Subgroups — C₁₃×#21817 #15708156

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2298	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1980	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1963	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1962	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1789	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×#41	C₂²	1	2	yes	—
9	C₁₃×#537	—	2	2	no	—
10	C₁₃×#536	C₄	1	4	yes	complemented
11	C₁₃×#535	C₄	1	4	yes	complemented
12	C₁₃×#534	—	2	2	no	—
13	C₁₃×#532	C₂²	1	2	yes	—
14	C₁₃×#532	C₂²	1	2	yes	—
15	C₁₃×#525	—	2	4	no	—
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₁₃×#433	—	2	4	no	—
18	C₁₃×#423	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#104	C₂²	1	8	yes	complemented
20	C₂×C₁₃×#104	C₂²	1	8	yes	complemented
21	C₁₃×#407	C₂²	1	2	yes	—
22	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
23	C₁₃×#388	—	2	2	no	—
24	C₁₃×#387	—	2	2	no	—
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
26	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₁₃×#376	C₂²	1	1	yes	characteristic, complemented
28	C₄³×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#41	—	2	2	no	—
30	C₂×C₁₃×#41	—	2	2	no	—
31	C₂×C₁₃×#41	—	4	8	no	—
32	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
33	C₂×C₁₃×#41	C₂³	1	4	yes	—
34	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
35	C₂²×D₄×C₁₃	—	2	2	no	—
36	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₁₃	—	2	2	no	—
38	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
40	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
41	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
42	C₁₃×#127	C₂×C₄	1	2	yes	—
43	C₁₃×#127	C₂×C₄	1	2	yes	—
44	C₁₃×#124	C₂×C₄	1	4	yes	—
45	C₁₃×#124	C₂×C₄	1	4	yes	—
46	C₁₃×#123	—	2	8	no	—
47	C₁₃×C₂²⋊Q₈	—	2	8	no	—
48	C₁₃×#121	—	2	4	no	—
49	C₁₃×#121	—	2	4	no	—
50	C₁₃×#121	—	2	8	no	—
51	C₁₃×#120	—	2	8	no	—
52	C₄×D₄×C₁₃	—	2	4	no	—
53	C₄×D₄×C₁₃	—	2	4	no	—
54	C₁₃×#117	C₂×C₄	1	4	yes	—
55	C₁₃×#117	D₄	1	4	yes	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
60	C₂×C₄²×C₁₃	—	2	2	no	—
61	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊C₈	—	2	4	no	—
66	C₁₃×#104	—	4	8	no	—
67	C₁₃×#104	—	4	8	no	—
68	C₁₃×C₂²⋊C₈	—	2	4	no	—
69	C₁₃×#97	—	2	2	no	—
70	C₄×C₈×C₁₃	—	2	2	no	—
71	C₁₃×#95	—	2	2	no	—
72	C₁₃×#95	—	2	2	no	—
73	C₁₃×#95	—	2	2	no	—
74	#21817	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₃	—	2	2	no	—
76	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₁₃×#41	—	2	8	no	—
78	C₁₃×#41	—	2	8	no	—
79	C₁₃×#41	—	4	8	no	—
80	C₁₃×#41	—	4	8	no	—
81	C₁₃×#41	—	4	8	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	4	4	no	—
84	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
85	C₂×D₄×C₁₃	—	2	4	no	—
86	C₂×D₄×C₁₃	—	2	4	no	—
87	C₂×D₄×C₁₃	—	2	2	no	—
88	C₂×D₄×C₁₃	—	2	4	no	—
89	C₂×D₄×C₁₃	—	2	4	no	—
90	C₂×D₄×C₁₃	—	4	4	no	—
91	C₂×D₄×C₁₃	—	4	8	no	—
92	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	4	8	no	—
100	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₁₃×M₁₆	—	2	8	no	—
107	C₂×C₈×C₁₃	—	2	4	no	—
108	C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	4	4	no	—
111	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
112	C₁₃×C₂²⋊C₄	—	2	8	no	—
113	C₁₃×C₂²⋊C₄	—	2	8	no	—
114	C₁₃×C₂²⋊C₄	—	4	4	no	—
115	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	8	yes	—
116	C₄²×C₁₃	—	2	4	no	—
117	C₄²×C₁₃	—	2	4	no	—
118	C₄²×C₁₃	—	4	4	no	—
119	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
120	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₃	C₂×D₄	1	2	yes	—
122	C₄²×C₁₃	C₂×D₄	1	2	yes	—
123	#3449	C₂×C₁₃	1	1	yes	characteristic
