Subgroups — C₁₃×#29384 #15715723

Order 3328.

708 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2956	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2102	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2091	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2050	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2010	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1932	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1896	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1891	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1861	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1841	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#575	C₂²	1	1	yes	characteristic
13	C₁₃×#568	C₂²	1	2	yes	—
14	C₁₃×#525	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#444	—	2	2	no	—
17	C₁₃×#443	—	2	2	no	—
18	C₁₃×#432	—	2	2	no	—
19	C₁₃×#431	—	2	2	no	—
20	C₁₃×#430	C₂²	1	1	yes	characteristic
21	C₁₃×#430	C₂²	1	2	yes	—
22	C₁₃×#423	C₂²	1	1	yes	characteristic
23	C₁₃×#423	C₂²	1	1	yes	characteristic
24	C₁₃×#421	C₂²	1	2	yes	—
25	C₂×C₁₃×#104	C₂²	1	2	yes	—
26	C₂×C₁₃×#104	C₂²	1	2	yes	—
27	C₁₃×#413	C₂²	1	2	yes	—
28	C₁₃×#407	C₂²	1	1	yes	characteristic
29	C₁₃×#407	C₂²	1	1	yes	characteristic
30	C₁₃×#407	C₂²	1	2	yes	—
31	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
33	C₁₃×#344	C₂²	1	2	yes	—
34	C₁₃×#344	C₂²	1	2	yes	—
35	C₁₃×#339	C₂²	1	2	yes	—
36	C₁₃×#339	C₂²	1	2	yes	—
37	C₁₃×#338	C₂²	1	1	yes	characteristic
38	C₁₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#41	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃	—	2	1	no	—
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×#137	—	2	2	no	—
43	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
44	C₁₃×#135	—	2	2	no	—
45	C₁₃×#131	—	2	4	no	—
46	C₁₃×#131	—	4	2	no	—
47	C₂×C₁₃×M₁₆	—	4	2	no	—
48	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
51	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
52	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
54	C₁₃×#123	—	2	2	no	—
55	C₁₃×C₂²⋊Q₈	—	2	2	no	—
56	C₁₃×#121	—	2	2	no	—
57	C₁₃×#120	—	2	2	no	—
58	C₄×D₄×C₁₃	—	4	2	no	—
59	C₁₃×#117	C₂³	1	2	yes	—
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	—	2	1	no	—
63	C₂×C₄²×C₁₃	—	2	1	no	—
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#108	—	2	2	no	—
68	C₁₃×#108	—	4	2	no	—
69	C₁₃×C₄⋊C₈	—	2	2	no	—
70	C₁₃×C₄⋊C₈	—	2	2	no	—
71	C₁₃×#104	—	2	2	no	—
72	C₁₃×#104	—	2	2	no	—
73	C₁₃×#104	—	2	2	no	—
74	C₁₃×#104	—	2	2	no	—
75	C₁₃×#104	—	4	2	no	—
76	C₁₃×#101	—	2	2	no	—
77	C₁₃×#100	—	2	2	no	—
78	C₁₃×C₂²⋊C₈	—	2	2	no	—
79	C₁₃×C₂²⋊C₈	—	2	2	no	—
80	C₁₃×C₂²⋊C₈	—	4	2	no	—
81	C₁₃×#97	—	2	1	no	—
82	C₁₃×#97	D₄	1	2	yes	complemented
83	C₄×C₈×C₁₃	—	2	1	no	—
84	C₄×C₈×C₁₃	D₄	1	2	yes	complemented
85	#29384	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	#41	1	1	yes	characteristic
87	C₁₃×#41	—	2	2	no	—
88	C₁₃×#41	—	2	2	no	—
89	C₁₃×#41	—	2	2	no	—
90	C₁₃×#41	—	2	2	no	—
91	C₂×Q₈×C₁₃	#41	1	2	yes	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	4	2	no	—
94	C₂×D₄×C₁₃	#41	1	2	yes	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	4	4	no	—
107	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₁₃×Q₁₆	—	2	2	no	—
110	C₁₃×SD₁₆	—	2	4	no	—
111	C₁₃×D₈	—	2	2	no	—
112	C₁₃×M₁₆	—	2	2	no	—
113	C₁₃×M₁₆	—	2	2	no	—
114	C₁₃×M₁₆	—	2	2	no	—
115	C₁₃×M₁₆	—	2	2	no	—
116	C₁₃×M₁₆	—	2	2	no	—
