Subgroups — C₁₃×#23458 #15709797

Order 3328.

1250 conjugacy classes of subgroups.

The subgroup lattice has 594 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×#417	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2311	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2026	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2025	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2024	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#340	C₂	1	1	yes	maximal, characteristic, 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	C₁₃×#544	—	2	4	no	—
16	C₁₃×#544	—	2	4	no	—
17	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#125	—	2	1	no	—
20	C₂×C₁₃×#125	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₁₃×#417	—	2	4	no	—
27	C₁₃×#416	—	2	4	no	—
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₁₃×#391	C₂²	1	2	yes	—
35	C₁₃×#390	C₂²	1	2	yes	—
36	C₁₃×#386	—	2	2	no	—
37	C₁₃×#380	—	2	1	no	—
38	C₁₃×#380	—	2	1	no	—
39	C₁₃×#340	C₂²	1	2	yes	—
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	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	—	2	2	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂×C₁₃×#41	Q₈	1	4	yes	complemented
51	C₂²×Q₈×C₁₃	—	2	2	no	—
52	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	—	2	1	no	—
56	C₂³×C₄×C₁₃	—	2	1	no	—
57	C₂³×C₄×C₁₃	—	2	1	no	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂²×C₈×C₁₃	—	2	2	no	—
63	C₂²×C₈×C₁₃	—	2	2	no	—
64	C₂²×C₈×C₁₃	—	2	2	no	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
68	C₁₃×C₄⋊Q₈	—	2	8	no	—
69	C₁₃×C₄⋊Q₈	—	2	4	no	—
70	C₁₃×C₄⋊Q₈	—	2	4	no	—
71	C₁₃×#125	—	2	8	no	—
72	C₁₃×#125	—	2	4	no	—
73	C₁₃×#125	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	16	no	—
75	C₁₃×#117	—	2	2	no	—
76	C₁₃×#117	—	2	2	no	—
77	C₁₃×#117	—	2	2	no	—
78	C₁₃×#117	D₄	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
100	C₁₃×#103	—	2	2	no	—
101	C₁₃×#103	—	2	2	no	—
102	C₁₃×#103	—	2	4	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	—	2	2	no	—
105	C₁₃×#102	—	2	4	no	—
106	C₁₃×#95	—	2	2	no	—
107	C₁₃×#95	—	2	2	no	—
108	#23458	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	1	no	—
110	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₁₃×#41	—	2	8	no	—
112	C₁₃×#41	—	2	8	no	—
113	C₁₃×#41	—	4	4	no	—
114	C₁₃×#41	—	4	4	no	—
115	C₂×Q₈×C₁₃	—	2	8	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	2	1	no	—
119	C₂×Q₈×C₁₃	—	2	1	no	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	8	2	no	—
122	C₂×Q₈×C₁₃	—	8	2	no	—
123	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	2	1	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	4	2	no	—
131	C₂×D₄×C₁₃	—	4	2	no	—
132	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	—	4	2	no	—
143	C₂²×C₄×C₁₃	—	8	1	no	—
144	C₂²×C₄×C₁₃	—	8	1	no	—
145	C₂²×C₄×C₁₃	—	8	1	no	—
146	C₂²×C₄×C₁₃	—	8	1	no	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
153	C₂²×C₄×C₁₃	#41	1	2	yes	—
154	C₂²×C₄×C₁₃	#41	1	2	yes	—
155	C₂²×C₄×C₁₃	#41	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₁₃×M₁₆	—	4	4	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	4	4	no	—
168	C₁₃×C₄⋊C₄	—	2	8	no	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	2	8	no	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	4	2	no	—
180	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
183	C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	8	2	no	—
186	C₁₃×C₂²⋊C₄	—	8	2	no	—
187	C₄²×C₁₃	—	2	4	no	—
188	C₄²×C₁₃	—	2	2	no	—
189	C₄²×C₁₃	—	2	2	no	—
190	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
192	C₂×#416	C₂×C₁₃	1	1	yes	characteristic
193	#2311	C₂×C₁₃	1	1	yes	characteristic
194	#2026	C₂×C₁₃	1	2	yes	complemented
195	#2025	C₂×C₁₃	1	2	yes	complemented
196	#2024	C₂×C₁₃	1	2	yes	complemented
197	#2023	C₂×C₁₃	1	2	yes	complemented
198	#1736	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#340	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#1729	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂³×C₁₃	—	2	1	no	—
202	C₂³×C₁₃	—	2	1	no	—
203	C₂³×C₁₃	—	2	1	no	—
204	C₂³×C₁₃	—	2	1	no	—
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	4	1	no	—
207	C₂³×C₁₃	—	4	1	no	—
208	C₂³×C₁₃	—	4	1	no	—
