Subgroups — C₁₃×#23647 #15709986

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2896	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2879	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2079	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2078	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#343	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1738	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₁₃×#428	—	2	2	no	—
18	C₁₃×#428	—	2	2	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
21	C₁₃×#419	—	2	1	no	—
22	C₁₃×#418	—	2	1	no	—
23	C₁₃×#417	—	2	2	no	—
24	C₁₃×#417	C₂²	1	2	yes	—
25	C₁₃×#417	C₂²	1	4	yes	—
26	C₁₃×#417	C₂²	1	2	yes	—
27	C₁₃×#416	—	2	2	no	—
28	C₂×C₁₃×#103	—	2	1	no	—
29	C₂×C₁₃×#102	—	2	1	no	—
30	C₁₃×#408	—	2	2	no	—
31	C₁₃×#408	C₂²	1	4	yes	—
32	C₁₃×#407	—	2	2	no	—
33	C₁₃×#343	C₂²	1	4	yes	complemented
34	C₁₃×#343	C₂²	1	2	yes	complemented
35	C₁₃×#343	C₂²	1	2	yes	complemented
36	C₁₃×#341	C₂²	1	4	yes	complemented
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₂×C₁₃×#41	—	2	1	no	—
39	C₂×C₁₃×#41	—	2	2	no	—
40	C₂×C₁₃×#41	—	2	2	no	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂×C₁₃×#41	D₄	1	2	yes	—
44	C₂×C₁₃×#41	C₂³	1	2	yes	—
45	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	1	no	—
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	2	no	—
58	C₂×C₁₃×M₁₆	—	2	2	no	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
63	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
64	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
65	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
66	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₃	—	2	1	no	—
68	C₂²×C₈×C₁₃	—	2	1	no	—
69	C₂²×C₈×C₁₃	—	2	1	no	—
70	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
71	C₁₃×#117	—	2	1	no	—
72	C₁₃×#117	—	2	1	no	—
73	C₁₃×#117	—	2	1	no	—
74	C₁₃×#117	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₁₃×#107	—	2	4	no	—
86	C₁₃×#106	—	2	4	no	—
87	C₁₃×#103	—	2	4	no	—
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#103	—	2	2	no	—
90	C₁₃×#102	—	2	4	no	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×C₂²⋊C₈	—	2	8	no	—
94	#23647	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	1	no	—
96	C₂⁴×C₁₃	#41	1	1	yes	characteristic
97	C₁₃×#41	—	2	4	no	—
98	C₁₃×#41	—	2	4	no	—
99	C₁₃×#41	—	2	2	no	—
100	C₁₃×#41	—	2	2	no	—
101	C₁₃×#41	—	2	2	no	—
102	C₁₃×#41	—	2	2	no	—
103	C₁₃×#41	—	4	2	no	—
104	C₁₃×#41	—	4	2	no	—
105	C₁₃×#41	—	4	2	no	—
106	C₁₃×#41	—	4	2	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	4	2	no	—
117	C₂×D₄×C₁₃	—	4	2	no	—
118	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	4	2	no	—
126	C₂²×C₄×C₁₃	—	4	2	no	—
127	C₂²×C₄×C₁₃	—	4	1	no	—
128	C₂²×C₄×C₁₃	—	4	1	no	—
129	C₂²×C₄×C₁₃	—	8	2	no	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	#41	1	2	yes	—
136	C₂²×C₄×C₁₃	#41	1	2	yes	—
137	C₂²×C₄×C₁₃	#41	1	2	yes	—
138	C₂²×C₄×C₁₃	#41	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₁₃×M₁₆	—	2	4	no	—
141	C₁₃×M₁₆	—	2	4	no	—
142	C₁₃×M₁₆	—	2	2	no	—
143	C₁₃×M₁₆	—	2	2	no	—
144	C₁₃×M₁₆	—	2	2	no	—
