Subgroups — C₁₃×#32818 #15719157

Order 3328.

776 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2858	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2093	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2071	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2067	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2057	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2041	C₂	1	2	yes	maximal
8	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#125	—	2	1	no	—
12	C₂×C₁₃×#124	—	2	1	no	—
13	C₂×C₁₃×#124	—	2	1	no	—
14	C₂×C₁₃×#107	C₂²	1	4	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×#102	C₂²	1	4	yes	—
17	C₂×C₁₃×#102	C₂²	1	4	yes	—
18	C₁₃×#390	—	2	1	no	—
19	C₁₃×#390	—	2	1	no	—
20	C₁₃×#390	C₂²	1	2	yes	—
21	C₁₃×#390	C₂²	1	2	yes	—
22	C₁₃×#389	—	2	1	no	—
23	C₁₃×#389	—	2	1	no	—
24	C₁₃×#389	C₂²	1	2	yes	—
25	C₁₃×#389	C₂²	1	2	yes	—
26	C₁₃×#384	C₂²	1	1	yes	characteristic
27	C₁₃×#384	C₂²	1	1	yes	characteristic
28	C₁₃×#382	—	2	1	no	—
29	C₄³×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#340	C₂²	1	4	yes	—
31	C₁₃×#336	C₂²	1	2	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₃	—	2	1	no	—
34	C₂²×D₄×C₁₃	—	2	1	no	—
35	C₂²×D₄×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
38	C₁₃×C₄⋊Q₈	—	4	2	no	—
39	C₁₃×#127	—	4	2	no	—
40	C₁₃×#125	—	4	4	no	—
41	C₁₃×#124	—	4	4	no	—
42	C₁₃×#124	—	4	4	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
53	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#107	—	4	4	no	—
65	C₁₃×C₄⋊C₈	—	4	2	no	—
66	C₁₃×#102	—	4	4	no	—
67	C₁₃×#102	—	4	4	no	—
68	C₁₃×#95	—	2	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	#32818	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	2	2	no	—
72	C₂×Q₈×C₁₃	—	4	2	no	—
73	C₂×Q₈×C₁₃	—	4	2	no	—
74	C₂×Q₈×C₁₃	—	4	2	no	—
75	C₂×D₄×C₁₃	—	2	2	no	—
76	C₂×D₄×C₁₃	—	2	4	no	—
77	C₂×D₄×C₁₃	—	2	4	no	—
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	4	2	no	—
80	C₂×D₄×C₁₃	—	4	2	no	—
81	C₂×D₄×C₁₃	—	4	2	no	—
82	C₂×D₄×C₁₃	—	4	2	no	—
83	C₂×D₄×C₁₃	—	4	2	no	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	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	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₁₃	—	2	4	no	—
96	C₂×C₈×C₁₃	—	2	4	no	—
97	C₂×C₈×C₁₃	—	2	4	no	—
98	C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₁₃×C₄⋊C₄	—	2	4	no	—
100	C₁₃×C₄⋊C₄	—	2	4	no	—
101	C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₁₃×C₄⋊C₄	—	4	2	no	—
103	C₁₃×C₄⋊C₄	—	4	2	no	—
104	C₁₃×C₄⋊C₄	—	4	2	no	—
105	C₁₃×C₄⋊C₄	—	4	2	no	—
106	C₁₃×C₄⋊C₄	—	4	4	no	—
107	C₁₃×C₄⋊C₄	—	4	4	no	—
108	C₁₃×C₄⋊C₄	—	4	2	no	—
109	C₁₃×C₂²⋊C₄	—	4	4	no	—
110	C₁₃×C₂²⋊C₄	—	4	4	no	—
111	C₁₃×C₂²⋊C₄	—	4	4	no	—
112	C₁₃×C₂²⋊C₄	—	4	4	no	—
113	C₄²×C₁₃	—	2	2	no	—
114	C₄²×C₁₃	—	2	2	no	—
115	C₄²×C₁₃	—	2	1	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	—	2	1	no	—
119	C₄²×C₁₃	—	4	1	no	—
120	C₄²×C₁₃	D₈	1	4	yes	—
121	#2859	C₂×C₁₃	1	1	yes	characteristic, complemented
122	#2858	C₂×C₁₃	1	1	yes	characteristic
123	#2093	C₂×C₁₃	1	2	yes	complemented
124	#2071	C₂×C₁₃	1	2	yes	complemented
125	#2067	C₂×C₁₃	1	4	yes	complemented
126	#2057	C₂×C₁₃	1	2	yes	complemented
127	#2041	C₂×C₁₃	1	2	yes	—
128	#1831	C₂×C₁₃	1	1	yes	characteristic, complemented
129	C₂³×C₁₃	—	4	2	no	—
130	C₂³×C₁₃	—	4	2	no	—
131	C₂³×C₁₃	—	4	2	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	—	4	2	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₁₃	—	8	4	no	—
138	D₄×C₁₃	—	4	4	no	—
139	D₄×C₁₃	—	4	4	no	—
140	D₄×C₁₃	—	8	4	no	—
141	D₄×C₁₃	—	8	4	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	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	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	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
166	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₁₃	#137	1	2	yes	—
169	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
172	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
173	C₈×C₁₃	—	4	4	no	—
174	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
175	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×#125	—	2	1	no	—
177	C₂×#124	—	2	1	no	—
178	C₂×#124	—	2	1	no	—
179	C₂×#107	C₂²×C₁₃	1	4	yes	—
180	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
181	C₂×#102	C₂²×C₁₃	1	4	yes	—
182	C₂×#102	C₂²×C₁₃	1	4	yes	—
183	#390	—	2	1	no	—
184	#390	—	2	1	no	—
185	#390	C₂²×C₁₃	1	2	yes	—
186	#390	C₂²×C₁₃	1	2	yes	—
187	#389	—	2	1	no	—
188	#389	—	2	1	no	—
189	#389	C₂²×C₁₃	1	2	yes	—
190	#389	C₂²×C₁₃	1	2	yes	—
