Subgroups — C₁₃×#10998 #15697337

Order 3328.

1350 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
9	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₁₃×#536	—	2	2	no	—
13	C₁₃×#536	—	2	2	no	—
14	C₁₃×#536	—	2	2	no	—
15	C₁₃×#536	C₄	1	4	yes	complemented
16	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₃×#124	—	2	1	no	—
18	C₂×C₁₃×#123	—	2	2	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#104	—	2	2	no	—
24	C₂×C₁₃×#104	—	2	2	no	—
25	C₂×C₁₃×#104	—	2	2	no	—
26	C₁₃×#417	—	2	2	no	—
27	C₁₃×#417	—	2	2	no	—
28	C₂×C₁₃×#103	—	2	1	no	—
29	C₂×C₁₃×#102	—	2	1	no	—
30	C₂×C₁₃×#101	—	2	2	no	—
31	C₂×C₁₃×#101	—	2	2	no	—
32	C₂×C₁₃×#101	—	2	2	no	—
33	C₁₃×#391	—	2	2	no	—
34	C₁₃×#391	—	2	2	no	—
35	C₂×C₁₃×#95	—	2	2	no	—
36	C₁₃×#340	—	2	2	no	—
37	C₁₃×#339	—	2	2	no	—
38	C₂×C₁₃×#41	—	2	1	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	2	1	no	—
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂×C₁₃×#41	—	2	1	no	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂×C₁₃×#41	—	2	1	no	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×#41	D₄	1	2	yes	—
50	C₂²×Q₈×C₁₃	—	2	1	no	—
51	C₂²×Q₈×C₁₃	—	2	1	no	—
52	C₂²×Q₈×C₁₃	—	2	1	no	—
53	C₂²×Q₈×C₁₃	—	2	1	no	—
54	C₂²×Q₈×C₁₃	—	2	1	no	—
55	C₂²×Q₈×C₁₃	—	2	1	no	—
56	C₂²×Q₈×C₁₃	—	2	1	no	—
57	C₂²×Q₈×C₁₃	—	2	1	no	—
58	C₂²×Q₈×C₁₃	—	2	1	no	—
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×Q₈×C₁₃	—	2	1	no	—
61	C₂²×Q₈×C₁₃	—	2	1	no	—
62	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
63	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
65	C₂²×D₄×C₁₃	—	2	1	no	—
66	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂³×C₄×C₁₃	—	2	1	no	—
69	C₂³×C₄×C₁₃	—	2	1	no	—
70	C₂³×C₄×C₁₃	D₄	1	2	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	—	2	1	no	—
73	C₂×C₁₃×M₁₆	—	2	1	no	—
74	C₂×C₁₃×M₁₆	—	2	1	no	—
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂×C₁₃×M₁₆	—	2	1	no	—
77	C₂×C₁₃×M₁₆	—	2	1	no	—
78	C₂×C₁₃×M₁₆	—	2	1	no	—
79	C₂×C₁₃×M₁₆	—	2	1	no	—
80	C₂×C₁₃×M₁₆	—	2	1	no	—
81	C₂×C₁₃×M₁₆	—	2	1	no	—
82	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
83	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
84	C₂²×C₈×C₁₃	—	2	1	no	—
85	C₂²×C₈×C₁₃	—	2	1	no	—
86	C₁₃×C₄⋊Q₈	—	2	4	no	—
87	C₁₃×C₄⋊Q₈	—	2	4	no	—
88	C₁₃×#124	—	2	4	no	—
89	C₁₃×#124	—	2	4	no	—
90	C₁₃×#123	—	2	8	no	—
91	C₁₃×#123	—	2	8	no	—
92	C₁₃×C₂²⋊Q₈	—	2	8	no	—
93	C₁₃×C₂²⋊Q₈	—	2	8	no	—
94	C₁₃×#117	—	2	1	no	—
95	C₁₃×#117	—	2	1	no	—
96	C₁₃×#117	C₂×C₄	1	2	yes	—
97	C₁₃×#117	D₄	1	2	yes	—
98	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	—	2	1	no	—
110	C₂×C₄²×C₁₃	—	2	1	no	—
111	C₂×C₄²×C₁₃	—	2	1	no	—
112	C₂×C₄²×C₁₃	—	2	1	no	—
113	C₂×C₄²×C₁₃	—	2	1	no	—
114	C₂×C₄²×C₁₃	D₄	1	2	yes	—
115	C₁₃×#104	—	2	8	no	—
116	C₁₃×#103	—	2	4	no	—
117	C₁₃×#102	—	2	4	no	—
118	C₁₃×#101	—	2	8	no	—
119	C₁₃×#95	—	2	8	no	—
120	#10998	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	—	2	1	no	—
