Subgroups — C₁₃×#24831 #15711170

Order 3328.

792 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2351	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2084	C₂	1	2	yes	maximal
6	C₁₃×#2066	C₂	1	2	yes	maximal
7	C₁₃×#1993	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1878	C₂	1	2	yes	maximal
10	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1803	C₂	1	2	yes	maximal
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#475	—	2	4	no	—
18	C₁₃×#441	—	2	4	no	—
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
28	C₁₃×#395	—	2	1	no	—
29	C₁₃×#395	—	2	1	no	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#389	—	2	2	no	—
32	C₁₃×#389	—	2	2	no	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#384	C₂²	1	2	yes	—
35	C₁₃×#382	—	2	1	no	—
36	C₁₃×#382	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×Q₁₆	—	2	2	no	—
47	C₂×C₁₃×Q₁₆	—	2	2	no	—
48	C₂×C₁₃×Q₁₆	Q₈	1	4	yes	complemented
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₄×Q₈×C₁₃	—	2	2	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	4	2	no	—
59	C₄×Q₈×C₁₃	D₄	1	4	yes	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#106	—	2	2	no	—
78	C₁₃×#106	—	2	4	no	—
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	4	2	no	—
81	C₁₃×#103	—	2	2	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×#103	—	4	2	no	—
85	C₁₃×#97	—	2	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	D₄	1	1	yes	characteristic
92	C₁₃×#95	D₄	1	1	yes	characteristic
93	#24831	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	—	4	2	no	—
103	C₂×Q₈×C₁₃	—	8	2	no	—
104	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
106	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
107	C₂×Q₈×C₁₃	#41	1	2	yes	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	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	—	2	1	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×Q₁₆	—	2	8	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	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
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	1	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	4	4	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	4	no	—
142	C₁₃×C₄⋊C₄	—	8	2	no	—
143	C₁₃×C₄⋊C₄	—	8	2	no	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
145	C₄²×C₁₃	—	2	4	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	4	4	no	—
149	C₄²×C₁₃	—	4	2	no	—
150	C₄²×C₁₃	C₂×D₄	1	2	yes	—
151	C₄²×C₁₃	#41	1	2	yes	—
152	C₂×#475	C₂×C₁₃	1	1	yes	characteristic
153	C₂×#441	C₂×C₁₃	1	1	yes	characteristic
154	#2567	C₂×C₁₃	1	1	yes	characteristic
155	#2351	C₂×C₁₃	1	1	yes	characteristic
156	#2084	C₂×C₁₃	1	2	yes	—
157	#2066	C₂×C₁₃	1	2	yes	—
158	#1993	C₂×C₁₃	1	1	yes	characteristic
159	#1940	C₂×C₁₃	1	1	yes	characteristic
160	#1878	C₂×C₁₃	1	2	yes	—
161	#1805	C₂×C₁₃	1	1	yes	characteristic
162	#1803	C₂×C₁₃	1	2	yes	—
163	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₃	—	2	2	no	—
165	Q₈×C₁₃	—	2	2	no	—
166	Q₈×C₁₃	—	2	2	no	—
167	Q₈×C₁₃	—	2	2	no	—
168	Q₈×C₁₃	—	2	2	no	—
169	Q₈×C₁₃	—	4	1	no	—
170	Q₈×C₁₃	—	4	1	no	—
171	Q₈×C₁₃	—	8	4	no	—
172	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
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	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	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	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	#121	1	2	yes	—
197	C₂×C₄×C₁₃	#121	1	2	yes	—
198	C₂×C₄×C₁₃	#137	1	4	yes	—
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	4	1	no	—
207	C₈×C₁₃	—	4	2	no	—
208	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
212	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
213	#475	—	2	4	no	—
214	#441	—	2	4	no	—
215	C₂×#106	C₂²×C₁₃	1	2	yes	—
216	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
219	C₂×#103	C₂²×C₁₃	1	2	yes	—
220	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#103	C₂²×C₁₃	1	2	yes	—
223	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
224	#395	—	2	1	no	—
225	#395	—	2	1	no	—
226	#391	C₂²×C₁₃	1	2	yes	—
227	#389	—	2	2	no	—
228	#389	—	2	2	no	—
229	#389	C₂²×C₁₃	1	2	yes	—
230	#384	C₂²×C₁₃	1	2	yes	—
231	#382	—	2	1	no	—