124	#2921	C₂×C₁₃	1	1	yes	characteristic, complemented
125	#2298	C₂×C₁₃	1	1	yes	characteristic, complemented
126	#1980	C₂×C₁₃	1	4	yes	complemented
127	#1963	C₂×C₁₃	1	2	yes	complemented
128	#1962	C₂×C₁₃	1	2	yes	complemented
129	#1789	C₂×C₁₃	1	4	yes	complemented
130	C₂³×C₁₃	—	2	2	no	—
131	C₂³×C₁₃	—	2	4	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	—	4	4	no	—
134	C₂³×C₁₃	—	8	4	no	—
135	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₁₃	—	2	8	no	—
138	Q₈×C₁₃	—	4	4	no	—
139	D₄×C₁₃	—	2	8	no	—
140	D₄×C₁₃	—	4	4	no	—
141	D₄×C₁₃	—	4	8	no	—
142	D₄×C₁₃	—	4	8	no	—
143	D₄×C₁₃	—	8	4	no	—
144	D₄×C₁₃	—	8	4	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	—	2	4	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	8	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	4	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	4	no	—
157	C₂×C₄×C₁₃	—	4	4	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
163	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
167	C₈×C₁₃	—	4	4	no	—
168	C₂²×#41	C₂²×C₁₃	1	2	yes	—
169	#537	—	2	2	no	—
170	#536	C₄×C₁₃	1	4	yes	complemented
171	#535	C₄×C₁₃	1	4	yes	complemented
172	#534	—	2	2	no	—
173	#532	C₂²×C₁₃	1	2	yes	—
174	#532	C₂²×C₁₃	1	2	yes	—
175	#525	—	2	4	no	—
176	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
177	#433	—	2	4	no	—
178	#423	C₂²×C₁₃	1	2	yes	complemented
179	C₂×#104	C₂²×C₁₃	1	8	yes	complemented
180	C₂×#104	C₂²×C₁₃	1	8	yes	complemented
181	#407	C₂²×C₁₃	1	2	yes	—
182	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
183	#388	—	2	2	no	—
184	#387	—	2	2	no	—
185	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
186	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
187	#376	C₂²×C₁₃	1	1	yes	characteristic, complemented
188	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	2	2	no	—
191	C₂²×C₁₃	—	2	4	no	—
192	C₂²×C₁₃	—	4	4	no	—
193	C₂²×C₁₃	—	4	8	no	—
194	C₂²×C₁₃	—	8	2	no	—
195	C₂²×C₁₃	—	8	8	no	—
196	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₁₃	#535	1	2	yes	—
198	C₄×C₁₃	—	2	2	no	—
199	C₄×C₁₃	—	2	4	no	—
200	C₄×C₁₃	—	2	4	no	—
201	C₄×C₁₃	—	4	4	no	—
202	C₄×C₁₃	—	4	4	no	—
203	C₄×C₁₃	—	8	2	no	—
204	C₄×C₁₃	#518	1	2	yes	—
205	C₄×C₁₃	#535	1	2	yes	—
206	C₂×#41	—	2	2	no	—
207	C₂×#41	—	2	2	no	—
208	C₂×#41	—	4	8	no	—
209	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
210	C₂×#41	C₂³×C₁₃	1	4	yes	—
211	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
212	C₂²×D₄	—	2	2	no	—
213	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
214	C₂³×C₄	—	2	2	no	—
215	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
216	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
217	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
218	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
219	#127	C₂×C₄×C₁₃	1	2	yes	—
220	#127	C₂×C₄×C₁₃	1	2	yes	—
221	#124	C₂×C₄×C₁₃	1	4	yes	—
222	#124	C₂×C₄×C₁₃	1	4	yes	—
223	#123	—	2	8	no	—
224	C₂²⋊Q₈	—	2	8	no	—
225	#121	—	2	4	no	—
226	#121	—	2	4	no	—
227	#121	—	2	8	no	—
228	#120	—	2	8	no	—
229	C₄×D₄	—	2	4	no	—
230	C₄×D₄	—	2	4	no	—
231	#117	C₂×C₄×C₁₃	1	4	yes	—
232	#117	D₄×C₁₃	1	4	yes	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
239	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
240	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
242	C₄⋊C₈	—	2	4	no	—
243	#104	—	4	8	no	—
244	#104	—	4	8	no	—
245	C₂²⋊C₈	—	2	4	no	—
246	#97	—	2	2	no	—
247	C₄×C₈	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	C₂×C₁₃	—	2	2	no	—
252	C₂×C₁₃	—	4	2	no	—
253	C₂×C₁₃	—	8	4	no	—
254	C₂×C₁₃	#2309	1	1	yes	characteristic
255	C₂×C₁₃	#2901	1	2	yes	—
