Subgroups — C₁₃×#24315 #15710654

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3078	C₂	1	2	yes	maximal
3	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2060	C₂	1	2	yes	maximal
5	C₁₃×#2028	C₂	1	2	yes	maximal
6	C₁₃×#1994	C₂	1	2	yes	maximal
7	C₁₃×#1886	C₂	1	2	yes	maximal
8	C₁₃×#1857	C₂	1	2	yes	maximal
9	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₁₃	—	2	2	no	—
11	C₁₃×#557	—	2	2	no	—
12	C₁₃×#557	—	2	4	no	—
13	C₁₃×#544	—	2	2	no	—
14	C₁₃×#544	C₂²	1	2	yes	—
15	C₁₃×#533	—	2	2	no	—
16	C₁₃×#533	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₁₃×#519	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#479	—	2	4	no	—
22	C₁₃×#477	—	2	2	no	—
23	C₁₃×#475	—	2	2	no	—
24	C₁₃×#428	C₂²	1	4	yes	—
25	C₁₃×#423	C₂²	1	2	yes	—
26	C₁₃×#419	C₂²	1	4	yes	—
27	C₂×C₁₃×#101	C₂²	1	2	yes	—
28	C₁₃×#391	C₂²	1	1	yes	characteristic
29	C₁₃×#391	C₂²	1	1	yes	characteristic
30	C₁₃×#389	—	2	2	no	—
31	C₁₃×#384	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
33	C₄³×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#343	C₂²	1	2	yes	—
35	C₁₃×#339	C₂²	1	4	yes	—
36	C₁₃×#339	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
40	C₁₃×C₄⋊Q₈	—	2	2	no	—
41	C₁₃×C₄⋊Q₈	—	2	2	no	—
42	C₁₃×C₄⋊Q₈	—	2	8	no	—
43	C₁₃×C₄⋊Q₈	—	2	2	no	—
44	C₁₃×C₄⋊Q₈	—	2	4	no	—
45	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
46	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
47	C₁₃×C₄⋊Q₈	Q₈	1	4	yes	complemented
48	C₁₃×#125	—	2	4	no	—
49	C₁₃×#125	—	2	8	no	—
50	C₁₃×#125	—	2	4	no	—
51	C₁₃×#125	D₄	1	4	yes	—
52	C₁₃×C₂²⋊Q₈	—	2	2	no	—
53	C₁₃×C₂²⋊Q₈	—	2	4	no	—
54	C₁₃×C₂²⋊Q₈	—	2	2	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	2	4	no	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	2	2	no	—
62	C₄×Q₈×C₁₃	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	2	no	—
64	C₄×Q₈×C₁₃	—	2	2	no	—
65	C₁₃×#117	—	2	4	no	—
66	C₁₃×#117	C₂³	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#107	—	2	4	no	—
81	C₁₃×#106	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×C₄⋊C₈	—	2	2	no	—
84	C₁₃×#103	—	2	4	no	—
85	C₁₃×#103	—	2	4	no	—
86	C₁₃×#101	—	2	4	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	#24315	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
99	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
100	C₂×Q₈×C₁₃	#41	1	2	yes	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₁₃×M₁₆	—	2	4	no	—
111	C₁₃×M₁₆	—	2	4	no	—
112	C₂×C₈×C₁₃	—	2	4	no	—
113	C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	—	2	8	no	—
117	C₁₃×C₄⋊C₄	—	2	4	no	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	4	no	—
122	C₁₃×C₄⋊C₄	—	2	8	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	4	4	no	—
126	C₁₃×C₄⋊C₄	—	4	2	no	—
127	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
128	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
129	C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₄²×C₁₃	—	2	4	no	—
131	C₄²×C₁₃	—	2	8	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	2	4	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	4	2	no	—
138	C₄²×C₁₃	—	4	1	no	—
139	C₄²×C₁₃	—	4	1	no	—
140	C₄²×C₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₃	C₂×D₄	1	2	yes	—
142	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
143	#3502	C₂×C₁₃	1	1	yes	characteristic
144	#3078	C₂×C₁₃	1	2	yes	—
145	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
146	#2060	C₂×C₁₃	1	2	yes	—
147	#2028	C₂×C₁₃	1	2	yes	—
148	#1994	C₂×C₁₃	1	2	yes	—
149	#1886	C₂×C₁₃	1	2	yes	—
150	#1857	C₂×C₁₃	1	2	yes	—
151	#1801	C₂×C₁₃	1	1	yes	characteristic
152	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₁₃	—	2	4	no	—
154	Q₈×C₁₃	—	2	4	no	—
155	Q₈×C₁₃	—	2	4	no	—
156	Q₈×C₁₃	—	4	2	no	—
157	Q₈×C₁₃	—	4	4	no	—
158	Q₈×C₁₃	—	8	2	no	—
159	Q₈×C₁₃	—	8	4	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
180	C₂×C₄×C₁₃	#120	1	2	yes	—
181	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
187	C₈×C₁₃	—	4	4	no	—
188	Q₈²	—	2	2	no	—
189	#557	—	2	2	no	—
190	#557	—	2	4	no	—
191	#544	—	2	2	no	—
192	#544	C₂²×C₁₃	1	2	yes	—
193	#533	—	2	2	no	—
194	#533	C₂²×C₁₃	1	2	yes	—
195	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	#519	C₂²×C₁₃	1	2	yes	—
197	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
199	#479	—	2	4	no	—
200	#477	—	2	2	no	—
201	#475	—	2	2	no	—
202	#428	C₂²×C₁₃	1	4	yes	—
203	#423	C₂²×C₁₃	1	2	yes	—
