Subgroups — C₂×C₁₃×#2184 #15719849

Order 3328.

1434 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×D₁₆	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2184	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#357	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₁₃	—	2	1	no	—
8	C₂²×C₁₃×D₈	—	2	8	no	—
9	C₂²×C₁₃×D₈	—	2	1	no	—
10	C₂²×C₁₃×D₈	—	2	2	no	—
11	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
12	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	—	2	1	no	—
16	C₂×C₁₃×D₁₆	—	2	8	no	—
17	C₂×C₁₃×D₁₆	C₂²	1	8	yes	complemented
18	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
19	C₁₃×#466	—	2	2	no	—
20	C₁₃×#466	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#102	—	2	1	no	—
23	C₁₃×#357	C₂²	1	8	yes	complemented
24	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
25	C₂⁵×C₁₃	—	4	1	no	—
26	C₂²×D₄×C₁₃	—	2	8	no	—
27	C₂²×D₄×C₁₃	—	2	2	no	—
28	C₂²×D₄×C₁₃	—	2	4	no	—
29	C₂²×D₄×C₁₃	—	2	1	no	—
30	C₂²×D₄×C₁₃	—	4	4	no	—
31	C₂²×D₄×C₁₃	—	4	1	no	—
32	C₂²×D₄×C₁₃	—	4	2	no	—
33	C₂²×D₄×C₁₃	—	4	1	no	—
34	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
35	C₂×C₁₃×D₈	—	2	8	no	—
36	C₂×C₁₃×D₈	—	2	16	no	—
37	C₂×C₁₃×D₈	—	2	16	no	—
38	C₂×C₁₃×D₈	—	2	2	no	—
39	C₂×C₁₃×D₈	—	2	4	no	—
40	C₂×C₁₃×D₈	—	2	4	no	—
41	C₂×C₁₃×D₈	—	2	4	no	—
42	C₂×C₁₃×D₈	—	2	1	no	—
43	C₂×C₁₃×D₈	D₄	1	8	yes	complemented
44	C₂×C₁₃×D₈	C₂³	1	4	yes	—
45	C₂×C₁₃×D₈	C₂³	1	2	yes	complemented
46	C₂²×C₈×C₁₃	—	2	4	no	—
47	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	D₄	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×#121	—	2	4	no	—
52	C₁₃×#121	—	4	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
55	C₁₃×D₁₆	—	2	16	no	—
56	C₂×C₁₃×C₁₆	—	2	4	no	—
57	C₂×C₁₃×C₁₆	C₂³	1	4	yes	complemented
58	C₁₃×#107	—	2	1	no	—
59	C₁₃×#107	C₂³	1	2	yes	complemented
60	C₁₃×#102	—	2	4	no	—
61	C₂×#2184	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂⁴×C₁₃	—	4	8	no	—
63	C₂⁴×C₁₃	—	4	4	no	—
64	C₂⁴×C₁₃	—	4	2	no	—
65	C₂⁴×C₁₃	—	4	1	no	—
66	C₂⁴×C₁₃	—	8	4	no	—
67	C₂⁴×C₁₃	—	8	4	no	—
68	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
69	C₂×D₄×C₁₃	—	2	16	no	—
70	C₂×D₄×C₁₃	—	2	8	no	—
71	C₂×D₄×C₁₃	—	2	4	no	—
72	C₂×D₄×C₁₃	—	2	2	no	—
73	C₂×D₄×C₁₃	—	4	8	no	—
74	C₂×D₄×C₁₃	—	4	8	no	—
75	C₂×D₄×C₁₃	—	4	16	no	—
76	C₂×D₄×C₁₃	—	4	4	no	—
77	C₂×D₄×C₁₃	—	4	2	no	—
78	C₂×D₄×C₁₃	—	4	4	no	—
79	C₂×D₄×C₁₃	—	4	2	no	—
80	C₂×D₄×C₁₃	—	4	1	no	—
81	C₂×D₄×C₁₃	—	4	4	no	—
82	C₂×D₄×C₁₃	—	4	2	no	—
83	C₂×D₄×C₁₃	—	8	4	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	4	1	no	—
87	C₂²×C₄×C₁₃	D₈	1	2	yes	—
88	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₁₃×D₈	—	2	16	no	—
92	C₁₃×D₈	—	2	8	no	—
93	C₁₃×D₈	—	2	4	no	—
94	C₁₃×D₈	—	2	4	no	—
95	C₁₃×D₈	—	4	2	no	—
96	C₁₃×D₈	C₂×D₄	1	8	yes	complemented
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	4	no	—
99	C₂×C₈×C₁₃	—	2	4	no	—
100	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
