Subgroups — C₁₃×#24680 #15711019

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2071	C₂	1	2	yes	maximal
6	C₁₃×#2055	C₂	1	2	yes	maximal
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1948	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	—	2	1	no	—
17	C₁₃×#476	—	2	4	no	—
18	C₄×C₁₃×SD₁₆	—	2	4	no	—
19	C₂×C₁₃×#106	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#395	—	2	2	no	—
29	C₁₃×#391	C₂²	1	2	yes	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#389	—	2	1	no	—
32	C₁₃×#389	—	2	1	no	—
33	C₁₃×#388	—	2	2	no	—
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₁₃×#384	C₂²	1	2	yes	—
36	C₁₃×#380	—	2	1	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₄×Q₈×C₁₃	—	2	2	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	D₄	1	4	yes	—
59	C₁₃×#117	—	4	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₄²×C₁₃	—	2	2	no	—
76	C₂×C₄²×C₁₃	—	2	1	no	—
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#106	—	2	2	no	—
80	C₁₃×#106	—	2	4	no	—
81	C₁₃×C₄⋊C₈	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#102	—	2	2	no	—
86	C₁₃×#102	—	2	4	no	—
87	C₄×C₈×C₁₃	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	D₄	1	2	yes	—
92	#24680	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	8	1	no	—
101	C₂×Q₈×C₁₃	—	8	1	no	—
102	C₂×Q₈×C₁₃	#41	1	2	yes	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₁₃×SD₁₆	—	2	8	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	#41	1	2	yes	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	—	8	1	no	—
144	C₁₃×C₄⋊C₄	—	8	2	no	—
145	C₁₃×C₄⋊C₄	—	8	2	no	—
146	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	complemented
147	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
148	C₁₃×C₂²⋊C₄	—	2	4	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₁₃×C₂²⋊C₄	—	8	2	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	—	4	2	no	—
154	C₄²×C₁₃	—	4	4	no	—
155	C₄²×C₁₃	C₂×D₄	1	2	yes	—
156	C₄²×C₁₃	#41	1	2	yes	—
157	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
158	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
159	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#2354	C₂×C₁₃	1	1	yes	characteristic
161	#2071	C₂×C₁₃	1	2	yes	—
162	#2055	C₂×C₁₃	1	2	yes	—
163	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1948	C₂×C₁₃	1	2	yes	complemented
165	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1927	C₂×C₁₃	1	2	yes	complemented
167	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	4	1	no	—
170	C₂³×C₁₃	—	4	1	no	—
171	C₂³×C₁₃	—	4	1	no	—
172	C₂³×C₁₃	—	4	1	no	—
173	C₂³×C₁₃	—	4	1	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	2	2	no	—
178	Q₈×C₁₃	—	4	1	no	—
179	Q₈×C₁₃	—	4	1	no	—
180	Q₈×C₁₃	—	8	4	no	—
181	D₄×C₁₃	—	2	2	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	4	1	no	—
184	D₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	8	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	#121	1	2	yes	—
209	C₂×C₄×C₁₃	#121	1	2	yes	—
210	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
211	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
212	C₂×C₄×C₁₃	#137	1	2	yes	—
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
218	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
219	C₈×C₁₃	—	2	2	no	—
220	C₈×C₁₃	—	4	2	no	—
221	C₈×C₁₃	—	4	1	no	—
222	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#117	—	2	1	no	—
227	#476	—	2	4	no	—
228	C₄×SD₁₆	—	2	4	no	—
229	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#106	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
232	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#103	C₂²×C₁₃	1	2	yes	—
234	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#102	C₂²×C₁₃	1	2	yes	—
236	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
238	#395	—	2	2	no	—
239	#391	C₂²×C₁₃	1	2	yes	—
240	#390	C₂²×C₁₃	1	2	yes	—
241	#389	—	2	1	no	—
242	#389	—	2	1	no	—
243	#388	—	2	2	no	—
244	#384	C₂²×C₁₃	1	2	yes	—
245	#384	C₂²×C₁₃	1	1	yes	characteristic
246	#380	—	2	1	no	—
247	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
248	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
249	#340	C₂²×C₁₃	1	2	yes	—
250	#340	C₂²×C₁₃	1	2	yes	—
251	#340	C₂²×C₁₃	1	2	yes	—
252	#336	C₂²×C₁₃	1	2	yes	—
253	C₂²×C₁₃	—	4	2	no	—
254	C₂²×C₁₃	—	4	2	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	8	1	no	—
257	C₂²×C₁₃	—	8	1	no	—
258	C₂²×C₁₃	—	8	1	no	—
259	C₂²×C₁₃	—	8	1	no	—
260	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
261	C₂²×C₁₃	#547	1	1	yes	characteristic
262	C₂²×C₁₃	#548	1	1	yes	characteristic
263	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
264	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
265	C₂²×C₁₃	#576	1	1	yes	characteristic
