Subgroups — C₁₃×#26082 #15712421

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 432 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×#3084	C₂	1	2	yes	maximal
3	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2090	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2061	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×#1860	C₂	1	2	yes	maximal
9	C₁₃×#1846	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×#476	—	2	2	no	—
21	C₁₃×#475	—	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	1	yes	characteristic
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#106	C₂²	1	2	yes	—
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×#382	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	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#108	—	2	2	no	—
71	C₁₃×#107	—	2	1	no	—
72	C₁₃×#107	—	2	1	no	—
73	C₁₃×#107	—	2	1	no	—
74	C₁₃×#107	—	2	1	no	—
75	C₁₃×#107	—	2	2	no	—
76	C₁₃×#107	—	2	2	no	—
77	C₁₃×#107	—	2	2	no	—
78	C₁₃×#107	D₄	1	1	yes	characteristic
79	C₁₃×#107	D₄	1	1	yes	characteristic
80	C₁₃×#106	—	2	2	no	—
81	C₁₃×#106	—	2	2	no	—
82	C₁₃×#106	—	2	2	no	—
83	C₁₃×#106	—	2	2	no	—
84	C₁₃×#106	—	2	2	no	—
85	C₁₃×#106	D₄	1	2	yes	—
86	C₁₃×C₄⋊C₈	—	2	2	no	—
87	C₁₃×C₄⋊C₈	—	2	2	no	—
88	C₁₃×#104	Q₈	1	4	yes	complemented
89	C₁₃×#103	—	2	2	no	—
90	C₁₃×#103	D₄	1	1	yes	characteristic
91	C₁₃×#103	D₄	1	1	yes	characteristic
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×#102	D₄	1	1	yes	characteristic
94	C₁₃×#102	D₄	1	1	yes	characteristic
95	C₁₃×#97	—	2	1	no	—
96	C₄×C₈×C₁₃	—	2	1	no	—
97	C₄×C₈×C₁₃	—	2	2	no	—
98	C₁₃×#95	—	4	2	no	—
99	#26082	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	C₂×D₄	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
143	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
145	C₁₃×C₂²⋊C₄	—	2	2	no	—
146	C₁₃×C₂²⋊C₄	—	2	1	no	—
147	C₁₃×C₂²⋊C₄	—	4	2	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	4	2	no	—
152	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
153	#3164	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#3084	C₂×C₁₃	1	2	yes	—
155	#2913	C₂×C₁₃	1	1	yes	characteristic
156	#2090	C₂×C₁₃	1	2	yes	complemented
157	#2061	C₂×C₁₃	1	2	yes	complemented
158	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1945	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1860	C₂×C₁₃	1	2	yes	—
161	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1816	C₂×C₁₃	1	1	yes	characteristic
163	#1764	C₂×C₁₃	1	1	yes	characteristic
164	C₂³×C₁₃	—	2	1	no	—
165	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
166	Q₈×C₁₃	—	2	1	no	—
167	Q₈×C₁₃	—	16	2	no	—
168	Q₈×C₁₃	C₄⋊Q₈	1	2	yes	—
169	D₄×C₁₃	—	2	2	no	—
170	D₄×C₁₃	—	2	2	no	—
171	D₄×C₁₃	—	2	1	no	—
172	D₄×C₁₃	C₄⋊Q₈	1	2	yes	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	4	1	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	—	8	2	no	—
186	C₂×C₄×C₁₃	—	8	2	no	—
187	C₂×C₄×C₁₃	—	16	2	no	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
194	C₈×C₁₃	—	2	2	no	—
195	C₈×C₁₃	—	2	1	no	—
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	2	2	no	—
198	C₈×C₁₃	—	4	2	no	—
199	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
200	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
201	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
202	#544	C₂²×C₁₃	1	2	yes	—
203	#520	C₂²×C₁₃	1	2	yes	—
204	#501	—	2	2	no	—
205	#500	—	2	1	no	—
206	#499	—	2	1	no	—
207	#479	—	2	2	no	—
208	#478	—	2	2	no	—
209	#476	—	2	2	no	—
210	#475	—	2	2	no	—
211	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
212	#428	—	2	2	no	—
213	#428	C₂²×C₁₃	1	2	yes	—
214	#428	C₂²×C₁₃	1	2	yes	—
215	#428	C₂²×C₁₃	1	2	yes	—
216	#427	—	2	1	no	—
217	#427	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#107	—	2	1	no	—
219	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#106	C₂²×C₁₃	1	2	yes	—
222	#424	C₂²×C₁₃	1	2	yes	—
223	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
224	#417	C₂²×C₁₃	1	2	yes	—
225	#416	C₂²×C₁₃	1	1	yes	characteristic
226	#405	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
228	#382	C₂²×C₁₃	1	2	yes	—
229	#343	C₂²×C₁₃	1	2	yes	—
230	#343	C₂²×C₁₃	1	2	yes	—
231	#341	C₂²×C₁₃	1	1	yes	characteristic
232	#339	C₂²×C₁₃	1	1	yes	characteristic
233	#339	C₂²×C₁₃	1	2	yes	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	4	1	no	—
238	C₂²×C₁₃	—	4	1	no	—
239	C₂²×C₁₃	#544	1	1	yes	characteristic
240	C₂²×C₁₃	D₄²	1	1	yes	characteristic
241	C₂²×C₁₃	#554	1	1	yes	characteristic
242	C₄×C₁₃	—	2	2	no	—
243	C₄×C₁₃	—	4	2	no	—