209	C₂³×C₁₃	—	4	1	no	—
210	C₂³×C₁₃	—	4	1	no	—
211	C₂³×C₁₃	—	4	1	no	—
212	C₂³×C₁₃	#120	1	2	yes	—
213	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
214	C₂³×C₁₃	#124	1	2	yes	—
215	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	Q₈×C₁₃	—	2	2	no	—
217	Q₈×C₁₃	—	2	2	no	—
218	Q₈×C₁₃	—	4	1	no	—
219	Q₈×C₁₃	—	4	1	no	—
220	Q₈×C₁₃	—	8	8	no	—
221	D₄×C₁₃	—	2	2	no	—
222	D₄×C₁₃	—	2	2	no	—
223	D₄×C₁₃	—	4	8	no	—
224	D₄×C₁₃	—	4	1	no	—
225	D₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	8	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	8	4	no	—
249	C₂×C₄×C₁₃	—	8	4	no	—
250	C₂×C₄×C₁₃	#120	1	2	yes	—
251	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
252	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
253	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
254	C₂×C₄×C₁₃	#124	1	4	yes	—
255	C₂×C₄×C₁₃	#124	1	4	yes	—
256	C₂×C₄×C₁₃	#124	1	2	yes	—
257	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
263	C₈×C₁₃	—	4	1	no	—
264	C₈×C₁₃	—	4	1	no	—
265	C₈×C₁₃	—	4	2	no	—
266	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
267	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
268	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
269	#544	—	2	4	no	—
270	#544	—	2	4	no	—
271	C₂×C₄⋊Q₈	—	2	1	no	—
272	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
273	C₂×#125	—	2	1	no	—
274	C₂×#125	C₂²×C₁₃	1	2	yes	—
275	C₂×C₂²⋊Q₈	—	2	2	no	—
276	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
278	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
280	#417	—	2	4	no	—
281	#416	—	2	4	no	—
282	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#103	C₂²×C₁₃	1	2	yes	—
285	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#102	C₂²×C₁₃	1	2	yes	—
288	#391	C₂²×C₁₃	1	2	yes	—
289	#390	C₂²×C₁₃	1	2	yes	—
290	#386	—	2	2	no	—
291	#380	—	2	1	no	—
292	#380	—	2	1	no	—
293	#340	C₂²×C₁₃	1	2	yes	—
294	#340	C₂²×C₁₃	1	2	yes	—
295	#340	C₂²×C₁₃	1	2	yes	—
296	#340	C₂²×C₁₃	1	2	yes	—
297	#336	C₂²×C₁₃	1	2	yes	—
298	#336	C₂²×C₁₃	1	2	yes	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	—	2	2	no	—
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	4	2	no	—
306	C₂²×C₁₃	—	4	2	no	—
307	C₂²×C₁₃	—	4	2	no	—
308	C₂²×C₁₃	—	8	1	no	—
309	C₂²×C₁₃	—	8	1	no	—
310	C₂²×C₁₃	—	8	1	no	—
311	C₂²×C₁₃	—	8	1	no	—
312	C₂²×C₁₃	#393	1	4	yes	—
313	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
314	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
315	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
316	C₂²×C₁₃	#576	1	1	yes	characteristic
317	C₂²×C₁₃	#577	1	1	yes	characteristic
318	C₂²×C₁₃	#577	1	1	yes	characteristic
319	C₂²×C₁₃	#578	1	1	yes	characteristic
320	C₄×C₁₃	—	4	2	no	—
321	C₄×C₁₃	—	4	2	no	—
322	C₄×C₁₃	—	4	4	no	—
323	C₄×C₁₃	—	4	2	no	—
324	C₄×C₁₃	—	4	2	no	—
325	C₄×C₁₃	—	4	2	no	—
326	C₄×C₁₃	—	8	2	no	—
327	C₄×C₁₃	#393	1	4	yes	—
328	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
329	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
330	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
331	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	Q₈×C₁₃	1	4	yes	complemented
338	C₂²×Q₈	—	2	2	no	—
339	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×M₁₆	—	2	2	no	—
347	C₂×M₁₆	—	2	2	no	—
348	C₂×M₁₆	—	2	2	no	—
349	C₂²×C₈	—	2	2	no	—
350	C₂²×C₈	—	2	2	no	—
351	C₂²×C₈	—	2	2	no	—
352	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
355	C₄⋊Q₈	—	2	8	no	—
356	C₄⋊Q₈	—	2	4	no	—
357	C₄⋊Q₈	—	2	4	no	—
358	#125	—	2	8	no	—
359	#125	—	2	4	no	—
360	#125	—	2	4	no	—
361	C₂²⋊Q₈	—	2	16	no	—
362	#117	—	2	2	no	—
363	#117	—	2	2	no	—
364	#117	—	2	2	no	—
365	#117	D₄×C₁₃	1	4	yes	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
387	#103	—	2	2	no	—
388	#103	—	2	2	no	—
389	#103	—	2	4	no	—
390	#102	—	2	2	no	—
391	#102	—	2	2	no	—
392	#102	—	2	4	no	—
393	#95	—	2	2	no	—
394	#95	—	2	2	no	—
395	C₂×C₁₃	—	2	4	no	—
396	C₂×C₁₃	—	8	2	no	—
397	C₂×C₁₃	C₂×#393	1	1	yes	characteristic
398	C₂×C₁₃	#3012	1	1	yes	characteristic
399	C₂×C₁₃	#3013	1	1	yes	characteristic
400	C₂×C₁₃	#3083	1	1	yes	characteristic
401	C₂×C₁₃	#3084	1	1	yes	characteristic
402	C₂×C₁₃	#3136	1	1	yes	characteristic
403	C₂×C₁₃	#3137	1	1	yes	characteristic
404	C₂⁴	—	2	1	no	—
