Subgroups — C₁₃×#26255 #15712594

Order 3328.

814 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2446	C₂	1	2	yes	maximal
4	C₁₃×#2056	C₂	1	2	yes	maximal
5	C₁₃×#2043	C₂	1	2	yes	maximal
6	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1878	C₂	1	2	yes	maximal
11	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#494	—	2	4	no	—
18	C₄×C₁₃×Q₁₆	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#400	—	2	2	no	—
30	C₁₃×#398	—	2	2	no	—
31	C₁₃×#391	C₂²	1	2	yes	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#391	C₂²	1	2	yes	—
34	C₁₃×#389	C₂²	1	2	yes	—
35	C₁₃×#387	—	2	2	no	—
36	C₁₃×#387	—	2	2	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
43	C₂×C₁₃×Q₁₆	—	2	4	no	—
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	—	2	2	no	—
46	C₂×C₁₃×Q₁₆	—	2	2	no	—
47	C₂×C₁₃×Q₁₆	—	2	4	no	—
48	C₂×C₁₃×Q₁₆	—	2	2	no	—
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂×C₁₃×Q₁₆	—	4	2	no	—
51	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×C₄⋊Q₈	—	2	4	no	—
57	C₁₃×C₄⋊Q₈	—	4	2	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	4	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₃	—	2	2	no	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×#107	—	2	2	no	—
73	C₁₃×#107	—	2	2	no	—
74	C₁₃×C₄⋊C₈	—	2	2	no	—
75	C₁₃×#103	—	2	4	no	—
76	C₁₃×#103	—	4	2	no	—
77	C₁₃×#103	—	4	2	no	—
78	C₁₃×#103	—	4	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	D₄	1	1	yes	characteristic
90	C₁₃×#95	D₄	1	1	yes	characteristic
91	#26255	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	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	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×Q₁₆	—	2	8	no	—
116	C₁₃×Q₁₆	—	4	8	no	—
117	C₁₃×Q₁₆	—	4	4	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	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	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₁₃	#41	1	2	yes	—
128	C₂×C₈×C₁₃	#41	1	2	yes	—
129	C₂×C₈×C₁₃	#41	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	4	4	no	—
136	C₁₃×C₄⋊C₄	—	4	4	no	—
137	C₁₃×C₄⋊C₄	—	4	4	no	—
138	C₁₃×C₄⋊C₄	—	4	4	no	—
139	C₁₃×C₄⋊C₄	Q₁₆	1	4	yes	complemented
140	C₄²×C₁₃	—	2	1	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	2	1	no	—
146	C₄²×C₁₃	—	4	4	no	—
147	C₂×#494	C₂×C₁₃	1	1	yes	characteristic
148	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
149	#2446	C₂×C₁₃	1	2	yes	—
150	#2056	C₂×C₁₃	1	2	yes	—
151	#2043	C₂×C₁₃	1	2	yes	—
152	#1969	C₂×C₁₃	1	1	yes	characteristic
153	#1969	C₂×C₁₃	1	1	yes	characteristic
154	#1969	C₂×C₁₃	1	1	yes	characteristic
155	#1942	C₂×C₁₃	1	1	yes	characteristic
156	#1878	C₂×C₁₃	1	2	yes	—
157	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
158	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₁₃	—	2	4	no	—
160	Q₈×C₁₃	—	2	4	no	—
161	Q₈×C₁₃	—	4	2	no	—
162	Q₈×C₁₃	—	4	2	no	—
163	Q₈×C₁₃	—	4	2	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	Q₈×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	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	C₂×Q₁₆	1	2	yes	—
194	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
195	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
196	C₂×C₄×C₁₃	#135	1	2	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	—	4	1	no	—
205	C₈×C₁₃	—	4	1	no	—
206	C₈×C₁₃	#123	1	4	yes	—
207	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
208	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
209	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
212	#494	—	2	4	no	—
213	C₄×Q₁₆	—	2	4	no	—
214	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#103	C₂²×C₁₃	1	2	yes	—
218	C₂×#103	C₂²×C₁₃	1	2	yes	—
219	C₂×#103	C₂²×C₁₃	1	2	yes	—
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
224	#400	—	2	2	no	—
225	#398	—	2	2	no	—
226	#391	C₂²×C₁₃	1	2	yes	—
227	#391	C₂²×C₁₃	1	2	yes	—
228	#391	C₂²×C₁₃	1	2	yes	—
229	#389	C₂²×C₁₃	1	2	yes	—
230	#387	—	2	2	no	—
231	#387	—	2	2	no	—
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	#340	C₂²×C₁₃	1	2	yes	—
234	#336	C₂²×C₁₃	1	1	yes	characteristic
235	#336	C₂²×C₁₃	1	1	yes	characteristic
236	C₂²×C₁₃	#532	1	1	yes	characteristic
237	C₂²×C₁₃	D₄²	1	1	yes	characteristic
238	C₂²×C₁₃	#550	1	1	yes	characteristic
