Subgroups — C₁₃×#23738 #15710077

Order 3328.

1098 conjugacy classes of subgroups.

The subgroup lattice has 512 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	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2311	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2097	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2096	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2094	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2092	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#428	—	2	4	no	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	—	2	4	no	—
22	C₂×C₁₃×#106	C₂²	1	2	yes	—
23	C₂×C₁₃×#106	C₂²	1	2	yes	—
24	C₂×C₁₃×#106	C₂²	1	2	yes	—
25	C₁₃×#417	—	2	4	no	—
26	C₁₃×#416	—	2	4	no	—
27	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₁₃×#391	C₂²	1	2	yes	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#389	—	2	2	no	—
36	C₁₃×#386	—	2	2	no	—
37	C₁₃×#385	—	2	2	no	—
38	C₁₃×#384	C₂²	1	2	yes	—
39	C₁₃×#382	C₂²	1	2	yes	—
40	C₁₃×#380	—	2	2	no	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	2	no	—
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	—	2	2	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	Q₈	1	4	yes	—
49	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	—	2	1	no	—
51	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×M₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	2	no	—
58	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₂²×C₈×C₁₃	—	2	2	no	—
61	C₂²×C₈×C₁₃	D₄	1	4	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
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	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
83	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
84	C₂×C₄²×C₁₃	—	2	1	no	—
85	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
86	C₁₃×#107	—	2	4	no	—
87	C₁₃×#106	—	2	4	no	—
88	C₁₃×#106	—	2	4	no	—
89	C₁₃×#106	—	2	4	no	—
90	C₁₃×#103	—	2	2	no	—
91	C₁₃×#103	—	2	2	no	—
92	C₁₃×#103	—	2	4	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	—	2	2	no	—
95	C₁₃×#102	—	2	4	no	—
96	C₁₃×#95	—	2	4	no	—
97	C₁₃×#95	—	2	4	no	—
98	#23738	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	—	2	1	no	—
100	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₁₃×#41	—	2	8	no	—
102	C₁₃×#41	—	2	8	no	—
103	C₁₃×#41	—	4	4	no	—
104	C₁₃×#41	—	4	4	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	—	2	1	no	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
111	C₂×D₄×C₁₃	—	2	4	no	—
112	C₂×D₄×C₁₃	—	2	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	1	no	—
117	C₂×D₄×C₁₃	—	4	2	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	4	2	no	—
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	—	4	2	no	—
129	C₂²×C₄×C₁₃	—	4	2	no	—
130	C₂²×C₄×C₁₃	—	8	2	no	—
131	C₂²×C₄×C₁₃	—	8	2	no	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
137	C₂²×C₄×C₁₃	#41	1	2	yes	—
138	C₂²×C₄×C₁₃	#41	1	2	yes	—
139	C₂²×C₄×C₁₃	#41	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₁₃×M₁₆	—	2	8	no	—
142	C₂×C₈×C₁₃	—	2	8	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	4	2	no	—
162	C₁₃×C₄⋊C₄	—	4	2	no	—
163	C₁₃×C₄⋊C₄	—	8	4	no	—
164	C₁₃×C₂²⋊C₄	—	2	4	no	—
165	C₁₃×C₂²⋊C₄	—	4	2	no	—
166	C₁₃×C₂²⋊C₄	—	8	4	no	—
167	C₄²×C₁₃	—	2	2	no	—
168	C₄²×C₁₃	—	2	2	no	—
169	C₄²×C₁₃	—	4	2	no	—
170	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
173	C₂×#416	C₂×C₁₃	1	1	yes	characteristic
174	#2317	C₂×C₁₃	1	1	yes	characteristic, complemented
175	#2311	C₂×C₁₃	1	1	yes	characteristic
176	#2097	C₂×C₁₃	1	2	yes	complemented
177	#2096	C₂×C₁₃	1	2	yes	complemented
178	#2094	C₂×C₁₃	1	2	yes	complemented
179	#2092	C₂×C₁₃	1	2	yes	complemented
180	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	4	1	no	—