103	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₁₃×C₂²⋊C₄	—	4	4	no	—
107	C₁₃×C₁₆	—	2	4	no	—
108	C₂³×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
109	C₂²×D₁₆	C₂×C₁₃	1	2	yes	complemented
110	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
111	#2184	C₂×C₁₃	1	8	yes	direct product factor
112	C₂×#357	C₂×C₁₃	1	2	yes	complemented
113	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
114	C₂³×C₁₃	—	2	2	no	—
115	C₂³×C₁₃	—	2	2	no	—
116	C₂³×C₁₃	—	4	16	no	—
117	C₂³×C₁₃	—	4	4	no	—
118	C₂³×C₁₃	—	4	8	no	—
119	C₂³×C₁₃	—	4	2	no	—
120	C₂³×C₁₃	—	8	8	no	—
121	C₂³×C₁₃	—	8	32	no	—
122	C₂³×C₁₃	—	8	4	no	—
123	C₂³×C₁₃	—	8	8	no	—
124	C₂³×C₁₃	—	8	4	no	—
125	C₂³×C₁₃	—	8	2	no	—
126	C₂³×C₁₃	—	8	2	no	—
127	C₂³×C₁₃	—	8	2	no	—
128	C₂³×C₁₃	D₁₆	1	4	yes	complemented
129	C₂³×C₁₃	C₂×D₈	1	2	yes	—
130	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
131	D₄×C₁₃	—	2	8	no	—
132	D₄×C₁₃	—	4	16	no	—
133	D₄×C₁₃	—	4	2	no	—
134	D₄×C₁₃	—	4	4	no	—
135	D₄×C₁₃	—	4	2	no	—
136	D₄×C₁₃	—	4	8	no	—
137	D₄×C₁₃	—	8	8	no	—
138	D₄×C₁₃	—	8	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	4	2	no	—
144	C₂×C₄×C₁₃	—	8	2	no	—
145	C₂×C₄×C₁₃	#120	1	2	yes	—
146	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
147	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
150	C₈×C₁₃	—	2	2	no	—
151	C₈×C₁₃	#120	1	2	yes	—
152	C₈×C₁₃	C₂²×D₄	1	2	yes	—
153	C₂³×D₄	—	2	1	no	—
154	C₂²×D₈	—	2	8	no	—
155	C₂²×D₈	—	2	1	no	—
156	C₂²×D₈	—	2	2	no	—
157	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
158	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
159	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
161	C₂×#121	—	2	1	no	—
162	C₂×D₁₆	—	2	8	no	—
163	C₂×D₁₆	C₂²×C₁₃	1	8	yes	complemented
164	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
165	#466	—	2	2	no	—
166	#466	C₂²×C₁₃	1	4	yes	complemented
167	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
168	C₂×#102	—	2	1	no	—
169	#357	C₂²×C₁₃	1	8	yes	complemented
170	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
171	C₂²×C₁₃	—	2	2	no	—
172	C₂²×C₁₃	—	2	8	no	—
173	C₂²×C₁₃	—	2	2	no	—
174	C₂²×C₁₃	—	4	8	no	—
175	C₂²×C₁₃	—	8	32	no	—
176	C₂²×C₁₃	—	8	4	no	—
177	C₂²×C₁₃	—	8	4	no	—
178	C₂²×C₁₃	—	8	16	no	—
179	C₂²×C₁₃	—	8	2	no	—
180	C₂²×C₁₃	—	8	2	no	—
181	C₂²×C₁₃	—	8	2	no	—
182	C₂²×C₁₃	—	16	4	no	—
183	C₂²×C₁₃	#447	1	2	yes	—
184	C₂²×C₁₃	C₂×D₁₆	1	2	yes	—
185	C₂²×C₁₃	C₂×D₁₆	1	4	yes	complemented
186	C₂²×C₁₃	#509	1	2	yes	—
187	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
188	C₄×C₁₃	—	2	2	no	—
189	C₄×C₁₃	—	8	2	no	—
190	C₄×C₁₃	#447	1	2	yes	—
191	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
192	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂⁵	—	4	1	no	—
194	C₂²×D₄	—	2	8	no	—
195	C₂²×D₄	—	2	2	no	—
196	C₂²×D₄	—	2	4	no	—
197	C₂²×D₄	—	2	1	no	—
198	C₂²×D₄	—	4	4	no	—
199	C₂²×D₄	—	4	1	no	—
200	C₂²×D₄	—	4	1	no	—
201	C₂²×D₄	—	4	2	no	—
202	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
