Subgroups — C₁₃×#26081 #15712420

Order 3328.

690 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3084	C₂	1	2	yes	maximal
3	C₁₃×#2912	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2090	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2060	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1951	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×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1815	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×#499	—	2	1	no	—
17	C₁₃×#498	—	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×#106	—	2	1	no	—
30	C₂×C₁₃×#106	C₂²	1	2	yes	—
31	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#106	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	2	no	—
73	C₁₃×#107	—	2	2	no	—
74	C₁₃×#107	—	2	2	no	—
75	C₁₃×#107	D₄	1	2	yes	—
76	C₁₃×#106	—	2	1	no	—
77	C₁₃×#106	—	2	1	no	—
78	C₁₃×#106	—	2	2	no	—
79	C₁₃×#106	—	2	2	no	—
80	C₁₃×#106	—	2	1	no	—
81	C₁₃×#106	—	2	1	no	—
82	C₁₃×#106	—	2	2	no	—
83	C₁₃×#106	—	2	2	no	—
84	C₁₃×#106	—	2	2	no	—
85	C₁₃×#106	D₄	1	1	yes	characteristic
86	C₁₃×#106	D₄	1	1	yes	characteristic
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	2	yes	—
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×#102	D₄	1	2	yes	—
94	C₁₃×#97	—	2	1	no	—
95	C₄×C₈×C₁₃	—	2	1	no	—
96	C₄×C₈×C₁₃	—	2	2	no	—
97	#26081	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₁₃×#41	—	2	1	no	—
99	C₁₃×#41	—	2	1	no	—
100	C₁₃×#41	C₂×Q₈	1	2	yes	—
101	C₁₃×#41	C₂×Q₈	1	2	yes	—
102	C₂×Q₈×C₁₃	—	4	2	no	—
103	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₁₃×M₁₆	—	2	1	no	—
113	C₁₃×M₁₆	—	2	1	no	—
114	C₁₃×M₁₆	—	2	4	no	—
115	C₁₃×M₁₆	—	2	2	no	—
116	C₁₃×M₁₆	—	2	2	no	—
117	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
118	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	4	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
129	C₂×C₈×C₁₃	#41	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	8	4	no	—
139	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
140	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
142	C₁₃×C₂²⋊C₄	—	2	2	no	—
143	C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	4	2	no	—
149	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
150	#3163	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#3084	C₂×C₁₃	1	2	yes	—
152	#2912	C₂×C₁₃	1	1	yes	characteristic
153	#2090	C₂×C₁₃	1	2	yes	complemented
154	#2060	C₂×C₁₃	1	2	yes	complemented
155	#1951	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#1945	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1859	C₂×C₁₃	1	2	yes	—
158	#1844	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1815	C₂×C₁₃	1	1	yes	characteristic
160	#1764	C₂×C₁₃	1	1	yes	characteristic
161	C₂³×C₁₃	—	2	1	no	—
162	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
163	Q₈×C₁₃	—	2	1	no	—
164	Q₈×C₁₃	—	16	2	no	—
165	Q₈×C₁₃	C₄⋊Q₈	1	2	yes	—
166	D₄×C₁₃	—	2	2	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	2	1	no	—
169	D₄×C₁₃	C₄⋊Q₈	1	2	yes	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	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	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	8	2	no	—
181	C₂×C₄×C₁₃	—	8	2	no	—
182	C₂×C₄×C₁₃	—	16	2	no	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₈×C₁₃	—	2	2	no	—
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	—	2	2	no	—
192	C₈×C₁₃	—	4	2	no	—
193	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
194	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
195	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
196	#544	C₂²×C₁₃	1	2	yes	—
197	#520	C₂²×C₁₃	1	2	yes	—
198	#501	—	2	2	no	—
199	#499	—	2	1	no	—
200	#498	—	2	1	no	—
201	#479	—	2	2	no	—
202	#478	—	2	2	no	—
203	#476	—	2	2	no	—
204	#475	—	2	2	no	—
205	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
206	#428	—	2	2	no	—
207	#428	C₂²×C₁₃	1	2	yes	—
208	#428	C₂²×C₁₃	1	2	yes	—
209	#428	C₂²×C₁₃	1	2	yes	—
210	#427	—	2	1	no	—
211	#427	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#106	—	2	1	no	—
213	C₂×#106	C₂²×C₁₃	1	2	yes	—
214	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
216	#424	C₂²×C₁₃	1	2	yes	—
217	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
218	#417	C₂²×C₁₃	1	2	yes	—
219	#416	C₂²×C₁₃	1	1	yes	characteristic
220	#405	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
222	#384	C₂²×C₁₃	1	2	yes	—
223	#343	C₂²×C₁₃	1	2	yes	—
224	#343	C₂²×C₁₃	1	2	yes	—
225	#341	C₂²×C₁₃	1	1	yes	characteristic
226	#339	C₂²×C₁₃	1	1	yes	characteristic
227	#339	C₂²×C₁₃	1	2	yes	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	4	2	no	—
231	C₂²×C₁₃	#544	1	1	yes	characteristic
232	C₂²×C₁₃	D₄²	1	1	yes	characteristic
233	C₂²×C₁₃	#554	1	1	yes	characteristic
234	C₄×C₁₃	—	2	4	no	—
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	4	2	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	8	2	no	—
240	C₄×C₁₃	—	8	2	no	—
241	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
242	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
243	C₄×C₁₃	#547	1	1	yes	characteristic
244	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
245	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
246	#131	—	2	2	no	—
247	#131	Q₈×C₁₃	1	4	yes	complemented
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
250	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
251	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	#125	—	2	2	no	—
258	#125	—	2	2	no	—
259	C₂²⋊Q₈	—	4	2	no	—
260	C₄×Q₈	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	4	2	no	—
263	#117	—	2	2	no	—
264	#117	C₂³×C₁₃	1	2	yes	—
265	#117	C₂³×C₁₃	1	1	yes	characteristic
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	4	2	no	—
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
270	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
271	#108	—	2	2	no	—
272	#107	—	2	2	no	—
273	#107	—	2	2	no	—
274	#107	—	2	2	no	—
275	#107	D₄×C₁₃	1	2	yes	—
276	#106	—	2	1	no	—
277	#106	—	2	1	no	—
278	#106	—	2	2	no	—
279	#106	—	2	2	no	—
280	#106	—	2	1	no	—
281	#106	—	2	1	no	—
282	#106	—	2	2	no	—
283	#106	—	2	2	no	—
284	#106	—	2	2	no	—
285	#106	D₄×C₁₃	1	1	yes	characteristic
286	#106	D₄×C₁₃	1	1	yes	characteristic
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	#104	Q₈×C₁₃	1	4	yes	complemented
290	#103	—	2	2	no	—
291	#103	D₄×C₁₃	1	2	yes	—
292	#102	—	2	2	no	—
293	#102	D₄×C₁₃	1	2	yes	—
294	#97	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	—	2	2	no	—
297	C₂×C₁₃	—	2	1	no	—
298	C₂×C₁₃	—	2	1	no	—
299	C₂×C₁₃	—	4	2	no	—
300	C₂×C₁₃	#2440	1	1	yes	characteristic
301	C₂×C₁₃	#3291	1	2	yes	—
302	#41	—	2	1	no	—
303	#41	—	2	1	no	—
304	#41	C₂×Q₈×C₁₃	1	2	yes	—
305	#41	C₂×Q₈×C₁₃	1	2	yes	—
306	C₂×Q₈	—	4	2	no	—
307	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	1	no	—
318	M₁₆	—	2	4	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
322	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
333	C₂×C₈	C₁₃×#41	1	2	yes	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	8	4	no	—
343	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
344	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
345	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	4	2	no	—
353	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
354	C₁₃	#26081	1	1	yes	characteristic, direct product factor, Sylow
355	C₂³	—	2	1	no	—
356	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
357	Q₈	—	2	1	no	—
358	Q₈	—	16	2	no	—
359	Q₈	C₁₃×C₄⋊Q₈	1	2	yes	—
360	D₄	—	2	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	2	1	no	—
363	D₄	C₁₃×C₄⋊Q₈	1	2	yes	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	8	2	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	—	16	2	no	—
377	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
379	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
380	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
382	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	2	2	no	—
385	C₈	—	2	2	no	—
386	C₈	—	4	2	no	—
387	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
388	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	C₁₃×#544	1	1	yes	characteristic
393	C₂²	D₄²×C₁₃	1	1	yes	characteristic
394	C₂²	C₁₃×#554	1	1	yes	characteristic
395	C₄	—	2	4	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	2	no	—
402	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
403	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
404	C₄	C₁₃×#547	1	1	yes	characteristic
405	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	4	2	no	—
409	C₂	C₁₃×#2440	1	1	yes	characteristic
410	C₂	C₁₃×#3291	1	2	yes	—

