Subgroups — C₁₃×#23735 #15710074

Order 3328.

1210 conjugacy classes of subgroups.

The subgroup lattice has 506 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	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2309	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2094	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2093	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2092	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	C₂³×D₄×C₁₃	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	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#428	—	2	4	no	—
20	C₁₃×#427	—	2	4	no	—
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#418	—	2	4	no	—
28	C₂×C₁₃×#102	—	2	4	no	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×#102	C₂²	1	2	yes	—
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₁₃×#390	—	2	2	no	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#390	C₂²	1	2	yes	—
36	C₁₃×#389	—	2	2	no	—
37	C₁₃×#385	—	2	2	no	—
38	C₁₃×#384	C₂²	1	2	yes	complemented
39	C₁₃×#382	C₂²	1	2	yes	complemented
40	C₁₃×#379	—	2	2	no	—
41	C₁₃×#336	C₂²	1	2	yes	complemented
42	C₁₃×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	Q₈	1	4	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×M₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
57	C₂²×C₈×C₁₃	—	2	2	no	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₃	D₄	1	4	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#117	—	2	2	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	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	4	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	—	2	1	no	—
86	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
87	C₁₃×#107	—	2	2	no	—
88	C₁₃×#107	—	2	2	no	—
89	C₁₃×#107	—	2	4	no	—
90	C₁₃×#106	—	2	2	no	—
91	C₁₃×#106	—	2	2	no	—
92	C₁₃×#106	—	2	4	no	—
93	C₁₃×#102	—	2	4	no	—
94	C₁₃×#102	—	2	4	no	—
95	C₁₃×#102	—	2	4	no	—
96	C₁₃×#102	—	2	4	no	—
97	C₁₃×#95	—	2	4	no	—
98	#23735	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	—	2	2	no	—
100	C₂⁴×C₁₃	—	2	4	no	—
101	C₂⁴×C₁₃	—	4	2	no	—
102	C₂⁴×C₁₃	—	4	2	no	—
103	C₂⁴×C₁₃	—	8	2	no	—
104	C₂⁴×C₁₃	—	8	2	no	—
105	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₃	—	2	8	no	—
107	C₂×D₄×C₁₃	—	2	8	no	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	4	4	no	—
115	C₂×D₄×C₁₃	—	4	4	no	—
116	C₂×D₄×C₁₃	—	4	2	no	—
117	C₂×D₄×C₁₃	—	4	2	no	—
118	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₃	—	8	2	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
131	C₂²×C₄×C₁₃	#41	1	2	yes	—
132	C₂²×C₄×C₁₃	#41	1	2	yes	—
133	C₂²×C₄×C₁₃	#41	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×M₁₆	—	2	8	no	—
136	C₂×C₈×C₁₃	—	2	8	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
145	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	4	2	no	—
158	C₁₃×C₄⋊C₄	—	8	4	no	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₁₃×C₂²⋊C₄	—	4	2	no	—
161	C₁₃×C₂²⋊C₄	—	4	2	no	—
162	C₁₃×C₂²⋊C₄	—	8	4	no	—
163	C₁₃×C₂²⋊C₄	—	8	4	no	—
164	C₄²×C₁₃	—	2	2	no	—
165	C₄²×C₁₃	—	2	2	no	—
166	C₄²×C₁₃	—	4	2	no	—
167	C₄²×C₁₃	—	4	2	no	—
168	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂×#418	C₂×C₁₃	1	1	yes	characteristic
171	C₂²×#102	C₂×C₁₃	1	1	yes	characteristic
172	#2317	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#2309	C₂×C₁₃	1	1	yes	characteristic
174	#2094	C₂×C₁₃	1	2	yes	complemented
175	#2093	C₂×C₁₃	1	2	yes	complemented
176	#2092	C₂×C₁₃	1	2	yes	complemented
177	#2092	C₂×C₁₃	1	2	yes	complemented
178	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	4	no	—
182	C₂³×C₁₃	—	4	2	no	—
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	—	4	4	no	—
185	C₂³×C₁₃	—	4	4	no	—
186	C₂³×C₁₃	—	4	8	no	—
187	C₂³×C₁₃	—	8	8	no	—
188	C₂³×C₁₃	—	8	8	no	—
189	C₂³×C₁₃	—	8	4	no	—
190	C₂³×C₁₃	—	8	4	no	—
191	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
192	C₂³×C₁₃	#123	1	2	yes	—
193	C₂³×C₁₃	#127	1	2	yes	—
194	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	D₄×C₁₃	—	2	4	no	—
196	D₄×C₁₃	—	2	4	no	—
197	D₄×C₁₃	—	4	2	no	—
198	D₄×C₁₃	—	4	2	no	—
199	D₄×C₁₃	—	4	8	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	8	4	no	—
214	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
215	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
216	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
217	C₂×C₄×C₁₃	#123	1	4	yes	—
218	C₂×C₄×C₁₃	#123	1	4	yes	—
219	C₂×C₄×C₁₃	#123	1	2	yes	—
220	C₂×C₄×C₁₃	#127	1	2	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	2	2	no	—
229	C₈×C₁₃	—	2	4	no	—
230	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
232	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
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	#428	—	2	4	no	—
238	#427	—	2	4	no	—
239	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
240	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
241	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
242	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
243	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
244	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
245	#418	—	2	4	no	—
246	C₂×#102	—	2	4	no	—
247	C₂×#102	C₂²×C₁₃	1	2	yes	—
