Subgroups — C₁₃×#33789 #15720128

Order 3328.

562 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3177	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2247	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2245	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2211	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2209	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2189	C₂	1	2	yes	maximal
10	C₁₃×#2188	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₁₃×#541	—	2	1	no	—
16	C₁₃×#536	—	2	1	no	—
17	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
20	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
21	C₁₃×#499	C₂²	1	1	yes	characteristic
22	C₁₃×#497	—	2	1	no	—
23	C₁₃×#497	—	2	1	no	—
24	C₁₃×#495	C₂²	1	1	yes	characteristic
25	C₁₃×#495	C₂²	1	1	yes	characteristic
26	C₁₃×#494	C₂²	1	1	yes	characteristic
27	C₁₃×#494	C₂²	1	1	yes	characteristic
28	C₁₃×#494	C₂²	1	1	yes	characteristic
29	C₁₃×#491	—	2	1	no	—
30	C₁₃×#470	—	2	1	no	—
31	C₁₃×#467	C₂²	1	2	yes	—
32	C₁₃×#441	—	2	1	no	—
33	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
34	C₁₃×#405	C₂²	1	1	yes	characteristic
35	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
36	C₁₃×#358	C₂²	1	2	yes	—
37	C₁₃×#358	C₂²	1	2	yes	—
38	C₁₃×#358	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	—
40	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₁₃×#346	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂²×Q₈×C₁₃	—	2	1	no	—
45	C₁₃×#137	—	4	4	no	—
46	C₁₃×#135	—	4	2	no	—
47	C₂×C₁₃×Q₁₆	—	2	1	no	—
48	C₂×C₁₃×Q₁₆	—	2	1	no	—
49	C₂×C₁₃×Q₁₆	—	2	1	no	—
50	C₂×C₁₃×Q₁₆	—	2	1	no	—
51	C₂×C₁₃×Q₁₆	—	4	2	no	—
52	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
56	C₂×C₁₃×SD₁₆	—	2	1	no	—
57	C₂×C₁₃×SD₁₆	—	2	1	no	—
58	C₂×C₁₃×SD₁₆	—	2	1	no	—
59	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	no	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₁₃×#126	—	4	2	no	—
66	C₁₃×#125	—	2	1	no	—
67	C₁₃×#125	—	4	2	no	—
68	C₁₃×#124	—	2	1	no	—
69	C₁₃×#124	—	2	1	no	—
70	C₁₃×#123	—	4	2	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	4	2	no	—
73	C₄×Q₈×C₁₃	—	2	2	no	—
74	C₁₃×#117	D₄	1	1	yes	characteristic
75	C₁₃×Q₃₂	—	4	2	no	—
76	C₁₃×Q₃₂	—	4	2	no	—
77	C₁₃×Q₃₂	—	4	2	no	—
78	C₁₃×SD₃₂	—	4	2	no	—
79	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
80	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
81	C₁₃×#107	C₂³	1	2	yes	—
82	C₁₃×#106	—	2	1	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#97	D₄	1	1	yes	characteristic
86	C₁₃×#97	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	#33789	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₁₃×#41	—	4	2	no	—
91	C₁₃×#41	—	4	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂×Q₈×C₁₃	—	4	2	no	—
98	C₂×Q₈×C₁₃	—	4	1	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂²×C₄×C₁₃	—	4	1	no	—
102	C₂²×C₄×C₁₃	—	4	1	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₁₃×Q₁₆	—	2	2	no	—
105	C₁₃×Q₁₆	—	2	2	no	—
106	C₁₃×Q₁₆	—	2	2	no	—
107	C₁₃×Q₁₆	—	2	2	no	—
108	C₁₃×Q₁₆	—	2	2	no	—
109	C₁₃×Q₁₆	—	4	2	no	—
110	C₁₃×Q₁₆	—	4	2	no	—
111	C₁₃×Q₁₆	—	4	2	no	—
112	C₁₃×Q₁₆	—	4	2	no	—
113	C₁₃×SD₁₆	—	4	2	no	—
114	C₁₃×SD₁₆	—	4	2	no	—
115	C₁₃×SD₁₆	—	4	2	no	—
116	C₁₃×D₈	—	2	2	no	—
117	C₁₃×M₁₆	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	4	2	no	—
125	C₁₃×C₄⋊C₄	—	4	2	no	—
126	C₁₃×C₄⋊C₄	—	4	2	no	—
127	C₁₃×C₄⋊C₄	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
135	C₄²×C₁₃	—	4	2	no	—
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₁₃×C₁₆	—	2	2	no	—
