Subgroups — C₁₃×#17340 #15703679

Order 3328.

704 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2965	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2965	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1455	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1454	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1454	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1450	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₁₃×#446	C₄	1	2	yes	—
18	C₁₃×#446	C₄	1	2	yes	—
19	C₁₃×#436	C₄	1	2	yes	—
20	C₁₃×#436	C₄	1	2	yes	—
21	C₁₃×#435	C₄	1	2	yes	—
22	C₁₃×#435	C₄	1	2	yes	—
23	C₁₃×#435	C₄	1	2	yes	—
24	C₁₃×#435	C₄	1	2	yes	—
25	C₁₃×#433	C₄	1	2	yes	—
26	C₁₃×#433	C₄	1	2	yes	—
27	C₁₃×#431	C₂²	1	1	yes	characteristic
28	C₁₃×#431	C₂²	1	1	yes	characteristic
29	C₁₃×#431	C₂²	1	1	yes	characteristic
30	C₁₃×#431	C₂²	1	1	yes	characteristic
31	C₁₃×#431	C₂²	1	1	yes	characteristic
32	C₁₃×#431	C₂²	1	1	yes	characteristic
33	C₁₃×#431	C₂²	1	1	yes	characteristic
34	C₁₃×#431	C₂²	1	1	yes	characteristic
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₁₃×#431	C₂²	1	1	yes	characteristic
37	C₁₃×#424	C₄	1	2	yes	—
38	C₁₃×#408	C₄	1	2	yes	—
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#322	C₂²	1	1	yes	characteristic
48	C₁₃×#322	C₂²	1	1	yes	characteristic
49	C₁₃×#322	C₂²	1	1	yes	characteristic
50	C₁₃×#322	C₂²	1	1	yes	characteristic
51	C₁₃×#322	C₂²	1	1	yes	characteristic
52	C₁₃×#322	C₂²	1	1	yes	characteristic
53	C₁₃×#322	C₂²	1	1	yes	characteristic
54	C₁₃×#322	C₂²	1	1	yes	characteristic
55	C₁₃×#322	C₂²	1	1	yes	characteristic
56	C₁₃×#322	C₂²	1	1	yes	characteristic
57	C₁₃×#322	C₂²	1	1	yes	characteristic
58	C₁₃×#322	C₂²	1	1	yes	characteristic
59	C₈²×C₁₃	C₂²	1	1	yes	characteristic
60	C₈²×C₁₃	C₂²	1	1	yes	characteristic
61	C₈²×C₁₃	C₂²	1	1	yes	characteristic
62	C₈²×C₁₃	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
65	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
66	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
72	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
73	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
77	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
78	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
79	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
81	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
87	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
89	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
90	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
92	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
94	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
95	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
96	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
97	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
98	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
99	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
100	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
101	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
102	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
103	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
104	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
105	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
106	C₁₃×#97	C₂×C₄	1	2	yes	—
107	C₁₃×#97	C₂×C₄	1	2	yes	—
108	C₁₃×#97	C₂×C₄	1	2	yes	—
109	C₁₃×#97	C₂×C₄	1	2	yes	—
110	C₁₃×#97	C₂×C₄	1	2	yes	—
111	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
112	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
113	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
114	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
115	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
119	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
126	#17340	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₁₃×#41	—	4	2	no	—
128	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
131	C₂×D₄×C₁₃	C₄²	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	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₁₃×M₁₆	—	2	4	no	—
142	C₁₃×M₁₆	—	2	4	no	—
143	C₁₃×M₁₆	—	4	2	no	—
144	C₁₃×M₁₆	—	4	2	no	—
145	C₁₃×M₁₆	—	4	2	no	—
146	C₂×C₈×C₁₃	—	2	4	no	—
147	C₂×C₈×C₁₃	—	4	2	no	—
148	C₂×C₈×C₁₃	—	4	2	no	—
149	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
159	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
160	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
162	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
163	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
164	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
165	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
167	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
168	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
169	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
171	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
172	C₁₃×C₂²⋊C₄	C₄²	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	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
183	#2965	C₂×C₁₃	1	1	yes	characteristic
184	#2965	C₂×C₁₃	1	1	yes	characteristic
185	#2922	C₂×C₁₃	1	1	yes	characteristic