248	C₂×#102	C₂²×C₁₃	1	2	yes	—
249	C₂×#102	C₂²×C₁₃	1	2	yes	—
250	C₂×#102	C₂²×C₁₃	1	2	yes	—
251	#390	—	2	2	no	—
252	#390	C₂²×C₁₃	1	2	yes	—
253	#390	C₂²×C₁₃	1	2	yes	—
254	#389	—	2	2	no	—
255	#385	—	2	2	no	—
256	#384	C₂²×C₁₃	1	2	yes	complemented
257	#382	C₂²×C₁₃	1	2	yes	complemented
258	#379	—	2	2	no	—
259	#336	C₂²×C₁₃	1	2	yes	complemented
260	#336	C₂²×C₁₃	1	2	yes	complemented
261	C₂²×C₁₃	—	2	4	no	—
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	2	2	no	—
265	C₂²×C₁₃	—	4	8	no	—
266	C₂²×C₁₃	—	4	4	no	—
267	C₂²×C₁₃	—	8	16	no	—
268	C₂²×C₁₃	—	8	4	no	—
269	C₂²×C₁₃	—	8	2	no	—
270	C₂²×C₁₃	—	8	2	no	—
271	C₂²×C₁₃	#399	1	4	yes	—
272	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
273	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
274	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
275	C₂²×C₁₃	#576	1	2	yes	—
276	C₂²×C₁₃	#577	1	2	yes	—
277	C₄×C₁₃	—	4	4	no	—
278	C₄×C₁₃	—	8	1	no	—
279	C₄×C₁₃	—	8	1	no	—
280	C₄×C₁₃	—	8	1	no	—
281	C₄×C₁₃	—	8	1	no	—
282	C₄×C₁₃	—	8	2	no	—
283	C₄×C₁₃	#399	1	4	yes	—
284	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
285	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
286	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
287	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
288	C₂⁵	—	2	1	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	Q₈×C₁₃	1	4	yes	—
296	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	2	no	—
304	C₂²×C₈	D₄×C₁₃	1	4	yes	—
305	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
308	#117	—	2	2	no	—
309	#117	—	2	2	no	—
310	#117	—	2	2	no	—
311	#117	—	2	2	no	—
312	#117	—	2	2	no	—
313	#117	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	4	no	—
318	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	4	no	—
327	C₂×C₂²⋊C₄	—	2	4	no	—
328	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
332	#107	—	2	2	no	—
333	#107	—	2	2	no	—
334	#107	—	2	4	no	—
335	#106	—	2	2	no	—
336	#106	—	2	2	no	—
337	#106	—	2	4	no	—
338	#102	—	2	4	no	—
339	#102	—	2	4	no	—
340	#102	—	2	4	no	—
341	#102	—	2	4	no	—
342	#95	—	2	4	no	—
343	C₂×C₁₃	—	2	4	no	—
344	C₂×C₁₃	—	8	4	no	—
345	C₂×C₁₃	C₂×#399	1	1	yes	characteristic
346	C₂×C₁₃	#3081	1	2	yes	—
347	C₂×C₁₃	#3096	1	2	yes	—
348	C₂×C₁₃	#3154	1	1	yes	characteristic
349	C₂×C₁₃	#3155	1	1	yes	characteristic
350	C₂⁴	—	2	2	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	4	2	no	—
353	C₂⁴	—	4	2	no	—
354	C₂⁴	—	8	2	no	—
355	C₂⁴	—	8	2	no	—
356	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	4	no	—
367	C₂×D₄	—	4	4	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	8	2	no	—
377	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
378	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
381	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
382	C₂²×C₄	C₁₃×#41	1	2	yes	—
383	C₂²×C₄	C₁₃×#41	1	2	yes	—
384	C₂²×C₄	C₁₃×#41	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
386	M₁₆	—	2	8	no	—
387	C₂×C₈	—	2	8	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
395	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
396	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	8	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	8	4	no	—
414	C₂²⋊C₄	—	8	4	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	4	2	no	—
418	C₄²	—	4	2	no	—
419	C₁₃	#23735	1	1	yes	characteristic, direct product factor, Sylow
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	8	8	no	—
429	C₂³	—	8	8	no	—
430	C₂³	—	8	4	no	—
431	C₂³	—	8	4	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	D₄	—	2	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	4	8	no	—
439	D₄	—	4	2	no	—
440	D₄	—	4	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	8	4	no	—
455	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
456	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
457	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
458	C₂×C₄	C₁₃×#123	1	2	yes	—
459	C₂×C₄	C₁₃×#123	1	4	yes	—
460	C₂×C₄	C₁₃×#123	1	4	yes	—
461	C₂×C₄	C₁₃×#127	1	2	yes	—
462	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
465	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
466	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
467	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	8	16	no	—
478	C₂²	—	8	4	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	C₁₃×#399	1	4	yes	—
482	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
483	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
484	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
485	C₂²	C₁₃×#576	1	2	yes	—
486	C₂²	C₁₃×#577	1	2	yes	—
487	C₄	—	4	4	no	—
488	C₄	—	8	1	no	—
489	C₄	—	8	1	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	1	no	—
492	C₄	—	8	2	no	—
493	C₄	C₁₃×#399	1	4	yes	—
494	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
495	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
496	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
497	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
498	C₂	—	2	4	no	—
499	C₂	—	8	4	no	—
500	C₂	C₂×C₁₃×#399	1	1	yes	characteristic
501	C₂	C₁₃×#3081	1	2	yes	—
502	C₂	C₁₃×#3096	1	2	yes	—
503	C₂	C₁₃×#3154	1	1	yes	characteristic
504	C₂	C₁₃×#3155	1	1	yes	characteristic