117	C₁₃×M₁₆	—	2	2	no	—
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	—	2	2	no	—
120	C₁₃×M₁₆	—	4	4	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	4	4	no	—
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₄²×C₁₃	—	2	1	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃	#41	1	1	yes	characteristic
143	C₄²×C₁₃	#41	1	1	yes	characteristic
144	#2956	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2102	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2091	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2050	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2010	C₂×C₁₃	1	1	yes	characteristic
150	#1932	C₂×C₁₃	1	2	yes	complemented
151	#1896	C₂×C₁₃	1	2	yes	complemented
152	#1891	C₂×C₁₃	1	2	yes	complemented
153	#1861	C₂×C₁₃	1	2	yes	complemented
154	#1841	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂³×C₁₃	—	2	1	no	—
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	4	2	no	—
159	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
160	Q₈×C₁₃	—	2	2	no	—
161	Q₈×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	4	2	no	—
166	D₄×C₁₃	—	8	4	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	—	2	2	no	—
192	C₈×C₁₃	—	4	1	no	—
193	C₈×C₁₃	—	4	2	no	—
194	C₈×C₁₃	—	4	1	no	—
195	C₈×C₁₃	—	4	2	no	—
196	#575	C₂²×C₁₃	1	1	yes	characteristic
197	#568	C₂²×C₁₃	1	2	yes	—
198	#525	C₂²×C₁₃	1	2	yes	—
199	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
200	#444	—	2	2	no	—
201	#443	—	2	2	no	—
202	#432	—	2	2	no	—
203	#431	—	2	2	no	—
204	#430	C₂²×C₁₃	1	1	yes	characteristic
205	#430	C₂²×C₁₃	1	2	yes	—
206	#423	C₂²×C₁₃	1	1	yes	characteristic
207	#423	C₂²×C₁₃	1	1	yes	characteristic
208	#421	C₂²×C₁₃	1	2	yes	—
209	C₂×#104	C₂²×C₁₃	1	2	yes	—
210	C₂×#104	C₂²×C₁₃	1	2	yes	—
211	#413	C₂²×C₁₃	1	2	yes	—
212	#407	C₂²×C₁₃	1	1	yes	characteristic
213	#407	C₂²×C₁₃	1	1	yes	characteristic
214	#407	C₂²×C₁₃	1	2	yes	—
215	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
216	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	#344	C₂²×C₁₃	1	2	yes	—
218	#344	C₂²×C₁₃	1	2	yes	—
219	#339	C₂²×C₁₃	1	2	yes	—
220	#339	C₂²×C₁₃	1	2	yes	—
221	#338	C₂²×C₁₃	1	1	yes	characteristic
222	H(3,ℤ/4)	C₂²×C₁₃	1	1	yes	characteristic
223	C₂²×C₁₃	—	2	2	no	—
224	C₂²×C₁₃	—	2	4	no	—
225	C₂²×C₁₃	—	4	1	no	—
226	C₂²×C₁₃	—	4	1	no	—
227	C₂²×C₁₃	—	4	2	no	—
228	C₂²×C₁₃	—	4	1	no	—
229	C₂²×C₁₃	—	4	2	no	—
230	C₂²×C₁₃	—	8	2	no	—
231	C₂²×C₁₃	#525	1	1	yes	characteristic
232	C₂²×C₁₃	#551	1	2	yes	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	4	1	no	—
236	C₄×C₁₃	—	4	1	no	—
237	C₄×C₁₃	—	4	1	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	#525	1	1	yes	characteristic
241	C₄×C₁₃	#535	1	1	yes	characteristic
242	C₄×C₁₃	#553	1	2	yes	—
243	C₂×#41	C₂³×C₁₃	1	2	yes	—
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
246	#137	—	2	2	no	—
247	AGL(1,ℤ/8)	—	2	2	no	—
248	#135	—	2	2	no	—
249	#131	—	2	4	no	—
250	#131	—	4	2	no	—
251	C₂×M₁₆	—	4	2	no	—
252	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
253	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
254	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
256	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
257	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
258	#123	—	2	2	no	—
259	C₂²⋊Q₈	—	2	2	no	—
260	#121	—	2	2	no	—
261	#120	—	2	2	no	—
262	C₄×D₄	—	4	2	no	—
