Subgroups — C₁₃×#33857 #15720196

Order 3328.

646 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	C₁₃×#3416	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3290	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2223	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2212	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2195	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2192	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2178	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2170	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#578	C₂²	1	2	yes	—
11	C₁₃×#577	—	2	2	no	—
12	C₁₃×#576	C₂²	1	2	yes	complemented
13	C₁₃×#510	—	2	2	no	—
14	C₁₃×#510	C₂²	1	2	yes	complemented
15	C₁₃×#509	—	2	2	no	—
16	C₁₃×#509	C₂²	1	2	yes	—
17	C₁₃×#508	—	2	2	no	—
18	C₁₃×#508	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₃×SD₃₂	—	2	2	no	—
21	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
22	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
23	C₁₃×#504	C₂²	1	2	yes	complemented
24	C₁₃×#495	C₂²	1	2	yes	complemented
25	C₁₃×#473	C₂²	1	2	yes	complemented
26	C₁₃×#472	C₂²	1	2	yes	—
27	C₁₃×#471	—	2	2	no	—
28	C₁₃×#455	—	2	2	no	—
29	C₁₃×#454	—	2	2	no	—
30	C₁₃×#443	C₂²	1	1	yes	characteristic
31	C₁₃×#443	C₂²	1	2	yes	complemented
32	C₁₃×#368	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#364	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#362	C₂²	1	2	yes	complemented
35	C₁₃×#361	C₂²	1	2	yes	complemented
36	C₁₃×#359	C₂²	1	2	yes	complemented
37	C₁₃×#350	C₂²	1	2	yes	complemented
38	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×2₋¹⁺⁴	—	2	2	no	—
40	C₁₃×H(5,𝔽₂)	—	2	2	no	—
41	C₁₃×#137	—	2	2	no	—
42	C₁₃×#137	—	2	2	no	—
43	C₁₃×#137	—	4	2	no	—
44	C₁₃×#137	—	4	2	no	—
45	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
46	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
47	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
48	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
49	C₁₃×#135	—	2	2	no	—
50	C₁₃×#135	—	2	2	no	—
51	C₁₃×#135	—	4	2	no	—
52	C₁₃×#135	D₄	1	1	yes	characteristic
53	C₁₃×#135	C₂³	1	2	yes	—
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×SD₁₆	—	4	2	no	—
58	C₂×C₁₃×D₈	—	2	2	no	—
59	C₂×C₁₃×D₈	C₂³	1	2	yes	—
60	C₁₃×#131	—	2	2	no	—
61	C₁₃×#131	C₂³	1	2	yes	—
62	C₁₃×#124	—	2	2	no	—
63	C₁₃×Q₃₂	—	2	2	no	—
64	C₁₃×Q₃₂	—	4	1	no	—
65	C₁₃×Q₃₂	D₄	1	1	yes	characteristic
66	C₁₃×SD₃₂	—	2	2	no	—
67	C₁₃×SD₃₂	—	2	2	no	—
68	C₁₃×SD₃₂	—	2	2	no	—
69	C₁₃×SD₃₂	—	2	2	no	—
70	C₁₃×SD₃₂	D₄	1	2	yes	—
71	C₁₃×D₁₆	—	2	2	no	—
72	C₁₃×D₁₆	—	4	1	no	—
73	C₁₃×D₁₆	D₄	1	1	yes	characteristic
74	C₁₃×M₃₂	—	2	2	no	—
75	C₁₃×M₃₂	C₂³	1	2	yes	—
76	C₂×C₁₃×C₁₆	—	2	2	no	—
77	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
79	C₁₃×#108	D₄	1	1	yes	characteristic
80	C₁₃×#108	C₂³	1	2	yes	—
81	C₁₃×#104	—	2	2	no	—
82	C₁₃×#104	D₄	1	2	yes	—
83	C₁₃×#101	—	2	2	no	—
84	C₁₃×#100	—	2	2	no	—
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	#33857	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₁₃×#41	—	2	2	no	—