	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×#3163	C₂	semidirect
4. C₁₃×#2090	C₂	semidirect
5. C₁₃×#2060	C₂	semidirect
6. C₁₃×#1951	C₂	semidirect
7. C₁₃×#1945	C₂	semidirect
9. C₁₃×#1844	C₂	semidirect
47. C₁₃×#131	Q₈	semidirect
89. C₁₃×#104	Q₈	semidirect
97. #26081	C₁₃	direct (N × H)
150. #3163	C₂×C₁₃	semidirect
153. #2090	C₂×C₁₃	semidirect
154. #2060	C₂×C₁₃	semidirect
155. #1951	C₂×C₁₃	semidirect
156. #1945	C₂×C₁₃	semidirect
158. #1844	C₂×C₁₃	semidirect
247. #131	Q₈×C₁₃	semidirect
289. #104	Q₈×C₁₃	semidirect
354. C₁₃	#26081	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×#3163	2
C₁₃×#3084	2
C₁₃×#2912	2
C₁₃×#2090	2
C₁₃×#2060	2
C₁₃×#1951	2
C₁₃×#1945	2
C₁₃×#1859	2
C₁₃×#1844	2
C₁₃×#1815	2
C₁₃×#1764	2
#26081	13

Subgroups — C13×#26081 #15712420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26081 #15712420