Subgroups — C₁₃×#24503 #15710842

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2854	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1968	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1933	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1874	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×#123	—	2	1	no	—
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#448	—	2	4	no	—
19	C₁₃×#431	—	2	4	no	—
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#391	—	2	1	no	—
30	C₁₃×#391	—	2	1	no	—
31	C₁₃×#391	C₂²	1	2	yes	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#390	C₂²	1	1	yes	characteristic
34	C₁₃×#390	C₂²	1	1	yes	characteristic
35	C₁₃×#389	C₂²	1	1	yes	characteristic
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#388	—	2	1	no	—
38	C₁₃×#388	—	2	1	no	—
39	C₁₃×#386	—	2	1	no	—
40	C₁₃×#380	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#95	—	2	1	no	—
42	C₂×C₁₃×#95	—	2	1	no	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	4	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	—	2	2	no	—
49	C₂²×Q₈×C₁₃	—	4	2	no	—
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×SD₁₆	—	2	4	no	—
59	C₂×C₁₃×SD₁₆	—	2	4	no	—
60	C₂×C₁₃×SD₁₆	—	4	2	no	—
61	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
63	C₁₃×#123	—	4	4	no	—
64	C₁₃×#121	—	2	2	no	—
65	C₁₃×#121	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₄²×C₁₃	—	2	2	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#106	—	4	2	no	—
87	C₁₃×C₄⋊C₈	—	2	4	no	—
88	C₁₃×#103	—	2	4	no	—
89	C₁₃×#103	—	2	4	no	—
90	C₁₃×#103	—	4	2	no	—
91	C₁₃×#102	—	4	2	no	—
92	C₁₃×C₂²⋊C₈	—	2	2	no	—
93	C₁₃×C₂²⋊C₈	D₄	1	4	yes	—
94	C₄×C₈×C₁₃	—	2	4	no	—
95	C₁₃×#95	—	2	1	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	2	no	—
99	C₁₃×#95	—	2	2	no	—
100	C₁₃×#95	—	2	2	no	—
101	C₁₃×#95	—	2	2	no	—
102	#24503	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×Q₈×C₁₃	—	2	4	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	4	8	no	—
112	C₂×Q₈×C₁₃	—	4	8	no	—
113	C₂×Q₈×C₁₃	—	4	2	no	—
114	C₂×Q₈×C₁₃	—	4	2	no	—
115	C₂×Q₈×C₁₃	#41	1	4	yes	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	4	2	no	—
121	C₂×D₄×C₁₃	—	4	2	no	—
122	C₂×D₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	4	1	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	complemented
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	#41	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₁₃×SD₁₆	—	4	8	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	4	2	no	—
164	C₁₃×C₄⋊C₄	—	4	2	no	—
165	C₁₃×C₄⋊C₄	—	4	2	no	—
166	C₁₃×C₂²⋊C₄	—	4	2	no	—
167	C₁₃×C₂²⋊C₄	—	4	2	no	—
168	C₁₃×C₂²⋊C₄	—	4	2	no	—
169	C₁₃×C₂²⋊C₄	—	4	2	no	—
170	C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₁₃×C₂²⋊C₄	—	4	2	no	—
172	C₄²×C₁₃	—	2	2	no	—
173	C₄²×C₁₃	—	2	2	no	—
174	C₄²×C₁₃	—	2	1	no	—
175	C₄²×C₁₃	—	2	1	no	—
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₂×#448	C₂×C₁₃	1	1	yes	characteristic
179	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#2854	C₂×C₁₃	1	1	yes	characteristic
181	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#2066	C₂×C₁₃	1	2	yes	complemented
183	#2055	C₂×C₁₃	1	2	yes	complemented
184	#1968	C₂×C₁₃	1	2	yes	complemented
185	#1933	C₂×C₁₃	1	2	yes	complemented
186	#1874	C₂×C₁₃	1	1	yes	characteristic
187	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂³×C₁₃	—	2	1	no	—
190	C₂³×C₁₃	—	2	1	no	—
191	C₂³×C₁₃	—	2	1	no	—
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	4	1	no	—
194	C₂³×C₁₃	—	4	1	no	—
195	C₂³×C₁₃	—	4	1	no	—
196	C₂³×C₁₃	—	4	1	no	—
197	C₂³×C₁₃	—	4	1	no	—
198	C₂³×C₁₃	—	4	1	no	—
199	C₂³×C₁₃	—	4	1	no	—
200	C₂³×C₁₃	#121	1	2	yes	—
201	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
202	C₂³×C₁₃	#135	1	2	yes	—
203	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₃	—	2	4	no	—
