Subgroups — C₁₃×#24316 #15710655

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2328	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2061	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2027	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1995	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1887	C₂	1	2	yes	maximal
8	C₁₃×#1856	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1800	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#554	—	2	2	no	—
11	C₁₃×#554	—	2	4	no	—
12	D₄×Q₈×C₁₃	—	2	2	no	—
13	C₁₃×#544	C₂²	1	2	yes	—
14	C₁₃×#543	—	2	2	no	—
15	C₁₃×#533	C₂²	1	2	yes	—
16	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
18	C₁₃×#518	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#478	—	2	4	no	—
22	C₁₃×#476	—	2	2	no	—
23	C₁₃×#474	—	2	2	no	—
24	C₁₃×#428	C₂²	1	4	yes	—
25	C₁₃×#423	C₂²	1	2	yes	—
26	C₁₃×#418	C₂²	1	4	yes	—
27	C₂×C₁₃×#100	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	1	yes	characteristic
29	C₁₃×#390	C₂²	1	1	yes	characteristic
30	C₁₃×#386	—	2	2	no	—
31	C₁₃×#386	—	2	2	no	—
32	C₁₃×#382	C₂²	1	1	yes	characteristic
33	C₁₃×#376	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	—	2	2	no	—
38	C₂²×D₄×C₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	—	2	1	no	—
42	C₂³×C₄×C₁₃	D₄	1	2	yes	—
43	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
44	C₁₃×C₄⋊Q₈	—	2	4	no	—
45	C₁₃×C₄⋊Q₈	D₄	1	2	yes	complemented
46	C₁₃×C₄⋊Q₈	D₄	1	2	yes	complemented
47	C₁₃×#127	—	2	2	no	—
48	C₁₃×#127	Q₈	1	4	yes	complemented
49	C₁₃×#125	—	2	4	no	—
50	C₁₃×#125	D₄	1	4	yes	complemented
51	C₁₃×C₂²⋊Q₈	—	2	4	no	—
52	C₁₃×C₂²⋊Q₈	—	2	4	no	—
53	C₁₃×C₂²⋊Q₈	—	2	8	no	—
54	C₁₃×C₂²⋊Q₈	—	2	8	no	—
55	C₁₃×C₂²⋊Q₈	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	2	4	no	—
57	C₁₃×C₂²⋊Q₈	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	2	2	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×D₄×C₁₃	—	2	4	no	—
61	C₄×D₄×C₁₃	—	2	4	no	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₁₃×#117	C₂³	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	—	2	4	no	—
80	C₁₃×#106	—	2	4	no	—
81	C₁₃×C₄⋊C₈	—	2	2	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×#100	—	2	4	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	#24316	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
92	C₂×Q₈×C₁₃	—	2	4	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	8	4	no	—
96	C₂×D₄×C₁₃	—	2	8	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	8	2	no	—
103	C₂×D₄×C₁₃	—	8	2	no	—
104	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
105	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	complemented
106	C₂×D₄×C₁₃	#41	1	2	yes	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	—	8	2	no	—
116	C₂²×C₄×C₁₃	—	8	2	no	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×M₁₆	—	2	4	no	—
122	C₁₃×M₁₆	—	2	4	no	—
123	C₂×C₈×C₁₃	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	8	no	—
126	C₁₃×C₄⋊C₄	—	2	4	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	4	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
133	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
134	C₁₃×C₂²⋊C₄	—	2	8	no	—
135	C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₁₃×C₂²⋊C₄	—	2	4	no	—
137	C₁₃×C₂²⋊C₄	—	4	1	no	—
138	C₁₃×C₂²⋊C₄	—	4	1	no	—
139	C₁₃×C₂²⋊C₄	—	8	2	no	—
140	C₁₃×C₂²⋊C₄	—	8	2	no	—