232	#382	C₂²×C₁₃	1	1	yes	characteristic
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
235	#340	C₂²×C₁₃	1	2	yes	—
236	#340	C₂²×C₁₃	1	2	yes	—
237	#340	C₂²×C₁₃	1	2	yes	—
238	#336	C₂²×C₁₃	1	2	yes	—
239	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
240	C₂²×C₁₃	#546	1	1	yes	characteristic
241	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×#137	1	2	yes	—
243	C₂²×C₁₃	#577	1	2	yes	—
244	C₄×C₁₃	—	2	4	no	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	2	4	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	8	1	no	—
252	C₄×C₁₃	—	8	2	no	—
253	C₄×C₁₃	—	8	2	no	—
254	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
255	C₄×C₁₃	#537	1	1	yes	characteristic
256	C₄×C₁₃	#552	1	1	yes	characteristic
257	C₄×C₁₃	#554	1	1	yes	characteristic
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
260	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	Q₈×C₁₃	1	4	yes	complemented
264	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₄⋊Q₈	—	2	2	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	4	2	no	—
274	C₄×Q₈	D₄×C₁₃	1	4	yes	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
292	#106	—	2	2	no	—
293	#106	—	2	4	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	4	2	no	—
296	#103	—	2	2	no	—
297	#103	—	2	4	no	—
298	#103	—	2	2	no	—
299	#103	—	4	2	no	—
300	#97	—	2	2	no	—
301	#95	—	2	1	no	—
302	#95	—	2	2	no	—
303	#95	—	2	1	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	D₄×C₁₃	1	1	yes	characteristic
307	#95	D₄×C₁₃	1	1	yes	characteristic
308	C₂×C₁₃	#2417	1	1	yes	characteristic
309	C₂×C₁₃	#3039	1	1	yes	characteristic
310	C₂×C₁₃	#3043	1	1	yes	characteristic
311	C₂×C₁₃	#3316	1	2	yes	—
312	C₂×C₁₃	#3387	1	2	yes	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	—	8	2	no	—
323	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
324	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
325	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
326	C₂×Q₈	C₁₃×#41	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
337	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
338	Q₁₆	—	2	8	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	8	2	no	—
362	C₄⋊C₄	—	8	2	no	—
363	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
364	C₄²	—	2	4	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	4	4	no	—
368	C₄²	—	4	2	no	—
369	C₄²	C₂×D₄×C₁₃	1	2	yes	—
370	C₄²	C₁₃×#41	1	2	yes	—
371	C₁₃	#24831	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
373	Q₈	—	2	2	no	—
374	Q₈	—	2	2	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	2	2	no	—
378	Q₈	—	4	1	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	8	4	no	—
381	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₁₃×#121	1	2	yes	—
406	C₂×C₄	C₁₃×#121	1	2	yes	—
407	C₂×C₄	C₁₃×#137	1	4	yes	—
408	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
410	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
411	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
412	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	2	no	—
417	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
418	C₂²	C₁₃×#546	1	1	yes	characteristic
419	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
420	C₂²	C₂×C₁₃×#137	1	2	yes	—
421	C₂²	C₁₃×#577	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	4	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	2	no	—
432	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
433	C₄	C₁₃×#537	1	1	yes	characteristic
434	C₄	C₁₃×#552	1	1	yes	characteristic
435	C₄	C₁₃×#554	1	1	yes	characteristic
436	C₂	C₁₃×#2417	1	1	yes	characteristic
437	C₂	C₁₃×#3039	1	1	yes	characteristic
438	C₂	C₁₃×#3043	1	1	yes	characteristic
439	C₂	C₁₃×#3316	1	2	yes	—
440	C₂	C₁₃×#3387	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
48. C₂×C₁₃×Q₁₆	Q₈	semidirect
93. #24831	C₁₃	direct (N × H)
263. C₂×Q₁₆	Q₈×C₁₃	semidirect
371. C₁₃	#24831	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×#475	2
C₂×C₁₃×#441	2
C₁₃×#2567	2
C₁₃×#2351	2
C₁₃×#2084	2
C₁₃×#2066	2
C₁₃×#1993	2
C₁₃×#1940	2
C₁₃×#1878	2
C₁₃×#1805	2
C₁₃×#1803	2
#24831	13

Subgroups — C13×#24831 #15711170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24831 #15711170