205	Q₈×C₁₃	—	2	4	no	—
206	Q₈×C₁₃	—	4	8	no	—
207	Q₈×C₁₃	—	4	2	no	—
208	Q₈×C₁₃	—	4	2	no	—
209	D₄×C₁₃	—	4	2	no	—
210	D₄×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	8	4	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	8	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	4	4	no	—
228	C₂×C₄×C₁₃	—	4	8	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	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	1	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	8	4	no	—
244	C₂×C₄×C₁₃	#121	1	2	yes	—
245	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
246	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
247	C₂×C₄×C₁₃	#137	1	2	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
250	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
252	C₈×C₁₃	—	2	4	no	—
253	C₈×C₁₃	—	4	2	no	—
254	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
256	C₂×#123	—	2	1	no	—
257	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
259	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
260	#448	—	2	4	no	—
261	#431	—	2	4	no	—
262	C₂×#106	C₂²×C₁₃	1	2	yes	—
263	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
264	C₂×#103	C₂²×C₁₃	1	2	yes	—
265	C₂×#103	C₂²×C₁₃	1	2	yes	—
266	C₂×#103	C₂²×C₁₃	1	2	yes	—
267	C₂×#102	C₂²×C₁₃	1	2	yes	—
268	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
271	#391	—	2	1	no	—
272	#391	—	2	1	no	—
273	#391	C₂²×C₁₃	1	2	yes	—
274	#391	C₂²×C₁₃	1	2	yes	—
275	#390	C₂²×C₁₃	1	1	yes	characteristic
276	#390	C₂²×C₁₃	1	1	yes	characteristic
277	#389	C₂²×C₁₃	1	1	yes	characteristic
278	#389	C₂²×C₁₃	1	1	yes	characteristic
279	#388	—	2	1	no	—
280	#388	—	2	1	no	—
281	#386	—	2	1	no	—
282	#380	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#95	—	2	1	no	—
284	C₂×#95	—	2	1	no	—
285	#340	C₂²×C₁₃	1	2	yes	—
286	#340	C₂²×C₁₃	1	2	yes	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	2	2	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	8	1	no	—
294	C₂²×C₁₃	—	8	1	no	—
295	C₂²×C₁₃	—	8	1	no	—
296	C₂²×C₁₃	—	8	1	no	—
297	C₂²×C₁₃	—	8	1	no	—
298	C₂²×C₁₃	—	8	1	no	—
299	C₂²×C₁₃	—	8	1	no	—
300	C₂²×C₁₃	#465	1	4	yes	—
301	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
302	C₂²×C₁₃	#525	1	1	yes	characteristic
303	C₂²×C₁₃	#535	1	1	yes	characteristic
304	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
305	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
306	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
307	C₂²×C₁₃	#575	1	1	yes	characteristic
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	2	2	no	—
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	4	4	no	—
313	C₄×C₁₃	—	4	1	no	—
314	C₄×C₁₃	—	8	1	no	—
315	C₄×C₁₃	—	8	1	no	—
316	C₄×C₁₃	—	8	2	no	—
317	C₄×C₁₃	—	8	1	no	—
318	C₄×C₁₃	#546	1	2	yes	—
319	C₄×C₁₃	#551	1	2	yes	—
320	C₂²×Q₈	—	2	4	no	—
321	C₂²×Q₈	—	2	1	no	—
322	C₂²×Q₈	—	2	2	no	—
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	—	4	2	no	—
325	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	—	2	1	no	—
330	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×SD₁₆	—	2	4	no	—
334	C₂×SD₁₆	—	2	4	no	—
335	C₂×SD₁₆	—	4	2	no	—
336	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
337	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
338	#123	—	4	4	no	—
339	#121	—	2	2	no	—
340	#121	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	4	2	no	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₄²	—	2	2	no	—
356	C₂×C₄²	—	2	2	no	—
357	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
358	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
361	#106	—	4	2	no	—
362	C₄⋊C₈	—	2	4	no	—
363	#103	—	2	4	no	—
364	#103	—	2	4	no	—
365	#103	—	4	2	no	—
366	#102	—	4	2	no	—
367	C₂²⋊C₈	—	2	2	no	—
368	C₂²⋊C₈	D₄×C₁₃	1	4	yes	—
369	C₄×C₈	—	2	4	no	—