186	#1455	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#1454	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1454	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1453	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#1453	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#1453	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1452	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1451	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#1451	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#1450	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
199	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
200	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
201	Q₈×C₁₃	—	4	1	no	—
202	D₄×C₁₃	—	4	1	no	—
203	D₄×C₁₃	—	4	1	no	—
204	D₄×C₁₃	—	4	1	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	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
226	C₈×C₁₃	—	2	2	no	—
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	2	2	no	—
229	C₈×C₁₃	—	2	2	no	—
230	C₈×C₁₃	—	2	2	no	—
231	C₈×C₁₃	—	2	2	no	—
232	C₈×C₁₃	—	2	2	no	—
233	C₈×C₁₃	—	2	2	no	—
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	2	2	no	—
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	#131	1	4	yes	—
238	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
239	#446	C₄×C₁₃	1	2	yes	—
240	#446	C₄×C₁₃	1	2	yes	—
241	#436	C₄×C₁₃	1	2	yes	—
242	#436	C₄×C₁₃	1	2	yes	—
243	#435	C₄×C₁₃	1	2	yes	—
244	#435	C₄×C₁₃	1	2	yes	—
245	#435	C₄×C₁₃	1	2	yes	—
246	#435	C₄×C₁₃	1	2	yes	—
247	#433	C₄×C₁₃	1	2	yes	—
248	#433	C₄×C₁₃	1	2	yes	—
249	#431	C₂²×C₁₃	1	1	yes	characteristic
250	#431	C₂²×C₁₃	1	1	yes	characteristic
251	#431	C₂²×C₁₃	1	1	yes	characteristic
252	#431	C₂²×C₁₃	1	1	yes	characteristic
253	#431	C₂²×C₁₃	1	1	yes	characteristic
254	#431	C₂²×C₁₃	1	1	yes	characteristic
255	#431	C₂²×C₁₃	1	1	yes	characteristic
256	#431	C₂²×C₁₃	1	1	yes	characteristic
257	#431	C₂²×C₁₃	1	1	yes	characteristic
258	#431	C₂²×C₁₃	1	1	yes	characteristic
259	#424	C₄×C₁₃	1	2	yes	—
260	#408	C₄×C₁₃	1	2	yes	—
261	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
262	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
263	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
264	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
265	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
269	#322	C₂²×C₁₃	1	1	yes	characteristic
270	#322	C₂²×C₁₃	1	1	yes	characteristic
271	#322	C₂²×C₁₃	1	1	yes	characteristic
272	#322	C₂²×C₁₃	1	1	yes	characteristic
273	#322	C₂²×C₁₃	1	1	yes	characteristic
274	#322	C₂²×C₁₃	1	1	yes	characteristic
275	#322	C₂²×C₁₃	1	1	yes	characteristic
276	#322	C₂²×C₁₃	1	1	yes	characteristic
277	#322	C₂²×C₁₃	1	1	yes	characteristic
278	#322	C₂²×C₁₃	1	1	yes	characteristic
279	#322	C₂²×C₁₃	1	1	yes	characteristic
280	#322	C₂²×C₁₃	1	1	yes	characteristic
281	C₈²	C₂²×C₁₃	1	1	yes	characteristic
282	C₈²	C₂²×C₁₃	1	1	yes	characteristic
283	C₈²	C₂²×C₁₃	1	1	yes	characteristic
284	C₈²	C₂²×C₁₃	1	1	yes	characteristic
285	C₂²×C₁₃	—	2	1	no	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	—	2	1	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	2	1	no	—
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	—	2	1	no	—
294	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	1	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	C₂×#131	1	2	yes	—
305	C₄×C₁₃	#568	1	2	yes	—
306	C₄×C₁₃	#568	1	2	yes	—
307	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
308	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
309	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
310	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
311	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
312	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
313	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
314	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
315	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
316	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
317	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
318	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
319	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
320	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
321	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
322	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
323	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
324	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
325	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
326	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
330	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
331	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
332	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
333	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
334	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
335	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
336	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
337	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
338	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
339	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
340	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
341	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
342	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
343	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
344	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
345	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