88	C₁₃×#41	—	4	2	no	—
89	C₁₃×#41	—	4	2	no	—
90	C₁₃×#41	—	4	2	no	—
91	C₁₃×#41	—	4	2	no	—
92	C₁₃×#41	—	8	2	no	—
93	C₁₃×#41	C₂×D₄	1	2	yes	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	8	2	no	—
101	C₁₃×Q₁₆	—	2	2	no	—
102	C₁₃×Q₁₆	—	2	2	no	—
103	C₁₃×Q₁₆	—	4	2	no	—
104	C₁₃×Q₁₆	—	4	2	no	—
105	C₁₃×Q₁₆	D₈	1	1	yes	characteristic
106	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
107	C₁₃×SD₁₆	—	2	2	no	—
108	C₁₃×SD₁₆	—	4	2	no	—
109	C₁₃×SD₁₆	—	4	2	no	—
110	C₁₃×SD₁₆	—	4	2	no	—
111	C₁₃×SD₁₆	—	4	2	no	—
112	C₁₃×SD₁₆	—	4	2	no	—
113	C₁₃×SD₁₆	—	4	2	no	—
114	C₁₃×SD₁₆	D₈	1	2	yes	—
115	C₁₃×D₈	—	2	2	no	—
116	C₁₃×D₈	—	2	2	no	—
117	C₁₃×D₈	—	4	2	no	—
118	C₁₃×D₈	—	4	2	no	—
119	C₁₃×D₈	D₈	1	1	yes	characteristic
120	C₁₃×D₈	C₂×D₄	1	2	yes	—
121	C₁₃×M₁₆	—	2	2	no	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	—	4	2	no	—
124	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	4	2	no	—
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×C₂²⋊C₄	—	8	2	no	—
130	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₁₃×C₁₆	—	2	2	no	—
132	C₁₃×C₁₆	—	2	1	no	—
133	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
134	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
135	#3416	C₂×C₁₃	1	2	yes	complemented
136	#3290	C₂×C₁₃	1	2	yes	complemented
137	#2249	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#2223	C₂×C₁₃	1	2	yes	complemented
139	#2212	C₂×C₁₃	1	2	yes	complemented
140	#2195	C₂×C₁₃	1	2	yes	complemented
141	#2192	C₂×C₁₃	1	2	yes	complemented
142	#2178	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2170	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂³×C₁₃	—	4	2	no	—
145	C₂³×C₁₃	—	8	2	no	—
146	Q₈×C₁₃	—	2	2	no	—
147	Q₈×C₁₃	—	4	2	no	—
148	Q₈×C₁₃	—	4	2	no	—
149	Q₈×C₁₃	—	8	2	no	—
150	Q₈×C₁₃	C₂×D₈	1	2	yes	—
151	D₄×C₁₃	—	2	2	no	—
152	D₄×C₁₃	—	2	2	no	—
153	D₄×C₁₃	—	4	2	no	—
154	D₄×C₁₃	—	4	2	no	—
155	D₄×C₁₃	—	4	2	no	—
156	D₄×C₁₃	—	8	2	no	—
157	D₄×C₁₃	—	8	2	no	—
158	D₄×C₁₃	—	8	2	no	—
159	D₄×C₁₃	C₂×D₈	1	2	yes	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	8	2	no	—
165	C₂×C₄×C₁₃	—	8	2	no	—
166	C₂×C₄×C₁₃	—	8	2	no	—
167	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	C₈×C₁₃	—	2	2	no	—
169	C₈×C₁₃	—	4	2	no	—
170	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
171	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
172	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
174	#578	C₂²×C₁₃	1	2	yes	—
175	#577	—	2	2	no	—
176	#576	C₂²×C₁₃	1	2	yes	complemented
177	#510	—	2	2	no	—
178	#510	C₂²×C₁₃	1	2	yes	complemented
179	#509	—	2	2	no	—
180	#509	C₂²×C₁₃	1	2	yes	—
181	#508	—	2	2	no	—
182	#508	C₂²×C₁₃	1	1	yes	characteristic
183	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
184	C₂×SD₃₂	—	2	2	no	—
185	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
186	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
187	#504	C₂²×C₁₃	1	2	yes	complemented
188	#495	C₂²×C₁₃	1	2	yes	complemented
189	#473	C₂²×C₁₃	1	2	yes	complemented