139	C₁₃×C₁₆	—	2	2	no	—
140	#3177	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#3156	C₂×C₁₃	1	1	yes	characteristic
142	#2251	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2247	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2245	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2242	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2211	C₂×C₁₃	1	2	yes	complemented
147	#2209	C₂×C₁₃	1	2	yes	complemented
148	#2189	C₂×C₁₃	1	2	yes	—
149	#2188	C₂×C₁₃	1	2	yes	complemented
150	#2164	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	4	1	no	—
152	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
153	Q₈×C₁₃	—	4	1	no	—
154	Q₈×C₁₃	—	4	1	no	—
155	Q₈×C₁₃	—	4	1	no	—
156	Q₈×C₁₃	—	4	2	no	—
157	Q₈×C₁₃	—	4	1	no	—
158	Q₈×C₁₃	—	4	1	no	—
159	Q₈×C₁₃	—	4	1	no	—
160	Q₈×C₁₃	—	4	2	no	—
161	Q₈×C₁₃	—	8	2	no	—
162	D₄×C₁₃	—	4	1	no	—
163	D₄×C₁₃	—	4	1	no	—
164	D₄×C₁₃	—	8	2	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	8	2	no	—
173	C₂×C₄×C₁₃	—	8	2	no	—
174	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
176	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₁₃	—	2	1	no	—
179	C₈×C₁₃	—	2	1	no	—
180	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
181	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
182	C₂×#137	—	2	1	no	—
183	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
184	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
185	#541	—	2	1	no	—
186	#536	—	2	1	no	—
187	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
188	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
189	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
190	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
191	#499	C₂²×C₁₃	1	1	yes	characteristic
192	#497	—	2	1	no	—
193	#497	—	2	1	no	—
194	#495	C₂²×C₁₃	1	1	yes	characteristic
195	#495	C₂²×C₁₃	1	1	yes	characteristic
196	#494	C₂²×C₁₃	1	1	yes	characteristic
197	#494	C₂²×C₁₃	1	1	yes	characteristic
198	#494	C₂²×C₁₃	1	1	yes	characteristic
199	#491	—	2	1	no	—
200	#470	—	2	1	no	—
201	#467	C₂²×C₁₃	1	2	yes	—
202	#441	—	2	1	no	—
203	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
204	#405	C₂²×C₁₃	1	1	yes	characteristic
205	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
206	#358	C₂²×C₁₃	1	2	yes	—
207	#358	C₂²×C₁₃	1	2	yes	—
208	#358	C₂²×C₁₃	1	2	yes	—
209	#357	C₂²×C₁₃	1	2	yes	—
210	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
211	#346	C₂²×C₁₃	1	1	yes	characteristic
212	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
213	C₂²×C₁₃	—	2	2	no	—
214	C₂²×C₁₃	—	2	1	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	—	8	1	no	—
217	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
218	C₄×C₁₃	—	2	2	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	8	2	no	—
222	C₄×C₁₃	—	8	1	no	—
223	C₄×C₁₃	—	8	1	no	—
224	C₄×C₁₃	—	8	1	no	—
225	C₄×C₁₃	—	8	2	no	—
226	C₄×C₁₃	#535	1	1	yes	characteristic
227	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₂×#41	—	2	1	no	—
229	C₂²×Q₈	—	2	1	no	—
230	#137	—	4	4	no	—
231	#135	—	4	2	no	—
232	C₂×Q₁₆	—	2	1	no	—
233	C₂×Q₁₆	—	2	1	no	—
234	C₂×Q₁₆	—	2	1	no	—
235	C₂×Q₁₆	—	2	1	no	—
236	C₂×Q₁₆	—	4	2	no	—
237	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
238	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
239	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
240	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
241	C₂×SD₁₆	—	2	1	no	—
242	C₂×SD₁₆	—	2	1	no	—
