Subgroups — C₁₃×#17593 #15703932

Order 3328.

1042 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1521	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1515	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1514	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1504	C₂	1	4	yes	maximal, complemented
8	C₁₃×#533	C₄	1	1	yes	characteristic, complemented
9	C₁₃×#533	C₄	1	1	yes	characteristic, complemented
10	C₁₃×#533	C₂²	1	1	yes	characteristic
11	C₁₃×#532	C₄	1	1	yes	characteristic, complemented
12	C₁₃×#532	C₄	1	1	yes	characteristic, complemented
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₁₃×#529	—	2	1	no	—
15	C₁₃×#529	—	2	1	no	—
16	C₁₃×#529	—	2	1	no	—
17	C₁₃×#529	—	2	1	no	—
18	C₁₃×#529	C₄	1	2	yes	complemented
19	C₁₃×#529	C₂²	1	2	yes	—
20	C₁₃×#525	—	2	1	no	—
21	C₁₃×#525	—	2	1	no	—
22	C₁₃×#525	C₂²	1	2	yes	—
23	C₄×C₁₃×#41	—	2	1	no	—
24	C₄×C₁₃×#41	—	2	1	no	—
25	C₄×C₁₃×#41	C₄	1	2	yes	complemented
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#432	—	2	1	no	—
28	C₁₃×#432	C₂²	1	2	yes	—
29	C₁₃×#431	—	2	1	no	—
30	C₁₃×#431	C₂²	1	2	yes	—
31	C₁₃×#423	—	2	1	no	—
32	C₁₃×#407	C₂²	1	2	yes	—
33	C₄×C₁₃×M₁₆	—	2	1	no	—
34	C₁₃×#383	—	2	1	no	—
35	C₁₃×#383	—	2	1	no	—
36	C₁₃×#383	C₂²	1	2	yes	—
37	C₁₃×#383	C₂²	1	2	yes	—
38	C₂×C₁₃×#95	—	2	1	no	—
39	C₂×C₁₃×#95	—	2	1	no	—
40	C₂×C₁₃×#95	C₂²	1	2	yes	—
41	C₁₃×#328	C₂²	1	8	yes	—
42	C₁₃×#327	C₂²	1	8	yes	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₃	—	2	2	no	—
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
54	C₁₃×#127	C₂×C₄	1	1	yes	characteristic, complemented
55	C₁₃×#126	—	2	2	no	—
56	C₁₃×#126	—	2	2	no	—
57	C₁₃×#125	—	2	1	no	—
58	C₁₃×#125	—	2	1	no	—
59	C₁₃×#125	C₂×C₄	1	2	yes	complemented
60	C₁₃×#124	—	2	1	no	—
61	C₁₃×#124	—	2	1	no	—
62	C₁₃×#124	C₂×C₄	1	2	yes	complemented
63	C₁₃×#123	—	2	2	no	—
64	C₁₃×#123	—	2	2	no	—
65	C₁₃×#123	—	2	2	no	—
66	C₁₃×C₂²⋊Q₈	—	2	1	no	—
67	C₁₃×C₂²⋊Q₈	—	2	1	no	—
68	C₁₃×C₂²⋊Q₈	—	2	1	no	—
69	C₁₃×C₂²⋊Q₈	—	2	1	no	—
70	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
71	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
72	C₁₃×#121	—	2	1	no	—
73	C₁₃×#121	—	2	1	no	—
74	C₁₃×#121	—	2	1	no	—
75	C₁₃×#121	—	2	1	no	—
76	C₁₃×#121	C₂×C₄	1	2	yes	—
77	C₁₃×#121	C₂³	1	2	yes	—
78	C₁₃×#120	—	2	2	no	—
79	C₄×Q₈×C₁₃	—	2	1	no	—
80	C₄×Q₈×C₁₃	—	2	1	no	—
81	C₄×Q₈×C₁₃	—	2	1	no	—
82	C₄×Q₈×C₁₃	—	2	1	no	—
83	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	complemented
84	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	complemented
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	complemented
96	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	complemented
97	C₁₃×#117	—	2	1	no	—
98	C₁₃×#117	—	2	1	no	—
99	C₁₃×#117	—	2	2	no	—
100	C₁₃×#117	—	2	2	no	—
101	C₁₃×#117	—	2	2	no	—
102	C₁₃×#117	C₂×C₄	1	2	yes	—
103	C₂×C₄²×C₁₃	—	2	2	no	—
104	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	—	2	2	no	—
117	C₁₃×C₄⋊C₈	—	2	2	no	—
118	C₁₃×C₂²⋊C₈	—	2	2	no	—
119	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
120	C₁₃×#97	—	2	2	no	—
121	C₄×C₈×C₁₃	—	2	2	no	—
122	C₁₃×#95	—	2	2	no	—
123	C₁₃×#95	—	2	2	no	—
124	C₁₃×#95	—	2	2	no	—
125	C₁₃×#95	—	2	2	no	—
126	C₁₃×#95	—	2	2	no	—
127	C₁₃×#95	C₂³	1	4	yes	—
128	#17593	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₁₃×#41	—	4	4	no	—
131	C₁₃×#41	—	4	4	no	—
132	C₁₃×#41	—	4	4	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	2	2	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	4	2	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	4	2	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	—	4	4	no	—