244	C₄×C₁₃	—	4	1	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	1	no	—
248	C₄×C₁₃	—	8	2	no	—
249	C₄×C₁₃	—	8	2	no	—
250	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
251	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
252	C₄×C₁₃	#547	1	1	yes	characteristic
253	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
254	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
255	#131	—	2	2	no	—
256	#131	Q₈×C₁₃	1	4	yes	complemented
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
259	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	#125	—	2	2	no	—
267	#125	—	2	2	no	—
268	C₂²⋊Q₈	—	4	2	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	—	4	2	no	—
272	#117	—	2	2	no	—
273	#117	C₂³×C₁₃	1	2	yes	—
274	#117	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
278	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
279	#108	—	2	2	no	—
280	#107	—	2	1	no	—
281	#107	—	2	1	no	—
282	#107	—	2	1	no	—
283	#107	—	2	1	no	—
284	#107	—	2	2	no	—
285	#107	—	2	2	no	—
286	#107	—	2	2	no	—
287	#107	D₄×C₁₃	1	1	yes	characteristic
288	#107	D₄×C₁₃	1	1	yes	characteristic
289	#106	—	2	2	no	—
290	#106	—	2	2	no	—
291	#106	—	2	2	no	—
292	#106	—	2	2	no	—
293	#106	—	2	2	no	—
294	#106	D₄×C₁₃	1	2	yes	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	2	2	no	—
297	#104	Q₈×C₁₃	1	4	yes	complemented
298	#103	—	2	2	no	—
299	#103	D₄×C₁₃	1	1	yes	characteristic
300	#103	D₄×C₁₃	1	1	yes	characteristic
301	#102	—	2	2	no	—
302	#102	D₄×C₁₃	1	1	yes	characteristic
303	#102	D₄×C₁₃	1	1	yes	characteristic
304	#97	—	2	1	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	—	2	2	no	—
307	#95	—	4	2	no	—
308	C₂×C₁₃	—	2	1	no	—
309	C₂×C₁₃	—	2	1	no	—
310	C₂×C₁₃	—	4	2	no	—
311	C₂×C₁₃	#2440	1	1	yes	characteristic
312	C₂×C₁₃	#3290	1	1	yes	characteristic
313	C₂×C₁₃	#3290	1	1	yes	characteristic
314	#41	—	2	1	no	—
315	#41	—	2	1	no	—
316	#41	C₂×Q₈×C₁₃	1	2	yes	—
317	#41	C₂×Q₈×C₁₃	1	2	yes	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
328	M₁₆	—	2	1	no	—
329	M₁₆	—	2	1	no	—
330	M₁₆	—	2	4	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
334	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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×Q₈×C₁₃	1	2	yes	—
346	C₂×C₈	C₁₃×#41	1	2	yes	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
358	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	4	2	no	—
366	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
367	C₁₃	#26082	1	1	yes	characteristic, direct product factor, Sylow
368	C₂³	—	2	1	no	—
369	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
370	Q₈	—	2	1	no	—
371	Q₈	—	16	2	no	—
372	Q₈	C₁₃×C₄⋊Q₈	1	2	yes	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	2	1	no	—
376	D₄	C₁₃×C₄⋊Q₈	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
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	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	16	2	no	—
392	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
397	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	2	2	no	—
402	C₈	—	4	2	no	—
403	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
404	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₁₃×#544	1	1	yes	characteristic
411	C₂²	D₄²×C₁₃	1	1	yes	characteristic
412	C₂²	C₁₃×#554	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	2	no	—
421	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
422	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
423	C₄	C₁₃×#547	1	1	yes	characteristic
424	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	4	2	no	—
428	C₂	C₁₃×#2440	1	1	yes	characteristic
429	C₂	C₁₃×#3290	1	1	yes	characteristic
430	C₂	C₁₃×#3290	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×#2090	C₂	semidirect
5. C₁₃×#2061	C₂	semidirect
6. C₁₃×#1952	C₂	semidirect
7. C₁₃×#1945	C₂	semidirect
9. C₁₃×#1846	C₂	semidirect
47. C₁₃×#131	Q₈	semidirect
88. C₁₃×#104	Q₈	semidirect
99. #26082	C₁₃	direct (N × H)
153. #3164	C₂×C₁₃	semidirect
156. #2090	C₂×C₁₃	semidirect
157. #2061	C₂×C₁₃	semidirect
158. #1952	C₂×C₁₃	semidirect
159. #1945	C₂×C₁₃	semidirect
161. #1846	C₂×C₁₃	semidirect
256. #131	Q₈×C₁₃	semidirect
297. #104	Q₈×C₁₃	semidirect
367. C₁₃	#26082	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×#3084	2
C₁₃×#2913	2
C₁₃×#2090	2
C₁₃×#2061	2
C₁₃×#1952	2
C₁₃×#1945	2
C₁₃×#1860	2
C₁₃×#1846	2
C₁₃×#1816	2
C₁₃×#1764	2
#26082	13

Subgroups — C13×#26082 #15712421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26082 #15712421