122	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	—	2	2	no	—
127	C₁₃×#41	—	2	2	no	—
128	C₁₃×#41	—	2	2	no	—
129	C₁₃×#41	—	2	2	no	—
130	C₁₃×#41	—	2	2	no	—
131	C₁₃×#41	—	4	1	no	—
132	C₁₃×#41	—	4	1	no	—
133	C₁₃×#41	—	4	1	no	—
134	C₁₃×#41	—	4	1	no	—
135	C₁₃×#41	—	4	1	no	—
136	C₁₃×#41	—	4	1	no	—
137	C₁₃×#41	—	4	1	no	—
138	C₁₃×#41	—	4	1	no	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	—	2	2	no	—
142	C₂×Q₈×C₁₃	—	2	2	no	—
143	C₂×Q₈×C₁₃	—	2	2	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	—	2	2	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	1	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	—	4	1	no	—
157	C₂×Q₈×C₁₃	—	4	1	no	—
158	C₂×Q₈×C₁₃	—	4	1	no	—
159	C₂×Q₈×C₁₃	—	4	1	no	—
160	C₂×Q₈×C₁₃	—	4	1	no	—
161	C₂×Q₈×C₁₃	—	4	1	no	—
162	C₂×Q₈×C₁₃	—	4	1	no	—
163	C₂×Q₈×C₁₃	—	4	1	no	—
164	C₂×Q₈×C₁₃	—	4	1	no	—
165	C₂×Q₈×C₁₃	—	4	1	no	—
166	C₂×Q₈×C₁₃	—	4	1	no	—
167	C₂×Q₈×C₁₃	—	4	1	no	—
168	C₂×Q₈×C₁₃	—	4	1	no	—
169	C₂×Q₈×C₁₃	—	4	1	no	—
170	C₂×Q₈×C₁₃	—	4	1	no	—
171	C₂×Q₈×C₁₃	—	4	1	no	—
172	C₂×Q₈×C₁₃	C₂²⋊C₄	1	2	yes	—
173	C₂×D₄×C₁₃	—	2	2	no	—
174	C₂×D₄×C₁₃	—	2	2	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	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	4	1	no	—
181	C₂×D₄×C₁₃	—	4	1	no	—
182	C₂×D₄×C₁₃	—	4	1	no	—
183	C₂×D₄×C₁₃	—	4	1	no	—
184	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	2	2	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	2	no	—
189	C₂²×C₄×C₁₃	—	2	2	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	2	2	no	—
193	C₂²×C₄×C₁₃	—	2	2	no	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	2	no	—
196	C₂²×C₄×C₁₃	—	2	2	no	—
197	C₂²×C₄×C₁₃	—	2	2	no	—
198	C₂²×C₄×C₁₃	—	4	2	no	—
199	C₂²×C₄×C₁₃	—	4	1	no	—
200	C₂²×C₄×C₁₃	—	4	1	no	—
201	C₂²×C₄×C₁₃	—	4	1	no	—
202	C₂²×C₄×C₁₃	—	4	1	no	—
203	C₂²×C₄×C₁₃	—	4	1	no	—
204	C₂²×C₄×C₁₃	—	4	1	no	—
205	C₂²×C₄×C₁₃	—	4	4	no	—
206	C₂²×C₄×C₁₃	—	4	1	no	—
207	C₂²×C₄×C₁₃	—	4	1	no	—
208	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
209	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
223	C₁₃×M₁₆	—	2	2	no	—
224	C₁₃×M₁₆	—	2	2	no	—
225	C₁₃×M₁₆	—	2	2	no	—
226	C₁₃×M₁₆	—	2	2	no	—
227	C₁₃×M₁₆	—	4	1	no	—
228	C₁₃×M₁₆	—	4	1	no	—
229	C₁₃×M₁₆	—	4	1	no	—
230	C₁₃×M₁₆	—	4	1	no	—
231	C₂×C₈×C₁₃	—	2	2	no	—
232	C₂×C₈×C₁₃	—	2	2	no	—
233	C₂×C₈×C₁₃	—	4	1	no	—
234	C₂×C₈×C₁₃	—	4	1	no	—
235	C₂×C₈×C₁₃	—	4	1	no	—
236	C₂×C₈×C₁₃	—	4	1	no	—
237	C₁₃×C₄⋊C₄	—	2	16	no	—
238	C₁₃×C₄⋊C₄	—	2	2	no	—
239	C₁₃×C₄⋊C₄	—	2	2	no	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	4	1	no	—
242	C₁₃×C₄⋊C₄	—	4	1	no	—
243	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
244	C₁₃×C₂²⋊C₄	—	2	16	no	—
245	C₁₃×C₂²⋊C₄	—	2	2	no	—
246	C₁₃×C₂²⋊C₄	—	2	2	no	—
247	C₄²×C₁₃	—	2	2	no	—
248	C₄²×C₁₃	—	2	2	no	—
249	C₄²×C₁₃	—	2	2	no	—
250	C₄²×C₁₃	—	2	2	no	—
251	C₄²×C₁₃	—	4	1	no	—
252	C₄²×C₁₃	—	4	1	no	—
253	C₂×#536	C₂×C₁₃	1	1	yes	characteristic
