Subgroups — C₁₃×#24693 #15711032

Order 3328.

828 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2073	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2054	C₂	1	2	yes	maximal
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1949	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#474	—	2	4	no	—
17	C₁₃×#442	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
27	C₁₃×#393	—	2	1	no	—
28	C₁₃×#393	—	2	1	no	—
29	C₁₃×#390	C₂²	1	2	yes	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#388	—	2	2	no	—
32	C₁₃×#382	C₂²	1	1	yes	characteristic
33	C₁₃×#382	C₂²	1	2	yes	—
34	C₁₃×#381	—	2	1	no	—
35	C₁₃×#380	—	2	2	no	—
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂×C₁₃×D₈	—	2	2	no	—
49	C₂×C₁₃×D₈	—	2	2	no	—
50	C₂×C₁₃×D₈	—	2	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₄×D₄×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	D₄	1	4	yes	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#107	—	2	4	no	—
76	C₁₃×#106	—	2	2	no	—
77	C₁₃×C₄⋊C₈	—	2	4	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×#102	—	2	2	no	—
80	C₁₃×#102	—	2	4	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×#102	—	2	2	no	—
83	C₁₃×#97	—	2	2	no	—
84	C₁₃×#95	—	2	1	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	D₄	1	1	yes	characteristic
90	C₁₃×#95	D₄	1	1	yes	characteristic
91	#24693	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	1	no	—
93	C₂⁴×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	4	2	no	—
95	C₂×Q₈×C₁₃	—	8	2	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₁₃	#41	1	2	yes	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	4	4	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	—	8	2	no	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
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×D₈	—	2	8	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	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	#41	1	2	yes	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	4	2	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
141	C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₁₃×C₂²⋊C₄	—	4	4	no	—
143	C₁₃×C₂²⋊C₄	—	4	2	no	—
144	C₁₃×C₂²⋊C₄	—	8	2	no	—
145	C₁₃×C₂²⋊C₄	—	8	2	no	—
146	C₁₃×C₂²⋊C₄	—	8	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	8	2	no	—
150	C₄²×C₁₃	C₂×D₄	1	2	yes	—
151	C₄²×C₁₃	#41	1	2	yes	—
152	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂×#442	C₂×C₁₃	1	1	yes	characteristic
154	#2563	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2357	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2073	C₂×C₁₃	1	2	yes	complemented
157	#2054	C₂×C₁₃	1	2	yes	—
158	#1993	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#1949	C₂×C₁₃	1	2	yes	complemented
160	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1925	C₂×C₁₃	1	2	yes	complemented
162	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	4	1	no	—
167	C₂³×C₁₃	—	4	1	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	—	4	2	no	—
172	C₂³×C₁₃	—	4	2	no	—
173	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₃	—	8	4	no	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	—	2	2	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	4	1	no	—
180	D₄×C₁₃	—	4	1	no	—
181	D₄×C₁₃	—	4	1	no	—
182	D₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	8	4	no	—
202	C₂×C₄×C₁₃	—	8	4	no	—
203	C₂×C₄×C₁₃	#121	1	2	yes	—
204	C₂×C₄×C₁₃	#121	1	2	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
211	C₈×C₁₃	—	2	2	no	—
212	C₈×C₁₃	—	4	2	no	—
213	C₈×C₁₃	—	4	1	no	—
214	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
218	#474	—	2	4	no	—
219	#442	—	2	4	no	—
220	C₂×#107	C₂²×C₁₃	1	2	yes	—
221	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#102	C₂²×C₁₃	1	2	yes	—
225	C₂×#102	C₂²×C₁₃	1	2	yes	—
226	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
229	#393	—	2	1	no	—
230	#393	—	2	1	no	—
231	#390	C₂²×C₁₃	1	2	yes	—
232	#390	C₂²×C₁₃	1	2	yes	—
233	#388	—	2	2	no	—
234	#382	C₂²×C₁₃	1	2	yes	—
235	#382	C₂²×C₁₃	1	1	yes	characteristic
236	#381	—	2	1	no	—
237	#380	—	2	2	no	—
238	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
239	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
240	C₄×C₂²⋊C₄	—	2	1	no	—
241	#340	C₂²×C₁₃	1	2	yes	—
242	#340	C₂²×C₁₃	1	2	yes	—
243	#340	C₂²×C₁₃	1	2	yes	—
244	#336	C₂²×C₁₃	1	2	yes	—
245	C₂²×C₁₃	—	4	4	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	—	8	2	no	—
252	C₂²×C₁₃	—	8	2	no	—
