Subgroups — C₁₃×#26321 #15712660

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2548	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2092	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2073	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1926	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#124	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#394	—	2	2	no	—
25	C₁₃×#391	—	2	1	no	—
26	C₁₃×#390	—	2	1	no	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#387	—	2	2	no	—
30	C₁₃×#384	C₂²	1	1	yes	characteristic
31	C₁₃×#382	C₂²	1	2	yes	—
32	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₁₃×#340	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×#127	—	2	2	no	—
49	C₁₃×#127	—	2	2	no	—
50	C₁₃×#124	—	4	4	no	—
51	C₄×Q₈×C₁₃	—	2	2	no	—
52	C₄×Q₈×C₁₃	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
56	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₄²×C₁₃	—	2	1	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄²×C₁₃	—	2	2	no	—
69	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#107	—	4	2	no	—
72	C₁₃×#106	—	2	2	no	—
73	C₁₃×#106	—	2	2	no	—
74	C₁₃×C₄⋊C₈	—	2	2	no	—
75	C₁₃×#102	—	2	4	no	—
76	C₁₃×#102	—	2	4	no	—
77	C₁₃×#102	—	4	2	no	—
78	C₁₃×#102	—	4	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	1	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	2	no	—
85	#26321	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	4	2	no	—
97	C₂×D₄×C₁₃	—	4	2	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	8	1	no	—
101	C₂×D₄×C₁₃	—	8	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	#41	1	2	yes	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₄⋊C₄	—	8	1	no	—
134	C₁₃×C₄⋊C₄	#41	1	2	yes	—
135	C₁₃×C₂²⋊C₄	—	4	4	no	—
136	C₁₃×C₂²⋊C₄	—	4	4	no	—
137	C₁₃×C₂²⋊C₄	—	8	2	no	—
138	C₁₃×C₂²⋊C₄	—	8	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	4	2	no	—
142	C₄²×C₁₃	—	4	2	no	—
143	C₄²×C₁₃	—	8	2	no	—
144	C₄²×C₁₃	#41	1	2	yes	—
145	C₄²×C₁₃	#41	1	2	yes	—
146	#2548	C₂×C₁₃	1	1	yes	characteristic
147	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2092	C₂×C₁₃	1	2	yes	complemented
149	#2073	C₂×C₁₃	1	2	yes	complemented
150	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1982	C₂×C₁₃	1	1	yes	characteristic
152	#1957	C₂×C₁₃	1	1	yes	characteristic
153	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1926	C₂×C₁₃	1	2	yes	complemented
155	#1925	C₂×C₁₃	1	2	yes	complemented
156	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	—	4	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	2	no	—
164	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₃	—	4	4	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	4	2	no	—
168	D₄×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	8	4	no	—
171	D₄×C₁₃	—	8	4	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	#123	1	2	yes	—
196	C₂×C₄×C₁₃	#123	1	2	yes	—
197	C₂×C₄×C₁₃	#135	1	2	yes	—
198	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	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	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#124	—	2	1	no	—
210	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#107	C₂²×C₁₃	1	2	yes	—
212	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#102	C₂²×C₁₃	1	2	yes	—
216	C₂×#102	C₂²×C₁₃	1	2	yes	—
217	C₂×#102	C₂²×C₁₃	1	2	yes	—
218	C₂×#102	C₂²×C₁₃	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
220	#394	—	2	2	no	—
221	#391	—	2	1	no	—
222	#390	—	2	1	no	—
223	#390	C₂²×C₁₃	1	2	yes	—
224	#390	C₂²×C₁₃	1	2	yes	—
225	#387	—	2	2	no	—
226	#384	C₂²×C₁₃	1	1	yes	characteristic
227	#382	C₂²×C₁₃	1	2	yes	—
228	C₄×C₄⋊C₄	—	2	1	no	—
229	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
230	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
231	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
232	#340	C₂²×C₁₃	1	1	yes	characteristic
233	#340	C₂²×C₁₃	1	2	yes	—
234	#340	C₂²×C₁₃	1	1	yes	characteristic
235	#336	C₂²×C₁₃	1	2	yes	—
236	#336	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	—	8	2	no	—
240	C₂²×C₁₃	—	8	2	no	—
241	C₂²×C₁₃	—	8	2	no	—
242	C₂²×C₁₃	—	8	2	no	—
243	C₂²×C₁₃	—	8	2	no	—
