Subgroups — C₁₃×#26083 #15712422

Order 3328.

690 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3083	C₂	1	2	yes	maximal
3	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2089	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2060	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1945	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1859	C₂	1	2	yes	maximal
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1816	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1764	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
13	C₁₃×#544	C₂²	1	2	yes	—
14	C₁₃×#520	C₂²	1	2	yes	—
15	C₁₃×#501	—	2	2	no	—
16	C₁₃×#500	—	2	1	no	—
17	C₁₃×#499	—	2	1	no	—
18	C₁₃×#479	—	2	2	no	—
19	C₁₃×#478	—	2	2	no	—
20	C₁₃×#477	—	2	2	no	—
21	C₁₃×#474	—	2	2	no	—
22	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
23	C₁₃×#428	—	2	2	no	—
24	C₁₃×#428	C₂²	1	2	yes	—
25	C₁₃×#428	C₂²	1	2	yes	—
26	C₁₃×#428	C₂²	1	2	yes	—
27	C₁₃×#427	—	2	1	no	—
28	C₁₃×#427	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#107	—	2	1	no	—
30	C₂×C₁₃×#107	C₂²	1	2	yes	—
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₁₃×#424	C₂²	1	2	yes	—
34	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
35	C₁₃×#417	C₂²	1	2	yes	—
36	C₁₃×#416	C₂²	1	1	yes	characteristic
37	C₁₃×#405	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#384	C₂²	1	2	yes	—
40	C₁₃×#343	C₂²	1	2	yes	—
41	C₁₃×#343	C₂²	1	2	yes	—
42	C₁₃×#341	C₂²	1	1	yes	characteristic
43	C₁₃×#339	C₂²	1	1	yes	characteristic
44	C₁₃×#339	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₁₃×#131	—	2	2	no	—
47	C₁₃×#131	Q₈	1	4	yes	complemented
48	C₂×C₁₃×M₁₆	—	2	1	no	—
49	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
50	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	—	2	1	no	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×#125	—	2	2	no	—
58	C₁₃×#125	—	2	2	no	—
59	C₁₃×C₂²⋊Q₈	—	4	2	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	4	2	no	—
63	C₁₃×#117	—	2	2	no	—
64	C₁₃×#117	C₂³	1	1	yes	characteristic
65	C₁₃×#117	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#108	—	2	2	no	—
72	C₁₃×#107	—	2	1	no	—
73	C₁₃×#107	—	2	1	no	—
74	C₁₃×#107	—	2	2	no	—
75	C₁₃×#107	—	2	2	no	—
76	C₁₃×#107	—	2	1	no	—
77	C₁₃×#107	—	2	1	no	—
78	C₁₃×#107	—	2	2	no	—
79	C₁₃×#107	—	2	2	no	—
80	C₁₃×#107	—	2	2	no	—
81	C₁₃×#107	D₄	1	1	yes	characteristic
82	C₁₃×#107	D₄	1	1	yes	characteristic
83	C₁₃×#106	—	2	2	no	—
84	C₁₃×#106	—	2	2	no	—
85	C₁₃×#106	—	2	2	no	—
86	C₁₃×#106	D₄	1	2	yes	—
87	C₁₃×C₄⋊C₈	—	2	2	no	—
88	C₁₃×C₄⋊C₈	—	2	2	no	—
89	C₁₃×#104	Q₈	1	4	yes	complemented
90	C₁₃×#103	—	2	2	no	—
91	C₁₃×#103	D₄	1	1	yes	characteristic
92	C₁₃×#103	D₄	1	1	yes	characteristic
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	D₄	1	1	yes	characteristic
95	C₁₃×#102	D₄	1	1	yes	characteristic
96	C₁₃×#97	—	2	1	no	—
97	C₄×C₈×C₁₃	—	2	1	no	—
98	C₄×C₈×C₁₃	—	2	2	no	—
99	#26083	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₁₃×#41	—	2	1	no	—
101	C₁₃×#41	—	2	1	no	—
102	C₁₃×#41	C₂×Q₈	1	2	yes	—
103	C₁₃×#41	C₂×Q₈	1	2	yes	—
104	C₂×Q₈×C₁₃	—	4	2	no	—
105	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₁₃×M₁₆	—	2	1	no	—
115	C₁₃×M₁₆	—	2	1	no	—
116	C₁₃×M₁₆	—	2	4	no	—
117	C₁₃×M₁₆	—	2	2	no	—
118	C₁₃×M₁₆	—	2	2	no	—
119	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
120	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	4	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
132	C₂×C₈×C₁₃	#41	1	2	yes	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	8	4	no	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
143	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
144	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