405	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
406	#41	—	2	8	no	—
407	#41	—	2	8	no	—
408	#41	—	4	4	no	—
409	#41	—	4	4	no	—
410	C₂×Q₈	—	2	8	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	8	2	no	—
417	C₂×Q₈	—	8	2	no	—
418	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	—	4	2	no	—
427	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	8	1	no	—
439	C₂²×C₄	—	8	1	no	—
440	C₂²×C₄	—	8	1	no	—
441	C₂²×C₄	—	8	1	no	—
442	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
446	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
447	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
448	C₂²×C₄	C₁₃×#41	1	2	yes	—
449	C₂²×C₄	C₁₃×#41	1	2	yes	—
450	C₂²×C₄	C₁₃×#41	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
452	M₁₆	—	4	4	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	4	4	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
476	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
477	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	8	2	no	—
481	C₂²⋊C₄	—	8	2	no	—
482	C₄²	—	2	4	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	2	no	—
485	C₁₃	#23458	1	1	yes	characteristic, direct product factor, Sylow
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	C₁₃×#120	1	2	yes	—
498	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
499	C₂³	C₁₃×#124	1	2	yes	—
500	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
501	Q₈	—	2	2	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	8	8	no	—
506	D₄	—	2	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	4	8	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	—	8	4	no	—
535	C₂×C₄	C₁₃×#120	1	2	yes	—
536	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
537	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
538	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
539	C₂×C₄	C₁₃×#124	1	2	yes	—
540	C₂×C₄	C₁₃×#124	1	4	yes	—
541	C₂×C₄	C₁₃×#124	1	4	yes	—
542	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
545	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
546	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
547	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	8	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	C₁₃×#393	1	4	yes	—
565	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
566	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
567	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
568	C₂²	C₁₃×#576	1	1	yes	characteristic
569	C₂²	C₁₃×#577	1	1	yes	characteristic
570	C₂²	C₁₃×#577	1	1	yes	characteristic
571	C₂²	C₁₃×#578	1	1	yes	characteristic
572	C₄	—	4	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	8	2	no	—
579	C₄	C₁₃×#393	1	4	yes	—
580	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
581	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
582	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
583	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
584	C₂	—	2	4	no	—
585	C₂	—	8	2	no	—
586	C₂	C₂×C₁₃×#393	1	1	yes	characteristic
587	C₂	C₁₃×#3012	1	1	yes	characteristic
588	C₂	C₁₃×#3013	1	1	yes	characteristic
589	C₂	C₁₃×#3083	1	1	yes	characteristic
590	C₂	C₁₃×#3084	1	1	yes	characteristic
591	C₂	C₁₃×#3136	1	1	yes	characteristic
592	C₂	C₁₃×#3137	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×#544	C₂	semidirect
5. C₁₃×#2026	C₂	semidirect
6. C₁₃×#2025	C₂	semidirect
7. C₁₃×#2024	C₂	semidirect
8. C₁₃×#2023	C₂	semidirect
9. C₁₃×#1736	C₂	semidirect
10. C₂×C₁₃×#340	C₂	semidirect
11. C₁₃×#1729	C₂	semidirect
50. C₂×C₁₃×#41	Q₈	semidirect
108. #23458	C₁₃	direct (N × H)
190. C₂×#544	C₂×C₁₃	semidirect
194. #2026	C₂×C₁₃	semidirect
195. #2025	C₂×C₁₃	semidirect
196. #2024	C₂×C₁₃	semidirect
197. #2023	C₂×C₁₃	semidirect
198. #1736	C₂×C₁₃	semidirect
199. C₂×#340	C₂×C₁₃	semidirect
200. #1729	C₂×C₁₃	semidirect
337. C₂×#41	Q₈×C₁₃	semidirect
485. C₁₃	#23458	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×#417	2
C₂×C₁₃×#416	2
C₁₃×#2311	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#2024	2
C₁₃×#2023	2
C₁₃×#1736	2
C₂×C₁₃×#340	2
C₁₃×#1729	2
#23458	13

Subgroups — C13×#23458 #15709797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23458 #15709797