254	C₂²×#104	C₂×C₁₃	1	1	yes	characteristic
255	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
256	C₂²×#101	C₂×C₁₃	1	1	yes	characteristic, complemented
257	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#1736	C₂×C₁₃	1	1	yes	characteristic, complemented
259	C₂×#339	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	4	1	no	—
264	C₂³×C₁₃	—	4	1	no	—
265	C₂³×C₁₃	—	4	2	no	—
266	C₂³×C₁₃	—	4	2	no	—
267	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂³×C₁₃	#120	1	1	yes	characteristic
269	C₂³×C₁₃	#120	1	1	yes	characteristic
270	C₂³×C₁₃	#120	1	1	yes	characteristic
271	C₂³×C₁₃	#121	1	1	yes	characteristic
272	C₂³×C₁₃	#121	1	1	yes	characteristic
273	C₂³×C₁₃	#123	1	1	yes	characteristic
274	Q₈×C₁₃	—	2	2	no	—
275	Q₈×C₁₃	—	2	2	no	—
276	Q₈×C₁₃	—	4	2	no	—
277	Q₈×C₁₃	—	4	2	no	—
278	Q₈×C₁₃	—	4	2	no	—
279	Q₈×C₁₃	—	4	2	no	—
280	Q₈×C₁₃	—	4	2	no	—
281	Q₈×C₁₃	—	4	2	no	—
282	Q₈×C₁₃	—	4	1	no	—
283	Q₈×C₁₃	—	4	2	no	—
284	Q₈×C₁₃	—	4	2	no	—
285	Q₈×C₁₃	—	4	1	no	—
286	D₄×C₁₃	—	2	2	no	—
287	D₄×C₁₃	—	2	2	no	—
288	D₄×C₁₃	—	4	2	no	—
289	D₄×C₁₃	—	4	2	no	—
290	D₄×C₁₃	—	4	2	no	—
291	D₄×C₁₃	—	4	2	no	—
292	D₄×C₁₃	—	4	1	no	—
293	D₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	2	4	no	—
295	C₂×C₄×C₁₃	—	2	4	no	—
296	C₂×C₄×C₁₃	—	2	4	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	4	no	—
299	C₂×C₄×C₁₃	—	2	4	no	—
300	C₂×C₄×C₁₃	—	4	4	no	—
301	C₂×C₄×C₁₃	—	4	2	no	—
302	C₂×C₄×C₁₃	—	4	4	no	—
303	C₂×C₄×C₁₃	—	4	2	no	—
304	C₂×C₄×C₁₃	—	4	2	no	—
305	C₂×C₄×C₁₃	—	4	2	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	2	no	—
308	C₂×C₄×C₁₃	—	4	2	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	2	no	—
311	C₂×C₄×C₁₃	—	4	2	no	—
312	C₂×C₄×C₁₃	—	4	2	no	—
313	C₂×C₄×C₁₃	—	4	2	no	—
314	C₂×C₄×C₁₃	—	4	2	no	—
315	C₂×C₄×C₁₃	—	4	2	no	—
316	C₂×C₄×C₁₃	—	4	4	no	—
317	C₂×C₄×C₁₃	—	4	2	no	—
318	C₂×C₄×C₁₃	—	8	2	no	—
319	C₂×C₄×C₁₃	—	8	2	no	—
320	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
322	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
324	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
326	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
327	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
328	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
329	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
330	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
331	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
332	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
333	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
334	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
335	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
336	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
337	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
338	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
339	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