151	C₂²×C₄×C₁₃	—	4	4	no	—
152	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×M₁₆	—	4	4	no	—
171	C₂×C₈×C₁₃	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
183	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
184	C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₁₃×C₂²⋊C₄	—	2	2	no	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	2	no	—
188	C₁₃×C₂²⋊C₄	—	2	2	no	—
189	C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₁₃×C₂²⋊C₄	—	2	2	no	—
191	C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₁₃×C₂²⋊C₄	—	2	2	no	—
193	C₄²×C₁₃	—	2	2	no	—
194	C₄²×C₁₃	—	2	2	no	—
195	C₄²×C₁₃	—	2	2	no	—
196	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
197	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
198	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
199	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
200	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
201	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
212	#3444	C₂×C₁₃	1	1	yes	characteristic
213	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#383	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1521	C₂×C₁₃	1	4	yes	complemented
216	#1515	C₂×C₁₃	1	2	yes	complemented
217	#1514	C₂×C₁₃	1	2	yes	complemented
218	#1504	C₂×C₁₃	1	4	yes	complemented
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₁₃	—	4	2	no	—
227	Q₈×C₁₃	—	4	2	no	—
228	Q₈×C₁₃	—	4	2	no	—
229	D₄×C₁₃	—	4	2	no	—
230	D₄×C₁₃	—	4	2	no	—
231	D₄×C₁₃	—	4	2	no	—
232	D₄×C₁₃	—	4	4	no	—
233	D₄×C₁₃	—	4	4	no	—
234	D₄×C₁₃	—	4	4	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	4	no	—
257	C₂×C₄×C₁₃	—	4	4	no	—
258	C₂×C₄×C₁₃	—	4	4	no	—
259	C₂×C₄×C₁₃	—	4	4	no	—
260	C₂×C₄×C₁₃	—	4	4	no	—
261	C₂×C₄×C₁₃	—	4	4	no	—
262	C₂×C₄×C₁₃	—	8	8	no	—
263	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₈×C₁₃	—	4	4	no	—
276	#533	C₄×C₁₃	1	1	yes	characteristic, complemented
277	#533	C₄×C₁₃	1	1	yes	characteristic, complemented
278	#533	C₂²×C₁₃	1	1	yes	characteristic
279	#532	C₄×C₁₃	1	1	yes	characteristic, complemented
280	#532	C₄×C₁₃	1	1	yes	characteristic, complemented
281	#532	C₂²×C₁₃	1	1	yes	characteristic
282	#529	—	2	1	no	—
283	#529	—	2	1	no	—
284	#529	—	2	1	no	—
285	#529	—	2	1	no	—
286	#529	C₄×C₁₃	1	2	yes	complemented
287	#529	C₂²×C₁₃	1	2	yes	—
288	#525	—	2	1	no	—
289	#525	—	2	1	no	—
290	#525	C₂²×C₁₃	1	2	yes	—
291	C₄×#41	—	2	1	no	—
292	C₄×#41	—	2	1	no	—
293	C₄×#41	C₄×C₁₃	1	2	yes	complemented
294	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
295	#432	—	2	1	no	—
296	#432	C₂²×C₁₃	1	2	yes	—
297	#431	—	2	1	no	—
298	#431	C₂²×C₁₃	1	2	yes	—
299	#423	—	2	1	no	—
300	#407	C₂²×C₁₃	1	2	yes	—
301	C₄×M₁₆	—	2	1	no	—
302	#383	—	2	1	no	—
303	#383	—	2	1	no	—
304	#383	C₂²×C₁₃	1	2	yes	—
305	#383	C₂²×C₁₃	1	2	yes	—
306	C₂×#95	—	2	1	no	—
307	C₂×#95	—	2	1	no	—
308	C₂×#95	C₂²×C₁₃	1	2	yes	—
309	#328	C₂²×C₁₃	1	8	yes	—
310	#327	C₂²×C₁₃	1	8	yes	—
311	C₂²×C₁₃	—	2	8	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	4	2	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	#410	1	2	yes	—
322	C₂²×C₁₃	#421	1	2	yes	—
323	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
324	C₂²×C₁₃	#575	1	2	yes	—
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	4	2	no	—
338	C₄×C₁₃	—	4	2	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	8	4	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
