Subgroups — C₁₃×#34631 #15720970

Order 3328.

2138 conjugacy classes of subgroups.

The subgroup lattice has 578 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, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2664	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2663	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2660	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2658	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2642	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2640	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2621	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2620	C₂	1	2	yes	maximal
11	C₁₃×#2396	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2395	C₂	1	4	yes	maximal, complemented
13	C₄×C₁₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#124	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#533	—	2	8	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₃×#529	—	2	8	no	—
21	C₂×C₁₃×#126	C₂²	1	2	yes	—
22	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#125	C₂²	1	2	yes	—
24	C₂×C₁₃×#124	C₂²	1	2	yes	—
25	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#123	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	C₂²	1	2	yes	—
37	C₂×C₁₃×#117	C₂²	1	2	yes	—
38	C₂×C₁₃×#117	C₂²	1	2	yes	—
39	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#400	C₂²	1	4	yes	—
41	C₁₃×#400	C₂²	1	4	yes	—
42	C₁₃×#399	C₂²	1	4	yes	—
43	C₁₃×#399	C₂²	1	4	yes	—
44	C₁₃×#398	C₂²	1	8	yes	—
45	C₁₃×#398	C₂²	1	4	yes	—
46	C₁₃×#397	C₂²	1	8	yes	—
47	C₁₃×#397	C₂²	1	4	yes	—
48	C₁₃×#396	C₂²	1	8	yes	—
49	C₁₃×#395	C₂²	1	4	yes	—
50	C₁₃×#394	C₂²	1	8	yes	—
51	C₁₃×#393	C₂²	1	4	yes	—
52	C₁₃×#391	C₂²	1	2	yes	—
53	C₁₃×#391	C₂²	1	2	yes	—
54	C₁₃×#391	C₂²	1	2	yes	—
55	C₁₃×#390	C₂²	1	2	yes	—
56	C₁₃×#389	C₂²	1	8	yes	—
57	C₁₃×#388	C₂²	1	8	yes	—
58	C₁₃×#384	C₂²	1	2	yes	—
59	C₁₃×#382	C₂²	1	2	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
66	C₁₃×#376	C₂²	1	1	yes	characteristic
67	C₁₃×#376	C₂²	1	1	yes	characteristic
68	C₄³×C₁₃	C₂²	1	2	yes	—
69	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
71	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	—	2	4	no	—
79	C₁₃×C₄⋊Q₈	—	2	4	no	—
80	C₁₃×C₄⋊Q₈	—	2	8	no	—
81	C₁₃×#126	—	2	8	no	—
82	C₁₃×#125	—	2	4	no	—
83	C₁₃×#125	—	2	8	no	—
84	C₁₃×#124	—	2	4	no	—
85	C₁₃×#124	—	2	8	no	—
86	C₁₃×#123	—	2	8	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	—	2	8	no	—
89	C₁₃×C₂²⋊Q₈	—	2	8	no	—
90	C₁₃×#121	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	4	no	—
92	C₄×Q₈×C₁₃	—	2	8	no	—
93	C₄×Q₈×C₁₃	—	2	8	no	—
94	C₄×D₄×C₁₃	—	2	8	no	—
95	C₄×D₄×C₁₃	—	2	4	no	—
96	C₁₃×#117	—	2	8	no	—
97	C₁₃×#117	—	2	8	no	—
98	C₁₃×#117	—	2	8	no	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
123	C₂×C₄²×C₁₃	D₄	1	8	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
134	C₁₃×#95	C₂³	1	2	yes	—
135	C₁₃×#95	C₂³	1	2	yes	—
136	C₁₃×#95	C₂³	1	2	yes	—
137	C₁₃×#95	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	8	yes	—
139	C₁₃×#95	C₂³	1	8	yes	—
140	C₁₃×#95	C₂³	1	8	yes	—
141	C₁₃×#95	C₂³	1	8	yes	—
142	#34631	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
144	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	4	no	—
147	C₂×Q₈×C₁₃	—	2	4	no	—
148	C₂×Q₈×C₁₃	—	2	4	no	—
149	C₂×Q₈×C₁₃	—	2	4	no	—
150	C₂×Q₈×C₁₃	—	2	4	no	—
151	C₂×Q₈×C₁₃	—	4	4	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	4	4	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	8	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	4	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	8	no	—
185	C₁₃×C₄⋊C₄	—	2	8	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	8	no	—
190	C₁₃×C₄⋊C₄	—	2	16	no	—
191	C₁₃×C₄⋊C₄	—	4	8	no	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	8	no	—
199	C₁₃×C₂²⋊C₄	—	2	16	no	—
200	C₁₃×C₂²⋊C₄	—	4	8	no	—
201	C₄²×C₁₃	—	2	4	no	—
202	C₄²×C₁₃	—	2	8	no	—
203	C₄²×C₁₃	—	2	4	no	—
204	C₄²×C₁₃	—	2	8	no	—
205	C₄²×C₁₃	—	4	4	no	—
206	C₄²×C₁₃	C₂×D₄	1	4	yes	—
207	C₄²×C₁₃	C₂×D₄	1	4	yes	—
208	C₄²×C₁₃	C₂×D₄	1	4	yes	—
209	C₄²×C₁₃	C₂×D₄	1	4	yes	—
210	C₄²×C₁₃	#41	1	8	yes	—
211	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
213	#2664	C₂×C₁₃	1	4	yes	complemented
214	#2663	C₂×C₁₃	1	4	yes	complemented
215	#2660	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2658	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2642	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2640	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2621	C₂×C₁₃	1	2	yes	complemented
