Subgroups — C₁₃×#33617 #15719956

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3067	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2223	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2222	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2221	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2148	C₂	1	2	yes	maximal, complemented
9	C₁₃×#575	—	2	2	no	—
10	C₂×C₁₃×#135	C₂²	1	2	yes	—
11	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
12	C₁₃×#508	—	2	1	no	—
13	C₁₃×#508	—	2	1	no	—
14	C₁₃×#508	—	2	1	no	—
15	C₁₃×#508	—	2	1	no	—
16	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#504	—	2	1	no	—
20	C₁₃×#504	—	2	1	no	—
21	C₁₃×#504	C₂²	1	2	yes	—
22	C₁₃×#504	C₂²	1	2	yes	—
23	C₂×C₁₃×M₃₂	—	2	1	no	—
24	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₁₆	—	2	1	no	—
26	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
27	C₁₃×#473	C₂²	1	4	yes	—
28	C₁₃×#472	C₂²	1	4	yes	—
29	C₁₃×#471	—	2	4	no	—
30	C₂×C₁₃×#108	C₂²	1	2	yes	—
31	C₁₃×#413	—	2	2	no	—
32	C₁₃×#368	C₂²	1	2	yes	complemented
33	C₁₃×#368	C₂²	1	2	yes	complemented
34	C₁₃×#362	C₂²	1	4	yes	complemented
35	C₁₃×#361	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
38	C₁₃×#137	—	2	4	no	—
39	C₁₃×#137	—	4	2	no	—
40	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
41	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
42	C₁₃×#135	—	2	2	no	—
43	C₁₃×#135	—	2	2	no	—
44	C₁₃×#135	—	2	2	no	—
45	C₁₃×#135	—	2	2	no	—
46	C₁₃×#135	—	4	4	no	—
47	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×D₈	C₂³	1	2	yes	—
50	C₁₃×#131	—	2	1	no	—
51	C₁₃×#131	—	2	1	no	—
52	C₁₃×#131	D₄	1	2	yes	—
53	C₁₃×#131	C₂³	1	2	yes	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×Q₃₂	—	2	1	no	—
60	C₁₃×Q₃₂	—	2	1	no	—
61	C₁₃×SD₃₂	—	2	2	no	—
62	C₁₃×SD₃₂	—	2	2	no	—
63	C₁₃×D₁₆	—	2	1	no	—
64	C₁₃×D₁₆	—	2	1	no	—
65	C₁₃×M₃₂	—	2	1	no	—
66	C₁₃×M₃₂	—	2	2	no	—
67	C₁₃×M₃₂	—	2	2	no	—
68	C₁₃×M₃₂	C₂³	1	2	yes	—
69	C₂×C₁₃×C₁₆	—	2	1	no	—
70	C₂×C₁₃×C₁₆	—	2	2	no	—
71	C₂×C₁₃×C₁₆	—	2	2	no	—
72	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
73	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
74	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
75	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
76	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
78	C₁₃×#108	—	2	2	no	—
79	C₁₃×#108	C₂³	1	4	yes	—
80	C₁₃×#101	—	2	4	no	—
81	C₁₃×#100	—	2	4	no	—
82	#33617	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₁₃×#41	—	2	1	no	—
84	C₁₃×#41	—	2	1	no	—
85	C₁₃×#41	—	4	2	no	—
86	C₁₃×#41	—	4	2	no	—
87	C₁₃×#41	—	4	2	no	—
88	C₁₃×#41	—	4	2	no	—
89	C₁₃×#41	D₈	1	2	yes	—
90	C₁₃×#41	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	4	2	no	—
96	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₁₃×Q₁₆	—	2	2	no	—
101	C₁₃×Q₁₆	—	2	2	no	—
102	C₁₃×Q₁₆	—	4	4	no	—
103	C₁₃×SD₁₆	—	4	4	no	—
104	C₁₃×SD₁₆	—	4	4	no	—
105	C₁₃×SD₁₆	—	4	2	no	—
106	C₁₃×SD₁₆	—	4	2	no	—
107	C₁₃×D₈	—	2	2	no	—
108	C₁₃×D₈	—	2	2	no	—
109	C₁₃×D₈	—	4	4	no	—
110	C₁₃×M₁₆	—	2	1	no	—
111	C₁₃×M₁₆	—	2	2	no	—
112	C₁₃×M₁₆	—	2	2	no	—
113	C₁₃×M₁₆	—	2	4	no	—
114	C₁₃×M₁₆	—	4	2	no	—
115	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	4	2	no	—
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
124	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×C₁₆	—	2	2	no	—
127	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
128	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
129	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
130	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
131	C₂×#508	C₂×C₁₃	1	1	yes	characteristic, complemented
132	C₂×#504	C₂×C₁₃	1	1	yes	characteristic, complemented
133	#3067	C₂×C₁₃	1	2	yes	complemented
134	#2223	C₂×C₁₃	1	4	yes	complemented
