Subgroups — C₁₃×#33585 #15719924

Order 3328.

748 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2210	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2206	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₁₃×#535	—	2	1	no	—
15	C₁₃×#518	—	2	1	no	—
16	C₁₃×#509	—	2	4	no	—
17	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₁₃×D₁₆	—	2	4	no	—
19	C₂×C₁₃×D₁₆	C₂²	1	4	yes	—
20	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
21	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
23	C₁₃×#496	—	2	2	no	—
24	C₁₃×#495	C₂²	1	2	yes	complemented
25	C₁₃×#493	C₂²	1	2	yes	complemented
26	C₁₃×#442	—	2	2	no	—
27	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
28	C₁₃×#427	C₂²	1	1	yes	characteristic
29	C₁₃×#418	—	2	1	no	—
30	C₁₃×#405	C₂²	1	1	yes	characteristic
31	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	complemented
32	C₁₃×#358	C₂²	1	2	yes	complemented
33	C₁₃×#357	C₂²	1	2	yes	complemented
34	C₁₃×#357	C₂²	1	4	yes	complemented
35	C₂×C₁₃×#41	—	2	1	no	—
36	C₂²×D₄×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	—	2	1	no	—
38	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
39	C₁₃×#135	—	2	2	no	—
40	C₁₃×#135	—	2	2	no	—
41	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
42	C₂×C₁₃×SD₁₆	—	2	2	no	—
43	C₂×C₁₃×SD₁₆	—	2	1	no	—
44	C₂×C₁₃×D₈	—	2	1	no	—
45	C₂×C₁₃×D₈	—	2	2	no	—
46	C₂×C₁₃×D₈	—	2	2	no	—
47	C₂×C₁₃×D₈	—	2	1	no	—
48	C₂×C₁₃×D₈	—	2	2	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	D₄	1	4	yes	complemented
51	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×D₈	C₂³	1	2	yes	—
53	C₂×C₁₃×D₈	C₂³	1	2	yes	—
54	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#127	—	2	2	no	—
57	C₁₃×#124	—	2	2	no	—
58	C₁₃×#121	—	4	2	no	—
59	C₁₃×#120	—	4	2	no	—
60	C₄×D₄×C₁₃	—	2	4	no	—
61	C₄×D₄×C₁₃	—	4	2	no	—
62	C₁₃×#117	—	2	1	no	—
63	C₁₃×#117	D₄	1	1	yes	characteristic
64	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
65	C₁₃×SD₃₂	—	2	4	no	—
66	C₁₃×D₁₆	—	2	8	no	—
67	C₁₃×D₁₆	—	2	4	no	—
68	C₁₃×M₃₂	—	2	2	no	—
69	C₂×C₁₃×C₁₆	—	2	2	no	—
70	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
71	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
72	C₁₃×#107	C₂³	1	2	yes	—
73	C₁₃×#106	—	2	1	no	—
74	C₁₃×#102	—	2	4	no	—
75	C₁₃×#97	D₄	1	2	yes	—
76	C₄×C₈×C₁₃	C₂³	1	2	yes	—
77	#33585	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁴×C₁₃	—	4	1	no	—
79	C₂⁴×C₁₃	—	4	1	no	—
80	C₁₃×#41	—	4	2	no	—
81	C₁₃×#41	—	4	2	no	—
82	C₂×Q₈×C₁₃	—	2	1	no	—
83	C₂×D₄×C₁₃	—	2	4	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	4	1	no	—
88	C₂×D₄×C₁₃	—	4	2	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	4	1	no	—
91	C₂×D₄×C₁₃	—	4	4	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂²×C₄×C₁₃	—	4	1	no	—
95	C₂²×C₄×C₁₃	—	4	4	no	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₁₃×Q₁₆	—	2	1	no	—
98	C₁₃×Q₁₆	—	2	1	no	—
99	C₁₃×SD₁₆	—	4	4	no	—
100	C₁₃×SD₁₆	—	4	2	no	—
101	C₁₃×D₈	—	2	4	no	—
102	C₁₃×D₈	—	2	2	no	—
103	C₁₃×D₈	—	2	1	no	—
