Subgroups — C₁₃×#17652 #15703991

Order 3328.

1028 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3514	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1532	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1530	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1529	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1527	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1525	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1524	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1524	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#329	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#131	—	2	1	no	—
13	C₁₃×#559	C₄	1	1	yes	characteristic
14	C₁₃×#556	C₄	1	1	yes	characteristic
15	C₁₃×#555	—	2	1	no	—
16	C₁₃×#551	—	2	2	no	—
17	D₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
18	C₁₃×#548	C₄	1	2	yes	—
19	C₁₃×#546	—	2	1	no	—
20	C₁₃×#546	C₄	1	2	yes	—
21	D₄²×C₁₃	C₄	1	1	yes	characteristic
22	C₁₃×#542	—	2	1	no	—
23	C₁₃×#538	—	2	2	no	—
24	C₁₃×#532	C₂²	1	1	yes	characteristic
25	C₁₃×#529	C₂²	1	1	yes	characteristic
26	C₁₃×#529	C₂²	1	2	yes	—
27	C₂×C₁₃×#124	C₂²	1	2	yes	—
28	C₁₃×#518	—	2	1	no	—
29	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
30	C₁₃×#446	—	2	1	no	—
31	C₁₃×#435	—	2	2	no	—
32	C₈×D₄×C₁₃	—	2	1	no	—
33	C₁₃×#432	C₂²	1	2	yes	complemented
34	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#405	—	2	2	no	—
36	C₁₃×#405	—	2	1	no	—
37	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₁₃×M₁₆	C₂²	1	2	yes	complemented
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#330	C₂²	1	2	yes	complemented
45	C₁₃×#330	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#329	C₂²	1	1	yes	characteristic
47	C₁₃×#329	C₂²	1	2	yes	—
48	C₁₃×#329	C₂²	1	1	yes	characteristic
49	C₁₃×#329	C₂²	1	2	yes	complemented
50	C₁₃×#329	C₂²	1	2	yes	complemented
51	C₁₃×#329	C₂²	1	2	yes	complemented
52	C₁₃×#329	C₂²	1	2	yes	complemented
53	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
56	C₂²×D₄×C₁₃	—	2	1	no	—
57	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
58	C₁₃×#131	—	2	8	no	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	—	2	1	no	—
61	C₂×C₁₃×M₁₆	—	2	1	no	—
62	C₂²×C₈×C₁₃	—	2	2	no	—
63	C₂²×C₈×C₁₃	—	2	1	no	—
64	C₂²×C₈×C₁₃	—	2	2	no	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
67	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
68	C₁₃×#126	—	2	2	no	—
69	C₁₃×#126	—	2	2	no	—
70	C₁₃×#126	—	2	1	no	—
71	C₁₃×#125	C₂³	1	1	yes	characteristic
72	C₁₃×#124	—	2	1	no	—
73	C₁₃×#124	—	2	2	no	—
74	C₁₃×#124	—	2	2	no	—
75	C₁₃×#124	—	2	2	no	—
76	C₁₃×#124	C₂×C₄	1	2	yes	—
77	C₁₃×#124	C₂×C₄	1	2	yes	—
78	C₁₃×#124	C₂³	1	1	yes	characteristic
79	C₁₃×#124	C₂³	1	2	yes	—
80	C₁₃×#123	—	2	1	no	—
81	C₁₃×#123	—	2	2	no	—
82	C₁₃×#123	—	2	2	no	—
83	C₁₃×#123	—	2	2	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
88	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
89	C₁₃×#121	—	2	2	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	2	2	no	—
94	C₁₃×#121	C₂×C₄	1	2	yes	—
95	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
96	C₁₃×#120	—	2	2	no	—
97	C₁₃×#120	—	2	2	no	—
98	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
99	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
100	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
101	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	—	2	1	no	—
105	C₄×D₄×C₁₃	—	2	1	no	—
106	C₄×D₄×C₁₃	—	2	2	no	—
107	C₄×D₄×C₁₃	—	2	1	no	—
108	C₄×D₄×C₁₃	—	2	1	no	—
109	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
110	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
111	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
112	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
113	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
114	C₄×D₄×C₁₃	D₄	1	2	yes	—
115	C₁₃×#117	—	2	1	no	—
116	C₁₃×#117	—	2	1	no	—
117	C₁₃×#117	—	2	2	no	—
118	C₁₃×#117	D₄	1	2	yes	—
119	C₁₃×#117	D₄	1	1	yes	characteristic
120	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	2	no	—
127	C₁₃×C₂²⋊C₈	—	2	2	no	—
128	C₁₃×C₂²⋊C₈	—	2	1	no	—
129	C₁₃×#97	—	2	2	no	—
130	C₁₃×#97	—	2	1	no	—
131	C₁₃×#97	—	2	2	no	—
132	C₁₃×#97	C₂³	1	1	yes	characteristic
133	C₁₃×#97	C₂³	1	1	yes	characteristic
134	C₁₃×#97	C₂³	1	2	yes	—
