Subgroups — C₁₃×#25940 #15712279

Order 3328.

1098 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2026	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2025	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1879	C₂	1	2	yes	maximal
10	C₁₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₁₃×#554	—	2	4	no	—
15	C₁₃×#554	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	C₂²	1	2	yes	—
18	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
25	C₁₃×#489	—	2	4	no	—
26	C₁₃×#463	—	2	4	no	—
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
34	C₁₃×#397	—	2	1	no	—
35	C₁₃×#393	—	2	1	no	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#390	C₂²	1	2	yes	—
38	C₁₃×#388	—	2	2	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂³×C₄×C₁₃	—	2	2	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	—	2	4	no	—
54	C₂×C₁₃×D₈	—	2	2	no	—
55	C₂×C₁₃×D₈	—	2	4	no	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
61	C₁₃×#125	—	2	4	no	—
62	C₁₃×#125	—	2	4	no	—
63	C₁₃×#124	—	2	2	no	—
64	C₁₃×#124	—	2	2	no	—
65	C₁₃×C₂²⋊Q₈	—	2	8	no	—
66	C₁₃×C₂²⋊Q₈	—	2	16	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×D₄×C₁₃	—	2	4	no	—
70	C₄×D₄×C₁₃	—	2	4	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	D₄	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
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	2	yes	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊C₈	—	2	2	no	—
92	C₁₃×#103	—	2	2	no	—
93	C₁₃×#103	—	2	4	no	—
94	C₁₃×#102	—	2	4	no	—
95	C₁₃×#102	—	2	2	no	—
96	C₁₃×#102	—	2	4	no	—
97	C₁₃×#97	—	2	2	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	—	2	2	no	—
100	C₁₃×#95	—	2	2	no	—
101	#25940	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₃	—	2	1	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	—	4	2	no	—
111	C₂×Q₈×C₁₃	—	8	1	no	—
112	C₂×Q₈×C₁₃	—	8	1	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₁₃	#41	1	4	yes	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	8	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	4	4	no	—
128	C₂²×C₄×C₁₃	—	8	2	no	—
129	C₂²×C₄×C₁₃	—	8	2	no	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×SD₁₆	—	4	4	no	—
136	C₁₃×D₈	—	4	4	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
154	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
155	C₁₃×C₂²⋊C₄	—	2	8	no	—
156	C₁₃×C₂²⋊C₄	—	2	4	no	—
157	C₁₃×C₂²⋊C₄	—	4	4	no	—
158	C₁₃×C₂²⋊C₄	—	4	2	no	—
159	C₁₃×C₂²⋊C₄	—	4	2	no	—
160	C₁₃×C₂²⋊C₄	—	8	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	2	2	no	—
163	C₄²×C₁₃	—	8	1	no	—
164	C₄²×C₁₃	C₂×D₄	1	2	yes	—
165	C₄²×C₁₃	C₂×D₄	1	2	yes	—
166	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂×#463	C₂×C₁₃	1	1	yes	characteristic
169	#2592	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#2026	C₂×C₁₃	1	2	yes	complemented
171	#2025	C₂×C₁₃	1	2	yes	complemented
172	#1988	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1879	C₂×C₁₃	1	2	yes	—
175	#1877	C₂×C₁₃	1	2	yes	complemented
176	#1762	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	—	2	4	no	—
179	C₂³×C₁₃	—	4	2	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	—	4	1	no	—
182	C₂³×C₁₃	—	4	1	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	2	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	—	4	1	no	—
187	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₁₃	—	4	4	no	—
189	Q₈×C₁₃	—	4	1	no	—
190	Q₈×C₁₃	—	4	1	no	—
191	Q₈×C₁₃	—	4	2	no	—
192	Q₈×C₁₃	—	8	4	no	—
193	D₄×C₁₃	—	2	2	no	—
194	D₄×C₁₃	—	2	4	no	—
195	D₄×C₁₃	—	4	1	no	—
196	D₄×C₁₃	—	4	1	no	—
197	D₄×C₁₃	—	4	2	no	—
198	D₄×C₁₃	#124	1	4	yes	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	4	8	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	8	8	no	—
220	C₂×C₄×C₁₃	#120	1	2	yes	—
221	C₂×C₄×C₁₃	#120	1	2	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
226	C₈×C₁₃	—	4	1	no	—
227	C₈×C₁₃	—	4	1	no	—
228	C₈×C₁₃	—	4	2	no	—
229	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
230	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
231	#554	—	2	4	no	—
232	#554	—	2	4	no	—
233	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#125	C₂²×C₁₃	1	2	yes	—
235	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₂²⋊Q₈	—	2	1	no	—
237	C₂×C₂²⋊Q₈	—	2	2	no	—
238	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
240	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	—	2	1	no	—
242	#489	—	2	4	no	—
243	#463	—	2	4	no	—
244	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×#103	C₂²×C₁₃	1	2	yes	—
246	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×#102	C₂²×C₁₃	1	2	yes	—
248	C₂×#102	C₂²×C₁₃	1	2	yes	—
249	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
251	#397	—	2	1	no	—
252	#393	—	2	1	no	—
253	#391	C₂²×C₁₃	1	2	yes	—
254	#390	C₂²×C₁₃	1	2	yes	—
255	#388	—	2	2	no	—
256	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
257	#340	C₂²×C₁₃	1	2	yes	—