104	C₁₃×D₈	—	2	2	no	—
105	C₁₃×D₈	—	2	2	no	—
106	C₁₃×D₈	—	2	1	no	—
107	C₁₃×D₈	—	4	4	no	—
108	C₁₃×D₈	—	4	2	no	—
109	C₁₃×D₈	C₂×D₄	1	4	yes	—
110	C₁₃×M₁₆	—	2	2	no	—
111	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₁₃	#41	1	2	yes	—
115	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
118	C₁₃×C₂²⋊C₄	—	4	1	no	—
119	C₁₃×C₂²⋊C₄	—	4	4	no	—
120	C₁₃×C₂²⋊C₄	—	4	4	no	—
121	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
122	C₄²×C₁₃	—	4	1	no	—
123	C₄²×C₁₃	C₂×D₄	1	2	yes	—
124	C₁₃×C₁₆	—	2	2	no	—
125	C₁₃×C₁₆	—	2	2	no	—
126	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
127	C₂²×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
128	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
129	#2948	C₂×C₁₃	1	1	yes	characteristic, complemented
130	#2210	C₂×C₁₃	1	4	yes	complemented
131	#2206	C₂×C₁₃	1	4	yes	complemented
132	#2151	C₂×C₁₃	1	1	yes	characteristic, complemented
133	#2140	C₂×C₁₃	1	1	yes	characteristic, complemented
134	#2138	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	—	4	4	no	—
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	—	4	1	no	—
139	C₂³×C₁₃	—	8	2	no	—
140	C₂³×C₁₃	—	16	2	no	—
141	C₂³×C₁₃	—	16	2	no	—
142	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
143	Q₈×C₁₃	—	4	1	no	—
144	Q₈×C₁₃	—	4	1	no	—
145	D₄×C₁₃	—	2	4	no	—
146	D₄×C₁₃	—	4	2	no	—
147	D₄×C₁₃	—	4	1	no	—
148	D₄×C₁₃	—	4	2	no	—
149	D₄×C₁₃	—	4	1	no	—
150	D₄×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	4	4	no	—
152	D₄×C₁₃	—	8	2	no	—
153	D₄×C₁₃	—	8	2	no	—
154	D₄×C₁₃	—	16	4	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	1	no	—
157	C₂×C₄×C₁₃	—	8	2	no	—
158	C₂×C₄×C₁₃	—	16	4	no	—
159	C₂×C₄×C₁₃	#121	1	2	yes	—
160	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
161	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	C₈×C₁₃	—	2	2	no	—
165	C₈×C₁₃	#121	1	2	yes	—
166	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
168	C₂×AGL(1,ℤ/8)	—	2	1	no	—
169	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
170	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
171	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
172	#535	—	2	1	no	—
173	#518	—	2	1	no	—
174	#509	—	2	4	no	—
175	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
176	C₂×D₁₆	—	2	4	no	—
177	C₂×D₁₆	C₂²×C₁₃	1	4	yes	—
178	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
179	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
180	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
181	#496	—	2	2	no	—
182	#495	C₂²×C₁₃	1	2	yes	complemented
183	#493	C₂²×C₁₃	1	2	yes	complemented
184	#442	—	2	2	no	—
185	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
186	#427	C₂²×C₁₃	1	1	yes	characteristic
187	#418	—	2	1	no	—
188	#405	C₂²×C₁₃	1	1	yes	characteristic
189	C₄⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
190	#358	C₂²×C₁₃	1	2	yes	complemented
191	#357	C₂²×C₁₃	1	2	yes	complemented
192	#357	C₂²×C₁₃	1	4	yes	complemented
193	C₂²×C₁₃	—	2	2	no	—
194	C₂²×C₁₃	—	4	4	no	—
