Subgroups — C₁₃×#33581 #15719920

Order 3328.

706 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×#510	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2211	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2209	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2207	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2139	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#135	—	2	1	no	—
10	C₂×C₁₃×#135	C₂²	1	2	yes	—
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
12	C₁₃×#532	—	2	1	no	—
13	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
14	C₁₃×#510	—	2	8	no	—
15	C₂×C₁₃×Q₃₂	C₂²	1	4	yes	—
16	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	—
17	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
18	C₁₃×#495	—	2	1	no	—
19	C₁₃×#495	C₂²	1	2	yes	—
20	C₁₃×#494	C₂²	1	1	yes	characteristic
21	C₁₃×#493	C₂²	1	1	yes	characteristic
22	C₁₃×#492	—	2	1	no	—
23	C₄×C₁₃×Q₁₆	—	2	1	no	—
24	C₄×C₁₃×Q₁₆	—	2	1	no	—
25	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
26	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	—	2	1	no	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
31	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
32	C₁₃×#358	C₂²	1	4	yes	—
33	C₁₃×#357	C₂²	1	4	yes	—
34	C₂×C₁₃×#41	—	2	2	no	—
35	C₂²×Q₈×C₁₃	—	2	1	no	—
36	C₁₃×#135	—	2	4	no	—
37	C₁₃×#135	—	2	4	no	—
38	C₁₃×#135	—	4	4	no	—
39	C₂×C₁₃×Q₁₆	—	2	1	no	—
40	C₂×C₁₃×Q₁₆	—	2	1	no	—
41	C₂×C₁₃×Q₁₆	—	2	2	no	—
42	C₂×C₁₃×Q₁₆	D₄	1	4	yes	complemented
43	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
44	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
45	C₂×C₁₃×SD₁₆	—	2	2	no	—
46	C₂×C₁₃×SD₁₆	—	2	2	no	—
47	C₂×C₁₃×D₈	—	2	1	no	—
48	C₂×C₁₃×D₈	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	—	2	1	no	—
52	C₁₃×#127	—	2	1	no	—
53	C₁₃×#124	—	2	2	no	—
54	C₁₃×#121	—	4	1	no	—
55	C₁₃×#121	—	4	1	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	4	1	no	—
59	C₄×Q₈×C₁₃	—	4	1	no	—
60	C₄×D₄×C₁₃	—	4	1	no	—
61	C₄×D₄×C₁₃	—	4	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
64	C₂×C₄²×C₁₃	—	4	1	no	—
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₁₃×Q₃₂	—	2	8	no	—
67	C₁₃×SD₃₂	—	2	8	no	—
68	C₁₃×M₃₂	—	2	4	no	—
69	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
70	C₁₃×#107	—	2	1	no	—
71	C₁₃×#107	C₂³	1	2	yes	—
72	C₁₃×#103	—	2	2	no	—
73	C₁₃×#103	—	2	2	no	—
74	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	#33581	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₁₃×#41	—	4	4	no	—
80	C₁₃×#41	—	4	4	no	—
81	C₂×Q₈×C₁₃	—	2	4	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	4	1	no	—
85	C₂×Q₈×C₁₃	—	4	2	no	—
86	C₂×D₄×C₁₃	—	2	2	no	—
87	C₂×D₄×C₁₃	—	4	2	no	—
88	C₂×D₄×C₁₃	—	4	1	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂²×C₄×C₁₃	—	4	1	no	—
91	C₂²×C₄×C₁₃	—	4	1	no	—
92	C₂²×C₄×C₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₁₃×Q₁₆	—	2	4	no	—
97	C₁₃×Q₁₆	—	2	2	no	—
98	C₁₃×Q₁₆	—	2	2	no	—
99	C₁₃×Q₁₆	—	2	2	no	—
100	C₁₃×Q₁₆	—	4	2	no	—
101	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
102	C₁₃×SD₁₆	—	4	4	no	—
103	C₁₃×SD₁₆	—	4	4	no	—
104	C₁₃×D₈	—	2	2	no	—
105	C₁₃×D₈	—	2	2	no	—
106	C₁₃×D₈	—	4	2	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₃	#41	1	2	yes	—
113	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	4	1	no	—
116	C₁₃×C₄⋊C₄	—	4	2	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₄⋊C₄	—	4	1	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₂²⋊C₄	—	4	2	no	—
121	C₁₃×C₂²⋊C₄	—	4	2	no	—
122	C₄²×C₁₃	—	4	2	no	—
123	C₄²×C₁₃	—	4	2	no	—
124	C₄²×C₁₃	D₈	1	1	yes	characteristic
125	C₄²×C₁₃	D₈	1	1	yes	characteristic
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₁₃×C₁₆	—	2	4	no	—