135	#2222	C₂×C₁₃	1	2	yes	complemented
136	#2221	C₂×C₁₃	1	2	yes	complemented
137	C₂×#368	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#2148	C₂×C₁₃	1	2	yes	complemented
139	C₂³×C₁₃	—	2	1	no	—
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	#135	1	1	yes	characteristic
142	Q₈×C₁₃	—	2	1	no	—
143	Q₈×C₁₃	—	4	2	no	—
144	Q₈×C₁₃	—	4	2	no	—
145	Q₈×C₁₃	C₂×D₈	1	2	yes	—
146	D₄×C₁₃	—	2	2	no	—
147	D₄×C₁₃	—	2	2	no	—
148	D₄×C₁₃	—	2	1	no	—
149	D₄×C₁₃	—	4	2	no	—
150	D₄×C₁₃	—	4	2	no	—
151	D₄×C₁₃	—	8	2	no	—
152	D₄×C₁₃	—	8	2	no	—
153	D₄×C₁₃	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	8	2	no	—
159	C₂×C₄×C₁₃	—	8	2	no	—
160	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₁₃	—	2	2	no	—
167	C₈×C₁₃	—	4	4	no	—
168	C₈×C₁₃	#121	1	1	yes	characteristic
169	C₈×C₁₃	#121	1	1	yes	characteristic
170	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
172	#575	—	2	2	no	—
173	C₂×#135	C₂²×C₁₃	1	2	yes	—
174	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
175	#508	—	2	1	no	—
176	#508	—	2	1	no	—
177	#508	—	2	1	no	—
178	#508	—	2	1	no	—
179	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
180	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
181	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
182	#504	—	2	1	no	—
183	#504	—	2	1	no	—
184	#504	C₂²×C₁₃	1	2	yes	—
185	#504	C₂²×C₁₃	1	2	yes	—
186	C₂×M₃₂	—	2	1	no	—
187	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
188	C₂²×C₁₆	—	2	1	no	—
189	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
190	#473	C₂²×C₁₃	1	4	yes	—
191	#472	C₂²×C₁₃	1	4	yes	—
192	#471	—	2	4	no	—
193	C₂×#108	C₂²×C₁₃	1	2	yes	—
194	#413	—	2	2	no	—
195	#368	C₂²×C₁₃	1	2	yes	complemented
196	#368	C₂²×C₁₃	1	2	yes	complemented
197	#362	C₂²×C₁₃	1	4	yes	complemented
198	#361	C₂²×C₁₃	1	4	yes	complemented
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	4	1	no	—
201	C₂²×C₁₃	—	4	2	no	—
202	C₂²×C₁₃	—	8	2	no	—
203	C₂²×C₁₃	—	16	2	no	—
204	C₂²×C₁₃	#466	1	1	yes	characteristic
205	C₂²×C₁₃	#466	1	1	yes	characteristic
206	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
207	C₄×C₁₃	—	2	2	no	—
208	C₄×C₁₃	—	8	2	no	—
209	C₄×C₁₃	#466	1	1	yes	characteristic
210	C₄×C₁₃	#466	1	1	yes	characteristic
211	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
212	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
213	C₂×#41	—	2	2	no	—
214	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
215	#137	—	2	4	no	—
216	#137	—	4	2	no	—
217	AGL(1,ℤ/8)	—	2	4	no	—
218	AGL(1,ℤ/8)	—	4	2	no	—
219	#135	—	2	2	no	—
220	#135	—	2	2	no	—
221	#135	—	2	2	no	—
222	#135	—	2	2	no	—
223	#135	—	4	4	no	—
224	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
225	C₂×SD₁₆	—	2	2	no	—
226	C₂×D₈	C₂³×C₁₃	1	2	yes	—
227	#131	—	2	1	no	—
228	#131	—	2	1	no	—
229	#131	D₄×C₁₃	1	2	yes	—
230	#131	C₂³×C₁₃	1	2	yes	—
231	C₂×M₁₆	—	2	1	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
236	Q₃₂	—	2	1	no	—
237	Q₃₂	—	2	1	no	—
238	SD₃₂	—	2	2	no	—
239	SD₃₂	—	2	2	no	—
240	D₁₆	—	2	1	no	—
241	D₁₆	—	2	1	no	—
242	M₃₂	—	2	1	no	—
243	M₃₂	—	2	2	no	—
244	M₃₂	—	2	2	no	—
245	M₃₂	C₂³×C₁₃	1	2	yes	—
246	C₂×C₁₆	—	2	1	no	—
247	C₂×C₁₆	—	2	2	no	—
248	C₂×C₁₆	—	2	2	no	—
249	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
250	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
251	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
252	C₂×C₁₆	D₄×C₁₃	1	1	yes	characteristic
253	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
255	#108	—	2	2	no	—
256	#108	C₂³×C₁₃	1	4	yes	—
257	#101	—	2	4	no	—
258	#100	—	2	4	no	—
259	C₂×C₁₃	—	2	1	no	—
260	C₂×C₁₃	—	2	1	no	—
261	C₂×C₁₃	—	2	1	no	—
262	C₂×C₁₃	—	4	2	no	—
263	C₂×C₁₃	—	16	2	no	—
264	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
265	#41	—	2	1	no	—
