Subgroups — C₁₃×#33817 #15720156

Order 3328.

534 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2228	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2225	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2224	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2218	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2210	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#532	—	2	1	no	—
13	C₁₃×#529	—	2	1	no	—
14	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
15	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
16	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
17	C₁₃×#500	C₂²	1	1	yes	characteristic
18	C₁₃×#499	C₂²	1	1	yes	characteristic
19	C₁₃×#495	C₂²	1	1	yes	characteristic
20	C₁₃×#493	C₂²	1	1	yes	characteristic
21	C₁₃×#488	—	2	1	no	—
22	C₁₃×#486	—	2	1	no	—
23	C₁₃×#467	C₂²	1	1	yes	characteristic
24	C₁₃×#466	—	2	1	no	—
25	C₁₃×#466	C₂²	1	1	yes	characteristic
26	C₁₃×#466	C₂²	1	2	yes	—
27	C₁₃×#465	—	2	1	no	—
28	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×SD₁₆	—	2	1	no	—
30	C₄×C₁₃×D₈	—	2	1	no	—
31	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×D₈	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#367	C₂²	1	2	yes	—
35	C₁₃×#366	C₂²	1	2	yes	—
36	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
39	C₁₃×#358	C₂²	1	2	yes	—
40	C₁₃×#357	C₂²	1	2	yes	—
41	C₁₃×#357	C₂²	1	2	yes	—
42	C₁₃×#357	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	4	1	no	—
44	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×SD₁₆	—	2	1	no	—
46	C₂×C₁₃×D₈	—	2	1	no	—
47	C₂×C₁₃×D₈	C₂³	1	2	yes	—
48	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
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×#126	—	4	1	no	—
54	C₁₃×#125	—	2	1	no	—
55	C₁₃×#124	—	2	1	no	—
56	C₁₃×#124	—	4	1	no	—
57	C₁₃×#123	—	4	1	no	—
58	C₁₃×C₂²⋊Q₈	—	2	1	no	—
59	C₁₃×#121	—	2	1	no	—
60	C₁₃×#121	—	2	2	no	—
61	C₁₃×#121	—	4	1	no	—
62	C₄×Q₈×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	4	1	no	—
66	C₄×D₄×C₁₃	—	4	1	no	—
67	C₁₃×#117	—	4	1	no	—
68	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
69	C₁₃×SD₃₂	—	4	2	no	—
70	C₁₃×D₁₆	—	4	2	no	—
71	C₁₃×M₃₂	—	4	2	no	—
72	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
74	C₁₃×#107	—	2	1	no	—
75	C₁₃×#107	C₂³	1	1	yes	characteristic
76	C₁₃×#107	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	2	yes	—
78	C₁₃×#106	—	2	1	no	—
79	C₁₃×#103	—	2	1	no	—
80	C₁₃×#103	—	2	1	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×#102	—	2	1	no	—
83	C₁₃×#102	—	2	2	no	—
84	C₁₃×#102	—	2	1	no	—
85	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
86	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	#33817	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₁₃×#41	—	8	4	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	4	2	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂×D₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₁₃×Q₁₆	—	2	1	no	—
105	C₁₃×Q₁₆	—	2	1	no	—
106	C₁₃×SD₁₆	—	4	2	no	—
107	C₁₃×D₈	—	2	1	no	—
108	C₁₃×D₈	—	2	2	no	—
109	C₁₃×D₈	—	2	2	no	—
110	C₁₃×D₈	—	2	1	no	—
111	C₁₃×D₈	—	4	2	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	4	1	no	—
115	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₄⋊C₄	—	4	1	no	—
127	C₁₃×C₂²⋊C₄	—	4	1	no	—
128	C₁₃×C₂²⋊C₄	—	4	1	no	—
129	C₁₃×C₂²⋊C₄	—	4	1	no	—
130	C₁₃×C₂²⋊C₄	—	4	2	no	—
131	C₁₃×C₂²⋊C₄	—	4	1	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	1	no	—
134	C₄²×C₁₃	—	4	1	no	—
135	C₄²×C₁₃	D₈	1	1	yes	characteristic
136	C₄²×C₁₃	D₈	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₁₃×C₁₆	—	2	2	no	—