195	C₂²×C₁₃	—	8	4	no	—
196	C₂²×C₁₃	—	8	2	no	—
197	C₂²×C₁₃	—	8	4	no	—
198	C₂²×C₁₃	—	8	1	no	—
199	C₂²×C₁₃	—	8	2	no	—
200	C₂²×C₁₃	—	16	4	no	—
201	C₂²×C₁₃	—	16	4	no	—
202	C₂²×C₁₃	#459	1	2	yes	—
203	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
204	C₄×C₁₃	—	2	4	no	—
205	C₄×C₁₃	—	8	2	no	—
206	C₄×C₁₃	—	8	1	no	—
207	C₄×C₁₃	#459	1	2	yes	—
208	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
209	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₂×#41	—	2	1	no	—
211	C₂²×D₄	—	2	1	no	—
212	C₂²×D₄	—	2	1	no	—
213	AGL(1,ℤ/8)	—	4	4	no	—
214	#135	—	2	2	no	—
215	#135	—	2	2	no	—
216	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
217	C₂×SD₁₆	—	2	1	no	—
218	C₂×SD₁₆	—	2	2	no	—
219	C₂×D₈	—	2	1	no	—
220	C₂×D₈	—	2	2	no	—
221	C₂×D₈	—	2	1	no	—
222	C₂×D₈	—	2	2	no	—
223	C₂×D₈	—	2	2	no	—
224	C₂×D₈	—	2	2	no	—
225	C₂×D₈	D₄×C₁₃	1	4	yes	complemented
226	C₂×D₈	C₂³×C₁₃	1	2	yes	—
227	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
228	C₂×D₈	C₂³×C₁₃	1	2	yes	—
229	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
231	#127	—	2	2	no	—
232	#124	—	2	2	no	—
233	#121	—	4	2	no	—
234	#120	—	4	2	no	—
235	C₄×D₄	—	2	4	no	—
236	C₄×D₄	—	4	2	no	—
237	#117	—	2	1	no	—
238	#117	D₄×C₁₃	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	—	4	2	no	—
240	SD₃₂	—	2	4	no	—
241	D₁₆	—	2	8	no	—
242	D₁₆	—	2	4	no	—
243	M₃₂	—	2	2	no	—
244	C₂×C₁₆	—	2	2	no	—
245	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
246	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
247	#107	C₂³×C₁₃	1	2	yes	—
248	#106	—	2	1	no	—
249	#102	—	2	4	no	—
250	#97	D₄×C₁₃	1	2	yes	—
251	C₄×C₈	C₂³×C₁₃	1	2	yes	—
252	C₂×C₁₃	—	2	2	no	—
253	C₂×C₁₃	—	8	4	no	—
254	C₂×C₁₃	—	16	1	no	—
255	C₂×C₁₃	—	16	2	no	—
256	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
257	C₂×C₁₃	#3415	1	2	yes	—
258	C₂⁴	—	4	1	no	—
259	C₂⁴	—	4	1	no	—
260	#41	—	4	2	no	—
261	#41	—	4	2	no	—
262	C₂×Q₈	—	2	1	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	—	4	1	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	4	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	—	4	4	no	—
276	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
277	Q₁₆	—	2	1	no	—
278	Q₁₆	—	2	1	no	—
279	SD₁₆	—	4	4	no	—
280	SD₁₆	—	4	2	no	—
281	D₈	—	2	4	no	—
282	D₈	—	2	2	no	—
283	D₈	—	2	1	no	—
284	D₈	—	2	2	no	—
285	D₈	—	2	2	no	—
286	D₈	—	2	1	no	—
287	D₈	—	4	4	no	—
288	D₈	—	4	2	no	—
289	D₈	C₂×D₄×C₁₃	1	4	yes	—
290	M₁₆	—	2	2	no	—
291	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
292	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
294	C₂×C₈	C₁₃×#41	1	2	yes	—
295	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	C₁₃×D₈	1	2	yes	—
298	C₂²⋊C₄	—	4	1	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
302	C₄²	—	4	1	no	—
303	C₄²	C₂×D₄×C₁₃	1	2	yes	—
304	C₁₆	—	2	2	no	—
305	C₁₆	—	2	2	no	—
306	C₁₃	#33585	1	1	yes	characteristic, direct product factor, Sylow
307	C₂³	—	4	2	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	8	2	no	—
312	C₂³	—	16	2	no	—