145	C₁₃×M₁₆	—	2	2	no	—
146	C₁₃×M₁₆	—	2	2	no	—
147	C₁₃×M₁₆	—	2	2	no	—
148	C₁₃×M₁₆	—	4	2	no	—
149	C₁₃×M₁₆	—	4	2	no	—
150	C₁₃×M₁₆	—	4	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	4	2	no	—
157	C₂×C₈×C₁₃	—	4	2	no	—
158	C₂×C₈×C₁₃	—	4	2	no	—
159	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	4	1	no	—
167	C₁₃×C₄⋊C₄	—	4	1	no	—
168	C₁₃×C₂²⋊C₄	—	4	1	no	—
169	C₁₃×C₂²⋊C₄	—	4	1	no	—
170	C₄²×C₁₃	—	4	1	no	—
171	C₄²×C₁₃	—	4	1	no	—
172	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#2896	C₂×C₁₃	1	1	yes	characteristic
174	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
175	#2879	C₂×C₁₃	1	1	yes	characteristic
176	#2079	C₂×C₁₃	1	4	yes	complemented
177	#2078	C₂×C₁₃	1	4	yes	complemented
178	#1742	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂×#343	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#1738	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	1	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	8	1	no	—
186	C₂³×C₁₃	—	8	1	no	—
187	C₂³×C₁₃	#121	1	1	yes	characteristic
188	C₂³×C₁₃	#121	1	1	yes	characteristic
189	C₂³×C₁₃	#126	1	2	yes	—
190	C₂³×C₁₃	#126	1	2	yes	—
191	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
192	Q₈×C₁₃	—	2	2	no	—
193	Q₈×C₁₃	—	2	2	no	—
194	Q₈×C₁₃	—	4	2	no	—
195	D₄×C₁₃	—	2	2	no	—
196	D₄×C₁₃	—	2	2	no	—
197	D₄×C₁₃	—	4	2	no	—
198	D₄×C₁₃	—	4	2	no	—
199	D₄×C₁₃	—	4	4	no	—
200	D₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	8	2	no	—
210	C₂×C₄×C₁₃	—	8	2	no	—
211	C₂×C₄×C₁₃	—	8	1	no	—
212	C₂×C₄×C₁₃	—	8	1	no	—
213	C₂×C₄×C₁₃	—	8	2	no	—
214	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
215	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
216	C₂×C₄×C₁₃	#123	1	2	yes	—
217	C₂×C₄×C₁₃	#123	1	2	yes	—
218	C₂×C₄×C₁₃	#123	1	2	yes	—
219	C₂×C₄×C₁₃	#123	1	2	yes	—
220	C₂×C₄×C₁₃	#123	1	2	yes	—
221	C₂×C₄×C₁₃	#123	1	2	yes	—
222	C₂×C₄×C₁₃	#124	1	2	yes	—
223	C₂×C₄×C₁₃	#124	1	2	yes	—
224	C₂×C₄×C₁₃	#126	1	2	yes	—
225	C₂×C₄×C₁₃	#126	1	2	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
232	C₈×C₁₃	—	2	4	no	—
233	C₈×C₁₃	—	4	2	no	—
234	C₈×C₁₃	—	4	2	no	—
235	C₈×C₁₃	—	4	2	no	—
236	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
238	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
240	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
243	#428	—	2	2	no	—
244	#428	—	2	2	no	—
245	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
246	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
247	#419	—	2	1	no	—
248	#418	—	2	1	no	—
249	#417	—	2	2	no	—
250	#417	C₂²×C₁₃	1	2	yes	—
251	#417	C₂²×C₁₃	1	4	yes	—
252	#417	C₂²×C₁₃	1	2	yes	—
253	#416	—	2	2	no	—
254	C₂×#103	—	2	1	no	—
255	C₂×#102	—	2	1	no	—
256	#408	—	2	2	no	—
257	#408	C₂²×C₁₃	1	4	yes	—
258	#407	—	2	2	no	—
259	#343	C₂²×C₁₃	1	2	yes	complemented
260	#343	C₂²×C₁₃	1	4	yes	complemented
261	#343	C₂²×C₁₃	1	2	yes	complemented
262	#341	C₂²×C₁₃	1	4	yes	complemented
263	C₂²×C₁₃	—	2	1	no	—
264	C₂²×C₁₃	—	2	1	no	—
265	C₂²×C₁₃	—	2	1	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	—	4	2	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	8	4	no	—
275	C₂²×C₁₃	#397	1	2	yes	—