140	C₁₃×C₁₆	—	2	2	no	—
141	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2228	C₂×C₁₃	1	2	yes	complemented
144	#2225	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2224	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2220	C₂×C₁₃	1	2	yes	complemented
147	#2218	C₂×C₁₃	1	2	yes	complemented
148	#2210	C₂×C₁₃	1	2	yes	complemented
149	#2207	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#2206	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2150	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
155	Q₈×C₁₃	—	4	1	no	—
156	Q₈×C₁₃	—	4	1	no	—
157	Q₈×C₁₃	—	8	2	no	—
158	D₄×C₁₃	—	4	1	no	—
159	D₄×C₁₃	—	4	2	no	—
160	D₄×C₁₃	—	4	2	no	—
161	D₄×C₁₃	—	4	1	no	—
162	D₄×C₁₃	—	8	2	no	—
163	D₄×C₁₃	—	8	2	no	—
164	D₄×C₁₃	—	8	4	no	—
165	D₄×C₁₃	—	8	2	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	8	4	no	—
175	C₂×C₄×C₁₃	—	8	2	no	—
176	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₁₃	—	2	1	no	—
183	C₈×C₁₃	—	2	1	no	—
184	C₈×C₁₃	—	2	1	no	—
185	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
186	C₈×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
187	#532	—	2	1	no	—
188	#529	—	2	1	no	—
189	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
190	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
191	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
192	#500	C₂²×C₁₃	1	1	yes	characteristic
193	#499	C₂²×C₁₃	1	1	yes	characteristic
194	#495	C₂²×C₁₃	1	1	yes	characteristic
195	#493	C₂²×C₁₃	1	1	yes	characteristic
196	#488	—	2	1	no	—
197	#486	—	2	1	no	—
198	#467	C₂²×C₁₃	1	1	yes	characteristic
199	#466	—	2	1	no	—
200	#466	C₂²×C₁₃	1	1	yes	characteristic
201	#466	C₂²×C₁₃	1	2	yes	—
202	#465	—	2	1	no	—
203	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
204	C₄×SD₁₆	—	2	1	no	—
205	C₄×D₈	—	2	1	no	—
206	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₄×D₈	C₂²×C₁₃	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
209	#367	C₂²×C₁₃	1	2	yes	—
210	#366	C₂²×C₁₃	1	2	yes	—
211	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
212	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
213	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
214	#358	C₂²×C₁₃	1	2	yes	—
215	#357	C₂²×C₁₃	1	2	yes	—
216	#357	C₂²×C₁₃	1	2	yes	—
217	#357	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	—	8	1	no	—
223	C₂²×C₁₃	—	8	2	no	—
224	C₂²×C₁₃	—	8	1	no	—
225	C₂²×C₁₃	—	8	2	no	—
226	C₂²×C₁₃	—	8	1	no	—
227	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	8	1	no	—
233	C₄×C₁₃	—	8	2	no	—
234	C₄×C₁₃	—	8	1	no	—
235	C₄×C₁₃	—	8	1	no	—
236	C₄×C₁₃	#509	1	2	yes	—
237	C₄×C₁₃	#537	1	1	yes	characteristic
238	C₄×C₁₃	#575	1	1	yes	characteristic
239	C₂×#41	—	4	1	no	—
240	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
241	C₂×SD₁₆	—	2	1	no	—
242	C₂×D₈	—	2	1	no	—
243	C₂×D₈	C₂³×C₁₃	1	2	yes	—
244	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
245	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
247	C₄⋊Q₈	—	2	1	no	—
248	#127	—	2	1	no	—
249	#126	—	4	1	no	—
250	#125	—	2	1	no	—
251	#124	—	2	1	no	—
252	#124	—	4	1	no	—
253	#123	—	4	1	no	—
254	C₂²⋊Q₈	—	2	1	no	—
255	#121	—	2	1	no	—
256	#121	—	2	2	no	—
257	#121	—	4	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	4	1	no	—
262	C₄×D₄	—	4	1	no	—
263	#117	—	4	1	no	—
264	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
265	SD₃₂	—	4	2	no	—
266	D₁₆	—	4	2	no	—
267	M₃₂	—	4	2	no	—
268	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
269	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