185	C₂³×C₁₃	—	4	1	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
189	C₂³×C₁₃	#123	1	2	yes	—
190	C₂³×C₁₃	#127	1	2	yes	—
191	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₁₃	—	2	2	no	—
193	Q₈×C₁₃	—	2	2	no	—
194	Q₈×C₁₃	—	4	1	no	—
195	Q₈×C₁₃	—	4	1	no	—
196	D₄×C₁₃	—	2	2	no	—
197	D₄×C₁₃	—	2	2	no	—
198	D₄×C₁₃	—	4	8	no	—
199	D₄×C₁₃	—	4	1	no	—
200	D₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	8	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	2	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	4	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	8	4	no	—
217	C₂×C₄×C₁₃	—	8	4	no	—
218	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
219	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
220	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
221	C₂×C₄×C₁₃	#123	1	4	yes	—
222	C₂×C₄×C₁₃	#123	1	4	yes	—
223	C₂×C₄×C₁₃	#123	1	2	yes	—
224	C₂×C₄×C₁₃	#127	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×Q₈	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	C₈×C₁₃	—	2	2	no	—
232	C₈×C₁₃	—	2	2	no	—
233	C₈×C₁₃	—	2	4	no	—
234	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
235	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
236	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
241	#428	—	2	4	no	—
242	C₂×#107	C₂²×C₁₃	1	2	yes	—
243	C₂×#106	—	2	4	no	—
244	C₂×#106	C₂²×C₁₃	1	2	yes	—
245	C₂×#106	C₂²×C₁₃	1	2	yes	—
246	C₂×#106	C₂²×C₁₃	1	2	yes	—
247	#417	—	2	4	no	—
248	#416	—	2	4	no	—
249	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#103	C₂²×C₁₃	1	2	yes	—
251	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#102	C₂²×C₁₃	1	2	yes	—
254	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
255	#391	C₂²×C₁₃	1	2	yes	—
256	#390	C₂²×C₁₃	1	2	yes	—
257	#389	—	2	2	no	—
258	#386	—	2	2	no	—
259	#385	—	2	2	no	—
260	#384	C₂²×C₁₃	1	2	yes	—
261	#382	C₂²×C₁₃	1	2	yes	—
262	#380	—	2	2	no	—
263	#336	C₂²×C₁₃	1	2	yes	—
264	#336	C₂²×C₁₃	1	2	yes	—
265	C₂²×C₁₃	—	2	4	no	—
266	C₂²×C₁₃	—	2	4	no	—
267	C₂²×C₁₃	—	2	2	no	—
268	C₂²×C₁₃	—	2	2	no	—
269	C₂²×C₁₃	—	4	4	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	8	2	no	—
272	C₂²×C₁₃	—	8	1	no	—
273	C₂²×C₁₃	—	8	1	no	—
274	C₂²×C₁₃	#399	1	4	yes	—
275	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
276	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
277	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
278	C₂²×C₁₃	#577	1	2	yes	—
279	C₂²×C₁₃	#577	1	2	yes	—
280	C₄×C₁₃	—	4	4	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	8	1	no	—
283	C₄×C₁₃	—	8	1	no	—
284	C₄×C₁₃	—	8	2	no	—
285	C₄×C₁₃	—	8	2	no	—
286	C₄×C₁₃	#399	1	4	yes	—
287	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
288	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
289	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
290	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
291	C₂×#41	—	2	2	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	Q₈×C₁₃	1	4	yes	—
297	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₂²×D₄	—	2	1	no	—
299	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂³×C₄	—	2	1	no	—
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	D₄×C₁₃	1	4	yes	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	D₄×C₁₃	1	4	yes	—
310	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
313	#117	—	2	2	no	—
314	#117	—	2	2	no	—
315	#117	—	2	2	no	—
316	#117	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	4	no	—
324	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	4	no	—
331	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
334	#107	—	2	4	no	—
335	#106	—	2	4	no	—
336	#106	—	2	4	no	—
337	#106	—	2	4	no	—
338	#103	—	2	2	no	—
339	#103	—	2	2	no	—
340	#103	—	2	4	no	—
341	#102	—	2	2	no	—
342	#102	—	2	2	no	—
