Subgroups — C₁₃×#19266 #15705605

Order 3328.

786 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×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic
4	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1666	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1665	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂²×C₁₃×SD₁₆	—	2	2	no	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₁₃×#492	—	2	1	no	—
16	C₁₃×#492	—	2	1	no	—
17	C₁₃×#492	C₂²	1	4	yes	—
18	C₁₃×#477	—	2	1	no	—
19	C₁₃×#476	—	2	1	no	—
20	C₁₃×#475	C₂²	1	2	yes	complemented
21	C₁₃×#474	C₂²	1	2	yes	complemented
22	C₁₃×#460	—	2	1	no	—
23	C₁₃×#460	C₂²	1	2	yes	—
24	C₁₃×#459	—	2	1	no	—
25	C₁₃×#459	C₂²	1	2	yes	—
26	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
27	C₈×D₄×C₁₃	—	2	2	no	—
28	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
29	C₁₃×#431	—	2	1	no	—
30	C₁₃×#431	C₂²	1	1	yes	characteristic
31	C₁₃×#428	—	2	1	no	—
32	C₁₃×#423	C₂²	1	1	yes	characteristic
33	C₁₃×#423	C₂²	1	1	yes	characteristic
34	C₁₃×#418	—	2	1	no	—
35	C₁₃×#417	—	2	1	no	—
36	C₂×C₄×C₈×C₁₃	—	2	1	no	—
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#334	C₂²	1	4	yes	complemented
39	C₁₃×#332	C₂²	1	4	yes	complemented
40	C₁₃×#331	C₂²	1	4	yes	—
41	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
42	C₂²×Q₈×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	1	no	—
46	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
47	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	4	no	—
49	C₂×C₁₃×SD₁₆	—	2	4	no	—
50	C₂×C₁₃×SD₁₆	—	4	8	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×M₁₆	—	2	1	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₃	D₄	1	2	yes	—
56	C₁₃×C₄⋊Q₈	—	2	1	no	—
57	C₁₃×C₄⋊Q₈	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	—	2	1	no	—
59	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₃×#127	—	2	1	no	—
61	C₁₃×#127	—	2	1	no	—
62	C₁₃×#127	—	2	1	no	—
63	C₁₃×#127	C₂³	1	2	yes	—
64	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₄×D₄×C₁₃	—	2	1	no	—
67	C₄×D₄×C₁₃	—	2	1	no	—
68	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
69	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×#117	—	2	1	no	—
71	C₁₃×#117	D₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₄²×C₁₃	—	2	1	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	—	2	2	no	—
77	C₁₃×#106	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	1	no	—
80	C₁₃×C₄⋊C₈	—	2	1	no	—
81	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
82	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
83	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#102	—	2	2	no	—
86	C₁₃×#102	—	2	2	no	—
87	C₁₃×#102	—	2	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	1	no	—
89	C₁₃×C₂²⋊C₈	—	2	2	no	—
90	C₄×C₈×C₁₃	—	2	2	no	—
91	C₄×C₈×C₁₃	—	2	1	no	—
92	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
93	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
94	C₄×C₈×C₁₃	C₂³	1	2	yes	—
95	#19266	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₃	—	4	1	no	—
97	C₁₃×#41	—	2	2	no	—
98	C₁₃×#41	SD₁₆	1	4	yes	complemented
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	4	4	no	—
101	C₂×Q₈×C₁₃	—	4	1	no	—
102	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	4	4	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂×D₄×C₁₃	—	4	1	no	—
110	C₂×D₄×C₁₃	—	4	1	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	—	8	2	no	—
114	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	4	1	no	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
122	C₁₃×SD₁₆	—	4	8	no	—
123	C₁₃×SD₁₆	—	4	4	no	—
124	C₁₃×SD₁₆	—	4	8	no	—
125	C₁₃×D₈	—	4	4	no	—
126	C₁₃×M₁₆	—	4	2	no	—
127	C₁₃×M₁₆	—	4	2	no	—
128	C₂×C₈×C₁₃	—	2	4	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	4	4	no	—
133	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	4	1	no	—
140	C₁₃×C₄⋊C₄	—	4	1	no	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
143	C₁₃×C₂²⋊C₄	—	2	1	no	—
144	C₁₃×C₂²⋊C₄	—	2	1	no	—