204	#419	C₂²×C₁₃	1	4	yes	—
205	C₂×#101	C₂²×C₁₃	1	2	yes	—
206	#391	C₂²×C₁₃	1	1	yes	characteristic
207	#391	C₂²×C₁₃	1	1	yes	characteristic
208	#389	—	2	2	no	—
209	#384	C₂²×C₁₃	1	1	yes	characteristic
210	C₄×C₄⋊C₄	—	2	2	no	—
211	C₄³	C₂²×C₁₃	1	1	yes	characteristic
212	#343	C₂²×C₁₃	1	2	yes	—
213	#339	C₂²×C₁₃	1	4	yes	—
214	#339	C₂²×C₁₃	1	4	yes	—
215	C₂²×C₁₃	—	2	1	no	—
216	C₂²×C₁₃	—	2	1	no	—
217	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
218	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
219	C₂²×C₁₃	#536	1	1	yes	characteristic
220	C₄×C₁₃	—	2	4	no	—
221	C₄×C₁₃	—	2	4	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	4	2	no	—
225	C₄×C₁₃	—	4	2	no	—
226	C₄×C₁₃	—	4	4	no	—
227	C₄×C₁₃	—	4	2	no	—
228	C₄×C₁₃	—	4	4	no	—
229	C₄×C₁₃	—	8	1	no	—
230	C₄×C₁₃	#456	1	2	yes	—
231	C₄×C₁₃	#548	1	2	yes	—
232	C₄×C₁₃	D₄×Q₈	1	2	yes	—
233	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
234	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
235	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	—	2	8	no	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	—	2	4	no	—
241	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
242	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
243	C₄⋊Q₈	Q₈×C₁₃	1	4	yes	complemented
244	#125	—	2	4	no	—
245	#125	—	2	8	no	—
246	#125	—	2	4	no	—
247	#125	D₄×C₁₃	1	4	yes	—
248	C₂²⋊Q₈	—	2	2	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	C₂²⋊Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	—	2	4	no	—
254	C₄×Q₈	—	2	4	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×Q₈	—	2	2	no	—
260	C₄×Q₈	—	2	2	no	—
261	#117	—	2	4	no	—
262	#117	C₂³×C₁₃	1	4	yes	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	D₄×C₁₃	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
276	#107	—	2	4	no	—
277	#106	—	2	4	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	#103	—	2	4	no	—
281	#103	—	2	4	no	—
282	#101	—	2	4	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	C₂×C₁₃	—	2	1	no	—
286	C₂×C₁₃	—	2	1	no	—
287	C₂×C₁₃	#2409	1	1	yes	characteristic
288	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
289	C₂×C₁₃	#3018	1	1	yes	characteristic
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
299	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
300	C₂×Q₈	C₁₃×#41	1	2	yes	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
310	M₁₆	—	2	4	no	—
311	M₁₆	—	2	4	no	—
312	C₂×C₈	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
328	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	8	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	4	2	no	—
338	C₄²	—	4	1	no	—
339	C₄²	—	4	1	no	—
340	C₄²	C₂×D₄×C₁₃	1	2	yes	—
341	C₄²	C₂×D₄×C₁₃	1	2	yes	—
342	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
343	C₁₃	#24315	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
345	Q₈	—	2	4	no	—
346	Q₈	—	2	4	no	—
347	Q₈	—	2	4	no	—
348	Q₈	—	4	4	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	8	2	no	—
351	Q₈	—	8	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
372	C₂×C₄	C₁₃×#120	1	2	yes	—
373	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
374	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
375	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
376	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
378	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
379	C₈	—	4	4	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
383	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
384	C₂²	C₁₃×#536	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	4	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	8	1	no	—
395	C₄	C₁₃×#456	1	2	yes	—
396	C₄	C₁₃×#548	1	2	yes	—
397	C₄	D₄×Q₈×C₁₃	1	2	yes	—
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	C₁₃×#2409	1	1	yes	characteristic
401	C₂	C₂×C₁₃×#456	1	1	yes	characteristic
402	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×C₁₃	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
47. C₁₃×C₄⋊Q₈	Q₈	semidirect
89. #24315	C₁₃	direct (N × H)
243. C₄⋊Q₈	Q₈×C₁₃	semidirect
343. C₁₃	#24315	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×#3502	2
C₁₃×#3078	2
C₄×C₁₃×C₄⋊Q₈	2
C₁₃×#2060	2
C₁₃×#2028	2
C₁₃×#1994	2
C₁₃×#1886	2
C₁₃×#1857	2
C₁₃×#1801	2
#24315	13

Subgroups — C13×#24315 #15710654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24315 #15710654