370	#95	—	2	2	no	—
371	#95	—	2	2	no	—
372	#95	—	2	2	no	—
373	#95	—	2	2	no	—
374	#95	—	2	1	no	—
375	#95	—	2	1	no	—
376	#95	—	2	1	no	—
377	C₂×C₁₃	—	2	4	no	—
378	C₂×C₁₃	—	16	1	no	—
379	C₂×C₁₃	#2411	1	1	yes	characteristic
380	C₂×C₁₃	C₂×#465	1	1	yes	characteristic
381	C₂×C₁₃	#3056	1	1	yes	characteristic
382	C₂×C₁₃	#3103	1	1	yes	characteristic
383	C₂×C₁₃	#3108	1	1	yes	characteristic
384	C₂×C₁₃	#3206	1	1	yes	characteristic
385	C₂×C₁₃	#3211	1	1	yes	characteristic
386	C₂⁴	—	2	1	no	—
387	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	4	8	no	—
395	C₂×Q₈	—	4	8	no	—
396	C₂×Q₈	—	4	2	no	—
397	C₂×Q₈	—	4	2	no	—
398	C₂×Q₈	C₁₃×#41	1	4	yes	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	4	1	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	complemented
425	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₁₃×#41	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
433	SD₁₆	—	4	8	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	2	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₁₃	#24503	1	1	yes	characteristic, direct product factor, Sylow
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	C₁₃×#121	1	2	yes	—
474	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
475	C₂³	C₁₃×#135	1	2	yes	—
476	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
477	Q₈	—	2	4	no	—
478	Q₈	—	2	4	no	—
479	Q₈	—	4	8	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	8	4	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	8	4	no	—
517	C₂×C₄	C₁₃×#121	1	2	yes	—
518	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
519	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
520	C₂×C₄	C₁₃×#137	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
522	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
523	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
524	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
525	C₈	—	2	4	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	C₁₃×#465	1	4	yes	—
541	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
542	C₂²	C₁₃×#525	1	1	yes	characteristic
543	C₂²	C₁₃×#535	1	1	yes	characteristic
544	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
545	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
546	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
547	C₂²	C₁₃×#575	1	1	yes	characteristic
548	C₄	—	2	2	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	4	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	2	no	—
558	C₄	C₁₃×#546	1	2	yes	—
559	C₄	C₁₃×#551	1	2	yes	—
560	C₂	—	2	4	no	—
561	C₂	—	16	1	no	—
562	C₂	C₁₃×#2411	1	1	yes	characteristic
563	C₂	C₂×C₁₃×#465	1	1	yes	characteristic
564	C₂	C₁₃×#3056	1	1	yes	characteristic
565	C₂	C₁₃×#3103	1	1	yes	characteristic
566	C₂	C₁₃×#3108	1	1	yes	characteristic
567	C₂	C₁₃×#3206	1	1	yes	characteristic
568	C₂	C₁₃×#3211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₁₃×#431	C₂	semidirect
4. C₂×C₁₃×#391	C₂	semidirect
5. C₁₃×#2066	C₂	semidirect
6. C₁₃×#2055	C₂	semidirect
7. C₁₃×#1968	C₂	semidirect
8. C₁₃×#1933	C₂	semidirect
10. C₁₃×#1853	C₂	semidirect
11. C₁₃×#1787	C₂	semidirect
102. #24503	C₁₃	direct (N × H)
141. C₂²×C₄×C₁₃	SD₁₆	semidirect
179. C₂×#431	C₂×C₁₃	semidirect
181. C₂×#391	C₂×C₁₃	semidirect
182. #2066	C₂×C₁₃	semidirect
183. #2055	C₂×C₁₃	semidirect
184. #1968	C₂×C₁₃	semidirect
185. #1933	C₂×C₁₃	semidirect
187. #1853	C₂×C₁₃	semidirect
188. #1787	C₂×C₁₃	semidirect
424. C₂²×C₄	C₁₃×SD₁₆	semidirect
461. C₁₃	#24503	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×#448	2
C₂×C₁₃×#431	2
C₁₃×#2854	2
C₂×C₁₃×#391	2
C₁₃×#2066	2
C₁₃×#2055	2
C₁₃×#1968	2
C₁₃×#1933	2
C₁₃×#1874	2
C₁₃×#1853	2
C₁₃×#1787	2
#24503	13

Subgroups — C13×#24503 #15710842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24503 #15710842