220	#2620	C₂×C₁₃	1	2	yes	—
221	#2396	C₂×C₁₃	1	4	yes	complemented
222	#2395	C₂×C₁₃	1	4	yes	complemented
223	C₄×C₄⋊Q₈	C₂×C₁₃	1	2	yes	complemented
224	C₄×#124	C₂×C₁₃	1	2	yes	complemented
225	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	2	2	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
234	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
235	Q₈×C₁₃	—	4	8	no	—
236	Q₈×C₁₃	—	4	4	no	—
237	Q₈×C₁₃	—	4	8	no	—
238	D₄×C₁₃	—	4	8	no	—
239	D₄×C₁₃	—	4	4	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	8	no	—
247	C₂×C₄×C₁₃	—	2	8	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	8	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	4	4	no	—
263	C₂×C₄×C₁₃	—	4	8	no	—
264	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
271	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
272	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
273	#533	—	2	8	no	—
274	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
275	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
277	#529	—	2	8	no	—
278	C₂×#126	C₂²×C₁₃	1	2	yes	—
279	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×#125	C₂²×C₁₃	1	2	yes	—
281	C₂×#124	C₂²×C₁₃	1	2	yes	—
282	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#123	C₂²×C₁₃	1	2	yes	—
284	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
285	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
287	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
290	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
291	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
292	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#117	C₂²×C₁₃	1	2	yes	—
294	C₂×#117	C₂²×C₁₃	1	2	yes	—
295	C₂×#117	C₂²×C₁₃	1	2	yes	—
296	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
297	#400	C₂²×C₁₃	1	4	yes	—
298	#400	C₂²×C₁₃	1	4	yes	—
299	#399	C₂²×C₁₃	1	4	yes	—
300	#399	C₂²×C₁₃	1	4	yes	—
301	#398	C₂²×C₁₃	1	8	yes	—
302	#398	C₂²×C₁₃	1	4	yes	—
303	#397	C₂²×C₁₃	1	8	yes	—
304	#397	C₂²×C₁₃	1	4	yes	—
305	#396	C₂²×C₁₃	1	8	yes	—
306	#395	C₂²×C₁₃	1	4	yes	—
307	#394	C₂²×C₁₃	1	8	yes	—
308	#393	C₂²×C₁₃	1	4	yes	—
309	#391	C₂²×C₁₃	1	2	yes	—
310	#391	C₂²×C₁₃	1	2	yes	—
311	#391	C₂²×C₁₃	1	2	yes	—
312	#390	C₂²×C₁₃	1	2	yes	—
313	#389	C₂²×C₁₃	1	8	yes	—
314	#388	C₂²×C₁₃	1	8	yes	—
315	#384	C₂²×C₁₃	1	2	yes	—
316	#382	C₂²×C₁₃	1	2	yes	—
317	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
318	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
319	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
320	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
321	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
322	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
323	#376	C₂²×C₁₃	1	1	yes	characteristic
324	#376	C₂²×C₁₃	1	1	yes	characteristic
325	C₄³	C₂²×C₁₃	1	2	yes	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	4	4	no	—
330	C₂²×C₁₃	—	4	2	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	2	no	—
333	C₂²×C₁₃	—	4	8	no	—
334	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
335	C₂²×C₁₃	C₂²×#41	1	2	yes	—
336	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
337	C₂²×C₁₃	#585	1	2	yes	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	2	2	no	—
342	C₄×C₁₃	—	2	8	no	—
343	C₄×C₁₃	—	4	2	no	—
344	C₄×C₁₃	—	4	4	no	—
345	C₄×C₁₃	—	4	2	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	—	4	4	no	—
348	C₄×C₁₃	—	4	4	no	—
349	C₄×C₁₃	#532	1	4	yes	—
350	C₄×C₁₃	#536	1	4	yes	—
351	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
352	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
353	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
354	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
356	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
357	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₄⋊Q₈	—	2	4	no	—
361	C₄⋊Q₈	—	2	4	no	—
362	C₄⋊Q₈	—	2	8	no	—
363	#126	—	2	8	no	—
364	#125	—	2	4	no	—
365	#125	—	2	8	no	—
366	#124	—	2	4	no	—
367	#124	—	2	8	no	—
368	#123	—	2	8	no	—
369	C₂²⋊Q₈	—	2	4	no	—
370	C₂²⋊Q₈	—	2	8	no	—
371	C₂²⋊Q₈	—	2	8	no	—
372	#121	—	2	4	no	—
373	C₄×Q₈	—	2	4	no	—
374	C₄×Q₈	—	2	8	no	—
375	C₄×Q₈	—	2	8	no	—
376	C₄×D₄	—	2	8	no	—
377	C₄×D₄	—	2	4	no	—
378	#117	—	2	8	no	—
379	#117	—	2	8	no	—
380	#117	—	2	8	no	—
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
405	C₂×C₄²	D₄×C₁₃	1	8	yes	—