258	#340	C₂²×C₁₃	1	2	yes	—
259	#340	C₂²×C₁₃	1	2	yes	—
260	#336	C₂²×C₁₃	1	2	yes	—
261	#336	C₂²×C₁₃	1	2	yes	—
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	4	4	no	—
264	C₂²×C₁₃	—	4	4	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	8	2	no	—
268	C₂²×C₁₃	—	8	2	no	—
269	C₂²×C₁₃	—	8	1	no	—
270	C₂²×C₁₃	—	8	1	no	—
271	C₂²×C₁₃	—	8	1	no	—
272	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
273	C₂²×C₁₃	#548	1	2	yes	—
274	C₂²×C₁₃	#575	1	2	yes	—
275	C₂²×C₁₃	#576	1	1	yes	characteristic
276	C₂²×C₁₃	#577	1	1	yes	characteristic
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	4	2	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	4	4	no	—
283	C₄×C₁₃	—	8	2	no	—
284	C₄×C₁₃	—	8	1	no	—
285	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
286	C₄×C₁₃	#536	1	1	yes	characteristic
287	C₄×C₁₃	#548	1	2	yes	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	—	2	2	no	—
295	C₂×SD₁₆	—	2	2	no	—
296	C₂×SD₁₆	—	2	4	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂×D₈	—	2	4	no	—
299	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
304	#125	—	2	4	no	—
305	#125	—	2	4	no	—
306	#124	—	2	2	no	—
307	#124	—	2	2	no	—
308	C₂²⋊Q₈	—	2	8	no	—
309	C₂²⋊Q₈	—	2	16	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	D₄×C₁₃	1	4	yes	—
316	C₂×C₄⋊C₄	—	2	8	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
333	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
334	C₄⋊C₈	—	2	2	no	—
335	#103	—	2	2	no	—
336	#103	—	2	4	no	—
337	#102	—	2	4	no	—
338	#102	—	2	2	no	—
339	#102	—	2	4	no	—
340	#97	—	2	2	no	—
341	#95	—	2	1	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	C₂×C₁₃	—	4	4	no	—
345	C₂×C₁₃	—	16	1	no	—
346	C₂×C₁₃	#2436	1	1	yes	characteristic
347	C₂×C₁₃	#3005	1	1	yes	characteristic
348	C₂×C₁₃	#3012	1	1	yes	characteristic
349	C₂×C₁₃	#3370	1	2	yes	—
350	C₂×C₁₃	#3376	1	2	yes	—
351	C₂⁴	—	2	1	no	—
352	C₂⁴	—	2	1	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	8	1	no	—
361	C₂×Q₈	—	8	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂×D₄	C₁₃×#41	1	4	yes	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	8	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	8	2	no	—
378	C₂²×C₄	—	8	2	no	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
384	SD₁₆	—	4	4	no	—
385	D₈	—	4	4	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	8	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
403	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	—	8	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	8	1	no	—
413	C₄²	C₂×D₄×C₁₃	1	2	yes	—
414	C₄²	C₂×D₄×C₁₃	1	2	yes	—
415	C₁₃	#25940	1	1	yes	characteristic, direct product factor, Sylow
416	C₂³	—	2	2	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
427	Q₈	—	4	4	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	4	2	no	—
431	Q₈	—	8	4	no	—
432	D₄	—	2	2	no	—
433	D₄	—	2	4	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	2	no	—
437	D₄	C₁₃×#124	1	4	yes	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	4	8	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	8	8	no	—
459	C₂×C₄	C₁₃×#120	1	2	yes	—
460	C₂×C₄	C₁₃×#120	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
463	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
464	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
479	C₂²	C₁₃×#548	1	2	yes	—
480	C₂²	C₁₃×#575	1	2	yes	—
481	C₂²	C₁₃×#576	1	1	yes	characteristic
482	C₂²	C₁₃×#577	1	1	yes	characteristic
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	8	2	no	—
490	C₄	—	8	1	no	—
491	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
492	C₄	C₁₃×#536	1	1	yes	characteristic
493	C₄	C₁₃×#548	1	2	yes	—
494	C₂	—	4	4	no	—
495	C₂	—	16	1	no	—
496	C₂	C₁₃×#2436	1	1	yes	characteristic
497	C₂	C₁₃×#3005	1	1	yes	characteristic
498	C₂	C₁₃×#3012	1	1	yes	characteristic
499	C₂	C₁₃×#3370	1	2	yes	—
500	C₂	C₁₃×#3376	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	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
1. C₂×C₁₃×#554	C₂	semidirect
2. C₂×C₁₃×#489	C₂	semidirect
4. C₁₃×#2592	C₂	semidirect
5. C₁₃×#2026	C₂	semidirect
6. C₁₃×#2025	C₂	semidirect
7. C₁₃×#1988	C₂	semidirect
8. C₁₃×#1985	C₂	semidirect
10. C₁₃×#1877	C₂	semidirect
11. C₁₃×#1762	C₂	semidirect
101. #25940	C₁₃	direct (N × H)
166. C₂×#554	C₂×C₁₃	semidirect
167. C₂×#489	C₂×C₁₃	semidirect
169. #2592	C₂×C₁₃	semidirect
170. #2026	C₂×C₁₃	semidirect
171. #2025	C₂×C₁₃	semidirect
172. #1988	C₂×C₁₃	semidirect
173. #1985	C₂×C₁₃	semidirect
175. #1877	C₂×C₁₃	semidirect
176. #1762	C₂×C₁₃	semidirect
415. C₁₃	#25940	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×#554	2
C₂×C₁₃×#489	2
C₂×C₁₃×#463	2
C₁₃×#2592	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#1988	2
C₁₃×#1985	2
C₁₃×#1879	2
C₁₃×#1877	2
C₁₃×#1762	2
#25940	13

Subgroups — C13×#25940 #15712279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25940 #15712279