Subgroups — C₁₃×#24483 #15710822

Order 3328.

984 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2436	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2345	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1983	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#124	C₂²	1	2	yes	—
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₁₃×#481	—	2	4	no	—
18	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×#103	—	2	4	no	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₃×#393	—	2	2	no	—
31	C₁₃×#391	C₂²	1	2	yes	—
32	C₁₃×#389	C₂²	1	2	yes	—
33	C₁₃×#387	—	2	2	no	—
34	C₁₃×#386	—	2	1	no	—
35	C₁₃×#386	—	2	1	no	—
36	C₁₃×#380	—	2	1	no	—
37	C₁₃×#380	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	—	2	4	no	—
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	4	2	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₃	—	4	2	no	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
59	C₁₃×#124	—	2	4	no	—
60	C₁₃×#124	—	4	2	no	—
61	C₁₃×#121	—	2	2	no	—
62	C₁₃×#121	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	—	2	2	no	—
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₁₃×#106	—	2	2	no	—
80	C₁₃×#106	—	2	2	no	—
81	C₁₃×C₄⋊C₈	—	4	2	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	2	4	no	—
85	C₁₃×#103	—	4	2	no	—
86	C₁₃×#102	—	2	2	no	—
87	C₁₃×#102	—	2	2	no	—
88	C₁₃×#102	—	4	2	no	—
89	C₁₃×C₂²⋊C₈	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	2	no	—
94	C₁₃×#95	—	2	2	no	—
95	C₁₃×#95	D₄	1	2	yes	—
96	#24483	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	1	no	—
98	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	8	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	4	4	no	—
106	C₂×Q₈×C₁₃	—	4	8	no	—
107	C₂×Q₈×C₁₃	—	4	4	no	—
108	C₂×Q₈×C₁₃	—	4	2	no	—
109	C₂×Q₈×C₁₃	#41	1	4	yes	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	4	2	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	4	4	no	—
126	C₂²×C₄×C₁₃	—	4	2	no	—
127	C₂²×C₄×C₁₃	—	8	2	no	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	#41	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	4	4	no	—
142	C₁₃×C₄⋊C₄	—	2	4	no	—
143	C₁₃×C₄⋊C₄	—	2	1	no	—
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	8	2	no	—
150	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
152	C₁₃×C₂²⋊C₄	—	2	2	no	—
153	C₁₃×C₂²⋊C₄	—	2	2	no	—
154	C₁₃×C₂²⋊C₄	—	4	4	no	—
155	C₁₃×C₂²⋊C₄	—	4	4	no	—
156	C₁₃×C₂²⋊C₄	—	4	2	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	—	8	2	no	—
161	C₂×#481	C₂×C₁₃	1	1	yes	characteristic
162	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#2436	C₂×C₁₃	1	1	yes	characteristic
164	#2345	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#2066	C₂×C₁₃	1	2	yes	complemented
166	#2042	C₂×C₁₃	1	2	yes	complemented
167	#1983	C₂×C₁₃	1	2	yes	complemented
168	#1927	C₂×C₁₃	1	2	yes	complemented
169	#1893	C₂×C₁₃	1	1	yes	characteristic
170	#1850	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	#121	1	2	yes	—
180	C₂³×C₁₃	#135	1	2	yes	—
181	C₂³×C₁₃	#137	1	2	yes	—
182	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₃	—	2	4	no	—
184	Q₈×C₁₃	—	2	4	no	—
185	Q₈×C₁₃	—	4	8	no	—
186	Q₈×C₁₃	—	4	2	no	—
187	Q₈×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	4	1	no	—
189	D₄×C₁₃	—	4	1	no	—
190	D₄×C₁₃	—	4	2	no	—
191	D₄×C₁₃	—	8	4	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	4	8	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	8	4	no	—
217	C₂×C₄×C₁₃	#121	1	2	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
222	C₈×C₁₃	—	4	1	no	—
223	C₈×C₁₃	—	4	1	no	—
224	C₈×C₁₃	—	4	2	no	—
225	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#124	C₂²×C₁₃	1	2	yes	—
228	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
230	#481	—	2	4	no	—
231	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
234	C₂×#103	—	2	4	no	—
235	C₂×#103	C₂²×C₁₃	1	2	yes	—
236	C₂×#103	C₂²×C₁₃	1	2	yes	—
237	C₂×#103	C₂²×C₁₃	1	2	yes	—
238	C₂×#103	C₂²×C₁₃	1	2	yes	—
239	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#102	C₂²×C₁₃	1	2	yes	—
242	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
243	#393	—	2	2	no	—
244	#391	C₂²×C₁₃	1	2	yes	—
245	#389	C₂²×C₁₃	1	2	yes	—
246	#387	—	2	2	no	—
247	#386	—	2	1	no	—
248	#386	—	2	1	no	—
249	#380	—	2	1	no	—
250	#380	C₂²×C₁₃	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
252	C₄×C₂²⋊C₄	—	2	1	no	—
253	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
254	#340	C₂²×C₁₃	1	2	yes	—
255	#336	C₂²×C₁₃	1	2	yes	—
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	2	2	no	—
258	C₂²×C₁₃	—	2	4	no	—
259	C₂²×C₁₃	—	2	4	no	—
260	C₂²×C₁₃	—	8	1	no	—
261	C₂²×C₁₃	—	8	1	no	—
262	C₂²×C₁₃	—	8	1	no	—
263	C₂²×C₁₃	—	8	2	no	—
264	C₂²×C₁₃	—	8	2	no	—