340	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
341	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
342	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
343	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
344	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
345	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
346	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
347	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
348	C₈×C₁₃	—	4	2	no	—
349	C₈×C₁₃	—	4	2	no	—
350	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
351	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
352	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
353	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
354	#536	—	2	2	no	—
355	#536	—	2	2	no	—
356	#536	—	2	2	no	—
357	#536	C₄×C₁₃	1	4	yes	complemented
358	C₂×C₄⋊Q₈	—	2	1	no	—
359	C₂×#124	—	2	1	no	—
360	C₂×#123	—	2	2	no	—
361	C₂×C₂²⋊Q₈	—	2	2	no	—
362	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
363	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
364	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#104	—	2	2	no	—
366	C₂×#104	—	2	2	no	—
367	C₂×#104	—	2	2	no	—
368	#417	—	2	2	no	—
369	#417	—	2	2	no	—
370	C₂×#103	—	2	1	no	—
371	C₂×#102	—	2	1	no	—
372	C₂×#101	—	2	2	no	—
373	C₂×#101	—	2	2	no	—
374	C₂×#101	—	2	2	no	—
375	#391	—	2	2	no	—
376	#391	—	2	2	no	—
377	C₂×#95	—	2	2	no	—
378	#340	—	2	2	no	—
379	#339	—	2	2	no	—
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	2	2	no	—
382	C₂²×C₁₃	—	2	1	no	—
383	C₂²×C₁₃	—	2	1	no	—
384	C₂²×C₁₃	—	2	1	no	—
385	C₂²×C₁₃	—	2	1	no	—
386	C₂²×C₁₃	—	2	2	no	—
387	C₂²×C₁₃	—	2	2	no	—
388	C₂²×C₁₃	—	4	4	no	—
389	C₂²×C₁₃	—	4	2	no	—
390	C₂²×C₁₃	—	8	1	no	—
391	C₂²×C₁₃	—	8	1	no	—
392	C₂²×C₁₃	—	8	2	no	—
393	C₂²×C₁₃	#379	1	1	yes	characteristic
394	C₂²×C₁₃	#386	1	1	yes	characteristic
395	C₂²×C₁₃	#386	1	1	yes	characteristic
396	C₂²×C₁₃	#392	1	1	yes	characteristic
397	C₂²×C₁₃	#392	1	1	yes	characteristic
398	C₂²×C₁₃	#394	1	1	yes	characteristic
399	C₂²×C₁₃	#394	1	1	yes	characteristic
400	C₂²×C₁₃	#454	1	2	yes	—
401	C₂²×C₁₃	#456	1	2	yes	—
402	C₄×C₁₃	—	4	4	no	—
403	C₄×C₁₃	—	4	4	no	—
404	C₄×C₁₃	—	4	4	no	—
405	C₄×C₁₃	—	4	2	no	—
406	C₄×C₁₃	—	8	2	no	—
407	C₄×C₁₃	#386	1	1	yes	characteristic
408	C₄×C₁₃	#386	1	1	yes	characteristic
409	C₄×C₁₃	#390	1	1	yes	characteristic
410	C₄×C₁₃	#390	1	1	yes	characteristic
411	C₄×C₁₃	#392	1	1	yes	characteristic
412	C₄×C₁₃	#392	1	1	yes	characteristic
413	C₄×C₁₃	#394	1	1	yes	characteristic
414	C₄×C₁₃	#394	1	1	yes	characteristic
415	C₂×#41	—	2	1	no	—
416	C₂×#41	—	2	1	no	—
417	C₂×#41	—	2	1	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	—	2	1	no	—
420	C₂×#41	—	2	1	no	—
421	C₂×#41	—	2	1	no	—
422	C₂×#41	—	2	1	no	—
423	C₂×#41	—	2	1	no	—
424	C₂×#41	—	2	1	no	—
425	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