191	#384	C₂²×C₁₃	1	1	yes	characteristic
192	#384	C₂²×C₁₃	1	1	yes	characteristic
193	#382	—	2	1	no	—
194	C₄³	C₂²×C₁₃	1	1	yes	characteristic
195	#340	C₂²×C₁₃	1	4	yes	—
196	#336	C₂²×C₁₃	1	2	yes	—
197	#336	C₂²×C₁₃	1	2	yes	—
198	C₂²×C₁₃	—	8	2	no	—
199	C₂²×C₁₃	—	8	2	no	—
200	C₂²×C₁₃	—	8	2	no	—
201	C₂²×C₁₃	—	8	2	no	—
202	C₂²×C₁₃	—	8	2	no	—
203	C₂²×C₁₃	—	8	2	no	—
204	C₂²×C₁₃	—	8	2	no	—
205	C₂²×C₁₃	#535	1	1	yes	characteristic
206	C₂²×C₁₃	#536	1	1	yes	characteristic
207	C₂²×C₁₃	#537	1	1	yes	characteristic
208	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
209	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
211	C₂²×C₁₃	#575	1	1	yes	characteristic
212	C₄×C₁₃	—	2	2	no	—
213	C₄×C₁₃	—	2	2	no	—
214	C₄×C₁₃	—	2	2	no	—
215	C₄×C₁₃	—	2	2	no	—
216	C₄×C₁₃	—	2	2	no	—
217	C₄×C₁₃	—	4	1	no	—
218	C₄×C₁₃	—	8	2	no	—
219	C₄×C₁₃	—	8	2	no	—
220	C₄×C₁₃	—	8	2	no	—
221	C₄×C₁₃	#562	1	2	yes	—
222	C₄×C₁₃	#563	1	2	yes	—
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	2	1	no	—
226	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
227	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
228	C₄⋊Q₈	—	4	2	no	—
229	#127	—	4	2	no	—
230	#125	—	4	4	no	—
231	#124	—	4	4	no	—
232	#124	—	4	4	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
248	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
249	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
254	#107	—	4	4	no	—
255	C₄⋊C₈	—	4	2	no	—
256	#102	—	4	4	no	—
257	#102	—	4	4	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	C₂×C₁₃	—	16	2	no	—
261	C₂×C₁₃	#2820	1	1	yes	characteristic
262	C₂×C₁₃	#3205	1	1	yes	characteristic
263	C₂×C₁₃	#3215	1	1	yes	characteristic
264	C₂×C₁₃	#3226	1	1	yes	characteristic
265	C₂×C₁₃	#3234	1	1	yes	characteristic
266	C₂×C₁₃	#3245	1	1	yes	characteristic
267	C₂×C₁₃	#3254	1	1	yes	characteristic
268	C₂⁴	—	2	2	no	—
269	C₂×Q₈	—	4	2	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×Q₈	—	4	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	4	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	4	2	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	—	4	4	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	4	4	no	—
308	C₂²⋊C₄	—	4	4	no	—
309	C₂²⋊C₄	—	4	4	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	4	1	no	—
317	C₄²	C₁₃×D₈	1	4	yes	—
318	C₁₃	#32818	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
327	Q₈	—	8	4	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	4	no	—
330	D₄	—	8	4	no	—
331	D₄	—	8	4	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
355	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
356	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
357	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
358	C₂×C₄	C₁₃×#137	1	2	yes	—
359	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
361	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
362	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
363	C₈	—	4	4	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	C₁₃×#535	1	1	yes	characteristic
372	C₂²	C₁₃×#536	1	1	yes	characteristic
373	C₂²	C₁₃×#537	1	1	yes	characteristic
374	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
375	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
376	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
377	C₂²	C₁₃×#575	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	4	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₁₃×#562	1	2	yes	—
388	C₄	C₁₃×#563	1	2	yes	—
389	C₂	—	16	2	no	—
390	C₂	C₁₃×#2820	1	1	yes	characteristic
391	C₂	C₁₃×#3205	1	1	yes	characteristic
392	C₂	C₁₃×#3215	1	1	yes	characteristic
393	C₂	C₁₃×#3226	1	1	yes	characteristic
394	C₂	C₁₃×#3234	1	1	yes	characteristic
395	C₂	C₁₃×#3245	1	1	yes	characteristic
396	C₂	C₁₃×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2859	C₂	semidirect
3. C₁₃×#2093	C₂	semidirect
4. C₁₃×#2071	C₂	semidirect
5. C₁₃×#2067	C₂	semidirect
6. C₁₃×#2057	C₂	semidirect
8. C₁₃×#1831	C₂	semidirect
70. #32818	C₁₃	direct (N × H)
121. #2859	C₂×C₁₃	semidirect
123. #2093	C₂×C₁₃	semidirect
124. #2071	C₂×C₁₃	semidirect
125. #2067	C₂×C₁₃	semidirect
126. #2057	C₂×C₁₃	semidirect
128. #1831	C₂×C₁₃	semidirect
318. C₁₃	#32818	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×#2859	2
C₁₃×#2858	2
C₁₃×#2093	2
C₁₃×#2071	2
C₁₃×#2067	2
C₁₃×#2057	2
C₁₃×#2041	2
C₁₃×#1831	2
#32818	13

Subgroups — C13×#32818 #15719157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32818 #15719157