Subgroups — C₁₃×#32952 #15719291

Order 3328.

1266 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3573	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#473	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3022	C₂	1	2	yes	maximal
5	C₁₃×#1915	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1902	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1814	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1813	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#585	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#137	C₂²	1	4	yes	—
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
12	C₁₃×#568	—	2	4	no	—
13	C₁₃×#568	—	2	2	no	—
14	C₁₃×#568	C₂²	1	2	yes	—
15	C₁₃×#568	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#131	—	2	4	no	—
17	C₂×C₁₃×#131	—	2	2	no	—
18	C₂×C₁₃×#131	C₂²	1	2	yes	—
19	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
20	C₁₃×#536	C₂²	1	2	yes	—
21	C₁₃×#473	—	2	4	no	—
22	C₁₃×#473	—	2	4	no	—
23	C₁₃×#470	—	2	2	no	—
24	C₁₃×#467	—	2	2	no	—
25	C₁₃×#456	—	2	4	no	—
26	C₁₃×#455	—	2	4	no	—
27	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
28	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#421	C₂²	1	4	yes	—
30	C₁₃×#419	C₂²	1	2	yes	complemented
31	C₁₃×#413	C₂²	1	2	yes	—
32	C₂×C₁₃×#101	C₂²	1	4	yes	complemented
33	C₁₃×#344	C₂²	1	4	yes	complemented
34	C₁₃×#338	C₂²	1	2	yes	complemented
35	C₁₃×2₋¹⁺⁴	—	2	2	no	—
36	C₁₃×2₋¹⁺⁴	D₄	1	2	yes	—
37	C₁₃×H(5,𝔽₂)	—	2	2	no	—
38	C₁₃×H(5,𝔽₂)	—	2	2	no	—
39	C₁₃×H(5,𝔽₂)	D₄	1	2	yes	—
40	C₂×C₁₃×#41	—	2	4	no	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	C₂³	1	2	yes	—
43	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
45	C₁₃×#137	—	2	8	no	—
46	C₁₃×#137	—	2	8	no	—
47	C₂×C₁₃×Q₁₆	—	2	4	no	—
48	C₂×C₁₃×Q₁₆	—	2	1	no	—
49	C₂×C₁₃×Q₁₆	—	2	1	no	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	4	no	—
53	C₁₃×#131	—	2	4	no	—
54	C₁₃×#131	—	2	8	no	—
55	C₁₃×#131	—	2	4	no	—
56	C₁₃×#131	—	2	4	no	—
57	C₁₃×#131	—	2	4	no	—
58	C₁₃×#131	—	2	2	no	—
59	C₁₃×#131	—	2	2	no	—
60	C₁₃×#131	—	2	4	no	—
61	C₁₃×#131	—	2	2	no	—
62	C₁₃×#131	—	2	2	no	—
63	C₁₃×#131	D₄	1	4	yes	—
64	C₁₃×#131	D₄	1	4	yes	—
65	C₂×C₁₃×M₁₆	—	2	8	no	—
66	C₂×C₁₃×M₁₆	—	2	4	no	—
67	C₂×C₁₃×M₁₆	—	2	2	no	—
68	C₂×C₁₃×M₁₆	—	2	4	no	—
69	C₂×C₁₃×M₁₆	—	2	2	no	—
70	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
72	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	—	2	4	no	—
75	C₂²×C₈×C₁₃	—	2	2	no	—
76	C₂²×C₈×C₁₃	D₄	1	2	yes	—
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	—	2	2	no	—
79	C₁₃×#124	—	2	2	no	—
80	C₁₃×#123	—	2	4	no	—
81	C₁₃×C₂²⋊Q₈	—	2	4	no	—
82	C₁₃×#117	C₂³	1	2	yes	—
83	C₁₃×#108	—	2	2	no	—
84	C₁₃×#108	—	2	2	no	—
85	C₁₃×#107	—	2	1	no	—
86	C₁₃×#106	—	2	1	no	—
87	C₁₃×#104	—	2	8	no	—
88	C₁₃×#103	—	2	4	no	—
89	C₁₃×#101	—	2	2	no	—
90	C₁₃×#101	—	2	8	no	—
91	C₁₃×#100	—	2	2	no	—
92	#32952	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₁₃×#41	—	2	4	no	—
94	C₁₃×#41	—	2	8	no	—
95	C₁₃×#41	—	2	4	no	—
96	C₁₃×#41	—	2	4	no	—