276	C₂²×C₁₃	#397	1	2	yes	—
277	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
278	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
279	C₂²×C₁₃	C₂×#126	1	1	yes	characteristic
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	8	1	no	—
282	C₄×C₁₃	—	8	2	no	—
283	C₄×C₁₃	—	8	1	no	—
284	C₄×C₁₃	#397	1	2	yes	—
285	C₄×C₁₃	#397	1	2	yes	—
286	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
287	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
288	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
289	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
290	C₂×#41	—	2	1	no	—
291	C₂×#41	—	2	1	no	—
292	C₂×#41	—	2	2	no	—
293	C₂×#41	—	2	2	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	—	2	2	no	—
296	C₂×#41	D₄×C₁₃	1	2	yes	—
297	C₂×#41	C₂³×C₁₃	1	2	yes	—
298	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	2	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	2	2	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	—	2	2	no	—
315	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
316	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
317	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
318	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
319	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
320	C₂²×C₈	—	2	1	no	—
321	C₂²×C₈	—	2	1	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
324	#117	—	2	1	no	—
325	#117	—	2	1	no	—
326	#117	—	2	1	no	—
327	#117	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	#107	—	2	4	no	—
339	#106	—	2	4	no	—
340	#103	—	2	4	no	—
341	#103	—	2	2	no	—
342	#103	—	2	2	no	—
343	#102	—	2	4	no	—
344	#102	—	2	2	no	—
345	#102	—	2	2	no	—
346	C₂²⋊C₈	—	2	8	no	—
347	C₂×C₁₃	—	2	2	no	—
348	C₂×C₁₃	—	2	1	no	—
349	C₂×C₁₃	—	2	1	no	—
350	C₂×C₁₃	—	2	2	no	—
351	C₂×C₁₃	—	8	2	no	—
352	C₂×C₁₃	C₂×#397	1	1	yes	characteristic
353	C₂×C₁₃	#3068	1	1	yes	characteristic
354	C₂×C₁₃	#3069	1	1	yes	characteristic
355	C₂⁴	—	2	1	no	—
356	C₂⁴	C₁₃×#41	1	1	yes	characteristic
357	#41	—	2	4	no	—
358	#41	—	2	4	no	—
359	#41	—	2	2	no	—
360	#41	—	2	2	no	—
361	#41	—	2	2	no	—
362	#41	—	2	2	no	—
363	#41	—	4	2	no	—
364	#41	—	4	2	no	—
365	#41	—	4	2	no	—
366	#41	—	4	2	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	8	2	no	—
390	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
395	C₂²×C₄	C₁₃×#41	1	2	yes	—
396	C₂²×C₄	C₁₃×#41	1	2	yes	—
397	C₂²×C₄	C₁₃×#41	1	2	yes	—
398	C₂²×C₄	C₁₃×#41	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
400	M₁₆	—	2	4	no	—
401	M₁₆	—	2	4	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	2	2	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	4	2	no	—
409	M₁₆	—	4	2	no	—
410	M₁₆	—	4	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	4	2	no	—
417	C₂×C₈	—	4	2	no	—
418	C₂×C₈	—	4	2	no	—
419	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₂²⋊C₄	—	4	1	no	—
429	C₂²⋊C₄	—	4	1	no	—
430	C₄²	—	4	1	no	—
431	C₄²	—	4	1	no	—
432	C₁₃	#23647	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	2	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	8	1	no	—
438	C₂³	—	8	1	no	—
439	C₂³	C₁₃×#121	1	1	yes	characteristic