239	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
240	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
241	C₂²×C₁₃	#578	1	1	yes	characteristic
242	C₂²×C₁₃	#578	1	1	yes	characteristic
243	C₄×C₁₃	—	2	2	no	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	2	2	no	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	4	1	no	—
248	C₄×C₁₃	—	4	4	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	—	8	2	no	—
252	C₄×C₁₃	—	8	2	no	—
253	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
254	C₄×C₁₃	#540	1	1	yes	characteristic
255	C₄×C₁₃	#546	1	1	yes	characteristic
256	C₄×C₁₃	#559	1	1	yes	characteristic
257	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
258	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
259	C₂×Q₁₆	—	2	4	no	—
260	C₂×Q₁₆	—	2	2	no	—
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	—	2	4	no	—
264	C₂×Q₁₆	—	2	2	no	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×Q₁₆	—	4	2	no	—
267	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
268	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₄⋊Q₈	—	2	4	no	—
273	C₄⋊Q₈	—	4	2	no	—
274	C₄×Q₈	—	2	4	no	—
275	C₄×Q₈	—	4	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	#107	—	2	2	no	—
289	#107	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	#103	—	2	4	no	—
292	#103	—	4	2	no	—
293	#103	—	4	2	no	—
294	#103	—	4	2	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	D₄×C₁₃	1	1	yes	characteristic
306	#95	D₄×C₁₃	1	1	yes	characteristic
307	C₂×C₁₃	#2445	1	1	yes	characteristic
308	C₂×C₁₃	#3170	1	1	yes	characteristic
309	C₂×C₁₃	#3177	1	1	yes	characteristic
310	C₂×C₁₃	#3285	1	1	yes	characteristic
311	C₂×C₁₃	D₄×Q₁₆	1	1	yes	characteristic
312	C₂×C₁₃	#3393	1	1	yes	characteristic
313	C₂×C₁₃	#3395	1	1	yes	characteristic
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
337	Q₁₆	—	2	8	no	—
338	Q₁₆	—	4	8	no	—
339	Q₁₆	—	4	4	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
349	C₂×C₈	C₁₃×#41	1	2	yes	—
350	C₂×C₈	C₁₃×#41	1	2	yes	—
351	C₂×C₈	C₁₃×#41	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	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	4	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	C₁₃×Q₁₆	1	4	yes	complemented
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	4	4	no	—
369	C₁₃	#26255	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
371	Q₈	—	2	4	no	—
372	Q₈	—	2	4	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	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	C₂×C₁₃×Q₁₆	1	2	yes	—
406	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
407	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
408	C₂×C₄	C₁₃×#135	1	2	yes	—
409	C₂×C₄	C₂²×D₄×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	C₂×C₁₃×#41	1	1	yes	characteristic
413	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	C₁₃×#123	1	4	yes	—
419	C₂²	C₁₃×#532	1	1	yes	characteristic
420	C₂²	D₄²×C₁₃	1	1	yes	characteristic
421	C₂²	C₁₃×#550	1	1	yes	characteristic
422	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
423	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
424	C₂²	C₁₃×#578	1	1	yes	characteristic
425	C₂²	C₁₃×#578	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	—	8	2	no	—
436	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
437	C₄	C₁₃×#540	1	1	yes	characteristic
438	C₄	C₁₃×#546	1	1	yes	characteristic
439	C₄	C₁₃×#559	1	1	yes	characteristic
440	C₂	C₁₃×#2445	1	1	yes	characteristic
441	C₂	C₁₃×#3170	1	1	yes	characteristic
442	C₂	C₁₃×#3177	1	1	yes	characteristic
443	C₂	C₁₃×#3285	1	1	yes	characteristic
444	C₂	D₄×C₁₃×Q₁₆	1	1	yes	characteristic
445	C₂	C₁₃×#3393	1	1	yes	characteristic
446	C₂	C₁₃×#3395	1	1	yes	characteristic

	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
91. #26255	C₁₃	direct (N × H)
139. C₁₃×C₄⋊C₄	Q₁₆	semidirect
361. C₄⋊C₄	C₁₃×Q₁₆	semidirect
369. C₁₃	#26255	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×#494	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2446	2
C₁₃×#2056	2
C₁₃×#2043	2
C₁₃×#1969	2
C₁₃×#1942	2
C₁₃×#1878	2
C₈×C₁₃×C₄⋊C₄	2
#26255	13

Subgroups — C13×#26255 #15712594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26255 #15712594