Subgroups — C₁₃×#25850 #15712189

Order 3328.

1056 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2059	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2057	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1864	C₂	1	2	yes	maximal
10	C₁₃×#1862	C₂	1	2	yes	maximal
11	C₁₃×#1762	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#554	—	2	4	no	—
13	C₁₃×#554	—	2	4	no	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
26	C₁₃×#501	—	2	4	no	—
27	C₁₃×#474	—	2	4	no	—
28	C₂×C₁₃×#107	C₂²	1	2	yes	—
29	C₂×C₁₃×#107	C₂²	1	2	yes	—
30	C₂×C₁₃×#106	C₂²	1	2	yes	—
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
35	C₁₃×#395	—	2	1	no	—
36	C₁₃×#395	—	2	1	no	—
37	C₁₃×#391	—	2	1	no	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₁₃×#389	C₂²	1	2	yes	—
40	C₁₃×#384	—	2	1	no	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₁₃×#336	C₂²	1	2	yes	—
46	C₁₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×#125	—	2	2	no	—
61	C₁₃×#125	—	2	2	no	—
62	C₁₃×#125	—	2	2	no	—
63	C₁₃×#125	D₄	1	4	yes	—
64	C₁₃×C₂²⋊Q₈	—	2	8	no	—
65	C₁₃×C₂²⋊Q₈	—	2	8	no	—
66	C₁₃×C₂²⋊Q₈	—	2	8	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	D₄	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#107	—	2	4	no	—
100	C₁₃×#107	—	2	4	no	—
101	C₁₃×#106	—	2	4	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×#102	—	2	4	no	—
104	C₁₃×#102	Q₈	1	8	yes	complemented
105	C₁₃×#97	—	2	2	no	—
106	C₁₃×#95	—	2	1	no	—
107	C₁₃×#95	—	2	2	no	—
108	C₁₃×#95	—	2	2	no	—
109	#25850	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	4	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	4	1	no	—
115	C₂×Q₈×C₁₃	—	4	2	no	—
116	C₂×Q₈×C₁₃	—	8	2	no	—
117	C₂×Q₈×C₁₃	—	8	2	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	8	2	no	—
133	C₂²×C₄×C₁₃	—	8	2	no	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	4	no	—
145	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	4	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	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	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	4	2	no	—
161	C₁₃×C₄⋊C₄	—	8	2	no	—
162	C₁₃×C₄⋊C₄	—	8	2	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₄²×C₁₃	—	2	1	no	—
171	C₄²×C₁₃	—	2	1	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₄²×C₁₃	—	4	2	no	—
175	C₄²×C₁₃	C₂×D₄	1	2	yes	—
176	C₄²×C₁₃	C₂×D₄	1	2	yes	—
177	C₂×#554	C₂×C₁₃	1	1	yes	characteristic
178	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂×#474	C₂×C₁₃	1	1	yes	characteristic
180	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#2059	C₂×C₁₃	1	2	yes	complemented
182	#2057	C₂×C₁₃	1	2	yes	complemented
183	#1989	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#1864	C₂×C₁₃	1	2	yes	—
186	#1862	C₂×C₁₃	1	2	yes	—
187	#1762	C₂×C₁₃	1	1	yes	characteristic
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	4	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	4	1	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₁₃	—	4	4	no	—
195	Q₈×C₁₃	—	8	4	no	—
196	Q₈×C₁₃	—	8	4	no	—
197	D₄×C₁₃	—	2	2	no	—
198	D₄×C₁₃	—	2	4	no	—
199	D₄×C₁₃	C₄⋊Q₈	1	4	yes	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	4	8	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	8	4	no	—
227	C₂×C₄×C₁₃	—	8	4	no	—
228	C₂×C₄×C₁₃	#120	1	2	yes	—
229	C₂×C₄×C₁₃	#120	1	2	yes	—
230	C₂×C₄×C₁₃	#137	1	2	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
234	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
235	C₈×C₁₃	—	2	4	no	—
236	C₈×C₁₃	—	4	2	no	—
237	#554	—	2	4	no	—
238	#554	—	2	4	no	—
239	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₂²⋊Q₈	—	2	1	no	—
244	C₂×C₂²⋊Q₈	—	2	1	no	—
245	C₂×C₂²⋊Q₈	—	2	1	no	—
246	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
250	C₂²×C₄⋊C₄	—	2	1	no	—
251	#501	—	2	4	no	—
252	#474	—	2	4	no	—
253	C₂×#107	C₂²×C₁₃	1	2	yes	—
254	C₂×#107	C₂²×C₁₃	1	2	yes	—
255	C₂×#106	C₂²×C₁₃	1	2	yes	—
256	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#102	C₂²×C₁₃	1	2	yes	—
258	C₂×#102	C₂²×C₁₃	1	2	yes	—
259	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
260	#395	—	2	1	no	—
261	#395	—	2	1	no	—
262	#391	—	2	1	no	—
263	#389	C₂²×C₁₃	1	2	yes	—
264	#389	C₂²×C₁₃	1	2	yes	—
265	#384	—	2	1	no	—
266	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
267	#340	C₂²×C₁₃	1	2	yes	—
268	#340	C₂²×C₁₃	1	2	yes	—
269	#340	C₂²×C₁₃	1	2	yes	—
270	#336	C₂²×C₁₃	1	2	yes	—
271	#336	C₂²×C₁₃	1	2	yes	—
272	C₂²×C₁₃	—	2	4	no	—
273	C₂²×C₁₃	—	4	4	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	4	2	no	—