203	C₂×D₈	—	2	8	no	—
204	C₂×D₈	—	2	16	no	—
205	C₂×D₈	—	2	16	no	—
206	C₂×D₈	—	2	2	no	—
207	C₂×D₈	—	2	4	no	—
208	C₂×D₈	—	2	4	no	—
209	C₂×D₈	—	2	4	no	—
210	C₂×D₈	—	2	1	no	—
211	C₂×D₈	D₄×C₁₃	1	8	yes	complemented
212	C₂×D₈	C₂³×C₁₃	1	4	yes	—
213	C₂×D₈	C₂³×C₁₃	1	2	yes	complemented
214	C₂²×C₈	—	2	4	no	—
215	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
216	C₂²×C₈	D₄×C₁₃	1	2	yes	—
217	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
218	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
219	#121	—	2	4	no	—
220	#121	—	4	2	no	—
221	C₂×C₄⋊C₄	—	2	1	no	—
222	C₂×C₂²⋊C₄	—	4	1	no	—
223	D₁₆	—	2	16	no	—
224	C₂×C₁₆	—	2	4	no	—
225	C₂×C₁₆	C₂³×C₁₃	1	4	yes	complemented
226	#107	—	2	1	no	—
227	#107	C₂³×C₁₃	1	2	yes	complemented
228	#102	—	2	4	no	—
229	C₂×C₁₃	—	2	4	no	—
230	C₂×C₁₃	—	8	8	no	—
231	C₂×C₁₃	—	16	2	no	—
232	C₂×C₁₃	#2184	1	4	yes	direct product factor
233	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
234	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
235	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
236	C₂⁴	—	4	8	no	—
237	C₂⁴	—	4	4	no	—
238	C₂⁴	—	4	2	no	—
239	C₂⁴	—	4	1	no	—
240	C₂⁴	—	8	4	no	—
241	C₂⁴	—	8	4	no	—
242	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
243	C₂×D₄	—	2	16	no	—
244	C₂×D₄	—	2	8	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	—	2	2	no	—
247	C₂×D₄	—	4	8	no	—
248	C₂×D₄	—	4	16	no	—
249	C₂×D₄	—	4	8	no	—
250	C₂×D₄	—	4	4	no	—
251	C₂×D₄	—	4	2	no	—
252	C₂×D₄	—	4	4	no	—
253	C₂×D₄	—	4	2	no	—
254	C₂×D₄	—	4	1	no	—
255	C₂×D₄	—	4	4	no	—
256	C₂×D₄	—	4	2	no	—
257	C₂×D₄	—	8	4	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
262	C₂²×C₄	C₁₃×D₈	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
265	D₈	—	2	16	no	—
266	D₈	—	2	8	no	—
267	D₈	—	2	4	no	—
268	D₈	—	2	4	no	—
269	D₈	—	4	2	no	—
270	D₈	C₂×D₄×C₁₃	1	8	yes	complemented
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
275	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
276	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
277	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	4	1	no	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₁₆	—	2	4	no	—
282	C₁₃	C₂×#2184	1	1	yes	characteristic, direct product factor, Sylow
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	4	16	no	—
286	C₂³	—	4	8	no	—
287	C₂³	—	4	4	no	—
288	C₂³	—	4	2	no	—
289	C₂³	—	8	8	no	—
290	C₂³	—	8	32	no	—
291	C₂³	—	8	4	no	—
292	C₂³	—	8	8	no	—
293	C₂³	—	8	4	no	—
294	C₂³	—	8	2	no	—
295	C₂³	—	8	2	no	—
296	C₂³	—	8	2	no	—
297	C₂³	C₁₃×D₁₆	1	4	yes	complemented
298	C₂³	C₂×C₁₃×D₈	1	2	yes	—
299	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
300	D₄	—	2	8	no	—
301	D₄	—	4	16	no	—
302	D₄	—	4	8	no	—
303	D₄	—	4	2	no	—
304	D₄	—	4	4	no	—
305	D₄	—	4	2	no	—
306	D₄	—	8	8	no	—
307	D₄	—	8	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	8	2	no	—
314	C₂×C₄	C₁₃×#120	1	2	yes	—
