Subgroups — C₁₃×#24194 #15710533

Order 3328.

1138 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2014	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1958	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₁₃×#559	—	2	4	no	—
20	C₁₃×#559	—	2	4	no	—
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	—	2	1	no	—
23	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	—	2	1	no	—
26	C₂×C₁₃×#123	—	2	1	no	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	—	2	1	no	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#464	—	2	4	no	—
34	C₄×C₁₃×SD₁₆	—	2	4	no	—
35	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#400	—	2	1	no	—
49	C₁₃×#395	—	2	1	no	—
50	C₁₃×#391	C₂²	1	1	yes	characteristic
51	C₁₃×#391	C₂²	1	1	yes	characteristic
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	1	yes	characteristic
54	C₁₃×#387	—	2	1	no	—
55	C₁₃×#387	—	2	1	no	—
56	C₁₃×#382	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	—	2	1	no	—
71	C₂³×C₄×C₁₃	—	2	1	no	—
72	C₂×C₁₃×Q₁₆	—	2	2	no	—
73	C₂×C₁₃×Q₁₆	—	2	2	no	—
74	C₂×C₁₃×Q₁₆	—	4	1	no	—
75	C₂×C₁₃×SD₁₆	—	2	2	no	—
76	C₂×C₁₃×SD₁₆	—	2	2	no	—
77	C₂×C₁₃×SD₁₆	—	2	2	no	—
78	C₂×C₁₃×SD₁₆	—	2	2	no	—
79	C₂×C₁₃×SD₁₆	—	2	2	no	—
80	C₂×C₁₃×SD₁₆	—	4	1	no	—
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#127	—	2	2	no	—
86	C₁₃×#127	—	2	2	no	—
87	C₁₃×#124	—	2	8	no	—
88	C₁₃×#124	—	2	2	no	—
89	C₁₃×#124	—	2	2	no	—
90	C₁₃×#124	—	2	2	no	—
91	C₁₃×#124	D₄	1	4	yes	—
92	C₁₃×#123	—	2	8	no	—
93	C₁₃×#123	—	2	8	no	—
94	C₄×Q₈×C₁₃	—	2	2	no	—
95	C₄×Q₈×C₁₃	—	2	2	no	—
96	C₄×Q₈×C₁₃	—	2	2	no	—
97	C₄×Q₈×C₁₃	—	2	2	no	—
98	C₄×Q₈×C₁₃	—	2	2	no	—
99	C₄×Q₈×C₁₃	—	2	2	no	—
100	C₄×D₄×C₁₃	—	2	8	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	D₄	1	4	yes	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₄²×C₁₃	—	2	1	no	—
123	C₂×C₄²×C₁₃	—	2	1	no	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₁₃×#106	—	2	2	no	—
128	C₁₃×C₄⋊C₈	—	2	2	no	—
129	C₁₃×#103	—	2	2	no	—
130	C₁₃×#103	—	2	2	no	—
131	C₁₃×#103	—	2	2	no	—
132	C₁₃×#103	—	4	1	no	—
133	C₁₃×#102	—	2	2	no	—
134	C₁₃×#102	—	2	2	no	—
135	C₁₃×#102	—	2	2	no	—
136	C₁₃×#102	—	4	1	no	—
137	C₁₃×#102	—	4	1	no	—
138	C₁₃×#102	—	4	1	no	—
139	C₄×C₈×C₁₃	—	2	2	no	—
140	C₁₃×#95	—	2	1	no	—
141	C₁₃×#95	—	2	1	no	—
142	C₁₃×#95	—	2	1	no	—
143	C₁₃×#95	—	2	1	no	—
144	C₁₃×#95	—	2	1	no	—
145	C₁₃×#95	—	2	1	no	—
146	C₁₃×#95	—	2	1	no	—
147	C₁₃×#95	—	2	1	no	—
148	#24194	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂⁴×C₁₃	—	2	1	no	—
150	C₂⁴×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	2	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	4	1	no	—
164	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
165	C₂×Q₈×C₁₃	#41	1	2	yes	—
166	C₂×D₄×C₁₃	—	2	4	no	—
167	C₂×D₄×C₁₃	—	2	4	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	2	1	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	2	1	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	4	2	no	—
179	C₂×D₄×C₁₃	—	4	2	no	—
180	C₂×D₄×C₁₃	—	8	1	no	—
181	C₂×D₄×C₁₃	—	8	1	no	—
182	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