145	C₁₃×C₂²⋊C₄	—	2	1	no	—
146	C₄²×C₁₃	—	2	1	no	—
147	C₄²×C₁₃	—	2	1	no	—
148	C₄²×C₁₃	—	2	1	no	—
149	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₃	#41	1	1	yes	characteristic
152	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#3038	C₂×C₁₃	1	1	yes	characteristic
156	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1666	C₂×C₁₃	1	4	yes	complemented
158	#1665	C₂×C₁₃	1	4	yes	complemented
159	#1566	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1549	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#1545	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	—	8	2	no	—
165	C₂³×C₁₃	—	8	2	no	—
166	C₂³×C₁₃	—	8	2	no	—
167	C₂³×C₁₃	#121	1	1	yes	characteristic
168	Q₈×C₁₃	—	2	1	no	—
169	Q₈×C₁₃	—	4	4	no	—
170	Q₈×C₁₃	—	8	2	no	—
171	Q₈×C₁₃	C₂×SD₁₆	1	2	yes	complemented
172	D₄×C₁₃	—	2	4	no	—
173	D₄×C₁₃	—	2	1	no	—
174	D₄×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	4	4	no	—
177	D₄×C₁₃	—	8	2	no	—
178	D₄×C₁₃	—	8	2	no	—
179	D₄×C₁₃	—	8	2	no	—
180	D₄×C₁₃	—	8	2	no	—
181	D₄×C₁₃	C₂×SD₁₆	1	2	yes	complemented
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	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	—	8	2	no	—
192	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×SD₁₆	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	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	—	4	2	no	—
202	C₈×C₁₃	—	4	2	no	—
203	C₈×C₁₃	—	4	2	no	—
204	C₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
205	C₂×AGL(1,ℤ/8)	—	2	1	no	—
206	C₂²×SD₁₆	—	2	2	no	—
207	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
209	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
210	#492	—	2	1	no	—
211	#492	—	2	1	no	—
212	#492	C₂²×C₁₃	1	4	yes	—
213	#477	—	2	1	no	—
214	#476	—	2	1	no	—
215	#475	C₂²×C₁₃	1	2	yes	complemented
216	#474	C₂²×C₁₃	1	2	yes	complemented
217	#460	—	2	1	no	—
218	#460	C₂²×C₁₃	1	2	yes	—
219	#459	—	2	1	no	—
220	#459	C₂²×C₁₃	1	2	yes	—
221	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
222	C₈×D₄	—	2	2	no	—
223	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
224	#431	—	2	1	no	—
225	#431	C₂²×C₁₃	1	1	yes	characteristic
226	#428	—	2	1	no	—
227	#423	C₂²×C₁₃	1	1	yes	characteristic
228	#423	C₂²×C₁₃	1	1	yes	characteristic
229	#418	—	2	1	no	—
230	#417	—	2	1	no	—
231	C₂×C₄×C₈	—	2	1	no	—
232	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
233	#334	C₂²×C₁₃	1	4	yes	complemented
234	#332	C₂²×C₁₃	1	4	yes	complemented
235	#331	C₂²×C₁₃	1	4	yes	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	4	1	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	—	8	2	no	—
242	C₂²×C₁₃	—	8	2	no	—
243	C₂²×C₁₃	—	8	2	no	—
244	C₂²×C₁₃	—	16	4	no	—
245	C₂²×C₁₃	#465	1	2	yes	—
246	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	4	1	no	—
251	C₄×C₁₃	—	4	1	no	—
252	C₄×C₁₃	—	8	2	no	—
253	C₄×C₁₃	#465	1	2	yes	—
254	C₄×C₁₃	#471	1	2	yes	—
255	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
256	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
257	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
258	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	AGL(1,ℤ/8)	—	4	4	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×SD₁₆	—	2	4	no	—
266	C₂×SD₁₆	—	2	4	no	—
267	C₂×SD₁₆	—	4	8	no	—
268	C₂×D₈	—	2	2	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	D₄×C₁₃	1	2	yes	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
277	#127	—	2	1	no	—
278	#127	—	2	1	no	—
279	#127	—	2	1	no	—
280	#127	C₂³×C₁₃	1	2	yes	—
281	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
282	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
286	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
287	#117	—	2	1	no	—
288	#117	D₄×C₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	#106	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
299	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
300	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
301	#103	—	2	2	no	—
302	#102	—	2	2	no	—