344	C₂³×C₄	—	2	2	no	—
345	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×M₁₆	—	2	2	no	—
349	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
350	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
351	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
352	#127	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
353	#126	—	2	2	no	—
354	#126	—	2	2	no	—
355	#125	—	2	1	no	—
356	#125	—	2	1	no	—
357	#125	C₂×C₄×C₁₃	1	2	yes	complemented
358	#124	—	2	1	no	—
359	#124	—	2	1	no	—
360	#124	C₂×C₄×C₁₃	1	2	yes	complemented
361	#123	—	2	2	no	—
362	#123	—	2	2	no	—
363	#123	—	2	2	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
369	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
370	#121	—	2	1	no	—
371	#121	—	2	1	no	—
372	#121	—	2	1	no	—
373	#121	—	2	1	no	—
374	#121	C₂×C₄×C₁₃	1	2	yes	—
375	#121	C₂³×C₁₃	1	2	yes	—
376	#120	—	2	2	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	—	2	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
382	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	complemented
394	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	complemented
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	2	no	—
398	#117	—	2	2	no	—
399	#117	—	2	2	no	—
400	#117	C₂×C₄×C₁₃	1	2	yes	—
401	C₂×C₄²	—	2	2	no	—
402	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
403	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
404	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
405	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
406	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
407	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
408	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
409	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	C₄⋊C₈	—	2	2	no	—
415	C₄⋊C₈	—	2	2	no	—
416	C₂²⋊C₈	—	2	2	no	—
417	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
418	#97	—	2	2	no	—
419	C₄×C₈	—	2	2	no	—
420	#95	—	2	2	no	—
421	#95	—	2	2	no	—
422	#95	—	2	2	no	—
423	#95	—	2	2	no	—
424	#95	—	2	2	no	—
425	#95	C₂³×C₁₃	1	4	yes	—
426	C₂×C₁₃	—	2	2	no	—
427	C₂×C₁₃	—	2	2	no	—
428	C₂×C₁₃	—	2	2	no	—
429	C₂×C₁₃	—	8	2	no	—
430	C₂×C₁₃	C₂×#410	1	1	yes	characteristic
431	C₂×C₁₃	#2896	1	1	yes	characteristic
432	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
433	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
434	#41	—	4	4	no	—
435	#41	—	4	4	no	—
436	#41	—	4	4	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
457	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
458	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
459	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
460	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
461	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
462	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
463	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
464	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
474	M₁₆	—	4	4	no	—
475	C₂×C₈	—	2	4	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
487	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
501	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
502	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
503	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
504	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
505	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
506	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
507	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
