Subgroups — C₁₃×#23456 #15709795

Order 3328.

1362 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2309	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2025	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2023	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1735	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#544	—	2	4	no	—
14	C₁₃×#544	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
17	C₂×C₁₃×#125	—	2	1	no	—
18	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
19	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₁₃×#418	—	2	4	no	—
25	C₂×C₁₃×#102	—	2	4	no	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	4	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₁₃×#390	—	2	1	no	—
30	C₁₃×#390	—	2	1	no	—
31	C₁₃×#390	C₂²	1	4	yes	—
32	C₁₃×#379	—	2	2	no	—
33	C₁₃×#340	C₂²	1	2	yes	complemented
34	C₁₃×#340	C₂²	1	2	yes	complemented
35	C₁₃×#340	C₂²	1	4	yes	complemented
36	C₁₃×#336	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₃	—	2	1	no	—
38	C₂²×Q₈×C₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₃	—	2	2	no	—
40	C₂²×D₄×C₁₃	—	2	2	no	—
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	Q₈	1	4	yes	complemented
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₁₃×M₁₆	—	2	2	no	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₂²×C₈×C₁₃	—	2	2	no	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×C₄⋊Q₈	—	2	8	no	—
58	C₁₃×C₄⋊Q₈	—	2	4	no	—
59	C₁₃×C₄⋊Q₈	—	2	4	no	—
60	C₁₃×#125	—	2	8	no	—
61	C₁₃×#125	—	2	4	no	—
62	C₁₃×#125	—	2	4	no	—
63	C₁₃×C₂²⋊Q₈	—	2	16	no	—
64	C₁₃×#117	—	2	2	no	—
65	C₁₃×#117	—	2	2	no	—
66	C₁₃×#117	—	2	2	no	—
67	C₁₃×#117	—	2	2	no	—
68	C₁₃×#117	—	2	2	no	—
69	C₁₃×#117	D₄	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
86	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
87	C₂×C₄²×C₁₃	—	2	1	no	—
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₁₃×#102	—	2	8	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#102	—	2	4	no	—
93	#23456	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	2	no	—
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	—	4	2	no	—
97	C₂⁴×C₁₃	—	4	2	no	—
98	C₂⁴×C₁₃	—	8	2	no	—
99	C₂⁴×C₁₃	—	8	2	no	—
100	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₁₃	—	2	8	no	—
102	C₂×Q₈×C₁₃	—	8	4	no	—
103	C₂×D₄×C₁₃	—	2	8	no	—
104	C₂×D₄×C₁₃	—	2	8	no	—
105	C₂×D₄×C₁₃	—	2	4	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	4	no	—
113	C₂×D₄×C₁₃	—	4	4	no	—
114	C₂×D₄×C₁₃	—	4	2	no	—
115	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	8	2	no	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₁₃	#41	1	2	yes	—
129	C₂²×C₄×C₁₃	#41	1	2	yes	—
130	C₂²×C₄×C₁₃	#41	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₁₃×M₁₆	—	4	4	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	4	4	no	—
140	C₁₃×C₄⋊C₄	—	2	8	no	—
141	C₁₃×C₄⋊C₄	—	2	8	no	—
142	C₁₃×C₄⋊C₄	—	2	8	no	—
143	C₁₃×C₄⋊C₄	—	2	4	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₁₃×C₂²⋊C₄	—	2	4	no	—
155	C₁₃×C₂²⋊C₄	—	2	4	no	—
156	C₁₃×C₂²⋊C₄	—	4	2	no	—
157	C₁₃×C₂²⋊C₄	—	8	4	no	—
158	C₁₃×C₂²⋊C₄	—	8	4	no	—
159	C₄²×C₁₃	—	2	4	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	4	2	no	—
163	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
165	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic
166	#2309	C₂×C₁₃	1	1	yes	characteristic
167	#2025	C₂×C₁₃	1	4	yes	complemented
168	#2023	C₂×C₁₃	1	4	yes	complemented
169	#1736	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1735	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	4	no	—
175	C₂³×C₁₃	—	4	2	no	—
176	C₂³×C₁₃	—	4	2	no	—
177	C₂³×C₁₃	—	4	4	no	—
178	C₂³×C₁₃	—	4	4	no	—
179	C₂³×C₁₃	—	4	8	no	—
180	C₂³×C₁₃	—	8	8	no	—
181	C₂³×C₁₃	—	8	8	no	—
182	C₂³×C₁₃	—	8	4	no	—
183	C₂³×C₁₃	—	8	4	no	—
184	C₂³×C₁₃	#120	1	2	yes	—
185	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
186	C₂³×C₁₃	#124	1	2	yes	—