243	C₂×SD₁₆	—	2	1	no	—
244	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
245	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	#126	—	4	2	no	—
251	#125	—	2	1	no	—
252	#125	—	4	2	no	—
253	#124	—	2	1	no	—
254	#124	—	2	1	no	—
255	#123	—	4	2	no	—
256	C₂²⋊Q₈	—	2	2	no	—
257	C₂²⋊Q₈	—	4	2	no	—
258	C₄×Q₈	—	2	2	no	—
259	#117	D₄×C₁₃	1	1	yes	characteristic
260	Q₃₂	—	4	2	no	—
261	Q₃₂	—	4	2	no	—
262	Q₃₂	—	4	2	no	—
263	SD₃₂	—	4	2	no	—
264	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
265	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
266	#107	C₂³×C₁₃	1	2	yes	—
267	#106	—	2	1	no	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#97	D₄×C₁₃	1	1	yes	characteristic
271	#97	D₄×C₁₃	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×C₁₃	—	4	1	no	—
275	C₂×C₁₃	—	16	1	no	—
276	C₂×C₁₃	#3205	1	1	yes	characteristic
277	C₂×C₁₃	#3417	1	2	yes	—
278	#41	—	4	2	no	—
279	#41	—	4	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
292	Q₁₆	—	2	2	no	—
293	Q₁₆	—	2	2	no	—
294	Q₁₆	—	2	2	no	—
295	Q₁₆	—	2	2	no	—
296	Q₁₆	—	2	2	no	—
297	Q₁₆	—	4	2	no	—
298	Q₁₆	—	4	2	no	—
299	Q₁₆	—	4	2	no	—
300	Q₁₆	—	4	2	no	—
301	SD₁₆	—	4	2	no	—
302	SD₁₆	—	4	2	no	—
303	SD₁₆	—	4	2	no	—
304	D₈	—	2	2	no	—
305	M₁₆	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	C₁₃×D₈	1	2	yes	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
323	C₄²	—	4	2	no	—
324	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₁₆	—	2	2	no	—
327	C₁₆	—	2	2	no	—
328	C₁₃	#33789	1	1	yes	characteristic, direct product factor, Sylow
329	C₂³	—	4	1	no	—
330	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
331	Q₈	—	4	1	no	—
332	Q₈	—	4	1	no	—
333	Q₈	—	4	1	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	4	1	no	—
337	Q₈	—	4	1	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	8	2	no	—
340	D₄	—	4	1	no	—
341	D₄	—	4	1	no	—
342	D₄	—	8	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
353	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
354	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
359	C₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	8	2	no	—
363	C₂²	—	8	1	no	—
364	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	1	no	—
368	C₄	—	8	2	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	1	no	—
371	C₄	—	8	1	no	—
372	C₄	—	8	2	no	—
373	C₄	C₁₃×#535	1	1	yes	characteristic
374	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
375	C₂	—	4	1	no	—
376	C₂	—	16	1	no	—
377	C₂	C₁₃×#3205	1	1	yes	characteristic
378	C₂	C₁₃×#3417	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
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. C₁₃×#3177	C₂	semidirect
3. C₁₃×#2251	C₂	semidirect
4. C₁₃×#2247	C₂	semidirect
5. C₁₃×#2245	C₂	semidirect
6. C₁₃×#2242	C₂	semidirect
7. C₁₃×#2211	C₂	semidirect
8. C₁₃×#2209	C₂	semidirect
10. C₁₃×#2188	C₂	semidirect
11. C₁₃×#2164	C₂	semidirect
89. #33789	C₁₃	direct (N × H)
140. #3177	C₂×C₁₃	semidirect
142. #2251	C₂×C₁₃	semidirect
143. #2247	C₂×C₁₃	semidirect
144. #2245	C₂×C₁₃	semidirect
145. #2242	C₂×C₁₃	semidirect
146. #2211	C₂×C₁₃	semidirect
147. #2209	C₂×C₁₃	semidirect
149. #2188	C₂×C₁₃	semidirect
150. #2164	C₂×C₁₃	semidirect
328. C₁₃	#33789	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×#3177	2
C₁₃×#3156	2
C₁₃×#2251	2
C₁₃×#2247	2
C₁₃×#2245	2
C₁₃×#2242	2
C₁₃×#2211	2
C₁₃×#2209	2
C₁₃×#2189	2
C₁₃×#2188	2
C₁₃×#2164	2
#33789	13

Subgroups — C13×#33789 #15720128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33789 #15720128