266	#41	—	2	1	no	—
267	#41	—	4	2	no	—
268	#41	—	4	2	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	#41	C₁₃×D₈	1	2	yes	—
272	#41	C₂×D₄×C₁₃	1	2	yes	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
282	Q₁₆	—	2	2	no	—
283	Q₁₆	—	2	2	no	—
284	Q₁₆	—	4	4	no	—
285	SD₁₆	—	4	4	no	—
286	SD₁₆	—	4	4	no	—
287	SD₁₆	—	4	2	no	—
288	SD₁₆	—	4	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	2	no	—
291	D₈	—	4	4	no	—
292	M₁₆	—	2	1	no	—
293	M₁₆	—	2	2	no	—
294	M₁₆	—	2	2	no	—
295	M₁₆	—	2	4	no	—
296	M₁₆	—	4	2	no	—
297	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
306	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
307	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
308	C₁₆	—	2	2	no	—
309	C₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₁₃	#33617	1	1	yes	characteristic, direct product factor, Sylow
314	C₂³	—	2	1	no	—
315	C₂³	—	4	2	no	—
316	C₂³	C₁₃×#135	1	1	yes	characteristic
317	Q₈	—	2	1	no	—
318	Q₈	—	4	2	no	—
319	Q₈	—	4	2	no	—
320	Q₈	C₂×C₁₃×D₈	1	2	yes	—
321	D₄	—	2	2	no	—
322	D₄	—	2	2	no	—
323	D₄	—	2	1	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	8	2	no	—
327	D₄	—	8	2	no	—
328	D₄	C₂×C₁₃×D₈	1	2	yes	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	8	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
336	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
337	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
338	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
339	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
341	C₈	—	2	2	no	—
342	C₈	—	4	4	no	—
343	C₈	C₁₃×#121	1	1	yes	characteristic
344	C₈	C₁₃×#121	1	1	yes	characteristic
345	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
346	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
347	C₂²	—	2	2	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	16	2	no	—
352	C₂²	C₁₃×#466	1	1	yes	characteristic
353	C₂²	C₁₃×#466	1	1	yes	characteristic
354	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
355	C₄	—	2	2	no	—
356	C₄	—	8	2	no	—
357	C₄	C₁₃×#466	1	1	yes	characteristic
358	C₄	C₁₃×#466	1	1	yes	characteristic
359	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
360	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	—	2	1	no	—
364	C₂	—	4	2	no	—
365	C₂	—	16	2	no	—
366	C₂	C₂×C₁₃×#466	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#466
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×#466
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×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. C₂×C₁₃×#508	C₂	semidirect
2. C₂×C₁₃×#504	C₂	semidirect
3. C₁₃×#3067	C₂	semidirect
4. C₁₃×#2223	C₂	semidirect
5. C₁₃×#2222	C₂	semidirect
6. C₁₃×#2221	C₂	semidirect
7. C₂×C₁₃×#368	C₂	semidirect
8. C₁₃×#2148	C₂	semidirect
16. C₂×C₁₃×Q₃₂	C₂²	semidirect
17. C₂×C₁₃×SD₃₂	C₂²	semidirect
18. C₂×C₁₃×D₁₆	C₂²	semidirect
32. C₁₃×#368	C₂²	semidirect
33. C₁₃×#368	C₂²	semidirect
34. C₁₃×#362	C₂²	semidirect
35. C₁₃×#361	C₂²	semidirect
82. #33617	C₁₃	direct (N × H)
131. C₂×#508	C₂×C₁₃	semidirect
132. C₂×#504	C₂×C₁₃	semidirect
133. #3067	C₂×C₁₃	semidirect
134. #2223	C₂×C₁₃	semidirect
135. #2222	C₂×C₁₃	semidirect
136. #2221	C₂×C₁₃	semidirect
137. C₂×#368	C₂×C₁₃	semidirect
138. #2148	C₂×C₁₃	semidirect
179. C₂×Q₃₂	C₂²×C₁₃	semidirect
180. C₂×SD₃₂	C₂²×C₁₃	semidirect
181. C₂×D₁₆	C₂²×C₁₃	semidirect
195. #368	C₂²×C₁₃	semidirect
196. #368	C₂²×C₁₃	semidirect
197. #362	C₂²×C₁₃	semidirect
198. #361	C₂²×C₁₃	semidirect
313. C₁₃	#33617	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×#508	2
C₂×C₁₃×#504	2
C₁₃×#3067	2
C₁₃×#2223	2
C₁₃×#2222	2
C₁₃×#2221	2
C₂×C₁₃×#368	2
C₁₃×#2148	2
#33617	13

Subgroups — C13×#33617 #15719956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33617 #15719956