135	C₁₃×#97	C₂³	1	1	yes	characteristic
136	C₁₃×#97	C₂³	1	2	yes	—
137	C₁₃×#97	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₃	—	2	2	no	—
139	C₄×C₈×C₁₃	—	2	1	no	—
140	C₄×C₈×C₁₃	—	2	1	no	—
141	#17652	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂⁴×C₁₃	—	2	2	no	—
143	C₁₃×#41	—	2	4	no	—
144	C₁₃×#41	—	8	2	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	8	2	no	—
147	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	4	4	no	—
157	C₂×D₄×C₁₃	—	8	2	no	—
158	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
159	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₁₃×M₁₆	—	2	8	no	—
173	C₁₃×M₁₆	—	2	4	no	—
174	C₁₃×M₁₆	—	4	2	no	—
175	C₂×C₈×C₁₃	—	2	8	no	—
176	C₂×C₈×C₁₃	—	2	4	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	2	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	2	no	—
183	C₂×C₈×C₁₃	—	4	4	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
196	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₁₃×C₂²⋊C₄	—	2	1	no	—
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	2	2	no	—
211	C₁₃×C₂²⋊C₄	—	2	2	no	—
212	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
213	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
214	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
215	C₄²×C₁₃	—	2	2	no	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
218	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
219	C₄²×C₁₃	C₂×D₄	1	2	yes	—
220	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₁₃	C₂×D₄	1	2	yes	—
223	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
224	#3514	C₂×C₁₃	1	1	yes	characteristic
225	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2875	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1532	C₂×C₁₃	1	2	yes	complemented
228	#1530	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1529	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1527	C₂×C₁₃	1	2	yes	complemented
231	#1525	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1524	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1524	C₂×C₁₃	1	2	yes	complemented
234	C₂×#329	C₂×C₁₃	1	2	yes	complemented
235	C₂³×C₁₃	—	2	1	no	—
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	4	4	no	—
238	C₂³×C₁₃	—	8	2	no	—
239	C₂³×C₁₃	—	8	2	no	—
240	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
242	Q₈×C₁₃	—	2	2	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×C₁₃	—	4	2	no	—
245	Q₈×C₁₃	—	8	2	no	—
246	D₄×C₁₃	—	2	4	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	2	no	—
249	D₄×C₁₃	—	4	4	no	—
250	D₄×C₁₃	—	4	2	no	—
251	D₄×C₁₃	—	8	1	no	—
252	D₄×C₁₃	—	8	2	no	—
253	D₄×C₁₃	—	8	1	no	—
254	D₄×C₁₃	—	8	2	no	—
255	D₄×C₁₃	#104	1	4	yes	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	8	2	no	—
268	C₂×C₄×C₁₃	—	8	2	no	—
269	C₂×C₄×C₁₃	—	8	2	no	—
270	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
271	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
279	C₈×C₁₃	—	2	2	no	—
280	C₈×C₁₃	—	2	4	no	—
281	C₈×C₁₃	—	2	2	no	—
282	C₈×C₁₃	—	2	2	no	—
283	C₈×C₁₃	—	4	2	no	—
284	C₈×C₁₃	—	4	1	no	—
285	C₂×#131	—	2	1	no	—
286	#559	C₄×C₁₃	1	1	yes	characteristic
287	#556	C₄×C₁₃	1	1	yes	characteristic
288	#555	—	2	1	no	—
289	#551	—	2	2	no	—
290	D₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
291	#548	C₄×C₁₃	1	2	yes	—
292	#546	—	2	1	no	—
293	#546	C₄×C₁₃	1	2	yes	—
294	D₄²	C₄×C₁₃	1	1	yes	characteristic
295	#542	—	2	1	no	—
296	#538	—	2	2	no	—
297	#532	C₂²×C₁₃	1	1	yes	characteristic
298	#529	C₂²×C₁₃	1	1	yes	characteristic
299	#529	C₂²×C₁₃	1	2	yes	—
300	C₂×#124	C₂²×C₁₃	1	2	yes	—
301	#518	—	2	1	no	—
302	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
303	#446	—	2	1	no	—
304	#435	—	2	2	no	—
305	C₈×D₄	—	2	1	no	—
306	#432	C₂²×C₁₃	1	2	yes	complemented
307	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	#405	—	2	2	no	—
309	#405	—	2	1	no	—
310	C₄×M₁₆	C₂²×C₁₃	1	2	yes	complemented
311	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
312	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
313	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
314	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
315	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
316	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
317	#330	C₂²×C₁₃	1	2	yes	complemented