406	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
407	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
408	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
410	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
411	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
416	#95	C₂³×C₁₃	1	2	yes	—
417	#95	C₂³×C₁₃	1	2	yes	—
418	#95	C₂³×C₁₃	1	2	yes	—
419	#95	C₂³×C₁₃	1	2	yes	—
420	#95	C₂³×C₁₃	1	8	yes	—
421	#95	C₂³×C₁₃	1	8	yes	—
422	#95	C₂³×C₁₃	1	8	yes	—
423	#95	C₂³×C₁₃	1	8	yes	—
424	C₂×C₁₃	—	4	2	no	—
425	C₂×C₁₃	—	8	2	no	—
426	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
427	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
428	C₂×C₁₃	#3449	1	1	yes	characteristic
429	C₂×C₁₃	#3461	1	4	yes	—
430	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
431	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	4	no	—
434	C₂×Q₈	—	2	4	no	—
435	C₂×Q₈	—	2	4	no	—
436	C₂×Q₈	—	2	4	no	—
437	C₂×Q₈	—	2	4	no	—
438	C₂×Q₈	—	4	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	4	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	8	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
449	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
450	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	8	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	8	no	—
477	C₄⋊C₄	—	2	16	no	—
478	C₄⋊C₄	—	4	8	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	—	2	16	no	—
487	C₂²⋊C₄	—	4	8	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	8	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	8	no	—
492	C₄²	—	4	4	no	—
493	C₄²	C₂×D₄×C₁₃	1	4	yes	—
494	C₄²	C₂×D₄×C₁₃	1	4	yes	—
495	C₄²	C₂×D₄×C₁₃	1	4	yes	—
496	C₄²	C₂×D₄×C₁₃	1	4	yes	—
497	C₄²	C₁₃×#41	1	8	yes	—
498	C₁₃	#34631	1	1	yes	characteristic, direct product factor, Sylow
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	4	no	—
506	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
507	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
508	Q₈	—	4	8	no	—
509	Q₈	—	4	4	no	—
510	Q₈	—	4	8	no	—
511	D₄	—	4	8	no	—
512	D₄	—	4	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	8	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
538	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
540	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
541	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
543	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
544	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
545	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	8	no	—
554	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
555	C₂²	C₂²×C₁₃×#41	1	2	yes	—
556	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
557	C₂²	C₁₃×#585	1	2	yes	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	8	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	4	no	—
568	C₄	—	4	4	no	—
569	C₄	C₁₃×#532	1	4	yes	—
570	C₄	C₁₃×#536	1	4	yes	—
571	C₂	—	4	2	no	—
572	C₂	—	8	2	no	—
573	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
574	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
575	C₂	C₁₃×#3449	1	1	yes	characteristic
576	C₂	C₁₃×#3461	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#2664	C₂	semidirect
4. C₁₃×#2663	C₂	semidirect
5. C₁₃×#2660	C₂	semidirect
6. C₁₃×#2658	C₂	semidirect
7. C₁₃×#2642	C₂	semidirect
8. C₁₃×#2640	C₂	semidirect
9. C₁₃×#2621	C₂	semidirect
11. C₁₃×#2396	C₂	semidirect
12. C₁₃×#2395	C₂	semidirect
13. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
14. C₄×C₁₃×#124	C₂	semidirect
15. C₄×C₁₃×#117	C₂	semidirect
142. #34631	C₁₃	direct (N × H)
211. C₂×#533	C₂×C₁₃	semidirect
213. #2664	C₂×C₁₃	semidirect
214. #2663	C₂×C₁₃	semidirect
215. #2660	C₂×C₁₃	semidirect
216. #2658	C₂×C₁₃	semidirect
217. #2642	C₂×C₁₃	semidirect
218. #2640	C₂×C₁₃	semidirect
219. #2621	C₂×C₁₃	semidirect
221. #2396	C₂×C₁₃	semidirect
222. #2395	C₂×C₁₃	semidirect
223. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
224. C₄×#124	C₂×C₁₃	semidirect
225. C₄×#117	C₂×C₁₃	semidirect
498. C₁₃	#34631	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
C₂×C₁₃×#529	2
C₁₃×#2664	2
C₁₃×#2663	2
C₁₃×#2660	2
C₁₃×#2658	2
C₁₃×#2642	2
C₁₃×#2640	2
C₁₃×#2621	2
C₁₃×#2620	2
C₁₃×#2396	2
C₁₃×#2395	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#124	2
C₄×C₁₃×#117	2
#34631	13

Subgroups — C13×#34631 #15720970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34631 #15720970