145	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
146	C₁₃×C₂²⋊C₄	—	2	2	no	—
147	C₁₃×C₂²⋊C₄	—	2	1	no	—
148	C₁₃×C₂²⋊C₄	—	4	2	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	—	4	2	no	—
153	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
154	#3164	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#3083	C₂×C₁₃	1	2	yes	—
156	#2913	C₂×C₁₃	1	1	yes	characteristic
157	#2089	C₂×C₁₃	1	2	yes	complemented
158	#2060	C₂×C₁₃	1	2	yes	complemented
159	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1945	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1859	C₂×C₁₃	1	2	yes	—
162	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1816	C₂×C₁₃	1	1	yes	characteristic
164	#1764	C₂×C₁₃	1	1	yes	characteristic
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
167	Q₈×C₁₃	—	2	1	no	—
168	Q₈×C₁₃	—	16	2	no	—
169	Q₈×C₁₃	C₄⋊Q₈	1	2	yes	—
170	D₄×C₁₃	—	2	2	no	—
171	D₄×C₁₃	—	2	2	no	—
172	D₄×C₁₃	—	2	1	no	—
173	D₄×C₁₃	C₄⋊Q₈	1	2	yes	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	8	2	no	—
187	C₂×C₄×C₁₃	—	8	2	no	—
188	C₂×C₄×C₁₃	—	16	2	no	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
195	C₈×C₁₃	—	2	2	no	—
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	—	2	2	no	—
199	C₈×C₁₃	—	4	2	no	—
200	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
201	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
202	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
203	#544	C₂²×C₁₃	1	2	yes	—
204	#520	C₂²×C₁₃	1	2	yes	—
205	#501	—	2	2	no	—
206	#500	—	2	1	no	—
207	#499	—	2	1	no	—
208	#479	—	2	2	no	—
209	#478	—	2	2	no	—
210	#477	—	2	2	no	—
211	#474	—	2	2	no	—
212	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
213	#428	—	2	2	no	—
214	#428	C₂²×C₁₃	1	2	yes	—
215	#428	C₂²×C₁₃	1	2	yes	—
216	#428	C₂²×C₁₃	1	2	yes	—
217	#427	—	2	1	no	—
218	#427	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#107	—	2	1	no	—
220	C₂×#107	C₂²×C₁₃	1	2	yes	—
221	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
223	#424	C₂²×C₁₃	1	2	yes	—
224	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
225	#417	C₂²×C₁₃	1	2	yes	—
226	#416	C₂²×C₁₃	1	1	yes	characteristic
227	#405	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
229	#384	C₂²×C₁₃	1	2	yes	—
230	#343	C₂²×C₁₃	1	2	yes	—
231	#343	C₂²×C₁₃	1	2	yes	—
232	#341	C₂²×C₁₃	1	1	yes	characteristic
233	#339	C₂²×C₁₃	1	1	yes	characteristic
234	#339	C₂²×C₁₃	1	2	yes	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	4	1	no	—
239	C₂²×C₁₃	—	4	1	no	—
240	C₂²×C₁₃	#544	1	1	yes	characteristic
241	C₂²×C₁₃	D₄²	1	1	yes	characteristic
242	C₂²×C₁₃	#554	1	1	yes	characteristic
243	C₄×C₁₃	—	2	4	no	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	—	4	1	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	1	no	—
249	C₄×C₁₃	—	8	2	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
252	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
253	C₄×C₁₃	#547	1	1	yes	characteristic
254	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
255	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
256	#131	—	2	2	no	—
257	#131	Q₈×C₁₃	1	4	yes	complemented
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
260	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
261	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	#125	—	2	2	no	—
268	#125	—	2	2	no	—
269	C₂²⋊Q₈	—	4	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	—	4	2	no	—
273	#117	—	2	2	no	—
274	#117	C₂³×C₁₃	1	2	yes	—
275	#117	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	4	2	no	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
280	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
281	#108	—	2	2	no	—
