Subgroups — C₁₃×#17545 #15703884

Order 3328.

1084 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1508	C₂	1	4	yes	maximal
5	C₁₃×#1506	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1503	C₂	1	4	yes	maximal, complemented
7	C₁₃×#533	—	2	1	no	—
8	C₁₃×#533	—	2	1	no	—
9	C₁₃×#533	—	2	1	no	—
10	C₁₃×#533	—	2	1	no	—
11	C₁₃×#533	C₄	1	2	yes	complemented
12	C₁₃×#533	C₄	1	2	yes	complemented
13	C₁₃×#533	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	2	yes	—
15	C₂×C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
16	C₂×C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
17	C₂×C₁₃×#125	—	2	1	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₃	C₄	1	2	yes	complemented
22	C₂×C₁₃×#117	—	2	1	no	—
23	C₂×C₁₃×#117	—	2	1	no	—
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#432	—	2	1	no	—
26	C₁₃×#432	C₂²	1	2	yes	—
27	C₁₃×#431	—	2	1	no	—
28	C₁₃×#431	C₂²	1	2	yes	—
29	C₁₃×#423	—	2	1	no	—
30	C₁₃×#407	C₂²	1	2	yes	—
31	C₄×C₁₃×M₁₆	—	2	1	no	—
32	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
35	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₁₃×#376	C₂²	1	2	yes	—
37	C₄³×C₁₃	—	2	1	no	—
38	C₁₃×#328	C₂²	1	16	yes	—
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₁₃×M₁₆	—	2	2	no	—
45	C₁₃×C₄⋊Q₈	—	2	1	no	—
46	C₁₃×C₄⋊Q₈	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	—	2	1	no	—
48	C₁₃×C₄⋊Q₈	—	2	1	no	—
49	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
50	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
53	C₁₃×#125	—	2	2	no	—
54	C₁₃×#125	—	2	2	no	—
55	C₁₃×#125	—	2	2	no	—
56	C₁₃×#125	—	2	2	no	—
57	C₁₃×C₂²⋊Q₈	—	2	2	no	—
58	C₁₃×C₂²⋊Q₈	—	2	2	no	—
59	C₁₃×C₂²⋊Q₈	—	2	2	no	—
60	C₁₃×C₂²⋊Q₈	—	2	2	no	—
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×C₂²⋊Q₈	—	2	2	no	—
63	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
64	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
72	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
73	C₁₃×#117	—	2	8	no	—
74	C₁₃×#117	—	2	2	no	—
75	C₁₃×#117	—	2	2	no	—
76	C₁₃×#117	—	2	2	no	—
77	C₁₃×#117	—	2	2	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	2	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₄²×C₁₃	—	2	2	no	—
88	C₂×C₄²×C₁₃	—	2	2	no	—
89	C₂×C₄²×C₁₃	—	2	2	no	—
90	C₂×C₄²×C₁₃	—	2	2	no	—
91	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊C₈	—	2	2	no	—
104	C₁₃×C₄⋊C₈	—	2	2	no	—
105	C₁₃×C₂²⋊C₈	—	2	2	no	—
106	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
107	C₁₃×#97	—	2	2	no	—
108	C₄×C₈×C₁₃	—	2	2	no	—
109	C₁₃×#95	—	2	2	no	—
110	C₁₃×#95	C₂³	1	4	yes	—
111	#17545	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	4	4	no	—
117	C₂×Q₈×C₁₃	—	4	4	no	—
118	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	4	2	no	—
125	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×M₁₆	—	4	4	no	—
144	C₂×C₈×C₁₃	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₁₃×C₂²⋊C₄	—	2	4	no	—
161	C₄²×C₁₃	—	2	8	no	—
162	C₄²×C₁₃	—	2	4	no	—
163	C₄²×C₁₃	—	2	4	no	—
164	C₄²×C₁₃	—	4	4	no	—
165	C₄²×C₁₃	—	4	4	no	—
166	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
183	#2920	C₂×C₁₃	1	1	yes	characteristic
184	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
185	#1508	C₂×C₁₃	1	4	yes	—
186	#1506	C₂×C₁₃	1	4	yes	complemented
187	#1503	C₂×C₁₃	1	4	yes	complemented
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₁₃	—	4	4	no	—
195	Q₈×C₁₃	—	4	4	no	—
196	Q₈×C₁₃	—	4	4	no	—
197	Q₈×C₁₃	—	4	4	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	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	8	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	4	no	—
218	C₂×C₄×C₁₃	—	4	4	no	—
219	C₂×C₄×C₁₃	—	4	4	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	#104	1	4	yes	—
222	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	#137	1	4	yes	—
233	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₈×C₁₃	—	4	4	no	—
236	#533	—	2	1	no	—
237	#533	—	2	1	no	—
238	#533	—	2	1	no	—
239	#533	—	2	1	no	—
240	#533	C₄×C₁₃	1	2	yes	complemented
241	#533	C₄×C₁₃	1	2	yes	complemented
242	#533	C₂²×C₁₃	1	2	yes	—
243	#533	C₂²×C₁₃	1	2	yes	—
244	C₂×C₄⋊Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
245	C₂×C₄⋊Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
246	C₂×#125	—	2	1	no	—
247	C₂×C₂²⋊Q₈	—	2	1	no	—
248	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
249	C₂×C₄×Q₈	—	2	1	no	—
250	C₂×C₄×Q₈	C₄×C₁₃	1	2	yes	complemented
251	C₂×#117	—	2	1	no	—
252	C₂×#117	—	2	1	no	—
253	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
254	#432	—	2	1	no	—
255	#432	C₂²×C₁₃	1	2	yes	—
256	#431	—	2	1	no	—
257	#431	C₂²×C₁₃	1	2	yes	—
258	#423	—	2	1	no	—
259	#407	C₂²×C₁₃	1	2	yes	—
260	C₄×M₁₆	—	2	1	no	—
261	C₄×C₄⋊C₄	—	2	1	no	—
262	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
263	C₄×C₂²⋊C₄	—	2	1	no	—
264	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
265	#376	C₂²×C₁₃	1	2	yes	—
266	C₄³	—	2	1	no	—
267	#328	C₂²×C₁₃	1	16	yes	—
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	2	1	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	—	4	4	no	—
276	C₂²×C₁₃	C₂×#104	1	2	yes	—
277	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
278	C₂²×C₁₃	C₂×#137	1	2	yes	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	1	no	—
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	—	4	8	no	—
287	C₄×C₁₃	—	4	4	no	—
288	C₄×C₁₃	—	4	4	no	—
289	C₄×C₁₃	#410	1	2	yes	—
290	C₄×C₁₃	#419	1	2	yes	—
291	C₄×C₁₃	#419	1	2	yes	—
292	C₄×C₁₃	C₂×#104	1	2	yes	—
293	C₄×C₁₃	C₂×#104	1	2	yes	—