263	#117	C₂³×C₁₃	1	2	yes	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
271	#108	—	2	2	no	—
272	#108	—	4	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	2	no	—
275	#104	—	2	2	no	—
276	#104	—	2	2	no	—
277	#104	—	2	2	no	—
278	#104	—	2	2	no	—
279	#104	—	4	2	no	—
280	#101	—	2	2	no	—
281	#100	—	2	2	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	4	2	no	—
285	#97	—	2	1	no	—
286	#97	D₄×C₁₃	1	2	yes	complemented
287	C₄×C₈	—	2	1	no	—
288	C₄×C₈	D₄×C₁₃	1	2	yes	complemented
289	C₂×C₁₃	—	2	1	no	—
290	C₂×C₁₃	—	2	2	no	—
291	C₂×C₁₃	—	4	2	no	—
292	C₂×C₁₃	—	8	2	no	—
293	C₂×C₁₃	#2598	1	1	yes	characteristic
294	C₂⁴	C₁₃×#41	1	1	yes	characteristic
295	#41	—	2	2	no	—
296	#41	—	2	2	no	—
297	#41	—	2	2	no	—
298	#41	—	2	2	no	—
299	C₂×Q₈	C₁₃×#41	1	2	yes	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	C₁₃×#41	1	2	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
317	Q₁₆	—	2	2	no	—
318	SD₁₆	—	2	4	no	—
319	D₈	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	4	4	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	4	no	—
334	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
335	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	2	no	—
348	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₄²	C₁₃×#41	1	1	yes	characteristic
351	C₄²	C₁₃×#41	1	1	yes	characteristic
352	C₁₃	#29384	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	—	2	1	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
358	Q₈	—	2	2	no	—
359	Q₈	—	2	2	no	—
360	D₄	—	2	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	8	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
385	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
386	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
387	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	4	1	no	—
391	C₈	—	4	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	C₁₃×#525	1	1	yes	characteristic
403	C₂²	C₁₃×#551	1	2	yes	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₁₃×#525	1	1	yes	characteristic
412	C₄	C₁₃×#535	1	1	yes	characteristic
413	C₄	C₁₃×#553	1	2	yes	—
414	C₂	—	2	1	no	—
415	C₂	—	2	2	no	—
416	C₂	—	4	2	no	—
417	C₂	—	8	2	no	—
418	C₂	C₁₃×#2598	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#535
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂×C₁₃	#2598
prime radical	C₁₃×#2010	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2956	C₂	semidirect
2. C₁₃×#2920	C₂	semidirect
3. C₁₃×#2102	C₂	semidirect
4. C₁₃×#2091	C₂	semidirect
5. C₁₃×#2050	C₂	semidirect
7. C₁₃×#1932	C₂	semidirect
8. C₁₃×#1896	C₂	semidirect
9. C₁₃×#1891	C₂	semidirect
10. C₁₃×#1861	C₂	semidirect
11. C₁₃×#1841	C₂	semidirect
82. C₁₃×#97	D₄	semidirect
84. C₄×C₈×C₁₃	D₄	semidirect
85. #29384	C₁₃	direct (N × H)
144. #2956	C₂×C₁₃	semidirect
145. #2920	C₂×C₁₃	semidirect
146. #2102	C₂×C₁₃	semidirect
147. #2091	C₂×C₁₃	semidirect
148. #2050	C₂×C₁₃	semidirect
150. #1932	C₂×C₁₃	semidirect
151. #1896	C₂×C₁₃	semidirect
152. #1891	C₂×C₁₃	semidirect
153. #1861	C₂×C₁₃	semidirect
154. #1841	C₂×C₁₃	semidirect
286. #97	D₄×C₁₃	semidirect
288. C₄×C₈	D₄×C₁₃	semidirect
352. C₁₃	#29384	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×#2956	2
C₁₃×#2920	2
C₁₃×#2102	2
C₁₃×#2091	2
C₁₃×#2050	2
C₁₃×#2010	2
C₁₃×#1932	2
C₁₃×#1896	2
C₁₃×#1891	2
C₁₃×#1861	2
C₁₃×#1841	2
#29384	13

Subgroups — C13×#29384 #15715723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29384 #15715723