315	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
316	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
317	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
318	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
319	C₈	—	2	2	no	—
320	C₈	C₁₃×#120	1	2	yes	—
321	C₈	C₂²×D₄×C₁₃	1	2	yes	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	4	8	no	—
326	C₂²	—	8	32	no	—
327	C₂²	—	8	4	no	—
328	C₂²	—	8	4	no	—
329	C₂²	—	8	16	no	—
330	C₂²	—	8	2	no	—
331	C₂²	—	8	2	no	—
332	C₂²	—	8	2	no	—
333	C₂²	—	16	4	no	—
334	C₂²	C₁₃×#447	1	2	yes	—
335	C₂²	C₂×C₁₃×D₁₆	1	2	yes	—
336	C₂²	C₂×C₁₃×D₁₆	1	4	yes	complemented
337	C₂²	C₁₃×#509	1	2	yes	—
338	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
339	C₄	—	2	2	no	—
340	C₄	—	8	2	no	—
341	C₄	C₁₃×#447	1	2	yes	—
342	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
343	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
344	C₂	—	2	4	no	—
345	C₂	—	8	8	no	—
346	C₂	—	16	2	no	—
347	C₂	C₁₃×#2184	1	4	yes	direct product factor
348	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
349	C₂	C₂²×C₁₃×D₁₆	1	1	yes	characteristic
350	C₂	C₂×C₁₃×#509	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₃×D₈	C₂	semidirect
2. C₂²×C₁₃×D₁₆	C₂	semidirect
3. C₂×C₁₃×#466	C₂	semidirect
4. C₁₃×#2184	C₂	direct (N × H)
5. C₂×C₁₃×#357	C₂	semidirect
6. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
12. C₂²×C₁₃×D₈	C₂²	semidirect
13. C₂²×C₁₃×D₈	C₂²	semidirect
17. C₂×C₁₃×D₁₆	C₂²	semidirect
18. C₂²×C₁₃×C₁₆	C₂²	semidirect
20. C₁₃×#466	C₂²	semidirect
21. C₂×C₁₃×#107	C₂²	semidirect
23. C₁₃×#357	C₂²	semidirect
24. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
43. C₂×C₁₃×D₈	D₄	semidirect
45. C₂×C₁₃×D₈	C₂³	semidirect
57. C₂×C₁₃×C₁₆	C₂³	semidirect
59. C₁₃×#107	C₂³	semidirect
61. C₂×#2184	C₁₃	direct (N × H)
96. C₁₃×D₈	C₂×D₄	semidirect
108. C₂³×D₈	C₂×C₁₃	semidirect
109. C₂²×D₁₆	C₂×C₁₃	semidirect
110. C₂×#466	C₂×C₁₃	semidirect
111. #2184	C₂×C₁₃	direct (N × H)
112. C₂×#357	C₂×C₁₃	semidirect
113. C₂×C₂²⋊C₁₆	C₂×C₁₃	semidirect
128. C₂³×C₁₃	D₁₆	semidirect
158. C₂²×D₈	C₂²×C₁₃	semidirect
159. C₂²×D₈	C₂²×C₁₃	semidirect
163. C₂×D₁₆	C₂²×C₁₃	semidirect
164. C₂²×C₁₆	C₂²×C₁₃	semidirect
166. #466	C₂²×C₁₃	semidirect
167. C₂×#107	C₂²×C₁₃	semidirect
169. #357	C₂²×C₁₃	semidirect
170. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
185. C₂²×C₁₃	C₂×D₁₆	semidirect
211. C₂×D₈	D₄×C₁₃	semidirect
213. C₂×D₈	C₂³×C₁₃	semidirect
225. C₂×C₁₆	C₂³×C₁₃	semidirect
227. #107	C₂³×C₁₃	semidirect
232. C₂×C₁₃	#2184	direct (N × H)
270. D₈	C₂×D₄×C₁₃	semidirect
282. C₁₃	C₂×#2184	direct (N × H)
297. C₂³	C₁₃×D₁₆	semidirect
336. C₂²	C₂×C₁₃×D₁₆	semidirect
347. C₂	C₁₃×#2184	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×D₈	2
C₂²×C₁₃×D₁₆	2
C₂×C₁₃×#466	2
C₁₃×#2184	2
C₂×C₁₃×#357	2
C₂×C₁₃×C₂²⋊C₁₆	2
C₂×#2184	13

Subgroups — C2×C13×#2184 #15719849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2184 #15719849