129	C₂×#510	C₂×C₁₃	1	2	yes	complemented
130	#3147	C₂×C₁₃	1	1	yes	characteristic
131	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
132	#2211	C₂×C₁₃	1	4	yes	complemented
133	#2209	C₂×C₁₃	1	2	yes	complemented
134	#2207	C₂×C₁₃	1	2	yes	complemented
135	#2150	C₂×C₁₃	1	1	yes	characteristic, complemented
136	#2139	C₂×C₁₃	1	2	yes	complemented
137	C₂³×C₁₃	—	4	2	no	—
138	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
139	Q₈×C₁₃	—	2	4	no	—
140	Q₈×C₁₃	—	4	2	no	—
141	Q₈×C₁₃	—	4	4	no	—
142	Q₈×C₁₃	—	4	2	no	—
143	Q₈×C₁₃	—	4	2	no	—
144	D₄×C₁₃	—	4	2	no	—
145	D₄×C₁₃	—	4	2	no	—
146	D₄×C₁₃	—	8	2	no	—
147	D₄×C₁₃	—	8	4	no	—
148	D₄×C₁₃	—	8	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	4	1	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	8	2	no	—
156	C₂×C₄×C₁₃	—	8	4	no	—
157	C₂×C₄×C₁₃	#121	1	2	yes	—
158	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
164	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	C₈×C₁₃	—	2	1	no	—
166	C₈×C₁₃	—	2	1	no	—
167	C₈×C₁₃	#121	1	2	yes	—
168	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
170	C₂×#135	—	2	1	no	—
171	C₂×#135	C₂²×C₁₃	1	2	yes	—
172	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
173	#532	—	2	1	no	—
174	C₂×C₄×Q₈	—	2	1	no	—
175	#510	—	2	8	no	—
176	C₂×Q₃₂	C₂²×C₁₃	1	4	yes	—
177	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	—
178	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
179	#495	—	2	1	no	—
180	#495	C₂²×C₁₃	1	2	yes	—
181	#494	C₂²×C₁₃	1	1	yes	characteristic
182	#493	C₂²×C₁₃	1	1	yes	characteristic
183	#492	—	2	1	no	—
184	C₄×Q₁₆	—	2	1	no	—
185	C₄×Q₁₆	—	2	1	no	—
186	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
187	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
188	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#103	—	2	1	no	—
190	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
192	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
193	#358	C₂²×C₁₃	1	4	yes	—
194	#357	C₂²×C₁₃	1	4	yes	—
195	C₂²×C₁₃	—	2	1	no	—
196	C₂²×C₁₃	—	2	1	no	—
197	C₂²×C₁₃	—	8	2	no	—
198	C₂²×C₁₃	—	8	2	no	—
199	C₂²×C₁₃	—	8	2	no	—
200	C₂²×C₁₃	#459	1	2	yes	—
201	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
202	C₄×C₁₃	—	2	1	no	—
203	C₄×C₁₃	—	2	1	no	—
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	4	4	no	—
206	C₄×C₁₃	—	8	2	no	—
207	C₄×C₁₃	—	8	2	no	—
208	C₄×C₁₃	#459	1	2	yes	—
209	C₄×C₁₃	#510	1	2	yes	complemented
210	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
211	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂×#41	—	2	2	no	—
213	C₂²×Q₈	—	2	1	no	—
214	#135	—	2	4	no	—
215	#135	—	2	4	no	—
216	#135	—	4	4	no	—
217	C₂×Q₁₆	—	2	1	no	—
218	C₂×Q₁₆	—	2	1	no	—
219	C₂×Q₁₆	—	2	2	no	—
220	C₂×Q₁₆	D₄×C₁₃	1	4	yes	complemented
221	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
222	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
223	C₂×SD₁₆	—	2	2	no	—
224	C₂×SD₁₆	—	2	2	no	—
225	C₂×D₈	—	2	1	no	—
226	C₂×D₈	C₂³×C₁₃	1	2	yes	—
227	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
229	C₄⋊Q₈	—	2	1	no	—
230	#127	—	2	1	no	—
231	#124	—	2	2	no	—
232	#121	—	4	1	no	—
233	#121	—	4	1	no	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₄×Q₈	—	4	1	no	—
237	C₄×Q₈	—	4	1	no	—
238	C₄×D₄	—	4	1	no	—
239	C₄×D₄	—	4	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	4	1	no	—
242	C₂×C₄²	—	4	1	no	—
243	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
244	Q₃₂	—	2	8	no	—
245	SD₃₂	—	2	8	no	—
246	M₃₂	—	2	4	no	—
247	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
248	#107	—	2	1	no	—
249	#107	C₂³×C₁₃	1	2	yes	—
250	#103	—	2	2	no	—
251	#103	—	2	2	no	—
252	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