426	C₂×#41	D₄×C₁₃	1	2	yes	—
427	C₂²×Q₈	—	2	1	no	—
428	C₂²×Q₈	—	2	1	no	—
429	C₂²×Q₈	—	2	1	no	—
430	C₂²×Q₈	—	2	1	no	—
431	C₂²×Q₈	—	2	1	no	—
432	C₂²×Q₈	—	2	1	no	—
433	C₂²×Q₈	—	2	1	no	—
434	C₂²×Q₈	—	2	1	no	—
435	C₂²×Q₈	—	2	1	no	—
436	C₂²×Q₈	—	2	1	no	—
437	C₂²×Q₈	—	2	1	no	—
438	C₂²×Q₈	—	2	1	no	—
439	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
440	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
441	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
442	C₂²×D₄	—	2	1	no	—
443	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
444	C₂³×C₄	—	2	1	no	—
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	—	2	1	no	—
447	C₂³×C₄	D₄×C₁₃	1	2	yes	—
448	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
449	C₂×M₁₆	—	2	1	no	—
450	C₂×M₁₆	—	2	1	no	—
451	C₂×M₁₆	—	2	1	no	—
452	C₂×M₁₆	—	2	1	no	—
453	C₂×M₁₆	—	2	1	no	—
454	C₂×M₁₆	—	2	1	no	—
455	C₂×M₁₆	—	2	1	no	—
456	C₂×M₁₆	—	2	1	no	—
457	C₂×M₁₆	—	2	1	no	—
458	C₂×M₁₆	—	2	1	no	—
459	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
460	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
461	C₂²×C₈	—	2	1	no	—
462	C₂²×C₈	—	2	1	no	—
463	C₄⋊Q₈	—	2	4	no	—
464	C₄⋊Q₈	—	2	4	no	—
465	#124	—	2	4	no	—
466	#124	—	2	4	no	—
467	#123	—	2	8	no	—
468	#123	—	2	8	no	—
469	C₂²⋊Q₈	—	2	8	no	—
470	C₂²⋊Q₈	—	2	8	no	—
471	#117	—	2	1	no	—
472	#117	—	2	1	no	—
473	#117	C₂×C₄×C₁₃	1	2	yes	—
474	#117	D₄×C₁₃	1	2	yes	—
475	C₂×C₄⋊C₄	—	2	4	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
482	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
483	C₂×C₂²⋊C₄	—	2	4	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₄²	—	2	1	no	—
486	C₂×C₄²	—	2	1	no	—
487	C₂×C₄²	—	2	1	no	—
488	C₂×C₄²	—	2	1	no	—
489	C₂×C₄²	—	2	1	no	—
490	C₂×C₄²	—	2	1	no	—
491	C₂×C₄²	D₄×C₁₃	1	2	yes	—
492	#104	—	2	8	no	—
493	#103	—	2	4	no	—
494	#102	—	2	4	no	—
495	#101	—	2	8	no	—
496	#95	—	2	8	no	—
497	C₂×C₁₃	—	2	1	no	—
498	C₂×C₁₃	—	2	1	no	—
499	C₂×C₁₃	—	2	1	no	—
500	C₂×C₁₃	—	2	1	no	—
501	C₂×C₁₃	—	8	2	no	—
502	C₂×C₁₃	#1438	1	1	yes	characteristic
503	C₂×C₁₃	#1793	1	2	yes	—
504	C₂×C₁₃	#2003	1	1	yes	characteristic
505	C₂×C₁₃	#2005	1	1	yes	characteristic
506	C₂×C₁₃	#2038	1	2	yes	—
507	C₂⁴	—	2	1	no	—
508	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
509	#41	—	2	2	no	—
510	#41	—	2	2	no	—
511	#41	—	2	2	no	—
512	#41	—	2	2	no	—
513	#41	—	2	2	no	—
514	#41	—	2	2	no	—
515	#41	—	2	2	no	—
516	#41	—	2	2	no	—
517	#41	—	4	1	no	—
518	#41	—	4	1	no	—
519	#41	—	4	1	no	—
520	#41	—	4	1	no	—
521	#41	—	4	1	no	—
522	#41	—	4	1	no	—
523	#41	—	4	1	no	—
524	#41	—	4	1	no	—
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	4	1	no	—
543	C₂×Q₈	—	4	1	no	—
544	C₂×Q₈	—	4	1	no	—
545	C₂×Q₈	—	4	1	no	—
546	C₂×Q₈	—	4	1	no	—
547	C₂×Q₈	—	4	1	no	—
548	C₂×Q₈	—	4	1	no	—
549	C₂×Q₈	—	4	1	no	—
550	C₂×Q₈	—	4	1	no	—
551	C₂×Q₈	—	4	1	no	—
552	C₂×Q₈	—	4	1	no	—
553	C₂×Q₈	—	4	1	no	—
554	C₂×Q₈	—	4	1	no	—
555	C₂×Q₈	—	4	1	no	—