303	#102	—	2	2	no	—
304	#102	—	2	2	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₄×C₈	—	2	2	no	—
308	C₄×C₈	—	2	1	no	—
309	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
310	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₁₃	1	2	yes	—
312	C₂×C₁₃	—	2	2	no	—
313	C₂×C₁₃	—	4	2	no	—
314	C₂×C₁₃	—	16	2	no	—
315	C₂×C₁₃	#3038	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#465	1	1	yes	characteristic
317	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
318	C₂⁴	—	4	1	no	—
319	#41	—	2	2	no	—
320	#41	C₁₃×SD₁₆	1	4	yes	complemented
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	4	no	—
323	C₂×Q₈	—	4	1	no	—
324	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	8	2	no	—
336	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
344	SD₁₆	—	4	8	no	—
345	SD₁₆	—	4	4	no	—
346	SD₁₆	—	4	8	no	—
347	D₈	—	4	4	no	—
348	M₁₆	—	4	2	no	—
349	M₁₆	—	4	2	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	4	no	—
355	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
356	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
364	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₄²	C₁₃×#41	1	1	yes	characteristic
374	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
375	C₁₃	#19266	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³	—	2	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	C₁₃×#121	1	1	yes	characteristic
382	Q₈	—	2	1	no	—
383	Q₈	—	4	4	no	—
384	Q₈	—	8	2	no	—
385	Q₈	C₂×C₁₃×SD₁₆	1	2	yes	complemented
386	D₄	—	2	4	no	—
387	D₄	—	2	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	4	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	C₂×C₁₃×SD₁₆	1	2	yes	complemented
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
407	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
408	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
409	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
410	C₂×C₄	C₁₃×#135	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	16	4	no	—
428	C₂²	C₁₃×#465	1	2	yes	—
429	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	8	2	no	—
436	C₄	C₁₃×#465	1	2	yes	—
437	C₄	C₁₃×#471	1	2	yes	—
438	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
439	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
440	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
441	C₂	—	2	2	no	—
442	C₂	—	4	2	no	—
443	C₂	—	16	2	no	—
444	C₂	C₁₃×#3038	1	1	yes	characteristic
445	C₂	C₂×C₁₃×#465	1	1	yes	characteristic
446	C₂	C₂×C₁₃×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3038	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#492	C₂	semidirect
2. C₁₃×#3079	C₂	semidirect
4. C₈×C₁₃×#41	C₂	semidirect
5. C₁₃×#1666	C₂	semidirect
6. C₁₃×#1665	C₂	semidirect
7. C₁₃×#1566	C₂	semidirect
8. C₁₃×#1549	C₂	semidirect
9. C₁₃×#1545	C₂	semidirect
20. C₁₃×#475	C₂²	semidirect
21. C₁₃×#474	C₂²	semidirect
26. C₈×Q₈×C₁₃	C₂²	semidirect
28. C₈×D₄×C₁₃	C₂²	semidirect
38. C₁₃×#334	C₂²	semidirect
39. C₁₃×#332	C₂²	semidirect
95. #19266	C₁₃	direct (N × H)
98. C₁₃×#41	SD₁₆	semidirect
153. C₂×#492	C₂×C₁₃	semidirect
154. #3079	C₂×C₁₃	semidirect
156. C₈×#41	C₂×C₁₃	semidirect
157. #1666	C₂×C₁₃	semidirect
158. #1665	C₂×C₁₃	semidirect
159. #1566	C₂×C₁₃	semidirect
160. #1549	C₂×C₁₃	semidirect
161. #1545	C₂×C₁₃	semidirect
171. Q₈×C₁₃	C₂×SD₁₆	semidirect
181. D₄×C₁₃	C₂×SD₁₆	semidirect
204. C₈×C₁₃	AGL(1,ℤ/8)	semidirect
215. #475	C₂²×C₁₃	semidirect
216. #474	C₂²×C₁₃	semidirect
221. C₈×Q₈	C₂²×C₁₃	semidirect
223. C₈×D₄	C₂²×C₁₃	semidirect
233. #334	C₂²×C₁₃	semidirect
234. #332	C₂²×C₁₃	semidirect
320. #41	C₁₃×SD₁₆	semidirect
375. C₁₃	#19266	direct (N × H)
385. Q₈	C₂×C₁₃×SD₁₆	semidirect
395. D₄	C₂×C₁₃×SD₁₆	semidirect
418. C₈	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#492	2
C₁₃×#3079	2
C₁₃×#3038	2
C₈×C₁₃×#41	2
C₁₃×#1666	2
C₁₃×#1665	2
C₁₃×#1566	2
C₁₃×#1549	2
C₁₃×#1545	2
#19266	13

Subgroups — C13×#19266 #15705605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19266 #15705605