183	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	1	no	—
186	C₂²×C₄×C₁₃	—	2	1	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	2	4	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	8	1	no	—
193	C₂²×C₄×C₁₃	—	8	1	no	—
194	C₂²×C₄×C₁₃	—	8	1	no	—
195	C₂²×C₄×C₁₃	—	8	1	no	—
196	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₁₃×Q₁₆	—	4	4	no	—
204	C₁₃×SD₁₆	—	2	8	no	—
205	C₁₃×SD₁₆	—	4	4	no	—
206	C₂×C₈×C₁₃	—	2	1	no	—
207	C₂×C₈×C₁₃	—	2	1	no	—
208	C₂×C₈×C₁₃	—	2	1	no	—
209	C₂×C₈×C₁₃	—	2	1	no	—
210	C₂×C₈×C₁₃	—	2	1	no	—
211	C₂×C₈×C₁₃	—	2	1	no	—
212	C₂×C₈×C₁₃	—	2	1	no	—
213	C₂×C₈×C₁₃	—	2	1	no	—
214	C₂×C₈×C₁₃	—	2	1	no	—
215	C₂×C₈×C₁₃	—	2	1	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	#41	1	2	yes	—
218	C₁₃×C₄⋊C₄	—	2	4	no	—
219	C₁₃×C₄⋊C₄	—	2	2	no	—
220	C₁₃×C₄⋊C₄	—	2	2	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	1	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	4	2	no	—
230	C₁₃×C₄⋊C₄	—	4	2	no	—
231	C₁₃×C₄⋊C₄	—	4	2	no	—
232	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
233	C₁₃×C₂²⋊C₄	—	2	4	no	—
234	C₁₃×C₂²⋊C₄	—	2	4	no	—
235	C₁₃×C₂²⋊C₄	—	2	4	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₄²×C₁₃	—	2	4	no	—
240	C₄²×C₁₃	—	2	1	no	—
241	C₄²×C₁₃	—	2	1	no	—
242	C₄²×C₁₃	—	2	1	no	—
243	C₄²×C₁₃	—	2	1	no	—
244	C₄²×C₁₃	—	4	2	no	—
245	C₄²×C₁₃	C₂×D₄	1	2	yes	—
246	C₄²×C₁₃	C₂×D₄	1	2	yes	—
247	C₂×#559	C₂×C₁₃	1	1	yes	characteristic
248	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
249	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#2581	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#2041	C₂×C₁₃	1	1	yes	characteristic
253	#2015	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#2014	C₂×C₁₃	1	1	yes	characteristic
255	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#1958	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	4	1	no	—
265	C₂³×C₁₃	—	4	1	no	—
266	C₂³×C₁₃	—	4	1	no	—
267	C₂³×C₁₃	—	4	1	no	—
268	C₂³×C₁₃	—	4	1	no	—
269	C₂³×C₁₃	—	4	1	no	—
270	C₂³×C₁₃	—	4	1	no	—
271	C₂³×C₁₃	—	4	1	no	—
272	C₂³×C₁₃	—	4	1	no	—
273	C₂³×C₁₃	—	4	1	no	—
274	C₂³×C₁₃	—	4	1	no	—
275	C₂³×C₁₃	—	4	1	no	—
276	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
277	Q₈×C₁₃	—	2	2	no	—
278	Q₈×C₁₃	—	2	2	no	—
279	Q₈×C₁₃	—	2	2	no	—
280	Q₈×C₁₃	—	2	2	no	—
281	Q₈×C₁₃	—	4	4	no	—
282	Q₈×C₁₃	—	4	1	no	—
283	Q₈×C₁₃	—	4	1	no	—
284	Q₈×C₁₃	—	4	1	no	—
285	Q₈×C₁₃	—	4	1	no	—
286	D₄×C₁₃	—	2	2	no	—
287	D₄×C₁₃	—	2	2	no	—
288	D₄×C₁₃	—	2	2	no	—
289	D₄×C₁₃	—	2	2	no	—
290	D₄×C₁₃	—	4	8	no	—
291	D₄×C₁₃	—	4	1	no	—
292	D₄×C₁₃	—	4	1	no	—
293	D₄×C₁₃	—	4	1	no	—
294	D₄×C₁₃	—	4	1	no	—
295	D₄×C₁₃	—	8	4	no	—
296	C₂×C₄×C₁₃	—	2	1	no	—
297	C₂×C₄×C₁₃	—	2	1	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	1	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	1	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	1	no	—
304	C₂×C₄×C₁₃	—	2	1	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	1	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	—	4	1	no	—
320	C₂×C₄×C₁₃	—	4	1	no	—
321	C₂×C₄×C₁₃	—	4	1	no	—
322	C₂×C₄×C₁₃	—	4	1	no	—
