Subgroups — C₁₃×#33648 #15719987

Order 3328.

632 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2234	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2233	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2232	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2159	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2140	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#121	—	2	1	no	—
12	C₂×C₁₃×#117	—	2	1	no	—
13	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
14	C₁₃×#466	—	2	1	no	—
15	C₁₃×#466	—	2	1	no	—
16	C₁₃×#466	C₂²	1	2	yes	—
17	C₁₃×#466	C₂²	1	2	yes	—
18	C₁₃×#427	—	2	1	no	—
19	C₁₃×#427	—	2	1	no	—
20	C₁₃×#427	C₂²	1	2	yes	—
21	C₁₃×#427	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#106	—	2	1	no	—
26	C₂×C₁₃×#102	—	2	1	no	—
27	C₁₃×#367	C₂²	1	4	yes	complemented
28	C₁₃×#366	C₂²	1	4	yes	complemented
29	C₁₃×#357	C₂²	1	4	yes	complemented
30	C₁₃×#357	C₂²	1	4	yes	complemented
31	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
32	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
33	C₂²×D₄×C₁₃	—	2	1	no	—
34	C₂²×D₄×C₁₃	—	4	1	no	—
35	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂×C₁₃×D₈	—	2	1	no	—
37	C₂×C₁₃×D₈	—	2	4	no	—
38	C₂×C₁₃×D₈	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₃	—	2	4	no	—
40	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₁₃×#121	—	2	2	no	—
47	C₁₃×#121	—	2	2	no	—
48	C₁₃×#121	—	4	1	no	—
49	C₁₃×#121	—	4	1	no	—
50	C₁₃×#117	—	2	2	no	—
51	C₁₃×#117	—	2	2	no	—
52	C₁₃×#117	—	4	1	no	—
53	C₁₃×#117	—	4	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
59	C₂×C₄²×C₁₃	—	4	1	no	—
60	C₁₃×M₃₂	—	2	4	no	—
61	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
62	C₁₃×#107	—	2	1	no	—
63	C₁₃×#107	—	2	1	no	—
64	C₁₃×#107	—	2	1	no	—
65	C₁₃×#107	C₂³	1	2	yes	—
66	C₁₃×#107	C₂³	1	2	yes	—
67	C₁₃×#107	C₂³	1	2	yes	—
68	C₁₃×#106	—	2	2	no	—
69	C₁₃×#106	—	2	2	no	—
70	C₁₃×#102	—	2	2	no	—
71	C₁₃×#102	—	2	2	no	—
72	#33648	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	—	4	1	no	—
74	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
75	C₂×D₄×C₁₃	—	2	2	no	—
76	C₂×D₄×C₁₃	—	4	2	no	—
77	C₂×D₄×C₁₃	—	4	2	no	—
78	C₂×D₄×C₁₃	—	4	2	no	—
79	C₂×D₄×C₁₃	—	4	1	no	—
80	C₂×D₄×C₁₃	—	4	2	no	—
81	C₂×D₄×C₁₃	—	8	4	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	4	1	no	—
85	C₂²×C₄×C₁₃	—	4	1	no	—
86	C₂²×C₄×C₁₃	—	4	1	no	—
87	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₁₃×D₈	—	2	4	no	—
94	C₁₃×D₈	—	4	2	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	2	2	no	—
100	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₁₃	#41	1	4	yes	—
104	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	4	1	no	—
109	C₁₃×C₄⋊C₄	—	4	1	no	—
110	C₁₃×C₄⋊C₄	—	4	1	no	—
111	C₁₃×C₂²⋊C₄	—	4	2	no	—
112	C₁₃×C₂²⋊C₄	—	4	2	no	—
113	C₁₃×C₂²⋊C₄	—	4	2	no	—
114	C₁₃×C₂²⋊C₄	—	4	2	no	—
115	C₄²×C₁₃	—	4	2	no	—
116	C₄²×C₁₃	—	4	2	no	—
117	C₁₃×C₁₆	—	2	4	no	—
118	C₂×#466	C₂×C₁₃	1	1	yes	characteristic
119	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
120	#2234	C₂×C₁₃	1	4	yes	complemented
121	#2233	C₂×C₁₃	1	2	yes	complemented
122	#2232	C₂×C₁₃	1	2	yes	complemented
123	#2159	C₂×C₁₃	1	2	yes	complemented
124	#2140	C₂×C₁₃	1	2	yes	complemented
125	#2112	C₂×C₁₃	1	1	yes	characteristic, complemented
126	C₂³×C₁₃	—	2	2	no	—
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	—	4	1	no	—
129	C₂³×C₁₃	—	4	2	no	—
130	C₂³×C₁₃	—	8	2	no	—
131	C₂³×C₁₃	—	8	2	no	—
132	C₂³×C₁₃	—	8	2	no	—
133	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
134	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