277	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
278	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
279	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
280	C₂²×C₁₃	#575	1	1	yes	characteristic
281	C₂²×C₁₃	#576	1	2	yes	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	2	2	no	—
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	4	4	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₄×C₁₃	—	4	1	no	—
290	C₄×C₁₃	—	4	2	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	8	2	no	—
293	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
294	C₄×C₁₃	#536	1	1	yes	characteristic
295	C₄×C₁₃	D₄×Q₈	1	2	yes	—
296	C₂²×Q₈	—	2	1	no	—
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
299	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
304	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	—	2	2	no	—
309	#125	—	2	2	no	—
310	#125	—	2	2	no	—
311	#125	—	2	2	no	—
312	#125	D₄×C₁₃	1	4	yes	—
313	C₂²⋊Q₈	—	2	8	no	—
314	C₂²⋊Q₈	—	2	8	no	—
315	C₂²⋊Q₈	—	2	8	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	D₄×C₁₃	1	4	yes	—
324	C₂×C₄⋊C₄	—	2	8	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
348	#107	—	2	4	no	—
349	#107	—	2	4	no	—
350	#106	—	2	4	no	—
351	C₄⋊C₈	—	2	2	no	—
352	#102	—	2	4	no	—
353	#102	Q₈×C₁₃	1	8	yes	complemented
354	#97	—	2	2	no	—
355	#95	—	2	1	no	—
356	#95	—	2	2	no	—
357	#95	—	2	2	no	—
358	C₂×C₁₃	—	4	4	no	—
359	C₂×C₁₃	#2434	1	1	yes	characteristic
360	C₂×C₁₃	#3007	1	1	yes	characteristic
361	C₂×C₁₃	#3008	1	1	yes	characteristic
362	C₂×C₁₃	#3385	1	2	yes	—
363	C₂×C₁₃	#3389	1	2	yes	—
364	C₂⁴	—	2	1	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	4	1	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	—	8	2	no	—
371	C₂×Q₈	—	8	2	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
375	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	8	2	no	—
387	C₂²×C₄	—	8	2	no	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	8	2	no	—
416	C₄⋊C₄	—	8	2	no	—
417	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
418	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
419	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
420	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	4	2	no	—
429	C₄²	C₂×D₄×C₁₃	1	2	yes	—
430	C₄²	C₂×D₄×C₁₃	1	2	yes	—
431	C₁₃	#25850	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	2	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	2	no	—
437	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
438	Q₈	—	4	4	no	—
439	Q₈	—	8	4	no	—
440	Q₈	—	8	4	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	4	no	—
443	D₄	C₁₃×C₄⋊Q₈	1	4	yes	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	4	no	—
471	C₂×C₄	—	8	4	no	—
472	C₂×C₄	C₁₃×#120	1	2	yes	—
473	C₂×C₄	C₁₃×#120	1	2	yes	—
474	C₂×C₄	C₁₃×#137	1	2	yes	—
475	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
478	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
479	C₈	—	2	4	no	—
480	C₈	—	4	2	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
487	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
488	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
489	C₂²	C₁₃×#575	1	1	yes	characteristic
490	C₂²	C₁₃×#576	1	2	yes	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	4	no	—
501	C₄	—	8	2	no	—
502	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
503	C₄	C₁₃×#536	1	1	yes	characteristic
504	C₄	D₄×Q₈×C₁₃	1	2	yes	—
505	C₂	—	4	4	no	—
506	C₂	C₁₃×#2434	1	1	yes	characteristic
507	C₂	C₁₃×#3007	1	1	yes	characteristic
508	C₂	C₁₃×#3008	1	1	yes	characteristic
509	C₂	C₁₃×#3385	1	2	yes	—
510	C₂	C₁₃×#3389	1	2	yes	—

	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#501	C₂	semidirect
4. C₁₃×#2567	C₂	semidirect
5. C₁₃×#2059	C₂	semidirect
6. C₁₃×#2057	C₂	semidirect
7. C₁₃×#1989	C₂	semidirect
8. C₁₃×#1985	C₂	semidirect
104. C₁₃×#102	Q₈	semidirect
109. #25850	C₁₃	direct (N × H)
178. C₂×#501	C₂×C₁₃	semidirect
180. #2567	C₂×C₁₃	semidirect
181. #2059	C₂×C₁₃	semidirect
182. #2057	C₂×C₁₃	semidirect
183. #1989	C₂×C₁₃	semidirect
184. #1985	C₂×C₁₃	semidirect
353. #102	Q₈×C₁₃	semidirect
431. C₁₃	#25850	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×#554	2
C₂×C₁₃×#501	2
C₂×C₁₃×#474	2
C₁₃×#2567	2
C₁₃×#2059	2
C₁₃×#2057	2
C₁₃×#1989	2
C₁₃×#1985	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1762	2
#25850	13

Subgroups — C13×#25850 #15712189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25850 #15712189