318	#330	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	#329	C₂²×C₁₃	1	1	yes	characteristic
320	#329	C₂²×C₁₃	1	2	yes	—
321	#329	C₂²×C₁₃	1	1	yes	characteristic
322	#329	C₂²×C₁₃	1	2	yes	complemented
323	#329	C₂²×C₁₃	1	2	yes	complemented
324	#329	C₂²×C₁₃	1	2	yes	complemented
325	#329	C₂²×C₁₃	1	2	yes	complemented
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	1	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	2	no	—
335	C₂²×C₁₃	—	4	2	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	16	4	no	—
338	C₂²×C₁₃	C₂×#104	1	4	yes	—
339	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	2	no	—
345	C₄×C₁₃	—	2	1	no	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	—	2	1	no	—
348	C₄×C₁₃	—	4	2	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	1	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	C₂×#104	1	2	yes	—
353	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
354	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
355	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
358	#131	—	2	8	no	—
359	C₂×M₁₆	—	2	2	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂²×C₈	—	2	2	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	2	2	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
367	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
368	#126	—	2	2	no	—
369	#126	—	2	2	no	—
370	#126	—	2	1	no	—
371	#125	C₂³×C₁₃	1	1	yes	characteristic
372	#124	—	2	1	no	—
373	#124	—	2	2	no	—
374	#124	—	2	2	no	—
375	#124	—	2	2	no	—
376	#124	C₂×C₄×C₁₃	1	2	yes	—
377	#124	C₂×C₄×C₁₃	1	2	yes	—
378	#124	C₂³×C₁₃	1	1	yes	characteristic
379	#124	C₂³×C₁₃	1	2	yes	—
380	#123	—	2	1	no	—
381	#123	—	2	2	no	—
382	#123	—	2	2	no	—
383	#123	—	2	2	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
388	C₂²⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
389	#121	—	2	2	no	—
390	#121	—	2	1	no	—
391	#121	—	2	1	no	—
392	#121	—	2	1	no	—
393	#121	—	2	2	no	—
394	#121	C₂×C₄×C₁₃	1	2	yes	—
395	#121	C₂×C₄×C₁₃	1	1	yes	characteristic
396	#120	—	2	2	no	—
397	#120	—	2	2	no	—
398	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
399	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
400	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
401	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
410	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
411	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
412	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
413	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
414	C₄×D₄	D₄×C₁₃	1	2	yes	—
415	#117	—	2	1	no	—
416	#117	—	2	1	no	—
417	#117	—	2	2	no	—
418	#117	D₄×C₁₃	1	2	yes	—
419	#117	D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	—	2	2	no	—
421	C₂×C₂²⋊C₄	—	2	2	no	—
422	C₂×C₂²⋊C₄	—	2	2	no	—
423	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
425	C₄⋊C₈	—	2	1	no	—
426	C₄⋊C₈	—	2	2	no	—
427	C₂²⋊C₈	—	2	2	no	—
428	C₂²⋊C₈	—	2	1	no	—
429	#97	—	2	2	no	—
430	#97	—	2	1	no	—
431	#97	—	2	2	no	—
432	#97	C₂³×C₁₃	1	1	yes	characteristic
433	#97	C₂³×C₁₃	1	1	yes	characteristic
434	#97	C₂³×C₁₃	1	2	yes	—
435	#97	C₂³×C₁₃	1	1	yes	characteristic
436	#97	C₂³×C₁₃	1	2	yes	—
437	#97	C₂³×C₁₃	1	1	yes	characteristic
438	C₄×C₈	—	2	2	no	—
439	C₄×C₈	—	2	1	no	—
440	C₄×C₈	—	2	1	no	—
441	C₂×C₁₃	—	2	4	no	—
442	C₂×C₁₃	—	4	1	no	—
443	C₂×C₁₃	—	8	2	no	—
444	C₂×C₁₃	—	8	1	no	—
445	C₂×C₁₃	#2888	1	1	yes	characteristic
446	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
447	C₂×C₁₃	#2901	1	1	yes	characteristic
448	C₂⁴	—	2	2	no	—
449	#41	—	2	4	no	—
450	#41	—	8	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	8	2	no	—
453	C₂×Q₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
454	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
455	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	4	4	no	—
463	C₂×D₄	—	8	2	no	—
464	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
465	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
466	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
467	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
473	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	M₁₆	—	2	8	no	—
479	M₁₆	—	2	4	no	—
480	M₁₆	—	4	2	no	—
481	C₂×C₈	—	2	8	no	—
