	4	no	—
198	#509	C₂²×C₁₃	1	8	yes	complemented
199	C₂×SD₃₂	—	2	2	no	—
200	C₂×D₁₆	—	2	2	no	—
201	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
202	#469	C₂²×C₁₃	1	4	yes	complemented
203	#466	—	2	2	no	—
204	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
205	#418	—	2	1	no	—
206	#360	C₂²×C₁₃	1	8	yes	complemented
207	#349	C₂²×C₁₃	1	4	yes	complemented
208	C₂²×C₁₃	—	2	2	no	—
209	C₂²×C₁₃	—	4	1	no	—
210	C₂²×C₁₃	—	4	2	no	—
211	C₂²×C₁₃	—	4	4	no	—
212	C₂²×C₁₃	—	8	4	no	—
213	C₂²×C₁₃	—	8	2	no	—
214	C₂²×C₁₃	—	16	2	no	—
215	C₂²×C₁₃	—	16	4	no	—
216	C₂²×C₁₃	—	16	4	no	—
217	C₂²×C₁₃	#447	1	2	yes	—
218	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	4	4	no	—
221	C₄×C₁₃	—	8	2	no	—
222	C₄×C₁₃	#447	1	2	yes	—
223	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
224	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	2₋¹⁺⁴	—	2	4	no	—
226	2₋¹⁺⁴	—	4	1	no	—
227	H(5,𝔽₂)	—	2	4	no	—
228	H(5,𝔽₂)	—	4	2	no	—
229	H(5,𝔽₂)	—	4	1	no	—
230	C₂×#41	—	2	4	no	—
231	C₂×#41	—	2	2	no	—
232	C₂×#41	—	4	4	no	—
233	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
234	C₂²×D₄	—	2	1	no	—
235	#137	—	2	4	no	—
236	#137	—	2	8	no	—
237	AGL(1,ℤ/8)	—	2	4	no	—
238	AGL(1,ℤ/8)	—	2	8	no	—
239	#135	—	2	4	no	—
240	#135	—	2	4	no	—
241	#135	—	2	2	no	—
242	#135	—	2	4	no	—
243	#135	—	2	2	no	—
244	#135	D₄×C₁₃	1	4	yes	complemented
245	#135	C₂³×C₁₃	1	4	yes	—
246	C₂×Q₁₆	—	2	2	no	—
247	C₂×Q₁₆	D₄×C₁₃	1	2	yes	complemented
248	C₂×SD₁₆	—	2	4	no	—
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×D₈	—	2	2	no	—
251	C₂×D₈	—	2	2	no	—
252	C₂×D₈	—	2	2	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	D₄×C₁₃	1	2	yes	complemented
255	C₂×D₈	C₂³×C₁₃	1	2	yes	—
256	#131	—	2	2	no	—
257	#131	—	2	2	no	—
258	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
259	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
260	C₂²×C₈	D₄×C₁₃	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
262	#127	—	4	1	no	—
263	#124	—	4	1	no	—
264	#121	—	2	4	no	—
265	#120	—	4	2	no	—
266	#117	—	2	1	no	—
267	SD₃₂	—	2	8	no	—
268	D₁₆	—	2	8	no	—
269	M₃₂	—	2	2	no	—
270	M₃₂	C₂³×C₁₃	1	4	yes	—
271	C₂×C₁₆	—	2	2	no	—
272	#107	—	2	1	no	—
273	#106	C₂³×C₁₃	1	2	yes	—
274	#102	—	2	4	no	—
275	C₂×C₁₃	—	2	1	no	—
276	C₂×C₁₃	—	2	2	no	—
277	C₂×C₁₃	—	4	2	no	—
278	C₂×C₁₃	—	8	4	no	—
279	C₂×C₁₃	—	16	2	no	—
280	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
281	C₂⁴	—	4	1	no	—
282	#41	—	2	2	no	—
283	#41	—	2	2	no	—
284	#41	—	2	8	no	—
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	4	4	no	—
288	#41	—	4	8	no	—
289	#41	—	4	4	no	—
290	#41	—	4	4	no	—
291	#41	—	4	4	no	—
292	#41	—	4	2	no	—
293	#41	—	4	2	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	4	4	no	—
297	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	4	8	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	C₁₃×D₈	1	2	yes	—
310	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
311	C₂²×C₄	—	4	4	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	Q₁₆	—	2	4	no	—
316	Q₁₆	—	2	2	no	—
317	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
318	SD₁₆	—	2	8	no	—
319	SD₁₆	—	2	4	no	—
320	SD₁₆	—	2	4	no	—
321	D₈	—	2	4	no	—
322	D₈	—	2	2	no	—
323	D₈	—	2	4	no	—