253	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
254	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×C₁₃	—	2	2	no	—
257	C₂×C₁₃	—	16	2	no	—
258	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
259	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
260	C₂×C₁₃	#3414	1	1	yes	characteristic
261	#41	—	4	4	no	—
262	#41	—	4	4	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	4	1	no	—
267	C₂×Q₈	—	4	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
276	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
278	Q₁₆	—	2	4	no	—
279	Q₁₆	—	2	2	no	—
280	Q₁₆	—	2	2	no	—
281	Q₁₆	—	2	2	no	—
282	Q₁₆	—	4	2	no	—
283	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
284	SD₁₆	—	4	4	no	—
285	SD₁₆	—	4	4	no	—
286	D₈	—	2	2	no	—
287	D₈	—	2	2	no	—
288	D₈	—	4	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
291	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	—	4	1	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₄²	—	4	2	no	—
305	C₄²	—	4	2	no	—
306	C₄²	C₁₃×D₈	1	1	yes	characteristic
307	C₄²	C₁₃×D₈	1	1	yes	characteristic
308	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₁₆	—	2	4	no	—
311	C₁₃	#33581	1	1	yes	characteristic, direct product factor, Sylow
312	C₂³	—	4	2	no	—
313	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
314	Q₈	—	2	4	no	—
315	Q₈	—	4	4	no	—
316	Q₈	—	4	2	no	—
317	Q₈	—	4	2	no	—
318	Q₈	—	4	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	2	no	—
321	D₄	—	8	2	no	—
322	D₄	—	8	4	no	—
323	D₄	—	8	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	—	8	4	no	—
332	C₂×C₄	C₁₃×#121	1	2	yes	—
333	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
334	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
335	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
336	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
337	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
338	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
339	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
340	C₈	—	2	1	no	—
341	C₈	—	2	1	no	—
342	C₈	C₁₃×#121	1	2	yes	—
343	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
344	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	C₁₃×#459	1	2	yes	—
351	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	4	4	no	—
356	C₄	—	8	2	no	—
357	C₄	—	8	2	no	—
358	C₄	C₁₃×#459	1	2	yes	—
359	C₄	C₁₃×#510	1	2	yes	complemented
360	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
361	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂	—	2	2	no	—
363	C₂	—	16	2	no	—
364	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
365	C₂	C₂×C₁₃×#510	1	1	yes	characteristic
366	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3147	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#510	C₂	semidirect
3. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#2211	C₂	semidirect
5. C₁₃×#2209	C₂	semidirect
6. C₁₃×#2207	C₂	semidirect
7. C₁₃×#2150	C₂	semidirect
8. C₁₃×#2139	C₂	semidirect
42. C₂×C₁₃×Q₁₆	D₄	semidirect
78. #33581	C₁₃	direct (N × H)
129. C₂×#510	C₂×C₁₃	semidirect
131. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
132. #2211	C₂×C₁₃	semidirect
133. #2209	C₂×C₁₃	semidirect
134. #2207	C₂×C₁₃	semidirect
135. #2150	C₂×C₁₃	semidirect
136. #2139	C₂×C₁₃	semidirect
209. C₄×C₁₃	#510	semidirect
220. C₂×Q₁₆	D₄×C₁₃	semidirect
311. C₁₃	#33581	direct (N × H)
359. C₄	C₁₃×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#510	2
C₁₃×#3147	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2211	2
C₁₃×#2209	2
C₁₃×#2207	2
C₁₃×#2150	2
C₁₃×#2139	2
#33581	13

Subgroups — C13×#33581 #15719920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33581 #15719920