187	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₁₃	—	8	8	no	—
189	D₄×C₁₃	—	2	4	no	—
190	D₄×C₁₃	—	2	4	no	—
191	D₄×C₁₃	—	4	2	no	—
192	D₄×C₁₃	—	4	2	no	—
193	D₄×C₁₃	—	4	8	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	4	4	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	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	8	4	no	—
208	C₂×C₄×C₁₃	#120	1	2	yes	—
209	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
210	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
211	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
212	C₂×C₄×C₁₃	#124	1	4	yes	—
213	C₂×C₄×C₁₃	#124	1	4	yes	—
214	C₂×C₄×C₁₃	#124	1	2	yes	—
215	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₈×C₁₃	—	4	2	no	—
222	C₈×C₁₃	—	4	2	no	—
223	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
224	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
225	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
226	#544	—	2	4	no	—
227	#544	—	2	4	no	—
228	C₂×C₄⋊Q₈	—	2	1	no	—
229	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
230	C₂×#125	—	2	1	no	—
231	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
232	C₂×C₂²⋊Q₈	—	2	2	no	—
233	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
237	#418	—	2	4	no	—
238	C₂×#102	—	2	4	no	—
239	C₂×#102	C₂²×C₁₃	1	4	yes	—
240	C₂×#102	C₂²×C₁₃	1	2	yes	—
241	C₂×#102	C₂²×C₁₃	1	2	yes	—
242	#390	—	2	1	no	—
243	#390	—	2	1	no	—
244	#390	C₂²×C₁₃	1	4	yes	—
245	#379	—	2	2	no	—
246	#340	C₂²×C₁₃	1	2	yes	complemented
247	#340	C₂²×C₁₃	1	2	yes	complemented
248	#340	C₂²×C₁₃	1	4	yes	complemented
249	#336	C₂²×C₁₃	1	4	yes	complemented
250	C₂²×C₁₃	—	2	4	no	—
251	C₂²×C₁₃	—	2	4	no	—
252	C₂²×C₁₃	—	2	2	no	—
253	C₂²×C₁₃	—	2	2	no	—
254	C₂²×C₁₃	—	4	8	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	8	16	no	—
257	C₂²×C₁₃	—	8	4	no	—
258	C₂²×C₁₃	—	8	2	no	—
259	C₂²×C₁₃	—	8	2	no	—
260	C₂²×C₁₃	#393	1	4	yes	—
261	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
262	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
263	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
264	C₂²×C₁₃	#576	1	2	yes	—
265	C₂²×C₁₃	#577	1	2	yes	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	—	4	4	no	—
268	C₄×C₁₃	—	4	2	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	2	no	—
271	C₄×C₁₃	—	8	2	no	—
272	C₄×C₁₃	#393	1	4	yes	—
273	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
274	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
275	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
276	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
277	C₂⁵	—	2	1	no	—
278	C₂²×Q₈	—	2	2	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	Q₈×C₁₃	1	4	yes	complemented
286	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
287	C₂³×C₄	—	2	1	no	—
288	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
296	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
297	C₄⋊Q₈	—	2	8	no	—
298	C₄⋊Q₈	—	2	4	no	—
299	C₄⋊Q₈	—	2	4	no	—
300	#125	—	2	8	no	—
301	#125	—	2	4	no	—
302	#125	—	2	4	no	—
303	C₂²⋊Q₈	—	2	16	no	—
304	#117	—	2	2	no	—
305	#117	—	2	2	no	—
306	#117	—	2	2	no	—
307	#117	—	2	2	no	—
308	#117	—	2	2	no	—
309	#117	D₄×C₁₃	1	4	yes	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	4	no	—
325	C₂×C₂²⋊C₄	—	2	4	no	—
326	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
330	#102	—	2	8	no	—
331	#102	—	2	4	no	—
332	#102	—	2	4	no	—
333	C₂×C₁₃	—	2	4	no	—
334	C₂×C₁₃	—	8	4	no	—
335	C₂×C₁₃	C₂×#393	1	1	yes	characteristic
336	C₂×C₁₃	#3008	1	1	yes	characteristic
337	C₂×C₁₃	#3010	1	1	yes	characteristic
338	C₂×C₁₃	#3081	1	2	yes	—
339	C₂×C₁₃	#3136	1	2	yes	—
340	C₂⁴	—	2	2	no	—
341	C₂⁴	—	2	4	no	—
342	C₂⁴	—	4	2	no	—
343	C₂⁴	—	4	2	no	—
344	C₂⁴	—	8	2	no	—
345	C₂⁴	—	8	2	no	—
346	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂×Q₈	—	2	8	no	—
348	C₂×Q₈	—	8	4	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	8	2	no	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