265	C₂²×C₁₃	#464	1	4	yes	—
266	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
267	C₂²×C₁₃	#546	1	2	yes	—
268	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
269	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
270	C₂²×C₁₃	#577	1	2	yes	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	4	4	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	4	2	no	—
275	C₄×C₁₃	—	4	2	no	—
276	C₄×C₁₃	—	4	2	no	—
277	C₄×C₁₃	—	8	1	no	—
278	C₄×C₁₃	—	8	2	no	—
279	C₄×C₁₃	#525	1	1	yes	characteristic
280	C₄×C₁₃	#535	1	1	yes	characteristic
281	C₄×C₁₃	#551	1	2	yes	—
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	—	2	4	no	—
284	C₂²×Q₈	—	2	2	no	—
285	C₂²×Q₈	—	2	2	no	—
286	C₂²×Q₈	—	4	2	no	—
287	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂³×C₄	—	2	1	no	—
292	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	4	2	no	—
295	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
296	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
298	#124	—	2	4	no	—
299	#124	—	4	2	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
318	#106	—	2	2	no	—
319	#106	—	2	2	no	—
320	C₄⋊C₈	—	4	2	no	—
321	#103	—	2	4	no	—
322	#103	—	2	4	no	—
323	#103	—	2	4	no	—
324	#103	—	4	2	no	—
325	#102	—	2	2	no	—
326	#102	—	2	2	no	—
327	#102	—	4	2	no	—
328	C₂²⋊C₈	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	1	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	D₄×C₁₃	1	2	yes	—
335	C₂×C₁₃	—	2	4	no	—
336	C₂×C₁₃	—	16	1	no	—
337	C₂×C₁₃	#2411	1	1	yes	characteristic
338	C₂×C₁₃	C₂×#464	1	1	yes	characteristic
339	C₂×C₁₃	#3042	1	1	yes	characteristic
340	C₂×C₁₃	#3301	1	2	yes	—
341	C₂×C₁₃	#3316	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	8	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	4	4	no	—
351	C₂×Q₈	—	4	8	no	—
352	C₂×Q₈	—	4	4	no	—
353	C₂×Q₈	—	4	2	no	—
354	C₂×Q₈	C₁₃×#41	1	4	yes	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	8	2	no	—
373	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
377	C₂²×C₄	C₁₃×#41	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	4	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	8	2	no	—
395	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
396	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	8	2	no	—
406	C₁₃	#24483	1	1	yes	characteristic, direct product factor, Sylow
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	2	no	—
414	C₂³	C₁₃×#121	1	2	yes	—
415	C₂³	C₁₃×#135	1	2	yes	—
416	C₂³	C₁₃×#137	1	2	yes	—
417	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	Q₈	—	2	4	no	—
419	Q₈	—	2	4	no	—
420	Q₈	—	4	8	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	2	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	2	no	—
426	D₄	—	8	4	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	8	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	4	no	—
452	C₂×C₄	C₁₃×#121	1	2	yes	—
453	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
455	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
456	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
457	C₈	—	4	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	1	no	—
469	C₂²	C₁₃×#464	1	4	yes	—
470	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
471	C₂²	C₁₃×#546	1	2	yes	—
472	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
473	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
474	C₂²	C₁₃×#577	1	2	yes	—
475	C₄	—	2	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	4	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	2	no	—
483	C₄	C₁₃×#525	1	1	yes	characteristic
484	C₄	C₁₃×#535	1	1	yes	characteristic
485	C₄	C₁₃×#551	1	2	yes	—
486	C₂	—	2	4	no	—
487	C₂	—	16	1	no	—
488	C₂	C₁₃×#2411	1	1	yes	characteristic
489	C₂	C₂×C₁₃×#464	1	1	yes	characteristic
490	C₂	C₁₃×#3042	1	1	yes	characteristic
491	C₂	C₁₃×#3301	1	2	yes	—
492	C₂	C₁₃×#3316	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×#103	C₂	semidirect
4. C₁₃×#2345	C₂	semidirect
5. C₁₃×#2066	C₂	semidirect
6. C₁₃×#2042	C₂	semidirect
7. C₁₃×#1983	C₂	semidirect
8. C₁₃×#1927	C₂	semidirect
10. C₁₃×#1850	C₂	semidirect
11. C₁₃×#1787	C₂	semidirect
96. #24483	C₁₃	direct (N × H)
162. C₂²×#103	C₂×C₁₃	semidirect
164. #2345	C₂×C₁₃	semidirect
165. #2066	C₂×C₁₃	semidirect
166. #2042	C₂×C₁₃	semidirect
167. #1983	C₂×C₁₃	semidirect
168. #1927	C₂×C₁₃	semidirect
170. #1850	C₂×C₁₃	semidirect
171. #1787	C₂×C₁₃	semidirect
406. C₁₃	#24483	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×#481	2
C₂²×C₁₃×#103	2
C₁₃×#2436	2
C₁₃×#2345	2
C₁₃×#2066	2
C₁₃×#2042	2
C₁₃×#1983	2
C₁₃×#1927	2
C₁₃×#1893	2
C₁₃×#1850	2
C₁₃×#1787	2
#24483	13

Subgroups — C13×#24483 #15710822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24483 #15710822