135	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
136	D₄×C₁₃	—	4	2	no	—
137	D₄×C₁₃	—	4	2	no	—
138	D₄×C₁₃	—	8	4	no	—
139	D₄×C₁₃	—	8	4	no	—
140	D₄×C₁₃	—	8	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	8	2	no	—
152	C₂×C₄×C₁₃	—	8	2	no	—
153	C₂×C₄×C₁₃	—	8	2	no	—
154	C₂×C₄×C₁₃	#123	1	2	yes	—
155	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#137	1	2	yes	—
159	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₁₃	—	2	1	no	—
161	C₈×C₁₃	—	2	1	no	—
162	C₈×C₁₃	#123	1	2	yes	—
163	C₈×C₁₃	C₂×#41	1	2	yes	—
164	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
165	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
166	C₂×#121	—	2	1	no	—
167	C₂×#117	—	2	1	no	—
168	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
169	#466	—	2	1	no	—
170	#466	—	2	1	no	—
171	#466	C₂²×C₁₃	1	2	yes	—
172	#466	C₂²×C₁₃	1	2	yes	—
173	#427	—	2	1	no	—
174	#427	—	2	1	no	—
175	#427	C₂²×C₁₃	1	2	yes	—
176	#427	C₂²×C₁₃	1	2	yes	complemented
177	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
179	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
180	C₂×#106	—	2	1	no	—
181	C₂×#102	—	2	1	no	—
182	#367	C₂²×C₁₃	1	4	yes	complemented
183	#366	C₂²×C₁₃	1	4	yes	complemented
184	#357	C₂²×C₁₃	1	4	yes	complemented
185	#357	C₂²×C₁₃	1	4	yes	complemented
186	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
187	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
188	C₂²×C₁₃	—	2	1	no	—
189	C₂²×C₁₃	—	2	1	no	—
190	C₂²×C₁₃	—	2	1	no	—
191	C₂²×C₁₃	—	2	1	no	—
192	C₂²×C₁₃	—	2	1	no	—
193	C₂²×C₁₃	—	2	1	no	—
194	C₂²×C₁₃	—	2	1	no	—
195	C₂²×C₁₃	—	4	4	no	—
196	C₂²×C₁₃	—	8	2	no	—
197	C₂²×C₁₃	—	8	2	no	—
198	C₂²×C₁₃	—	8	2	no	—
199	C₂²×C₁₃	—	16	4	no	—
200	C₂²×C₁₃	#480	1	2	yes	—
201	C₂²×C₁₃	#509	1	2	yes	—
202	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
203	C₄×C₁₃	—	2	1	no	—
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	8	2	no	—
206	C₄×C₁₃	—	8	2	no	—
207	C₄×C₁₃	—	8	2	no	—
208	C₄×C₁₃	#480	1	2	yes	—
209	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
210	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
211	C₂²×D₄	—	2	1	no	—
212	C₂²×D₄	—	4	1	no	—
213	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
214	C₂×D₈	—	2	1	no	—
215	C₂×D₈	—	2	4	no	—
216	C₂×D₈	C₂³×C₁₃	1	2	yes	—
217	C₂²×C₈	—	2	4	no	—
218	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
219	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
220	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
224	#121	—	2	2	no	—
225	#121	—	2	2	no	—
226	#121	—	4	1	no	—
227	#121	—	4	1	no	—
228	#117	—	2	2	no	—
229	#117	—	2	2	no	—
230	#117	—	4	1	no	—
231	#117	—	4	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₂²⋊C₄	—	4	1	no	—
236	C₂×C₂²⋊C₄	—	4	1	no	—
237	C₂×C₄²	—	4	1	no	—
238	M₃₂	—	2	4	no	—
239	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
240	#107	—	2	1	no	—
241	#107	—	2	1	no	—
242	#107	—	2	1	no	—
243	#107	C₂³×C₁₃	1	2	yes	—
244	#107	C₂³×C₁₃	1	2	yes	—
245	#107	C₂³×C₁₃	1	2	yes	—
246	#106	—	2	2	no	—
247	#106	—	2	2	no	—
248	#102	—	2	2	no	—
249	#102	—	2	2	no	—
250	C₂×C₁₃	—	2	2	no	—
251	C₂×C₁₃	—	2	2	no	—
252	C₂×C₁₃	—	4	1	no	—
253	C₂×C₁₃	—	16	2	no	—
254	C₂×C₁₃	C₂×#480	1	1	yes	characteristic
255	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
256	C₂×C₁₃	#3414	1	1	yes	characteristic
257	C₂⁴	—	4	1	no	—
258	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	4	2	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂×D₄	—	4	2	no	—
265	C₂×D₄	—	8	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
272	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