282	#107	—	2	1	no	—
283	#107	—	2	1	no	—
284	#107	—	2	2	no	—
285	#107	—	2	2	no	—
286	#107	—	2	1	no	—
287	#107	—	2	1	no	—
288	#107	—	2	2	no	—
289	#107	—	2	2	no	—
290	#107	—	2	2	no	—
291	#107	D₄×C₁₃	1	1	yes	characteristic
292	#107	D₄×C₁₃	1	1	yes	characteristic
293	#106	—	2	2	no	—
294	#106	—	2	2	no	—
295	#106	—	2	2	no	—
296	#106	D₄×C₁₃	1	2	yes	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	#104	Q₈×C₁₃	1	4	yes	complemented
300	#103	—	2	2	no	—
301	#103	D₄×C₁₃	1	1	yes	characteristic
302	#103	D₄×C₁₃	1	1	yes	characteristic
303	#102	—	2	2	no	—
304	#102	D₄×C₁₃	1	1	yes	characteristic
305	#102	D₄×C₁₃	1	1	yes	characteristic
306	#97	—	2	1	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	2	2	no	—
309	C₂×C₁₃	—	2	1	no	—
310	C₂×C₁₃	—	2	1	no	—
311	C₂×C₁₃	—	4	2	no	—
312	C₂×C₁₃	#2440	1	1	yes	characteristic
313	C₂×C₁₃	#3292	1	1	yes	characteristic
314	C₂×C₁₃	#3293	1	1	yes	characteristic
315	#41	—	2	1	no	—
316	#41	—	2	1	no	—
317	#41	C₂×Q₈×C₁₃	1	2	yes	—
318	#41	C₂×Q₈×C₁₃	1	2	yes	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
329	M₁₆	—	2	1	no	—
330	M₁₆	—	2	1	no	—
331	M₁₆	—	2	4	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
335	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
346	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
347	C₂×C₈	C₁₃×#41	1	2	yes	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	8	4	no	—
357	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
360	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	4	2	no	—
368	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
369	C₁₃	#26083	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	2	1	no	—
371	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
372	Q₈	—	2	1	no	—
373	Q₈	—	16	2	no	—
374	Q₈	C₁₃×C₄⋊Q₈	1	2	yes	—
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	2	1	no	—
378	D₄	C₁₃×C₄⋊Q₈	1	2	yes	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	16	2	no	—
394	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
398	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
399	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	1	no	—
402	C₈	—	2	1	no	—
403	C₈	—	2	2	no	—
404	C₈	—	4	2	no	—
405	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
406	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	C₁₃×#544	1	1	yes	characteristic
413	C₂²	D₄²×C₁₃	1	1	yes	characteristic
414	C₂²	C₁₃×#554	1	1	yes	characteristic
415	C₄	—	2	4	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	1	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
424	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
425	C₄	C₁₃×#547	1	1	yes	characteristic
426	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	4	2	no	—
430	C₂	C₁₃×#2440	1	1	yes	characteristic
431	C₂	C₁₃×#3292	1	1	yes	characteristic
432	C₂	C₁₃×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3164	C₂	semidirect
4. C₁₃×#2089	C₂	semidirect
5. C₁₃×#2060	C₂	semidirect
6. C₁₃×#1952	C₂	semidirect
7. C₁₃×#1945	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
47. C₁₃×#131	Q₈	semidirect
89. C₁₃×#104	Q₈	semidirect
99. #26083	C₁₃	direct (N × H)
154. #3164	C₂×C₁₃	semidirect
157. #2089	C₂×C₁₃	semidirect
158. #2060	C₂×C₁₃	semidirect
159. #1952	C₂×C₁₃	semidirect
160. #1945	C₂×C₁₃	semidirect
162. #1845	C₂×C₁₃	semidirect
257. #131	Q₈×C₁₃	semidirect
299. #104	Q₈×C₁₃	semidirect
369. C₁₃	#26083	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×#3164	2
C₁₃×#3083	2
C₁₃×#2913	2
C₁₃×#2089	2
C₁₃×#2060	2
C₁₃×#1952	2
C₁₃×#1945	2
C₁₃×#1859	2
C₁₃×#1845	2
C₁₃×#1816	2
C₁₃×#1764	2
#26083	13

Subgroups — C13×#26083 #15712422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26083 #15712422