97	C₁₃×#41	—	2	4	no	—
98	C₁₃×#41	—	2	4	no	—
99	C₁₃×#41	—	2	2	no	—
100	C₁₃×#41	—	2	2	no	—
101	C₁₃×#41	—	2	2	no	—
102	C₁₃×#41	—	2	2	no	—
103	C₁₃×#41	C₂×D₄	1	4	yes	—
104	C₁₃×#41	C₂×D₄	1	4	yes	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	4	no	—
107	C₂×Q₈×C₁₃	—	2	4	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	2	4	no	—
111	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₃	#41	1	2	yes	—
113	C₂×D₄×C₁₃	—	2	8	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	4	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₁₃	#41	1	2	yes	—
120	C₂×D₄×C₁₃	#41	1	2	yes	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×Q₁₆	—	4	8	no	—
127	C₁₃×Q₁₆	—	4	1	no	—
128	C₁₃×Q₁₆	—	4	1	no	—
129	C₁₃×Q₁₆	—	4	2	no	—
130	C₁₃×SD₁₆	—	4	8	no	—
131	C₁₃×M₁₆	—	2	4	no	—
132	C₁₃×M₁₆	—	2	8	no	—
133	C₁₃×M₁₆	—	2	2	no	—
134	C₁₃×M₁₆	—	2	2	no	—
135	C₁₃×M₁₆	—	2	4	no	—
136	C₁₃×M₁₆	—	2	4	no	—
137	C₁₃×M₁₆	—	2	4	no	—
138	C₁₃×M₁₆	—	2	4	no	—
139	C₁₃×M₁₆	—	2	4	no	—
140	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
141	C₂×C₈×C₁₃	—	2	4	no	—
142	C₂×C₈×C₁₃	—	2	8	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	4	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	—	2	4	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	4	no	—
149	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	4	4	no	—
156	C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₁₃×C₂²⋊C₄	—	4	4	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	#3573	C₂×C₁₃	1	1	yes	characteristic
160	C₂×#473	C₂×C₁₃	1	2	yes	complemented
161	#3059	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#3022	C₂×C₁₃	1	2	yes	—
163	#1915	C₂×C₁₃	1	2	yes	complemented
164	#1902	C₂×C₁₃	1	4	yes	complemented
165	#1814	C₂×C₁₃	1	2	yes	complemented
166	#1813	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂³×C₁₃	—	2	4	no	—
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	#121	1	2	yes	—
170	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	4	no	—
172	Q₈×C₁₃	—	2	2	no	—
173	Q₈×C₁₃	—	2	2	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	Q₈×C₁₃	—	4	4	no	—
176	Q₈×C₁₃	—	4	2	no	—
177	Q₈×C₁₃	#121	1	4	yes	—
178	D₄×C₁₃	—	2	8	no	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	2	4	no	—
182	D₄×C₁₃	—	2	4	no	—
183	D₄×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	#121	1	4	yes	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	4	no	—
196	C₂×C₄×C₁₃	#121	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
201	C₈×C₁₃	—	2	4	no	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	4	4	no	—
204	C₈×C₁₃	#120	1	1	yes	characteristic
205	C₈×C₁₃	#120	1	2	yes	—
206	C₈×C₁₃	#120	1	1	yes	characteristic
207	#585	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#137	C₂²×C₁₃	1	4	yes	—
209	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
210	#568	—	2	4	no	—
211	#568	—	2	2	no	—
212	#568	C₂²×C₁₃	1	2	yes	—
213	#568	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#131	—	2	4	no	—
215	C₂×#131	—	2	2	no	—
216	C₂×#131	C₂²×C₁₃	1	2	yes	—