508	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
509	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
510	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
511	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₁₃	#17593	1	1	yes	characteristic, direct product factor, Sylow
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
522	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
523	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
524	Q₈	—	4	2	no	—
525	Q₈	—	4	2	no	—
526	Q₈	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	4	no	—
531	D₄	—	4	4	no	—
532	D₄	—	4	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	8	8	no	—
561	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
562	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
564	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
566	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
567	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
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	1	yes	characteristic
571	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
572	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
573	C₈	—	4	4	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	C₁₃×#410	1	2	yes	—
585	C₂²	C₁₃×#421	1	2	yes	—
586	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
587	C₂²	C₁₃×#575	1	2	yes	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	8	4	no	—
604	C₂	—	2	2	no	—
605	C₂	—	2	2	no	—
606	C₂	—	2	2	no	—
607	C₂	—	8	2	no	—
608	C₂	C₂×C₁₃×#410	1	1	yes	characteristic
609	C₂	C₁₃×#2896	1	1	yes	characteristic
610	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2920	C₂	semidirect
3. C₂×C₁₃×#383	C₂	semidirect
4. C₁₃×#1521	C₂	semidirect
5. C₁₃×#1515	C₂	semidirect
6. C₁₃×#1514	C₂	semidirect
7. C₁₃×#1504	C₂	semidirect
8. C₁₃×#533	C₄	semidirect
9. C₁₃×#533	C₄	semidirect
11. C₁₃×#532	C₄	semidirect
12. C₁₃×#532	C₄	semidirect
18. C₁₃×#529	C₄	semidirect
25. C₄×C₁₃×#41	C₄	semidirect
51. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
52. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
53. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
54. C₁₃×#127	C₂×C₄	semidirect
59. C₁₃×#125	C₂×C₄	semidirect
62. C₁₃×#124	C₂×C₄	semidirect
83. C₄×Q₈×C₁₃	C₂×C₄	semidirect
84. C₄×Q₈×C₁₃	C₂×C₄	semidirect
95. C₄×D₄×C₁₃	C₂×C₄	semidirect
96. C₄×D₄×C₁₃	C₂×C₄	semidirect
128. #17593	C₁₃	direct (N × H)
213. #2920	C₂×C₁₃	semidirect
214. C₂×#383	C₂×C₁₃	semidirect
215. #1521	C₂×C₁₃	semidirect
216. #1515	C₂×C₁₃	semidirect
217. #1514	C₂×C₁₃	semidirect
218. #1504	C₂×C₁₃	semidirect
276. #533	C₄×C₁₃	semidirect
277. #533	C₄×C₁₃	semidirect
279. #532	C₄×C₁₃	semidirect
280. #532	C₄×C₁₃	semidirect
286. #529	C₄×C₁₃	semidirect
293. C₄×#41	C₄×C₁₃	semidirect
349. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
350. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
351. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
352. #127	C₂×C₄×C₁₃	semidirect
357. #125	C₂×C₄×C₁₃	semidirect
360. #124	C₂×C₄×C₁₃	semidirect
381. C₄×Q₈	C₂×C₄×C₁₃	semidirect
382. C₄×Q₈	C₂×C₄×C₁₃	semidirect
393. C₄×D₄	C₂×C₄×C₁₃	semidirect
394. C₄×D₄	C₂×C₄×C₁₃	semidirect
516. C₁₃	#17593	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×#3444	2
C₁₃×#2920	2
C₂×C₁₃×#383	2
C₁₃×#1521	2
C₁₃×#1515	2
C₁₃×#1514	2
C₁₃×#1504	2
#17593	13

Subgroups — C13×#17593 #15703932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17593 #15703932