266	C₂²×C₁₃	#577	1	1	yes	characteristic
267	C₄×C₁₃	—	2	4	no	—
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	2	no	—
271	C₄×C₁₃	—	4	2	no	—
272	C₄×C₁₃	—	8	2	no	—
273	C₄×C₁₃	—	8	1	no	—
274	C₄×C₁₃	—	8	2	no	—
275	C₄×C₁₃	#461	1	4	yes	—
276	C₄×C₁₃	#525	1	1	yes	characteristic
277	C₄×C₁₃	#536	1	1	yes	characteristic
278	C₄×C₁₃	#552	1	1	yes	characteristic
279	C₄×C₁₃	#556	1	1	yes	characteristic
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₂³×C₄	—	2	1	no	—
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
289	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	D₄×C₁₃	1	4	yes	—
296	#117	—	4	4	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
315	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
316	#106	—	2	2	no	—
317	#106	—	2	4	no	—
318	C₄⋊C₈	—	2	4	no	—
319	C₄⋊C₈	—	2	2	no	—
320	#103	—	2	4	no	—
321	#103	—	2	2	no	—
322	#102	—	2	2	no	—
323	#102	—	2	4	no	—
324	C₄×C₈	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	D₄×C₁₃	1	2	yes	—
329	C₂×C₁₃	—	8	2	no	—
330	C₂×C₁₃	#2415	1	1	yes	characteristic
331	C₂×C₁₃	C₂×#461	1	1	yes	characteristic
332	C₂×C₁₃	#3045	1	1	yes	characteristic
333	C₂×C₁₃	#3335	1	1	yes	characteristic
334	C₂×C₁₃	#3357	1	1	yes	characteristic
335	C₂×C₁₃	#3362	1	1	yes	characteristic
336	C₂×C₁₃	#3369	1	1	yes	characteristic
337	C₂⁴	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	8	1	no	—
345	C₂×Q₈	—	8	1	no	—
346	C₂×Q₈	C₁₃×#41	1	2	yes	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
366	SD₁₆	—	2	8	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	C₁₃×#41	1	2	yes	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	8	1	no	—
388	C₄⋊C₄	—	8	2	no	—
389	C₄⋊C₄	—	8	2	no	—
390	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
391	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	8	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	4	2	no	—
398	C₄²	—	4	4	no	—
399	C₄²	C₂×D₄×C₁₃	1	2	yes	—
400	C₄²	C₁₃×#41	1	2	yes	—
401	C₁₃	#24680	1	1	yes	characteristic, direct product factor, Sylow
402	C₂³	—	2	2	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
410	Q₈	—	2	2	no	—
411	Q₈	—	2	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	8	4	no	—
415	D₄	—	2	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	C₁₃×#121	1	2	yes	—
443	C₂×C₄	C₁₃×#121	1	2	yes	—
444	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
445	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
446	C₂×C₄	C₁₃×#137	1	2	yes	—
447	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
448	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
449	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
450	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
451	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
452	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	4	2	no	—
455	C₈	—	4	1	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
464	C₂²	C₁₃×#547	1	1	yes	characteristic
465	C₂²	C₁₃×#548	1	1	yes	characteristic
466	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
467	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
468	C₂²	C₁₃×#576	1	1	yes	characteristic
469	C₂²	C₁₃×#577	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	2	4	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	1	no	—
476	C₄	—	8	2	no	—
477	C₄	—	8	2	no	—
478	C₄	C₁₃×#461	1	4	yes	—
479	C₄	C₁₃×#525	1	1	yes	characteristic
480	C₄	C₁₃×#536	1	1	yes	characteristic
481	C₄	C₁₃×#552	1	1	yes	characteristic
482	C₄	C₁₃×#556	1	1	yes	characteristic
483	C₂	—	8	2	no	—
484	C₂	C₁₃×#2415	1	1	yes	characteristic
485	C₂	C₂×C₁₃×#461	1	1	yes	characteristic
486	C₂	C₁₃×#3045	1	1	yes	characteristic
487	C₂	C₁₃×#3335	1	1	yes	characteristic
488	C₂	C₁₃×#3357	1	1	yes	characteristic
489	C₂	C₁₃×#3362	1	1	yes	characteristic
490	C₂	C₁₃×#3369	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2567	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
8. C₁₃×#1948	C₂	semidirect
9. C₁₃×#1939	C₂	semidirect
10. C₁₃×#1927	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
92. #24680	C₁₃	direct (N × H)
146. C₁₃×C₄⋊C₄	SD₁₆	semidirect
159. #2567	C₂×C₁₃	semidirect
163. #1990	C₂×C₁₃	semidirect
164. #1948	C₂×C₁₃	semidirect
165. #1939	C₂×C₁₃	semidirect
166. #1927	C₂×C₁₃	semidirect
167. #1803	C₂×C₁₃	semidirect
390. C₄⋊C₄	C₁₃×SD₁₆	semidirect
401. C₁₃	#24680	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×#476	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2567	2
C₁₃×#2354	2
C₁₃×#2071	2
C₁₃×#2055	2
C₁₃×#1990	2
C₁₃×#1948	2
C₁₃×#1939	2
C₁₃×#1927	2
C₁₃×#1803	2
#24680	13

Subgroups — C13×#24680 #15711019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24680 #15711019