217	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
218	#536	C₂²×C₁₃	1	2	yes	—
219	#473	—	2	4	no	—
220	#473	—	2	4	no	—
221	#470	—	2	2	no	—
222	#467	—	2	2	no	—
223	#456	—	2	4	no	—
224	#455	—	2	4	no	—
225	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
226	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
227	#421	C₂²×C₁₃	1	4	yes	—
228	#419	C₂²×C₁₃	1	2	yes	complemented
229	#413	C₂²×C₁₃	1	2	yes	—
230	C₂×#101	C₂²×C₁₃	1	4	yes	complemented
231	#344	C₂²×C₁₃	1	4	yes	complemented
232	#338	C₂²×C₁₃	1	2	yes	complemented
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	—	2	4	no	—
235	C₂²×C₁₃	—	4	1	no	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	4	no	—
239	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
240	C₂²×C₁₃	#525	1	2	yes	—
241	C₄×C₁₃	—	2	4	no	—
242	C₄×C₁₃	—	2	2	no	—
243	C₄×C₁₃	—	8	2	no	—
244	C₄×C₁₃	—	8	2	no	—
245	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
246	C₄×C₁₃	C₂×#121	1	2	yes	—
247	C₄×C₁₃	#525	1	1	yes	characteristic
248	2₋¹⁺⁴	—	2	2	no	—
249	2₋¹⁺⁴	D₄×C₁₃	1	2	yes	—
250	H(5,𝔽₂)	—	2	2	no	—
251	H(5,𝔽₂)	—	2	2	no	—
252	H(5,𝔽₂)	D₄×C₁₃	1	2	yes	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	—	2	2	no	—
255	C₂×#41	C₂³×C₁₃	1	2	yes	—
256	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
258	#137	—	2	8	no	—
259	#137	—	2	8	no	—
260	C₂×Q₁₆	—	2	4	no	—
261	C₂×Q₁₆	—	2	1	no	—
262	C₂×Q₁₆	—	2	1	no	—
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×SD₁₆	—	2	4	no	—
266	#131	—	2	4	no	—
267	#131	—	2	8	no	—
268	#131	—	2	4	no	—
269	#131	—	2	4	no	—
270	#131	—	2	4	no	—
271	#131	—	2	2	no	—
272	#131	—	2	2	no	—
273	#131	—	2	4	no	—
274	#131	—	2	2	no	—
275	#131	—	2	2	no	—
276	#131	D₄×C₁₃	1	4	yes	—
277	#131	D₄×C₁₃	1	4	yes	—
278	C₂×M₁₆	—	2	8	no	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	4	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
284	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
285	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
286	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
287	C₂²×C₈	—	2	4	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	D₄×C₁₃	1	2	yes	—
290	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₄⋊Q₈	—	2	2	no	—
292	#124	—	2	2	no	—
293	#123	—	2	4	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	#117	C₂³×C₁₃	1	2	yes	—
296	#108	—	2	2	no	—
297	#108	—	2	2	no	—
298	#107	—	2	1	no	—
299	#106	—	2	1	no	—
300	#104	—	2	8	no	—
301	#103	—	2	4	no	—
302	#101	—	2	2	no	—
303	#101	—	2	8	no	—
304	#100	—	2	2	no	—
305	C₂×C₁₃	—	2	1	no	—
306	C₂×C₁₃	—	2	2	no	—
307	C₂×C₁₃	—	4	2	no	—
308	C₂×C₁₃	—	4	4	no	—
309	C₂×C₁₃	#2847	1	1	yes	characteristic
310	#41	—	2	4	no	—
311	#41	—	2	8	no	—
312	#41	—	2	4	no	—
313	#41	—	2	4	no	—
314	#41	—	2	4	no	—
315	#41	—	2	4	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	C₂×D₄×C₁₃	1	4	yes	—
321	#41	C₂×D₄×C₁₃	1	4	yes	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
329	C₂×Q₈	C₁₃×#41	1	2	yes	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂×D₄	C₁₃×#41	1	2	yes	—