323	C₂×C₄×C₁₃	—	4	1	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	1	no	—
326	C₂×C₄×C₁₃	—	4	1	no	—
327	C₂×C₄×C₁₃	—	4	1	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	8	4	no	—
330	C₂×C₄×C₁₃	—	8	4	no	—
331	C₂×C₄×C₁₃	#120	1	2	yes	—
332	C₂×C₄×C₁₃	#120	1	2	yes	—
333	C₂×C₄×C₁₃	#135	1	2	yes	—
334	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
340	C₈×C₁₃	—	2	2	no	—
341	C₈×C₁₃	—	4	1	no	—
342	C₈×C₁₃	—	4	1	no	—
343	C₈×C₁₃	—	4	1	no	—
344	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
345	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
346	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
347	#559	—	2	4	no	—
348	#559	—	2	4	no	—
349	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#124	—	2	1	no	—
351	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#123	—	2	1	no	—
354	C₂×#123	—	2	1	no	—
355	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×C₄×D₄	—	2	1	no	—
359	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
361	#464	—	2	4	no	—
362	C₄×SD₁₆	—	2	4	no	—
363	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
373	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
374	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
376	#400	—	2	1	no	—
377	#395	—	2	1	no	—
378	#391	C₂²×C₁₃	1	1	yes	characteristic
379	#391	C₂²×C₁₃	1	1	yes	characteristic
380	#389	C₂²×C₁₃	1	1	yes	characteristic
381	#389	C₂²×C₁₃	1	1	yes	characteristic
382	#387	—	2	1	no	—
383	#387	—	2	1	no	—
384	#382	C₂²×C₁₃	1	1	yes	characteristic
385	#340	C₂²×C₁₃	1	1	yes	characteristic
386	#340	C₂²×C₁₃	1	1	yes	characteristic
387	#336	C₂²×C₁₃	1	1	yes	characteristic
388	#336	C₂²×C₁₃	1	1	yes	characteristic
389	#336	C₂²×C₁₃	1	1	yes	characteristic
390	#336	C₂²×C₁₃	1	1	yes	characteristic
391	C₂²×C₁₃	—	4	2	no	—
392	C₂²×C₁₃	—	4	2	no	—
393	C₂²×C₁₃	—	4	2	no	—
394	C₂²×C₁₃	—	4	2	no	—
395	C₂²×C₁₃	—	4	2	no	—
396	C₂²×C₁₃	—	4	2	no	—
397	C₂²×C₁₃	—	8	1	no	—
398	C₂²×C₁₃	—	8	1	no	—
399	C₂²×C₁₃	—	8	1	no	—
400	C₂²×C₁₃	—	8	1	no	—
401	C₂²×C₁₃	—	8	1	no	—
402	C₂²×C₁₃	—	8	1	no	—
403	C₂²×C₁₃	—	8	1	no	—
404	C₂²×C₁₃	—	8	1	no	—
405	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
406	C₂²×C₁₃	#548	1	1	yes	characteristic
407	C₂²×C₁₃	#550	1	1	yes	characteristic
408	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
409	C₂²×C₁₃	#575	1	1	yes	characteristic
410	C₂²×C₁₃	#577	1	1	yes	characteristic
411	C₂²×C₁₃	#577	1	1	yes	characteristic
412	C₄×C₁₃	—	2	2	no	—
413	C₄×C₁₃	—	2	2	no	—
414	C₄×C₁₃	—	2	2	no	—
415	C₄×C₁₃	—	4	2	no	—
416	C₄×C₁₃	—	4	2	no	—
417	C₄×C₁₃	—	4	1	no	—
418	C₄×C₁₃	—	4	1	no	—
419	C₄×C₁₃	—	4	1	no	—
420	C₄×C₁₃	—	4	2	no	—
421	C₄×C₁₃	—	8	1	no	—
422	C₄×C₁₃	—	8	1	no	—
423	C₄×C₁₃	—	8	1	no	—
424	C₄×C₁₃	#525	1	1	yes	characteristic
425	C₄×C₁₃	#537	1	1	yes	characteristic
426	C₄×C₁₃	#546	1	1	yes	characteristic
427	C₄×C₁₃	#547	1	1	yes	characteristic
428	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
429	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	—	2	1	no	—
433	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