190	#472	C₂²×C₁₃	1	2	yes	—
191	#471	—	2	2	no	—
192	#455	—	2	2	no	—
193	#454	—	2	2	no	—
194	#443	C₂²×C₁₃	1	1	yes	characteristic
195	#443	C₂²×C₁₃	1	2	yes	complemented
196	#368	C₂²×C₁₃	1	1	yes	characteristic, complemented
197	#364	C₂²×C₁₃	1	1	yes	characteristic, complemented
198	#362	C₂²×C₁₃	1	2	yes	complemented
199	#361	C₂²×C₁₃	1	2	yes	complemented
200	#359	C₂²×C₁₃	1	2	yes	complemented
201	#350	C₂²×C₁₃	1	2	yes	complemented
202	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
203	C₂²×C₁₃	—	2	2	no	—
204	C₂²×C₁₃	—	4	2	no	—
205	C₂²×C₁₃	—	8	2	no	—
206	C₂²×C₁₃	—	16	2	no	—
207	C₂²×C₁₃	—	32	2	no	—
208	C₂²×C₁₃	#576	1	1	yes	characteristic
209	C₄×C₁₃	—	2	2	no	—
210	C₄×C₁₃	—	4	1	no	—
211	C₄×C₁₃	—	4	2	no	—
212	C₄×C₁₃	—	8	2	no	—
213	C₄×C₁₃	D₄²	1	1	yes	characteristic
214	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
215	2₋¹⁺⁴	—	2	2	no	—
216	H(5,𝔽₂)	—	2	2	no	—
217	#137	—	2	2	no	—
218	#137	—	2	2	no	—
219	#137	—	4	2	no	—
220	#137	—	4	2	no	—
221	AGL(1,ℤ/8)	—	2	2	no	—
222	AGL(1,ℤ/8)	—	2	2	no	—
223	AGL(1,ℤ/8)	—	4	2	no	—
224	AGL(1,ℤ/8)	—	4	2	no	—
225	#135	—	2	2	no	—
226	#135	—	2	2	no	—
227	#135	—	4	2	no	—
228	#135	D₄×C₁₃	1	1	yes	characteristic
229	#135	C₂³×C₁₃	1	2	yes	—
230	C₂×Q₁₆	—	2	2	no	—
231	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×SD₁₆	—	4	2	no	—
234	C₂×D₈	—	2	2	no	—
235	C₂×D₈	C₂³×C₁₃	1	2	yes	—
236	#131	—	2	2	no	—
237	#131	C₂³×C₁₃	1	2	yes	—
238	#124	—	2	2	no	—
239	Q₃₂	—	2	2	no	—
240	Q₃₂	—	4	1	no	—
241	Q₃₂	D₄×C₁₃	1	1	yes	characteristic
242	SD₃₂	—	2	2	no	—
243	SD₃₂	—	2	2	no	—
244	SD₃₂	—	2	2	no	—
245	SD₃₂	—	2	2	no	—
246	SD₃₂	D₄×C₁₃	1	2	yes	—
247	D₁₆	—	2	2	no	—
248	D₁₆	—	4	1	no	—
249	D₁₆	D₄×C₁₃	1	1	yes	characteristic
250	M₃₂	—	2	2	no	—
251	M₃₂	C₂³×C₁₃	1	2	yes	—
252	C₂×C₁₆	—	2	2	no	—
253	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
255	#108	D₄×C₁₃	1	1	yes	characteristic
256	#108	C₂³×C₁₃	1	2	yes	—
257	#104	—	2	2	no	—
258	#104	D₄×C₁₃	1	2	yes	—
259	#101	—	2	2	no	—
260	#100	—	2	2	no	—
261	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×C₁₃	—	2	1	no	—
263	C₂×C₁₃	—	4	2	no	—
264	C₂×C₁₃	—	8	2	no	—
265	C₂×C₁₃	—	16	2	no	—
266	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
267	#41	—	2	2	no	—
268	#41	—	4	2	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	#41	—	8	2	no	—
273	#41	C₂×D₄×C₁₃	1	2	yes	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	8	2	no	—
281	Q₁₆	—	2	2	no	—
282	Q₁₆	—	2	2	no	—
283	Q₁₆	—	4	2	no	—
284	Q₁₆	—	4	2	no	—
285	Q₁₆	C₁₃×D₈	1	1	yes	characteristic
286	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
287	SD₁₆	—	2	2	no	—
288	SD₁₆	—	4	2	no	—
289	SD₁₆	—	4	2	no	—
290	SD₁₆	—	4	2	no	—
291	SD₁₆	—	4	2	no	—
292	SD₁₆	—	4	2	no	—
293	SD₁₆	—	4	2	no	—
294	SD₁₆	C₁₃×D₈	1	2	yes	—
295	D₈	—	2	2	no	—
296	D₈	—	2	2	no	—
297	D₈	—	4	2	no	—
298	D₈	—	4	2	no	—
299	D₈	C₁₃×D₈	1	1	yes	characteristic
300	D₈	C₂×D₄×C₁₃	1	2	yes	—
301	M₁₆	—	2	2	no	—
302	M₁₆	—	2	2	no	—
303	M₁₆	—	4	2	no	—
304	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
309	C₂²⋊C₄	—	8	2	no	—