337	C₂×D₄	C₁₃×#41	1	2	yes	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
343	Q₁₆	—	4	8	no	—
344	Q₁₆	—	4	1	no	—
345	Q₁₆	—	4	1	no	—
346	Q₁₆	—	4	2	no	—
347	SD₁₆	—	4	8	no	—
348	M₁₆	—	2	4	no	—
349	M₁₆	—	2	8	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	4	no	—
353	M₁₆	—	2	4	no	—
354	M₁₆	—	2	4	no	—
355	M₁₆	—	2	4	no	—
356	M₁₆	—	2	4	no	—
357	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
358	C₂×C₈	—	2	4	no	—
359	C₂×C₈	—	2	8	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
367	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₄²	—	2	2	no	—
376	C₁₃	#32952	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	—	2	4	no	—
378	C₂³	—	2	2	no	—
379	C₂³	C₁₃×#121	1	2	yes	—
380	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
381	Q₈	—	2	4	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	4	2	no	—
387	Q₈	C₁₃×#121	1	4	yes	—
388	D₄	—	2	8	no	—
389	D₄	—	2	4	no	—
390	D₄	—	2	4	no	—
391	D₄	—	2	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	C₁₃×#121	1	4	yes	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	C₁₃×#121	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
411	C₈	—	2	4	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	4	no	—
414	C₈	C₁₃×#120	1	1	yes	characteristic
415	C₈	C₁₃×#120	1	2	yes	—
416	C₈	C₁₃×#120	1	1	yes	characteristic
417	C₂²	—	2	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	4	no	—
423	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
424	C₂²	C₁₃×#525	1	2	yes	—
425	C₄	—	2	4	no	—
426	C₄	—	2	2	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	2	no	—
429	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
430	C₄	C₂×C₁₃×#121	1	2	yes	—
431	C₄	C₁₃×#525	1	1	yes	characteristic
432	C₂	—	2	1	no	—
433	C₂	—	2	2	no	—
434	C₂	—	4	2	no	—
435	C₂	—	4	4	no	—
436	C₂	C₁₃×#2847	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#585	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#473	C₂	semidirect
3. C₁₃×#3059	C₂	semidirect
5. C₁₃×#1915	C₂	semidirect
6. C₁₃×#1902	C₂	semidirect
7. C₁₃×#1814	C₂	semidirect
8. C₁₃×#1813	C₂	semidirect
11. C₂²×C₁₃×Q₁₆	C₂²	semidirect
27. C₂×C₁₃×#108	C₂²	semidirect
28. C₁₃×#427	C₂²	semidirect
30. C₁₃×#419	C₂²	semidirect
32. C₂×C₁₃×#101	C₂²	semidirect
33. C₁₃×#344	C₂²	semidirect
34. C₁₃×#338	C₂²	semidirect
92. #32952	C₁₃	direct (N × H)
160. C₂×#473	C₂×C₁₃	semidirect
161. #3059	C₂×C₁₃	semidirect
163. #1915	C₂×C₁₃	semidirect
164. #1902	C₂×C₁₃	semidirect
165. #1814	C₂×C₁₃	semidirect
166. #1813	C₂×C₁₃	semidirect
209. C₂²×Q₁₆	C₂²×C₁₃	semidirect
225. C₂×#108	C₂²×C₁₃	semidirect
226. #427	C₂²×C₁₃	semidirect
228. #419	C₂²×C₁₃	semidirect
230. C₂×#101	C₂²×C₁₃	semidirect
231. #344	C₂²×C₁₃	semidirect
232. #338	C₂²×C₁₃	semidirect
376. C₁₃	#32952	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×#3573	2
C₂×C₁₃×#473	2
C₁₃×#3059	2
C₁₃×#3022	2
C₁₃×#1915	2
C₁₃×#1902	2
C₁₃×#1814	2
C₁₃×#1813	2
#32952	13

Subgroups — C13×#32952 #15719291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32952 #15719291