	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×#428	C₂	semidirect
2. C₂×C₁₃×#427	C₂	semidirect
5. C₁₃×#2317	C₂	semidirect
7. C₁₃×#2094	C₂	semidirect
8. C₁₃×#2093	C₂	semidirect
9. C₁₃×#2092	C₂	semidirect
10. C₁₃×#2092	C₂	semidirect
11. C₁₃×#1729	C₂	semidirect
21. C₂×C₁₃×#107	C₂²	semidirect
22. C₂×C₁₃×#107	C₂²	semidirect
23. C₂×C₁₃×#107	C₂²	semidirect
24. C₂×C₁₃×#106	C₂²	semidirect
25. C₂×C₁₃×#106	C₂²	semidirect
26. C₂×C₁₃×#106	C₂²	semidirect
38. C₁₃×#384	C₂²	semidirect
39. C₁₃×#382	C₂²	semidirect
41. C₁₃×#336	C₂²	semidirect
42. C₁₃×#336	C₂²	semidirect
98. #23735	C₁₃	direct (N × H)
168. C₂×#428	C₂×C₁₃	semidirect
169. C₂×#427	C₂×C₁₃	semidirect
172. #2317	C₂×C₁₃	semidirect
174. #2094	C₂×C₁₃	semidirect
175. #2093	C₂×C₁₃	semidirect
176. #2092	C₂×C₁₃	semidirect
177. #2092	C₂×C₁₃	semidirect
178. #1729	C₂×C₁₃	semidirect
239. C₂×#107	C₂²×C₁₃	semidirect
240. C₂×#107	C₂²×C₁₃	semidirect
241. C₂×#107	C₂²×C₁₃	semidirect
242. C₂×#106	C₂²×C₁₃	semidirect
243. C₂×#106	C₂²×C₁₃	semidirect
244. C₂×#106	C₂²×C₁₃	semidirect
256. #384	C₂²×C₁₃	semidirect
257. #382	C₂²×C₁₃	semidirect
259. #336	C₂²×C₁₃	semidirect
260. #336	C₂²×C₁₃	semidirect
419. C₁₃	#23735	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
C₂×C₁₃×#427	2
C₂×C₁₃×#418	2
C₂²×C₁₃×#102	2
C₁₃×#2317	2
C₁₃×#2309	2
C₁₃×#2094	2
C₁₃×#2093	2
C₁₃×#2092	2
C₁₃×#1729	2
#23735	13

Subgroups — C13×#23735 #15710074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23735 #15710074