256	C₂⁴	—	2	2	no	—
257	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
258	#41	—	2	8	no	—
259	#41	—	2	8	no	—
260	#41	—	4	8	no	—
261	#41	—	4	8	no	—
262	#41	—	4	8	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	4	4	no	—
265	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	4	4	no	—
272	C₂×D₄	—	4	8	no	—
273	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	4	8	no	—
281	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
287	M₁₆	—	2	8	no	—
288	C₂×C₈	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	4	4	no	—
292	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	8	yes	—
293	C₂²⋊C₄	—	2	8	no	—
294	C₂²⋊C₄	—	2	8	no	—
295	C₂²⋊C₄	—	4	4	no	—
296	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	8	yes	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	4	no	—
299	C₄²	—	4	4	no	—
300	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
301	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
302	C₄²	C₂×D₄×C₁₃	1	2	yes	—
303	C₄²	C₂×D₄×C₁₃	1	2	yes	—
304	C₁₃	#21817	1	1	yes	characteristic, direct product factor, Sylow
305	C₂³	—	2	2	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	8	4	no	—
310	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
311	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
312	Q₈	—	2	8	no	—
313	Q₈	—	4	4	no	—
314	D₄	—	2	8	no	—
315	D₄	—	4	4	no	—
316	D₄	—	4	8	no	—
317	D₄	—	4	8	no	—
318	D₄	—	8	4	no	—
319	D₄	—	8	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	8	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
337	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
338	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
339	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
341	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
342	C₈	—	4	4	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	8	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	8	no	—
350	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
351	C₂²	C₁₃×#535	1	2	yes	—
352	C₄	—	2	2	no	—
353	C₄	—	2	4	no	—
354	C₄	—	2	4	no	—
355	C₄	—	4	4	no	—
356	C₄	—	4	4	no	—
357	C₄	—	8	2	no	—
358	C₄	C₁₃×#518	1	2	yes	—
359	C₄	C₁₃×#535	1	2	yes	—
360	C₂	—	2	2	no	—
361	C₂	—	4	2	no	—
362	C₂	—	8	4	no	—
363	C₂	C₁₃×#2309	1	1	yes	characteristic
364	C₂	C₁₃×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₁₃×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2921	C₂	semidirect
3. C₁₃×#2298	C₂	semidirect
4. C₁₃×#1980	C₂	semidirect
5. C₁₃×#1963	C₂	semidirect
6. C₁₃×#1962	C₂	semidirect
7. C₁₃×#1789	C₂	semidirect
10. C₁₃×#536	C₄	semidirect
11. C₁₃×#535	C₄	semidirect
18. C₁₃×#423	C₂²	semidirect
19. C₂×C₁₃×#104	C₂²	semidirect
20. C₂×C₁₃×#104	C₂²	semidirect
22. C₄×C₁₃×M₁₆	C₂²	semidirect
25. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
27. C₁₃×#376	C₂²	semidirect
28. C₄³×C₁₃	C₂²	semidirect
74. #21817	C₁₃	direct (N × H)
124. #2921	C₂×C₁₃	semidirect
125. #2298	C₂×C₁₃	semidirect
126. #1980	C₂×C₁₃	semidirect
127. #1963	C₂×C₁₃	semidirect
128. #1962	C₂×C₁₃	semidirect
129. #1789	C₂×C₁₃	semidirect
170. #536	C₄×C₁₃	semidirect
171. #535	C₄×C₁₃	semidirect
178. #423	C₂²×C₁₃	semidirect
179. C₂×#104	C₂²×C₁₃	semidirect
180. C₂×#104	C₂²×C₁₃	semidirect
182. C₄×M₁₆	C₂²×C₁₃	semidirect
185. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
187. #376	C₂²×C₁₃	semidirect
188. C₄³	C₂²×C₁₃	semidirect
304. C₁₃	#21817	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×#3449	2
C₁₃×#2921	2
C₁₃×#2298	2
C₁₃×#1980	2
C₁₃×#1963	2
C₁₃×#1962	2
C₁₃×#1789	2
#21817	13

Subgroups — C13×#21817 #15708156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21817 #15708156