270	#107	—	2	1	no	—
271	#107	C₂³×C₁₃	1	1	yes	characteristic
272	#107	C₂³×C₁₃	1	1	yes	characteristic
273	#107	C₂³×C₁₃	1	2	yes	—
274	#106	—	2	1	no	—
275	#103	—	2	1	no	—
276	#103	—	2	1	no	—
277	#102	—	2	2	no	—
278	#102	—	2	1	no	—
279	#102	—	2	2	no	—
280	#102	—	2	1	no	—
281	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
282	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₁₃	—	4	1	no	—
286	C₂×C₁₃	—	16	2	no	—
287	C₂×C₁₃	—	16	1	no	—
288	C₂×C₁₃	#3245	1	1	yes	characteristic
289	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
290	C₂×C₁₃	#3414	1	1	yes	characteristic
291	#41	—	8	4	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
303	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	Q₁₆	—	2	1	no	—
306	Q₁₆	—	2	1	no	—
307	SD₁₆	—	4	2	no	—
308	D₈	—	2	1	no	—
309	D₈	—	2	2	no	—
310	D₈	—	2	2	no	—
311	D₈	—	2	1	no	—
312	D₈	—	4	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₂²⋊C₄	—	4	1	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	1	no	—
335	C₄²	—	4	1	no	—
336	C₄²	C₁₃×D₈	1	1	yes	characteristic
337	C₄²	C₁₃×D₈	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₁₆	—	2	2	no	—
341	C₁₆	—	2	2	no	—
342	C₁₃	#33817	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	—	4	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
346	Q₈	—	4	1	no	—
347	Q₈	—	4	1	no	—
348	Q₈	—	8	2	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	1	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	8	4	no	—
356	D₄	—	8	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	—	8	2	no	—
367	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
368	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
369	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
370	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
371	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
373	C₈	—	2	1	no	—
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
377	C₈	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	1	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	1	no	—
387	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	8	1	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	1	no	—
396	C₄	C₁₃×#509	1	2	yes	—
397	C₄	C₁₃×#537	1	1	yes	characteristic
398	C₄	C₁₃×#575	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	16	2	no	—
401	C₂	—	16	1	no	—
402	C₂	C₁₃×#3245	1	1	yes	characteristic
403	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
404	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
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. C₁₃×#3169	C₂	semidirect
2. C₁₃×#3168	C₂	semidirect
3. C₁₃×#2228	C₂	semidirect
4. C₁₃×#2225	C₂	semidirect
5. C₁₃×#2224	C₂	semidirect
6. C₁₃×#2220	C₂	semidirect
7. C₁₃×#2218	C₂	semidirect
8. C₁₃×#2210	C₂	semidirect
9. C₁₃×#2207	C₂	semidirect
10. C₁₃×#2206	C₂	semidirect
11. C₁₃×#2150	C₂	semidirect
89. #33817	C₁₃	direct (N × H)
141. #3169	C₂×C₁₃	semidirect
142. #3168	C₂×C₁₃	semidirect
143. #2228	C₂×C₁₃	semidirect
144. #2225	C₂×C₁₃	semidirect
145. #2224	C₂×C₁₃	semidirect
146. #2220	C₂×C₁₃	semidirect
147. #2218	C₂×C₁₃	semidirect
148. #2210	C₂×C₁₃	semidirect
149. #2207	C₂×C₁₃	semidirect
150. #2206	C₂×C₁₃	semidirect
151. #2150	C₂×C₁₃	semidirect
342. C₁₃	#33817	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×#3169	2
C₁₃×#3168	2
C₁₃×#2228	2
C₁₃×#2225	2
C₁₃×#2224	2
C₁₃×#2220	2
C₁₃×#2218	2
C₁₃×#2210	2
C₁₃×#2207	2
C₁₃×#2206	2
C₁₃×#2150	2
#33817	13

Subgroups — C13×#33817 #15720156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33817 #15720156