440	C₂³	C₁₃×#121	1	1	yes	characteristic
441	C₂³	C₁₃×#126	1	2	yes	—
442	C₂³	C₁₃×#126	1	2	yes	—
443	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
444	Q₈	—	2	2	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	4	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	8	2	no	—
462	C₂×C₄	—	8	2	no	—
463	C₂×C₄	—	8	2	no	—
464	C₂×C₄	—	8	1	no	—
465	C₂×C₄	—	8	1	no	—
466	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
467	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
468	C₂×C₄	C₁₃×#123	1	2	yes	—
469	C₂×C₄	C₁₃×#123	1	2	yes	—
470	C₂×C₄	C₁₃×#123	1	2	yes	—
471	C₂×C₄	C₁₃×#123	1	2	yes	—
472	C₂×C₄	C₁₃×#123	1	2	yes	—
473	C₂×C₄	C₁₃×#123	1	2	yes	—
474	C₂×C₄	C₁₃×#124	1	2	yes	—
475	C₂×C₄	C₁₃×#124	1	2	yes	—
476	C₂×C₄	C₁₃×#126	1	2	yes	—
477	C₂×C₄	C₁₃×#126	1	2	yes	—
478	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
480	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
481	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
482	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
483	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
484	C₈	—	2	4	no	—
485	C₈	—	4	2	no	—
486	C₈	—	4	2	no	—
487	C₈	—	4	2	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	8	4	no	—
500	C₂²	C₁₃×#397	1	2	yes	—
501	C₂²	C₁₃×#397	1	2	yes	—
502	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
503	C₂²	C₂×C₁₃×#126	1	1	yes	characteristic
504	C₂²	C₂×C₁₃×#126	1	1	yes	characteristic
505	C₄	—	4	2	no	—
506	C₄	—	8	1	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	1	no	—
509	C₄	C₁₃×#397	1	2	yes	—
510	C₄	C₁₃×#397	1	2	yes	—
511	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
512	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
513	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
514	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
515	C₂	—	2	2	no	—
516	C₂	—	2	2	no	—
517	C₂	—	2	1	no	—
518	C₂	—	2	1	no	—
519	C₂	—	8	2	no	—
520	C₂	C₂×C₁₃×#397	1	1	yes	characteristic
521	C₂	C₁₃×#3068	1	1	yes	characteristic
522	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#428	C₂	semidirect
5. C₁₃×#2079	C₂	semidirect
6. C₁₃×#2078	C₂	semidirect
7. C₁₃×#1742	C₂	semidirect
8. C₂×C₁₃×#343	C₂	semidirect
9. C₁₃×#1738	C₂	semidirect
19. C₂×C₁₃×#107	C₂²	semidirect
20. C₂×C₁₃×#106	C₂²	semidirect
33. C₁₃×#343	C₂²	semidirect
34. C₁₃×#343	C₂²	semidirect
35. C₁₃×#343	C₂²	semidirect
36. C₁₃×#341	C₂²	semidirect
94. #23647	C₁₃	direct (N × H)
172. C₂×#428	C₂×C₁₃	semidirect
176. #2079	C₂×C₁₃	semidirect
177. #2078	C₂×C₁₃	semidirect
178. #1742	C₂×C₁₃	semidirect
179. C₂×#343	C₂×C₁₃	semidirect
180. #1738	C₂×C₁₃	semidirect
245. C₂×#107	C₂²×C₁₃	semidirect
246. C₂×#106	C₂²×C₁₃	semidirect
259. #343	C₂²×C₁₃	semidirect
260. #343	C₂²×C₁₃	semidirect
261. #343	C₂²×C₁₃	semidirect
262. #341	C₂²×C₁₃	semidirect
432. C₁₃	#23647	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×#428	2
C₁₃×#2896	2
C₂×C₁₃×#417	2
C₁₃×#2879	2
C₁₃×#2079	2
C₁₃×#2078	2
C₁₃×#1742	2
C₂×C₁₃×#343	2
C₁₃×#1738	2
#23647	13

Subgroups — C13×#23647 #15709986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23647 #15709986