313	C₂³	—	16	2	no	—
314	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
315	Q₈	—	4	1	no	—
316	Q₈	—	4	1	no	—
317	D₄	—	2	4	no	—
318	D₄	—	4	4	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	1	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	2	no	—
324	D₄	—	8	2	no	—
325	D₄	—	8	2	no	—
326	D₄	—	16	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	8	2	no	—
330	C₂×C₄	—	16	4	no	—
331	C₂×C₄	C₁₃×#121	1	2	yes	—
332	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
333	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
334	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
335	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	C₁₃×#121	1	2	yes	—
338	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
339	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
340	C₂²	—	2	2	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	8	4	no	—
343	C₂²	—	8	1	no	—
344	C₂²	—	8	2	no	—
345	C₂²	—	8	2	no	—
346	C₂²	—	8	4	no	—
347	C₂²	—	16	4	no	—
348	C₂²	—	16	4	no	—
349	C₂²	C₁₃×#459	1	2	yes	—
350	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	8	1	no	—
353	C₄	—	8	2	no	—
354	C₄	C₁₃×#459	1	2	yes	—
355	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
356	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₂	—	2	2	no	—
358	C₂	—	8	4	no	—
359	C₂	—	16	2	no	—
360	C₂	—	16	1	no	—
361	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
362	C₂	C₁₃×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#117 ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#509	C₂	semidirect
2. C₂²×C₁₃×D₁₆	C₂	semidirect
3. C₁₃×#3155	C₂	semidirect
4. C₁₃×#2948	C₂	semidirect
5. C₁₃×#2210	C₂	semidirect
6. C₁₃×#2206	C₂	semidirect
7. C₁₃×#2151	C₂	semidirect
8. C₁₃×#2140	C₂	semidirect
9. C₁₃×#2138	C₂	semidirect
17. C₂×C₁₃×SD₃₂	C₂²	semidirect
20. C₂×C₁₃×D₁₆	C₂²	semidirect
24. C₁₃×#495	C₂²	semidirect
25. C₁₃×#493	C₂²	semidirect
27. C₄×C₁₃×D₈	C₂²	semidirect
31. C₁₃×C₄⋊C₁₆	C₂²	semidirect
32. C₁₃×#358	C₂²	semidirect
33. C₁₃×#357	C₂²	semidirect
34. C₁₃×#357	C₂²	semidirect
50. C₂×C₁₃×D₈	D₄	semidirect
77. #33585	C₁₃	direct (N × H)
126. C₂×#509	C₂×C₁₃	semidirect
127. C₂²×D₁₆	C₂×C₁₃	semidirect
128. #3155	C₂×C₁₃	semidirect
129. #2948	C₂×C₁₃	semidirect
130. #2210	C₂×C₁₃	semidirect
131. #2206	C₂×C₁₃	semidirect
132. #2151	C₂×C₁₃	semidirect
133. #2140	C₂×C₁₃	semidirect
134. #2138	C₂×C₁₃	semidirect
175. C₂×SD₃₂	C₂²×C₁₃	semidirect
178. C₂×D₁₆	C₂²×C₁₃	semidirect
182. #495	C₂²×C₁₃	semidirect
183. #493	C₂²×C₁₃	semidirect
185. C₄×D₈	C₂²×C₁₃	semidirect
189. C₄⋊C₁₆	C₂²×C₁₃	semidirect
190. #358	C₂²×C₁₃	semidirect
191. #357	C₂²×C₁₃	semidirect
192. #357	C₂²×C₁₃	semidirect
225. C₂×D₈	D₄×C₁₃	semidirect
306. C₁₃	#33585	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#509	2
C₂²×C₁₃×D₁₆	2
C₁₃×#3155	2
C₁₃×#2948	2
C₁₃×#2210	2
C₁₃×#2206	2
C₁₃×#2151	2
C₁₃×#2140	2
C₁₃×#2138	2
#33585	13

Subgroups — C13×#33585 #15719924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33585 #15719924