556	C₂×Q₈	—	4	1	no	—
557	C₂×Q₈	—	4	1	no	—
558	C₂×Q₈	C₁₃×C₂²⋊C₄	1	2	yes	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	—	4	1	no	—
569	C₂×D₄	—	4	1	no	—
570	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	1	no	—
586	C₂²×C₄	—	4	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	—	4	1	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	—	4	1	no	—
593	C₂²×C₄	—	4	1	no	—
594	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
595	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
605	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
606	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
607	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
608	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
609	M₁₆	—	2	2	no	—
610	M₁₆	—	2	2	no	—
611	M₁₆	—	2	2	no	—
612	M₁₆	—	2	2	no	—
613	M₁₆	—	4	1	no	—
614	M₁₆	—	4	1	no	—
615	M₁₆	—	4	1	no	—
616	M₁₆	—	4	1	no	—
617	C₂×C₈	—	2	2	no	—
618	C₂×C₈	—	2	2	no	—
619	C₂×C₈	—	4	1	no	—
620	C₂×C₈	—	4	1	no	—
621	C₂×C₈	—	4	1	no	—
622	C₂×C₈	—	4	1	no	—
623	C₄⋊C₄	—	2	16	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	4	1	no	—
628	C₄⋊C₄	—	4	1	no	—
629	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
630	C₂²⋊C₄	—	2	16	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	4	1	no	—
638	C₄²	—	4	1	no	—
639	C₁₃	#10998	1	1	yes	characteristic, direct product factor, Sylow
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	2	no	—
647	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
648	C₂³	C₁₃×#120	1	1	yes	characteristic
649	C₂³	C₁₃×#120	1	1	yes	characteristic
650	C₂³	C₁₃×#120	1	1	yes	characteristic
651	C₂³	C₁₃×#121	1	1	yes	characteristic
652	C₂³	C₁₃×#121	1	1	yes	characteristic
653	C₂³	C₁₃×#123	1	1	yes	characteristic
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	4	2	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	4	2	no	—
662	Q₈	—	4	1	no	—
663	Q₈	—	4	2	no	—
664	Q₈	—	4	2	no	—
665	Q₈	—	4	1	no	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	4	2	no	—
669	D₄	—	4	2	no	—
670	D₄	—	4	2	no	—
671	D₄	—	4	2	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	1	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	4	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	2	no	—
694	C₂×C₄	—	4	2	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	—	8	2	no	—
700	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
701	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
702	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
703	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
704	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
705	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
706	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
707	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
708	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
709	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