434	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₂³×C₄	—	2	1	no	—
436	C₂³×C₄	—	2	1	no	—
437	C₂×Q₁₆	—	2	2	no	—
438	C₂×Q₁₆	—	2	2	no	—
439	C₂×Q₁₆	—	4	1	no	—
440	C₂×SD₁₆	—	2	2	no	—
441	C₂×SD₁₆	—	2	2	no	—
442	C₂×SD₁₆	—	2	2	no	—
443	C₂×SD₁₆	—	2	2	no	—
444	C₂×SD₁₆	—	2	2	no	—
445	C₂×SD₁₆	—	4	1	no	—
446	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
450	#127	—	2	2	no	—
451	#127	—	2	2	no	—
452	#124	—	2	8	no	—
453	#124	—	2	2	no	—
454	#124	—	2	2	no	—
455	#124	—	2	2	no	—
456	#124	D₄×C₁₃	1	4	yes	—
457	#123	—	2	8	no	—
458	#123	—	2	8	no	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	—	2	2	no	—
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×D₄	—	2	8	no	—
466	C₄×D₄	—	2	2	no	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	—	2	2	no	—
469	C₄×D₄	D₄×C₁₃	1	4	yes	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₄²	—	2	1	no	—
488	C₂×C₄²	—	2	1	no	—
489	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
492	#106	—	2	2	no	—
493	C₄⋊C₈	—	2	2	no	—
494	#103	—	2	2	no	—
495	#103	—	2	2	no	—
496	#103	—	2	2	no	—
497	#103	—	4	1	no	—
498	#102	—	2	2	no	—
499	#102	—	2	2	no	—
500	#102	—	2	2	no	—
501	#102	—	4	1	no	—
502	#102	—	4	1	no	—
503	#102	—	4	1	no	—
504	C₄×C₈	—	2	2	no	—
505	#95	—	2	1	no	—
506	#95	—	2	1	no	—
507	#95	—	2	1	no	—
508	#95	—	2	1	no	—
509	#95	—	2	1	no	—
510	#95	—	2	1	no	—
511	#95	—	2	1	no	—
512	#95	—	2	1	no	—
513	C₂×C₁₃	—	8	2	no	—
514	C₂×C₁₃	—	8	2	no	—
515	C₂×C₁₃	#2407	1	1	yes	characteristic
516	C₂×C₁₃	#3002	1	1	yes	characteristic
517	C₂×C₁₃	#3009	1	1	yes	characteristic
518	C₂×C₁₃	#3365	1	1	yes	characteristic
519	C₂×C₁₃	#3371	1	1	yes	characteristic
520	C₂×C₁₃	#3394	1	1	yes	characteristic
521	C₂×C₁₃	#3401	1	1	yes	characteristic
522	C₂⁴	—	2	1	no	—
523	C₂⁴	—	2	1	no	—
524	C₂×Q₈	—	2	2	no	—
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	4	1	no	—
537	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
538	C₂×Q₈	C₁₃×#41	1	2	yes	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	4	2	no	—
552	C₂×D₄	—	4	2	no	—
553	C₂×D₄	—	8	1	no	—
554	C₂×D₄	—	8	1	no	—
555	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
556	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	8	1	no	—
566	C₂²×C₄	—	8	1	no	—
567	C₂²×C₄	—	8	1	no	—
568	C₂²×C₄	—	8	1	no	—
569	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
576	Q₁₆	—	4	4	no	—
577	SD₁₆	—	2	8	no	—
578	SD₁₆	—	4	4	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	C₁₃×#41	1	2	yes	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	4	2	no	—
603	C₄⋊C₄	—	4	2	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₄²	—	2	4	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	4	2	no	—
618	C₄²	C₂×D₄×C₁₃	1	2	yes	—
619	C₄²	C₂×D₄×C₁₃	1	2	yes	—
620	C₁₃	#24194	1	1	yes	characteristic, direct product factor, Sylow
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	4	1	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
636	Q₈	—	2	2	no	—
637	Q₈	—	2	2	no	—
638	Q₈	—	2	2	no	—
639	Q₈	—	2	2	no	—
640	Q₈	—	4	4	no	—
641	Q₈	—	4	1	no	—
642	Q₈	—	4	1	no	—
643	Q₈	—	4	1	no	—
644	Q₈	—	4	1	no	—
645	D₄	—	2	2	no	—