273	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
277	D₈	—	2	4	no	—
278	D₈	—	4	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
285	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
286	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂×C₈	C₁₃×#41	1	4	yes	—
288	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	4	1	no	—
293	C₄⋊C₄	—	4	1	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₄²	—	4	2	no	—
300	C₄²	—	4	2	no	—
301	C₁₆	—	2	4	no	—
302	C₁₃	#33648	1	1	yes	characteristic, direct product factor, Sylow
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	—	4	2	no	—
307	C₂³	—	8	2	no	—
308	C₂³	—	8	2	no	—
309	C₂³	—	8	2	no	—
310	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
311	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
312	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
313	D₄	—	4	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	8	4	no	—
316	D₄	—	8	4	no	—
317	D₄	—	8	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	8	2	no	—
329	C₂×C₄	—	8	2	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	C₁₃×#123	1	2	yes	—
332	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
333	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
334	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
335	C₂×C₄	C₁₃×#137	1	2	yes	—
336	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
337	C₈	—	2	1	no	—
338	C₈	—	2	1	no	—
339	C₈	C₁₃×#123	1	2	yes	—
340	C₈	C₂×C₁₃×#41	1	2	yes	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	8	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	16	4	no	—
353	C₂²	C₁₃×#480	1	2	yes	—
354	C₂²	C₁₃×#509	1	2	yes	—
355	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	8	2	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	C₁₃×#480	1	2	yes	—
362	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
363	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	2	2	no	—
366	C₂	—	4	1	no	—
367	C₂	—	16	2	no	—
368	C₂	C₂×C₁₃×#480	1	1	yes	characteristic
369	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
370	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	C₂×C₁₃×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#427	C₂	semidirect
3. C₁₃×#2234	C₂	semidirect
4. C₁₃×#2233	C₂	semidirect
5. C₁₃×#2232	C₂	semidirect
6. C₁₃×#2159	C₂	semidirect
7. C₁₃×#2140	C₂	semidirect
8. C₁₃×#2112	C₂	semidirect
21. C₁₃×#427	C₂²	semidirect
23. C₂×C₁₃×#107	C₂²	semidirect
24. C₂×C₁₃×#107	C₂²	semidirect
27. C₁₃×#367	C₂²	semidirect
28. C₁₃×#366	C₂²	semidirect
29. C₁₃×#357	C₂²	semidirect
30. C₁₃×#357	C₂²	semidirect
31. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
32. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
72. #33648	C₁₃	direct (N × H)
119. C₂×#427	C₂×C₁₃	semidirect
120. #2234	C₂×C₁₃	semidirect
121. #2233	C₂×C₁₃	semidirect
122. #2232	C₂×C₁₃	semidirect
123. #2159	C₂×C₁₃	semidirect
124. #2140	C₂×C₁₃	semidirect
125. #2112	C₂×C₁₃	semidirect
176. #427	C₂²×C₁₃	semidirect
178. C₂×#107	C₂²×C₁₃	semidirect
179. C₂×#107	C₂²×C₁₃	semidirect
182. #367	C₂²×C₁₃	semidirect
183. #366	C₂²×C₁₃	semidirect
184. #357	C₂²×C₁₃	semidirect
185. #357	C₂²×C₁₃	semidirect
186. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
187. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
302. C₁₃	#33648	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×#466	2
C₂×C₁₃×#427	2
C₁₃×#2234	2
C₁₃×#2233	2
C₁₃×#2232	2
C₁₃×#2159	2
C₁₃×#2140	2
C₁₃×#2112	2
#33648	13

Subgroups — C13×#33648 #15719987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33648 #15719987