346	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
347	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
348	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
349	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
350	#97	C₂×C₄×C₁₃	1	2	yes	—
351	#97	C₂×C₄×C₁₃	1	2	yes	—
352	#97	C₂×C₄×C₁₃	1	2	yes	—
353	#97	C₂×C₄×C₁₃	1	2	yes	—
354	#97	C₂×C₄×C₁₃	1	2	yes	—
355	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
356	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
357	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
358	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
360	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
361	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
364	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
368	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×C₁₃	—	4	1	no	—
371	C₂×C₁₃	—	4	1	no	—
372	C₂×C₁₃	—	4	1	no	—
373	C₂×C₁₃	#2873	1	1	yes	characteristic
374	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
375	C₂×C₁₃	#2875	1	1	yes	characteristic
376	#41	—	4	2	no	—
377	C₂×Q₈	C₄²×C₁₃	1	1	yes	characteristic
378	C₂×D₄	C₄²×C₁₃	1	1	yes	characteristic
379	C₂×D₄	C₄²×C₁₃	1	1	yes	characteristic
380	C₂×D₄	C₄²×C₁₃	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
390	M₁₆	—	2	4	no	—
391	M₁₆	—	2	4	no	—
392	M₁₆	—	4	2	no	—
393	M₁₆	—	4	2	no	—
394	M₁₆	—	4	2	no	—
395	C₂×C₈	—	2	4	no	—
396	C₂×C₈	—	4	2	no	—
397	C₂×C₈	—	4	2	no	—
398	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
399	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
400	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
401	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
402	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
403	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
404	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
405	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
406	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
407	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
408	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
409	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
410	C₄⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
411	C₄⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
412	C₄⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
413	C₄⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
414	C₄⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
415	C₄⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
416	C₂²⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
417	C₂²⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
418	C₂²⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
419	C₂²⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
420	C₂²⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
421	C₂²⋊C₄	C₄²×C₁₃	1	1	yes	characteristic
422	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
423	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
424	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
425	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
426	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
427	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
428	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
429	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
430	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
431	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
432	C₁₃	#17340	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	C₂×C₄²×C₁₃	1	1	yes	characteristic
434	C₂³	C₂×C₄²×C₁₃	1	1	yes	characteristic
435	C₂³	C₂×C₄²×C₁₃	1	1	yes	characteristic
436	Q₈	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
455	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
457	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	2	2	no	—
466	C₈	—	2	2	no	—
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	2	2	no	—
471	C₈	—	2	2	no	—
472	C₈	C₁₃×#131	1	4	yes	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	C₂×C₁₃×#131	1	2	yes	—
493	C₄	C₁₃×#568	1	2	yes	—
494	C₄	C₁₃×#568	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	4	1	no	—
497	C₂	—	4	1	no	—
498	C₂	C₁₃×#2873	1	1	yes	characteristic
499	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
500	C₂	C₁₃×#2875	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1455	C₂	semidirect
5. C₁₃×#1454	C₂	semidirect
6. C₁₃×#1454	C₂	semidirect
7. C₁₃×#1453	C₂	semidirect
8. C₁₃×#1453	C₂	semidirect
9. C₁₃×#1453	C₂	semidirect
10. C₁₃×#1452	C₂	semidirect
11. C₁₃×#1451	C₂	semidirect
12. C₁₃×#1451	C₂	semidirect
13. C₁₃×#1450	C₂	semidirect
14. C₈×C₁₃×M₁₆	C₂	semidirect
15. C₈×C₁₃×M₁₆	C₂	semidirect
126. #17340	C₁₃	direct (N × H)
186. #1455	C₂×C₁₃	semidirect
187. #1454	C₂×C₁₃	semidirect
188. #1454	C₂×C₁₃	semidirect
189. #1453	C₂×C₁₃	semidirect
190. #1453	C₂×C₁₃	semidirect
191. #1453	C₂×C₁₃	semidirect
192. #1452	C₂×C₁₃	semidirect
193. #1451	C₂×C₁₃	semidirect
194. #1451	C₂×C₁₃	semidirect
195. #1450	C₂×C₁₃	semidirect
196. C₈×M₁₆	C₂×C₁₃	semidirect
197. C₈×M₁₆	C₂×C₁₃	semidirect
432. C₁₃	#17340	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×#2965	2
C₁₃×#2922	2
C₁₃×#1455	2
C₁₃×#1454	2
C₁₃×#1453	2
C₁₃×#1452	2
C₁₃×#1451	2
C₁₃×#1450	2
C₈×C₁₃×M₁₆	2
#17340	13

Subgroups — C13×#17340 #15703679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17340 #15703679