244	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
245	C₂²×C₁₃	#548	1	1	yes	characteristic
246	C₂²×C₁₃	#550	1	1	yes	characteristic
247	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂²×C₁₃	#576	1	1	yes	characteristic
250	C₂²×C₁₃	#577	1	1	yes	characteristic
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	—	8	1	no	—
256	C₄×C₁₃	—	8	1	no	—
257	C₄×C₁₃	—	8	1	no	—
258	C₄×C₁₃	—	8	2	no	—
259	C₄×C₁₃	#482	1	4	yes	—
260	C₄×C₁₃	#529	1	1	yes	characteristic
261	C₄×C₁₃	#542	1	1	yes	characteristic
262	C₄×C₁₃	#556	1	1	yes	characteristic
263	C₄×C₁₃	#559	1	1	yes	characteristic
264	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
268	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	#127	—	2	2	no	—
272	#127	—	2	2	no	—
273	#124	—	4	4	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
293	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
294	#107	—	4	2	no	—
295	#106	—	2	2	no	—
296	#106	—	2	2	no	—
297	C₄⋊C₈	—	2	2	no	—
298	#102	—	2	4	no	—
299	#102	—	2	4	no	—
300	#102	—	4	2	no	—
301	#102	—	4	2	no	—
302	C₄×C₈	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	1	no	—
305	#95	—	2	2	no	—
306	#95	—	2	1	no	—
307	#95	—	2	2	no	—
308	C₂×C₁₃	—	16	2	no	—
309	C₂×C₁₃	#2448	1	1	yes	characteristic
310	C₂×C₁₃	C₂×#482	1	1	yes	characteristic
311	C₂×C₁₃	#3096	1	1	yes	characteristic
312	C₂×C₁₃	#3361	1	1	yes	characteristic
313	C₂×C₁₃	#3368	1	1	yes	characteristic
314	C₂×C₁₃	#3394	1	1	yes	characteristic
315	C₂×C₁₃	#3399	1	1	yes	characteristic
316	C₂⁴	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	—	8	1	no	—
331	C₂×D₄	—	8	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	C₁₃×#41	1	2	yes	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	8	1	no	—
364	C₄⋊C₄	C₁₃×#41	1	2	yes	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	4	2	no	—
372	C₄²	—	4	2	no	—
373	C₄²	—	8	2	no	—
374	C₄²	C₁₃×#41	1	2	yes	—
375	C₄²	C₁₃×#41	1	2	yes	—
376	C₁₃	#26321	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
385	Q₈	—	4	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	8	4	no	—
391	D₄	—	8	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	C₁₃×#123	1	2	yes	—
416	C₂×C₄	C₁₃×#123	1	2	yes	—
417	C₂×C₄	C₁₃×#135	1	2	yes	—
418	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
419	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
422	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
423	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
436	C₂²	C₁₃×#548	1	1	yes	characteristic
437	C₂²	C₁₃×#550	1	1	yes	characteristic
438	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
439	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
440	C₂²	C₁₃×#576	1	1	yes	characteristic
441	C₂²	C₁₃×#577	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	2	no	—
450	C₄	C₁₃×#482	1	4	yes	—
451	C₄	C₁₃×#529	1	1	yes	characteristic
452	C₄	C₁₃×#542	1	1	yes	characteristic
453	C₄	C₁₃×#556	1	1	yes	characteristic
454	C₄	C₁₃×#559	1	1	yes	characteristic
455	C₂	—	16	2	no	—
456	C₂	C₁₃×#2448	1	1	yes	characteristic
457	C₂	C₂×C₁₃×#482	1	1	yes	characteristic
458	C₂	C₁₃×#3096	1	1	yes	characteristic
459	C₂	C₁₃×#3361	1	1	yes	characteristic
460	C₂	C₁₃×#3368	1	1	yes	characteristic
461	C₂	C₁₃×#3394	1	1	yes	characteristic
462	C₂	C₁₃×#3399	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2355	C₂	semidirect
3. C₁₃×#2092	C₂	semidirect
4. C₁₃×#2073	C₂	semidirect
5. C₁₃×#1984	C₂	semidirect
8. C₁₃×#1947	C₂	semidirect
9. C₁₃×#1926	C₂	semidirect
10. C₁₃×#1925	C₂	semidirect
11. C₄×C₁₃×#106	C₂	semidirect
85. #26321	C₁₃	direct (N × H)
147. #2355	C₂×C₁₃	semidirect
148. #2092	C₂×C₁₃	semidirect
149. #2073	C₂×C₁₃	semidirect
150. #1984	C₂×C₁₃	semidirect
153. #1947	C₂×C₁₃	semidirect
154. #1926	C₂×C₁₃	semidirect
155. #1925	C₂×C₁₃	semidirect
156. C₄×#106	C₂×C₁₃	semidirect
376. C₁₃	#26321	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×#2548	2
C₁₃×#2355	2
C₁₃×#2092	2
C₁₃×#2073	2
C₁₃×#1984	2
C₁₃×#1982	2
C₁₃×#1957	2
C₁₃×#1947	2
C₁₃×#1926	2
C₁₃×#1925	2
C₄×C₁₃×#106	2
#26321	13

Subgroups — C13×#26321 #15712660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26321 #15712660