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
296	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
297	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×M₁₆	—	2	2	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
305	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
306	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
307	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
308	#125	—	2	2	no	—
309	#125	—	2	2	no	—
310	#125	—	2	2	no	—
311	#125	—	2	2	no	—
312	C₂²⋊Q₈	—	2	2	no	—
313	C₂²⋊Q₈	—	2	2	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
319	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
327	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
328	#117	—	2	8	no	—
329	#117	—	2	2	no	—
330	#117	—	2	2	no	—
331	#117	—	2	2	no	—
332	#117	—	2	2	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
347	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
348	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
349	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
350	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
358	C₄⋊C₈	—	2	2	no	—
359	C₄⋊C₈	—	2	2	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
362	#97	—	2	2	no	—
363	C₄×C₈	—	2	2	no	—
364	#95	—	2	2	no	—
365	#95	C₂³×C₁₃	1	4	yes	—
366	C₂×C₁₃	—	2	2	no	—
367	C₂×C₁₃	—	2	2	no	—
368	C₂×C₁₃	—	4	1	no	—
369	C₂×C₁₃	C₂×#410	1	1	yes	characteristic
370	C₂×C₁₃	C₂×#419	1	1	yes	characteristic
371	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
372	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×Q₈	—	4	4	no	—
378	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
386	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
387	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
388	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
389	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
390	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
391	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
392	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
403	M₁₆	—	4	4	no	—
404	C₂×C₈	—	2	4	no	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₄²	—	2	8	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	4	4	no	—
425	C₄²	—	4	4	no	—
426	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
427	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
428	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
429	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
430	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
431	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
432	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
433	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
434	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
435	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
436	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
437	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
438	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₁₃	#17545	1	1	yes	characteristic, direct product factor, Sylow
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	4	1	no	—
446	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
447	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
448	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
449	Q₈	—	4	4	no	—
450	Q₈	—	4	4	no	—
451	Q₈	—	4	4	no	—
452	Q₈	—	4	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	C₁₃×#104	1	4	yes	—
477	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
478	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
479	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
480	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
481	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
483	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
484	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
485	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
486	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
487	C₂×C₄	C₁₃×#137	1	4	yes	—
488	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
490	C₈	—	4	4	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	4	4	no	—
499	C₂²	C₂×C₁₃×#104	1	2	yes	—
500	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
501	C₂²	C₂×C₁₃×#137	1	2	yes	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	8	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	4	no	—
512	C₄	C₁₃×#410	1	2	yes	—
513	C₄	C₁₃×#419	1	2	yes	—
514	C₄	C₁₃×#419	1	2	yes	—
515	C₄	C₂×C₁₃×#104	1	2	yes	—
516	C₄	C₂×C₁₃×#104	1	2	yes	—
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	C₂×C₁₃×#410	1	1	yes	characteristic
521	C₂	C₂×C₁₃×#419	1	1	yes	characteristic
522	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₁₃×#1506	C₂	semidirect
6. C₁₃×#1503	C₂	semidirect
11. C₁₃×#533	C₄	semidirect
12. C₁₃×#533	C₄	semidirect
15. C₂×C₁₃×C₄⋊Q₈	C₄	semidirect
16. C₂×C₁₃×C₄⋊Q₈	C₄	semidirect
21. C₂×C₄×Q₈×C₁₃	C₄	semidirect
111. #17545	C₁₃	direct (N × H)
186. #1506	C₂×C₁₃	semidirect
187. #1503	C₂×C₁₃	semidirect
240. #533	C₄×C₁₃	semidirect
241. #533	C₄×C₁₃	semidirect
244. C₂×C₄⋊Q₈	C₄×C₁₃	semidirect
245. C₂×C₄⋊Q₈	C₄×C₁₃	semidirect
250. C₂×C₄×Q₈	C₄×C₁₃	semidirect
442. C₁₃	#17545	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×#533	2
C₁₃×#2920	2
C₄×C₁₃×#117	2
C₁₃×#1508	2
C₁₃×#1506	2
C₁₃×#1503	2
#17545	13

Subgroups — C13×#17545 #15703884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17545 #15703884