646	D₄	—	2	2	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	2	no	—
649	D₄	—	4	8	no	—
650	D₄	—	4	1	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	8	4	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	8	4	no	—
689	C₂×C₄	—	8	4	no	—
690	C₂×C₄	C₁₃×#120	1	2	yes	—
691	C₂×C₄	C₁₃×#120	1	2	yes	—
692	C₂×C₄	C₁₃×#135	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
695	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
696	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
697	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
699	C₈	—	2	2	no	—
700	C₈	—	4	1	no	—
701	C₈	—	4	1	no	—
702	C₈	—	4	1	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	—	8	1	no	—
712	C₂²	—	8	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	—	8	1	no	—
716	C₂²	—	8	1	no	—
717	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
718	C₂²	C₁₃×#548	1	1	yes	characteristic
719	C₂²	C₁₃×#550	1	1	yes	characteristic
720	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
721	C₂²	C₁₃×#575	1	1	yes	characteristic
722	C₂²	C₁₃×#577	1	1	yes	characteristic
723	C₂²	C₁₃×#577	1	1	yes	characteristic
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	2	2	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	1	no	—
733	C₄	—	8	1	no	—
734	C₄	—	8	1	no	—
735	C₄	—	8	1	no	—
736	C₄	C₁₃×#525	1	1	yes	characteristic
737	C₄	C₁₃×#537	1	1	yes	characteristic
738	C₄	C₁₃×#546	1	1	yes	characteristic
739	C₄	C₁₃×#547	1	1	yes	characteristic
740	C₂	—	8	2	no	—
741	C₂	—	8	2	no	—
742	C₂	C₁₃×#2407	1	1	yes	characteristic
743	C₂	C₁₃×#3002	1	1	yes	characteristic
744	C₂	C₁₃×#3009	1	1	yes	characteristic
745	C₂	C₁₃×#3365	1	1	yes	characteristic
746	C₂	C₁₃×#3371	1	1	yes	characteristic
747	C₂	C₁₃×#3394	1	1	yes	characteristic
748	C₂	C₁₃×#3401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	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
2. C₂×C₁₃×#464	C₂	semidirect
3. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
4. C₁₃×#2581	C₂	semidirect
5. C₁₃×#2042	C₂	semidirect
7. C₁₃×#2015	C₂	semidirect
9. C₁₃×#1984	C₂	semidirect
10. C₁₃×#1958	C₂	semidirect
11. C₁₃×#1878	C₂	semidirect
12. C₁₃×#1877	C₂	semidirect
13. C₁₃×#1865	C₂	semidirect
14. C₁₃×#1864	C₂	semidirect
15. C₁₃×#1804	C₂	semidirect
148. #24194	C₁₃	direct (N × H)
248. C₂×#464	C₂×C₁₃	semidirect
249. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
250. #2581	C₂×C₁₃	semidirect
251. #2042	C₂×C₁₃	semidirect
253. #2015	C₂×C₁₃	semidirect
255. #1984	C₂×C₁₃	semidirect
256. #1958	C₂×C₁₃	semidirect
257. #1878	C₂×C₁₃	semidirect
258. #1877	C₂×C₁₃	semidirect
259. #1865	C₂×C₁₃	semidirect
260. #1864	C₂×C₁₃	semidirect
261. #1804	C₂×C₁₃	semidirect
620. C₁₃	#24194	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×#559	2
C₂×C₁₃×#464	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2581	2
C₁₃×#2042	2
C₁₃×#2041	2
C₁₃×#2015	2
C₁₃×#2014	2
C₁₃×#1984	2
C₁₃×#1958	2
C₁₃×#1878	2
C₁₃×#1877	2
C₁₃×#1865	2
C₁₃×#1864	2
C₁₃×#1804	2
#24194	13

Subgroups — C13×#24194 #15710533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24194 #15710533