141	C₄²×C₁₃	—	2	4	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	C₂×D₄	1	2	yes	—
145	C₄²×C₁₃	C₂×D₄	1	2	yes	—
146	C₄²×C₁₃	C₂×Q₈	1	2	yes	complemented
147	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#3077	C₂×C₁₃	1	2	yes	complemented
149	#2328	C₂×C₁₃	1	1	yes	characteristic
150	#2061	C₂×C₁₃	1	2	yes	complemented
151	#2027	C₂×C₁₃	1	2	yes	complemented
152	#1995	C₂×C₁₃	1	2	yes	complemented
153	#1887	C₂×C₁₃	1	2	yes	—
154	#1856	C₂×C₁₃	1	2	yes	complemented
155	#1800	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	C₂²⋊Q₈	1	4	yes	—
166	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₃	—	4	4	no	—
168	Q₈×C₁₃	—	8	2	no	—
169	Q₈×C₁₃	—	8	4	no	—
170	D₄×C₁₃	—	2	4	no	—
171	D₄×C₁₃	—	2	4	no	—
172	D₄×C₁₃	—	2	4	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	—	8	8	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	4	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	8	2	no	—
191	C₂×C₄×C₁₃	—	8	4	no	—
192	C₂×C₄×C₁₃	—	8	4	no	—
193	C₂×C₄×C₁₃	—	8	4	no	—
194	C₂×C₄×C₁₃	#120	1	2	yes	—
195	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
196	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
201	C₈×C₁₃	—	4	4	no	—
202	#554	—	2	2	no	—
203	#554	—	2	4	no	—
204	D₄×Q₈	—	2	2	no	—
205	#544	C₂²×C₁₃	1	2	yes	—
206	#543	—	2	2	no	—
207	#533	C₂²×C₁₃	1	2	yes	—
208	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₂²⋊Q₈	—	2	2	no	—
210	#518	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
213	#478	—	2	4	no	—
214	#476	—	2	2	no	—
215	#474	—	2	2	no	—
216	#428	C₂²×C₁₃	1	4	yes	—
217	#423	C₂²×C₁₃	1	2	yes	—
218	#418	C₂²×C₁₃	1	4	yes	—
219	C₂×#100	C₂²×C₁₃	1	2	yes	—
220	#390	C₂²×C₁₃	1	1	yes	characteristic
221	#390	C₂²×C₁₃	1	1	yes	characteristic
222	#386	—	2	2	no	—
223	#386	—	2	2	no	—
224	#382	C₂²×C₁₃	1	1	yes	characteristic
225	#376	C₂²×C₁₃	1	1	yes	characteristic
226	#343	C₂²×C₁₃	1	2	yes	—
227	#339	C₂²×C₁₃	1	4	yes	—
228	#339	C₂²×C₁₃	1	4	yes	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	2	4	no	—
232	C₂²×C₁₃	—	4	4	no	—
233	C₂²×C₁₃	—	4	4	no	—
234	C₂²×C₁₃	—	4	2	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	—	8	1	no	—
240	C₂²×C₁₃	—	8	1	no	—
241	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₂²×C₁₃	#536	1	1	yes	characteristic
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	4	no	—
250	C₄×C₁₃	—	4	4	no	—
251	C₄×C₁₃	—	8	1	no	—
252	C₄×C₁₃	—	8	1	no	—
253	C₄×C₁₃	#548	1	2	yes	—
254	C₄×C₁₃	D₄×Q₈	1	2	yes	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	D₄×C₁₃	1	2	yes	—
261	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
262	C₄⋊Q₈	—	2	4	no	—
263	C₄⋊Q₈	D₄×C₁₃	1	2	yes	complemented
264	C₄⋊Q₈	D₄×C₁₃	1	2	yes	complemented
265	#127	—	2	2	no	—
266	#127	Q₈×C₁₃	1	4	yes	complemented
267	#125	—	2	4	no	—
268	#125	D₄×C₁₃	1	4	yes	complemented
269	C₂²⋊Q₈	—	2	4	no	—
270	C₂²⋊Q₈	—	2	4	no	—
271	C₂²⋊Q₈	—	2	8	no	—
272	C₂²⋊Q₈	—	2	8	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	C₂²⋊Q₈	—	2	4	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	—	2	2	no	—
278	C₄×D₄	—	2	4	no	—
279	C₄×D₄	—	2	4	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	—	2	2	no	—
284	#117	C₂³×C₁₃	1	4	yes	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	4	no	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
294	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
297	#107	—	2	4	no	—
298	#106	—	2	4	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	#102	—	2	4	no	—