253	C₂²×C₁₃	—	8	1	no	—
254	C₂²×C₁₃	—	8	1	no	—
255	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
256	C₂²×C₁₃	#547	1	1	yes	characteristic
257	C₂²×C₁₃	#548	1	1	yes	characteristic
258	C₂²×C₁₃	#575	1	2	yes	—
259	C₂²×C₁₃	#576	1	2	yes	—
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	2	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	2	no	—
265	C₄×C₁₃	—	8	2	no	—
266	C₄×C₁₃	—	8	1	no	—
267	C₄×C₁₃	—	8	2	no	—
268	C₄×C₁₃	#525	1	1	yes	characteristic
269	C₄×C₁₃	#536	1	1	yes	characteristic
270	C₄×C₁₃	#552	1	1	yes	characteristic
271	C₄×C₁₃	#556	1	1	yes	characteristic
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
274	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	—	2	1	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	2	no	—
279	C₂×D₈	—	2	2	no	—
280	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄⋊Q₈	—	2	2	no	—
284	C₄⋊Q₈	—	2	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	D₄×C₁₃	1	4	yes	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
303	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
304	#107	—	2	4	no	—
305	#106	—	2	2	no	—
306	C₄⋊C₈	—	2	4	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	4	no	—
310	#102	—	2	4	no	—
311	#102	—	2	2	no	—
312	#97	—	2	2	no	—
313	#95	—	2	1	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	1	no	—
318	#95	D₄×C₁₃	1	1	yes	characteristic
319	#95	D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₁₃	—	8	2	no	—
321	C₂×C₁₃	—	8	2	no	—
322	C₂×C₁₃	#2415	1	1	yes	characteristic
323	C₂×C₁₃	#3040	1	1	yes	characteristic
324	C₂×C₁₃	#3041	1	1	yes	characteristic
325	C₂×C₁₃	#3347	1	2	yes	—
326	C₂×C₁₃	#3370	1	2	yes	—
327	C₂⁴	—	2	1	no	—
328	C₂⁴	—	2	1	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	8	2	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
342	C₂×D₄	C₁₃×#41	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	8	2	no	—
351	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
356	D₈	—	2	8	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	C₁₃×#41	1	2	yes	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	8	2	no	—
380	C₂²⋊C₄	—	8	2	no	—
381	C₂²⋊C₄	—	8	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	8	2	no	—
385	C₄²	C₂×D₄×C₁₃	1	2	yes	—
386	C₄²	C₁₃×#41	1	2	yes	—
387	C₁₃	#24693	1	1	yes	characteristic, direct product factor, Sylow
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
399	Q₈	—	8	4	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	1	no	—
405	D₄	—	4	1	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	8	4	no	—
427	C₂×C₄	—	8	4	no	—
428	C₂×C₄	C₁₃×#121	1	2	yes	—
429	C₂×C₄	C₁₃×#121	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
432	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
434	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
435	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
436	C₈	—	2	2	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
450	C₂²	C₁₃×#547	1	1	yes	characteristic
451	C₂²	C₁₃×#548	1	1	yes	characteristic
452	C₂²	C₁₃×#575	1	2	yes	—
453	C₂²	C₁₃×#576	1	2	yes	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	2	no	—
462	C₄	C₁₃×#525	1	1	yes	characteristic
463	C₄	C₁₃×#536	1	1	yes	characteristic
464	C₄	C₁₃×#552	1	1	yes	characteristic
465	C₄	C₁₃×#556	1	1	yes	characteristic
466	C₂	—	8	2	no	—
467	C₂	—	8	2	no	—
468	C₂	C₁₃×#2415	1	1	yes	characteristic
469	C₂	C₁₃×#3040	1	1	yes	characteristic
470	C₂	C₁₃×#3041	1	1	yes	characteristic
471	C₂	C₁₃×#3347	1	2	yes	—
472	C₂	C₁₃×#3370	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#474	C₂	semidirect
3. C₁₃×#2563	C₂	semidirect
4. C₁₃×#2357	C₂	semidirect
5. C₁₃×#2073	C₂	semidirect
7. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1949	C₂	semidirect
9. C₁₃×#1940	C₂	semidirect
10. C₁₃×#1925	C₂	semidirect
11. C₁₃×#1804	C₂	semidirect
91. #24693	C₁₃	direct (N × H)
152. C₂×#474	C₂×C₁₃	semidirect
154. #2563	C₂×C₁₃	semidirect
155. #2357	C₂×C₁₃	semidirect
156. #2073	C₂×C₁₃	semidirect
158. #1993	C₂×C₁₃	semidirect
159. #1949	C₂×C₁₃	semidirect
160. #1940	C₂×C₁₃	semidirect
161. #1925	C₂×C₁₃	semidirect
162. #1804	C₂×C₁₃	semidirect
387. C₁₃	#24693	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#474	2
C₂×C₁₃×#442	2
C₁₃×#2563	2
C₁₃×#2357	2
C₁₃×#2073	2
C₁₃×#2054	2
C₁₃×#1993	2
C₁₃×#1949	2
C₁₃×#1940	2
C₁₃×#1925	2
C₁₃×#1804	2
#24693	13

Subgroups — C13×#24693 #15711032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24693 #15711032