482	C₂×C₈	—	2	4	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	4	4	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
499	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
500	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
501	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
502	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
519	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
520	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	1	no	—
523	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
524	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
525	C₄²	C₂×D₄×C₁₃	1	2	yes	—
526	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₄²	C₂×D₄×C₁₃	1	2	yes	—
529	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
530	C₁₃	#17652	1	1	yes	characteristic, direct product factor, Sylow
531	C₂³	—	2	1	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	8	2	no	—
535	C₂³	—	8	2	no	—
536	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
537	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	8	2	no	—
542	D₄	—	2	4	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	2	no	—
547	D₄	—	8	2	no	—
548	D₄	—	8	1	no	—
549	D₄	—	8	1	no	—
550	D₄	—	8	2	no	—
551	D₄	C₁₃×#104	1	4	yes	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	2	no	—
565	C₂×C₄	—	8	2	no	—
566	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
567	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
568	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
569	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
570	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
571	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
572	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
574	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
575	C₈	—	2	2	no	—
576	C₈	—	2	4	no	—
577	C₈	—	2	2	no	—
578	C₈	—	2	2	no	—
579	C₈	—	4	2	no	—
580	C₈	—	4	1	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	16	4	no	—
593	C₂²	C₂×C₁₃×#104	1	4	yes	—
594	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	1	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	C₂×C₁₃×#104	1	2	yes	—
608	C₂	—	2	4	no	—
609	C₂	—	4	1	no	—
610	C₂	—	8	1	no	—
611	C₂	—	8	2	no	—
612	C₂	C₁₃×#2888	1	1	yes	characteristic
613	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic
614	C₂	C₁₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3514	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2970	C₂	semidirect
3. C₁₃×#2875	C₂	semidirect
4. C₁₃×#1532	C₂	semidirect
5. C₁₃×#1530	C₂	semidirect
6. C₁₃×#1529	C₂	semidirect
7. C₁₃×#1527	C₂	semidirect
8. C₁₃×#1525	C₂	semidirect
9. C₁₃×#1524	C₂	semidirect
10. C₁₃×#1524	C₂	semidirect
11. C₂×C₁₃×#329	C₂	semidirect
33. C₁₃×#432	C₂²	semidirect
34. C₁₃×#432	C₂²	semidirect
37. C₄×C₁₃×M₁₆	C₂²	semidirect
38. C₄×C₁₃×M₁₆	C₂²	semidirect
39. C₄×C₁₃×M₁₆	C₂²	semidirect
40. C₂×C₁₃×#97	C₂²	semidirect
41. C₂×C₁₃×#97	C₂²	semidirect
42. C₂×C₁₃×#97	C₂²	semidirect
43. C₁₃×#330	C₂²	semidirect
44. C₁₃×#330	C₂²	semidirect
45. C₁₃×#330	C₂²	semidirect
49. C₁₃×#329	C₂²	semidirect
50. C₁₃×#329	C₂²	semidirect
51. C₁₃×#329	C₂²	semidirect
52. C₁₃×#329	C₂²	semidirect
141. #17652	C₁₃	direct (N × H)
225. #2970	C₂×C₁₃	semidirect
226. #2875	C₂×C₁₃	semidirect
227. #1532	C₂×C₁₃	semidirect
228. #1530	C₂×C₁₃	semidirect
229. #1529	C₂×C₁₃	semidirect
230. #1527	C₂×C₁₃	semidirect
231. #1525	C₂×C₁₃	semidirect
232. #1524	C₂×C₁₃	semidirect
233. #1524	C₂×C₁₃	semidirect
234. C₂×#329	C₂×C₁₃	semidirect
306. #432	C₂²×C₁₃	semidirect
307. #432	C₂²×C₁₃	semidirect
310. C₄×M₁₆	C₂²×C₁₃	semidirect
311. C₄×M₁₆	C₂²×C₁₃	semidirect
312. C₄×M₁₆	C₂²×C₁₃	semidirect
313. C₂×#97	C₂²×C₁₃	semidirect
314. C₂×#97	C₂²×C₁₃	semidirect
315. C₂×#97	C₂²×C₁₃	semidirect
316. #330	C₂²×C₁₃	semidirect
317. #330	C₂²×C₁₃	semidirect
318. #330	C₂²×C₁₃	semidirect
322. #329	C₂²×C₁₃	semidirect
323. #329	C₂²×C₁₃	semidirect
324. #329	C₂²×C₁₃	semidirect
325. #329	C₂²×C₁₃	semidirect
530. C₁₃	#17652	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3514	2
C₁₃×#2970	2
C₁₃×#2875	2
C₁₃×#1532	2
C₁₃×#1530	2
C₁₃×#1529	2
C₁₃×#1527	2
C₁₃×#1525	2
C₁₃×#1524	2
C₂×C₁₃×#329	2
#17652	13

Subgroups — C13×#17652 #15703991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17652 #15703991