373	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
374	C₂²×C₄	C₁₃×#41	1	2	yes	—
375	C₂²×C₄	C₁₃×#41	1	2	yes	—
376	C₂²×C₄	C₁₃×#41	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
378	M₁₆	—	4	4	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	4	4	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
398	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
399	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	8	4	no	—
404	C₂²⋊C₄	—	8	4	no	—
405	C₄²	—	2	4	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	4	2	no	—
409	C₁₃	#23456	1	1	yes	characteristic, direct product factor, Sylow
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	8	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	4	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	8	8	no	—
419	C₂³	—	8	4	no	—
420	C₂³	—	8	4	no	—
421	C₂³	—	8	8	no	—
422	C₂³	C₁₃×#120	1	2	yes	—
423	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
424	C₂³	C₁₃×#124	1	2	yes	—
425	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
426	Q₈	—	8	8	no	—
427	D₄	—	2	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	4	8	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	8	4	no	—
446	C₂×C₄	C₁₃×#120	1	2	yes	—
447	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
448	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
449	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
450	C₂×C₄	C₁₃×#124	1	2	yes	—
451	C₂×C₄	C₁₃×#124	1	4	yes	—
452	C₂×C₄	C₁₃×#124	1	4	yes	—
453	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
457	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
458	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
459	C₈	—	4	2	no	—
460	C₈	—	4	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	4	8	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	8	16	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	4	no	—
471	C₂²	C₁₃×#393	1	4	yes	—
472	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
473	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
474	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
475	C₂²	C₁₃×#576	1	2	yes	—
476	C₂²	C₁₃×#577	1	2	yes	—
477	C₄	—	4	2	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	8	2	no	—
483	C₄	C₁₃×#393	1	4	yes	—
484	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
485	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
486	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
487	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
488	C₂	—	2	4	no	—
489	C₂	—	8	4	no	—
490	C₂	C₂×C₁₃×#393	1	1	yes	characteristic
491	C₂	C₁₃×#3008	1	1	yes	characteristic
492	C₂	C₁₃×#3010	1	1	yes	characteristic
493	C₂	C₁₃×#3081	1	2	yes	—
494	C₂	C₁₃×#3136	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#544	C₂	semidirect
5. C₁₃×#2025	C₂	semidirect
6. C₁₃×#2023	C₂	semidirect
7. C₁₃×#1736	C₂	semidirect
8. C₁₃×#1735	C₂	semidirect
9. C₁₃×#1729	C₂	semidirect
16. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₁₃×#125	C₂²	semidirect
33. C₁₃×#340	C₂²	semidirect
34. C₁₃×#340	C₂²	semidirect
35. C₁₃×#340	C₂²	semidirect
36. C₁₃×#336	C₂²	semidirect
45. C₂²×D₄×C₁₃	Q₈	semidirect
93. #23456	C₁₃	direct (N × H)
163. C₂×#544	C₂×C₁₃	semidirect
167. #2025	C₂×C₁₃	semidirect
168. #2023	C₂×C₁₃	semidirect
169. #1736	C₂×C₁₃	semidirect
170. #1735	C₂×C₁₃	semidirect
171. #1729	C₂×C₁₃	semidirect
229. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
231. C₂×#125	C₂²×C₁₃	semidirect
246. #340	C₂²×C₁₃	semidirect
247. #340	C₂²×C₁₃	semidirect
248. #340	C₂²×C₁₃	semidirect
249. #336	C₂²×C₁₃	semidirect
285. C₂²×D₄	Q₈×C₁₃	semidirect
409. C₁₃	#23456	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×#544	2
C₂×C₁₃×#418	2
C₂²×C₁₃×#102	2
C₁₃×#2309	2
C₁₃×#2025	2
C₁₃×#2023	2
C₁₃×#1736	2
C₁₃×#1735	2
C₁₃×#1729	2
#23456	13

Subgroups — C13×#23456 #15709795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23456 #15709795