343	#102	—	2	4	no	—
344	#95	—	2	4	no	—
345	#95	—	2	4	no	—
346	C₂×C₁₃	—	2	4	no	—
347	C₂×C₁₃	—	8	2	no	—
348	C₂×C₁₃	C₂×#399	1	1	yes	characteristic
349	C₂×C₁₃	#3084	1	2	yes	—
350	C₂×C₁₃	#3099	1	2	yes	—
351	C₂×C₁₃	#3154	1	1	yes	characteristic
352	C₂×C₁₃	#3154	1	1	yes	characteristic
353	C₂⁴	—	2	1	no	—
354	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
355	#41	—	2	8	no	—
356	#41	—	2	8	no	—
357	#41	—	4	4	no	—
358	#41	—	4	4	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	8	2	no	—
385	C₂²×C₄	—	8	2	no	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
390	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
391	C₂²×C₄	C₁₃×#41	1	2	yes	—
392	C₂²×C₄	C₁₃×#41	1	2	yes	—
393	C₂²×C₄	C₁₃×#41	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
395	M₁₆	—	2	8	no	—
396	C₂×C₈	—	2	8	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
404	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
405	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	8	4	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	8	4	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	4	2	no	—
424	C₁₃	#23738	1	1	yes	characteristic, direct product factor, Sylow
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
433	C₂³	C₁₃×#123	1	2	yes	—
434	C₂³	C₁₃×#127	1	2	yes	—
435	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	4	1	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	4	8	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	—	8	4	no	—
462	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
463	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
464	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
465	C₂×C₄	C₁₃×#123	1	2	yes	—
466	C₂×C₄	C₁₃×#123	1	4	yes	—
467	C₂×C₄	C₁₃×#123	1	4	yes	—
468	C₂×C₄	C₁₃×#127	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
472	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
473	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
474	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	C₁₃×#399	1	4	yes	—
488	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
489	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
490	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
491	C₂²	C₁₃×#577	1	2	yes	—
492	C₂²	C₁₃×#577	1	2	yes	—
493	C₄	—	4	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	2	no	—
498	C₄	—	8	2	no	—
499	C₄	C₁₃×#399	1	4	yes	—
500	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
501	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
502	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
503	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
504	C₂	—	2	4	no	—
505	C₂	—	8	2	no	—
506	C₂	C₂×C₁₃×#399	1	1	yes	characteristic
507	C₂	C₁₃×#3084	1	2	yes	—
508	C₂	C₁₃×#3099	1	2	yes	—
509	C₂	C₁₃×#3154	1	1	yes	characteristic
510	C₂	C₁₃×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	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×#428	C₂	semidirect
2. C₂²×C₁₃×#106	C₂	semidirect
5. C₁₃×#2317	C₂	semidirect
7. C₁₃×#2097	C₂	semidirect
8. C₁₃×#2096	C₂	semidirect
9. C₁₃×#2094	C₂	semidirect
10. C₁₃×#2092	C₂	semidirect
11. C₁₃×#1729	C₂	semidirect
98. #23738	C₁₃	direct (N × H)
170. C₂×#428	C₂×C₁₃	semidirect
171. C₂²×#106	C₂×C₁₃	semidirect
174. #2317	C₂×C₁₃	semidirect
176. #2097	C₂×C₁₃	semidirect
177. #2096	C₂×C₁₃	semidirect
178. #2094	C₂×C₁₃	semidirect
179. #2092	C₂×C₁₃	semidirect
180. #1729	C₂×C₁₃	semidirect
424. C₁₃	#23738	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
C₂²×C₁₃×#106	2
C₂×C₁₃×#417	2
C₂×C₁₃×#416	2
C₁₃×#2317	2
C₁₃×#2311	2
C₁₃×#2097	2
C₁₃×#2096	2
C₁₃×#2094	2
C₁₃×#2092	2
C₁₃×#1729	2
#23738	13

Subgroups — C13×#23738 #15710077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23738 #15710077