324	D₈	—	4	1	no	—
325	D₈	—	4	1	no	—
326	D₈	C₂×D₄×C₁₃	1	4	yes	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	2	4	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
332	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
334	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
335	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
336	C₄⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	4	no	—
339	C₄²	—	4	1	no	—
340	C₁₆	—	2	4	no	—
341	C₁₃	#33531	1	1	yes	characteristic, direct product factor, Sylow
342	C₂³	—	4	4	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	2	no	—
346	C₂³	—	16	2	no	—
347	C₂³	C₂×C₁₃×D₈	1	2	yes	—
348	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
349	Q₈	—	2	2	no	—
350	Q₈	—	2	4	no	—
351	Q₈	—	4	4	no	—
352	Q₈	—	4	2	no	—
353	D₄	—	2	4	no	—
354	D₄	—	2	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	8	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	2	no	—
364	D₄	—	16	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	C₁₃×#120	1	2	yes	—
374	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
375	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
376	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
377	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	C₁₃×#120	1	1	yes	characteristic
380	C₈	C₁₃×#120	1	1	yes	characteristic
381	C₈	C₂²×D₄×C₁₃	1	2	yes	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	8	4	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	16	2	no	—
389	C₂²	—	16	4	no	—
390	C₂²	—	16	4	no	—
391	C₂²	C₁₃×#447	1	2	yes	—
392	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	8	2	no	—
396	C₄	C₁₃×#447	1	2	yes	—
397	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
398	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	—	8	4	no	—
403	C₂	—	16	2	no	—
404	C₂	C₂×C₁₃×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3584	C₂	semidirect
2. C₂×C₁₃×#509	C₂	semidirect
3. C₁₃×#3058	C₂	semidirect
4. C₁₃×#2190	C₂	semidirect
5. C₁₃×#2145	C₂	semidirect
6. C₁₃×#2115	C₂	semidirect
12. C₁₃×#575	C₂²	semidirect
15. C₂²×C₁₃×D₈	C₂²	semidirect
19. C₁₃×#509	C₂²	semidirect
22. C₂×C₁₃×M₃₂	C₂²	semidirect
23. C₁₃×#469	C₂²	semidirect
25. C₁₃×#427	C₂²	semidirect
27. C₁₃×#360	C₂²	semidirect
28. C₁₃×#349	C₂²	semidirect
48. C₁₃×#135	D₄	semidirect
51. C₂×C₁₃×Q₁₆	D₄	semidirect
58. C₂×C₁₃×D₈	D₄	semidirect
79. #33531	C₁₃	direct (N × H)
140. #3584	C₂×C₁₃	semidirect
141. C₂×#509	C₂×C₁₃	semidirect
142. #3058	C₂×C₁₃	semidirect
143. #2190	C₂×C₁₃	semidirect
144. #2145	C₂×C₁₃	semidirect
145. #2115	C₂×C₁₃	semidirect
191. #575	C₂²×C₁₃	semidirect
194. C₂²×D₈	C₂²×C₁₃	semidirect
198. #509	C₂²×C₁₃	semidirect
201. C₂×M₃₂	C₂²×C₁₃	semidirect
202. #469	C₂²×C₁₃	semidirect
204. #427	C₂²×C₁₃	semidirect
206. #360	C₂²×C₁₃	semidirect
207. #349	C₂²×C₁₃	semidirect
244. #135	D₄×C₁₃	semidirect
247. C₂×Q₁₆	D₄×C₁₃	semidirect
254. C₂×D₈	D₄×C₁₃	semidirect
341. C₁₃	#33531	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×#3584	2
C₂×C₁₃×#509	2
C₁₃×#3058	2
C₁₃×#2190	2
C₁₃×#2145	2
C₁₃×#2115	2
#33531	13

Subgroups — C13×#33531 #15719870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33531 #15719870