710	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
711	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
712	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
713	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
714	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
715	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
716	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
717	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
718	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
719	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
720	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
721	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
722	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
723	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
724	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
725	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
726	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
727	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
728	C₈	—	4	2	no	—
729	C₈	—	4	2	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	2	no	—
743	C₂²	C₁₃×#379	1	1	yes	characteristic
744	C₂²	C₁₃×#386	1	1	yes	characteristic
745	C₂²	C₁₃×#386	1	1	yes	characteristic
746	C₂²	C₁₃×#392	1	1	yes	characteristic
747	C₂²	C₁₃×#392	1	1	yes	characteristic
748	C₂²	C₁₃×#394	1	1	yes	characteristic
749	C₂²	C₁₃×#394	1	1	yes	characteristic
750	C₂²	C₁₃×#454	1	2	yes	—
751	C₂²	C₁₃×#456	1	2	yes	—
752	C₄	—	4	4	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	4	no	—
755	C₄	—	4	2	no	—
756	C₄	—	8	2	no	—
757	C₄	C₁₃×#386	1	1	yes	characteristic
758	C₄	C₁₃×#386	1	1	yes	characteristic
759	C₄	C₁₃×#390	1	1	yes	characteristic
760	C₄	C₁₃×#390	1	1	yes	characteristic
761	C₄	C₁₃×#392	1	1	yes	characteristic
762	C₄	C₁₃×#392	1	1	yes	characteristic
763	C₄	C₁₃×#394	1	1	yes	characteristic
764	C₄	C₁₃×#394	1	1	yes	characteristic
765	C₂	—	2	1	no	—
766	C₂	—	2	1	no	—
767	C₂	—	2	1	no	—
768	C₂	—	2	1	no	—
769	C₂	—	8	2	no	—
770	C₂	C₁₃×#1438	1	1	yes	characteristic
771	C₂	C₁₃×#1793	1	2	yes	—
772	C₂	C₁₃×#2003	1	1	yes	characteristic
773	C₂	C₁₃×#2005	1	1	yes	characteristic
774	C₂	C₁₃×#2038	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂²×C₁₃×#101	C₂	semidirect
5. C₂×C₁₃×#391	C₂	semidirect
6. C₁₃×#1736	C₂	semidirect
7. C₂×C₁₃×#339	C₂	semidirect
15. C₁₃×#536	C₄	semidirect
120. #10998	C₁₃	direct (N × H)
256. C₂²×#101	C₂×C₁₃	semidirect
257. C₂×#391	C₂×C₁₃	semidirect
258. #1736	C₂×C₁₃	semidirect
259. C₂×#339	C₂×C₁₃	semidirect
357. #536	C₄×C₁₃	semidirect
639. C₁₃	#10998	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×#536	2
C₂²×C₁₃×#104	2
C₂×C₁₃×#417	2
C₂²×C₁₃×#101	2
C₂×C₁₃×#391	2
C₁₃×#1736	2
C₂×C₁₃×#339	2
#10998	13

Subgroups — C13×#10998 #15697337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10998 #15697337