302	#102	—	2	4	no	—
303	#100	—	2	4	no	—
304	#95	—	2	1	no	—
305	#95	—	2	1	no	—
306	#95	—	2	2	no	—
307	C₂×C₁₃	—	2	1	no	—
308	C₂×C₁₃	—	2	1	no	—
309	C₂×C₁₃	—	4	4	no	—
310	C₂×C₁₃	—	8	2	no	—
311	C₂×C₁₃	#2409	1	1	yes	characteristic
312	C₂×C₁₃	#3019	1	1	yes	characteristic
313	C₂×C₁₃	#3021	1	1	yes	characteristic
314	C₂⁴	—	2	1	no	—
315	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	8	4	no	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	8	2	no	—
327	C₂×D₄	—	8	2	no	—
328	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
329	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	complemented
330	C₂×D₄	C₁₃×#41	1	2	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	8	2	no	—
340	C₂²×C₄	—	8	2	no	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	4	no	—
347	C₂×C₈	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
357	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	8	2	no	—
364	C₂²⋊C₄	—	8	2	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	C₂×D₄×C₁₃	1	2	yes	—
369	C₄²	C₂×D₄×C₁₃	1	2	yes	—
370	C₄²	C₂×Q₈×C₁₃	1	2	yes	complemented
371	C₁₃	#24316	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	C₁₃×C₂²⋊Q₈	1	4	yes	—
382	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
383	Q₈	—	4	4	no	—
384	Q₈	—	8	2	no	—
385	Q₈	—	8	4	no	—
386	D₄	—	2	4	no	—
387	D₄	—	2	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	8	4	no	—
408	C₂×C₄	—	8	4	no	—
409	C₂×C₄	—	8	4	no	—
410	C₂×C₄	C₁₃×#120	1	2	yes	—
411	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
412	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
414	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
416	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
417	C₈	—	4	4	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
431	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
432	C₂²	C₁₃×#536	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	1	no	—
442	C₄	C₁₃×#548	1	2	yes	—
443	C₄	D₄×Q₈×C₁₃	1	2	yes	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	4	4	no	—
447	C₂	—	8	2	no	—
448	C₂	C₁₃×#2409	1	1	yes	characteristic
449	C₂	C₁₃×#3019	1	1	yes	characteristic
450	C₂	C₁₃×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
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
1. C₁₃×#3501	C₂	semidirect
2. C₁₃×#3077	C₂	semidirect
4. C₁₃×#2061	C₂	semidirect
5. C₁₃×#2027	C₂	semidirect
6. C₁₃×#1995	C₂	semidirect
8. C₁₃×#1856	C₂	semidirect
9. C₁₃×#1800	C₂	semidirect
45. C₁₃×C₄⋊Q₈	D₄	semidirect
46. C₁₃×C₄⋊Q₈	D₄	semidirect
48. C₁₃×#127	Q₈	semidirect
50. C₁₃×#125	D₄	semidirect
89. #24316	C₁₃	direct (N × H)
105. C₂×D₄×C₁₃	C₂×Q₈	semidirect
146. C₄²×C₁₃	C₂×Q₈	semidirect
147. #3501	C₂×C₁₃	semidirect
148. #3077	C₂×C₁₃	semidirect
150. #2061	C₂×C₁₃	semidirect
151. #2027	C₂×C₁₃	semidirect
152. #1995	C₂×C₁₃	semidirect
154. #1856	C₂×C₁₃	semidirect
155. #1800	C₂×C₁₃	semidirect
263. C₄⋊Q₈	D₄×C₁₃	semidirect
264. C₄⋊Q₈	D₄×C₁₃	semidirect
266. #127	Q₈×C₁₃	semidirect
268. #125	D₄×C₁₃	semidirect
329. C₂×D₄	C₂×Q₈×C₁₃	semidirect
370. C₄²	C₂×Q₈×C₁₃	semidirect
371. C₁₃	#24316	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×#3501	2
C₁₃×#3077	2
C₁₃×#2328	2
C₁₃×#2061	2
C₁₃×#2027	2
C₁₃×#1995	2
C₁₃×#1887	2
C₁₃×#1856	2
C₁₃×#1800	2
#24316	13

Subgroups — C13×#24316 #15710655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24316 #15710655