310	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₁₆	—	2	2	no	—
312	C₁₆	—	2	1	no	—
313	C₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₁₃	#33857	1	1	yes	characteristic, direct product factor, Sylow
316	C₂³	—	4	2	no	—
317	C₂³	—	8	2	no	—
318	Q₈	—	2	2	no	—
319	Q₈	—	4	2	no	—
320	Q₈	—	4	2	no	—
321	Q₈	—	8	2	no	—
322	Q₈	C₂×C₁₃×D₈	1	2	yes	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	D₄	—	8	2	no	—
331	D₄	C₂×C₁₃×D₈	1	2	yes	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
340	C₈	—	2	2	no	—
341	C₈	—	4	2	no	—
342	C₈	C₂×C₁₃×D₈	1	1	yes	characteristic
343	C₈	C₂×C₁₃×D₈	1	1	yes	characteristic
344	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
345	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂²	—	2	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	16	2	no	—
350	C₂²	—	32	2	no	—
351	C₂²	C₁₃×#576	1	1	yes	characteristic
352	C₄	—	2	2	no	—
353	C₄	—	4	1	no	—
354	C₄	—	4	2	no	—
355	C₄	—	8	2	no	—
356	C₄	D₄²×C₁₃	1	1	yes	characteristic
357	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
358	C₂	—	2	1	no	—
359	C₂	—	4	2	no	—
360	C₂	—	8	2	no	—
361	C₂	—	16	2	no	—
362	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	D₄×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#443 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3416	C₂	semidirect
2. C₁₃×#3290	C₂	semidirect
3. C₁₃×#2249	C₂	semidirect
4. C₁₃×#2223	C₂	semidirect
5. C₁₃×#2212	C₂	semidirect
6. C₁₃×#2195	C₂	semidirect
7. C₁₃×#2192	C₂	semidirect
8. C₁₃×#2178	C₂	semidirect
9. C₁₃×#2170	C₂	semidirect
12. C₁₃×#576	C₂²	semidirect
14. C₁₃×#510	C₂²	semidirect
19. C₂×C₁₃×Q₃₂	C₂²	semidirect
21. C₂×C₁₃×SD₃₂	C₂²	semidirect
23. C₁₃×#504	C₂²	semidirect
24. C₁₃×#495	C₂²	semidirect
25. C₁₃×#473	C₂²	semidirect
31. C₁₃×#443	C₂²	semidirect
32. C₁₃×#368	C₂²	semidirect
33. C₁₃×#364	C₂²	semidirect
34. C₁₃×#362	C₂²	semidirect
35. C₁₃×#361	C₂²	semidirect
36. C₁₃×#359	C₂²	semidirect
37. C₁₃×#350	C₂²	semidirect
38. C₄×C₁₃×C₁₆	C₂²	semidirect
86. #33857	C₁₃	direct (N × H)
135. #3416	C₂×C₁₃	semidirect
136. #3290	C₂×C₁₃	semidirect
137. #2249	C₂×C₁₃	semidirect
138. #2223	C₂×C₁₃	semidirect
139. #2212	C₂×C₁₃	semidirect
140. #2195	C₂×C₁₃	semidirect
141. #2192	C₂×C₁₃	semidirect
142. #2178	C₂×C₁₃	semidirect
143. #2170	C₂×C₁₃	semidirect
176. #576	C₂²×C₁₃	semidirect
178. #510	C₂²×C₁₃	semidirect
183. C₂×Q₃₂	C₂²×C₁₃	semidirect
185. C₂×SD₃₂	C₂²×C₁₃	semidirect
187. #504	C₂²×C₁₃	semidirect
188. #495	C₂²×C₁₃	semidirect
189. #473	C₂²×C₁₃	semidirect
195. #443	C₂²×C₁₃	semidirect
196. #368	C₂²×C₁₃	semidirect
197. #364	C₂²×C₁₃	semidirect
198. #362	C₂²×C₁₃	semidirect
199. #361	C₂²×C₁₃	semidirect
200. #359	C₂²×C₁₃	semidirect
201. #350	C₂²×C₁₃	semidirect
202. C₄×C₁₆	C₂²×C₁₃	semidirect
315. C₁₃	#33857	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×#3416	2
C₁₃×#3290	2
C₁₃×#2249	2
C₁₃×#2223	2
C₁₃×#2212	2
C₁₃×#2195	2
C₁₃×#2192	2
C₁₃×#2178	2
C₁₃×#2170	2
#33857	13

Subgroups — C13×#33857 #15720196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33857 #15720196