Subgroups — C₁₃×#34745 #15721084

Order 3328.

2522 conjugacy classes of subgroups.

The subgroup lattice has 668 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×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2454	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2453	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2452	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2451	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2450	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2449	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2396	C₂	1	4	yes	maximal, complemented
10	C₄×C₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₁₃×#533	—	2	8	no	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#125	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₄×C₁₃×#41	—	2	8	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#117	C₂²	1	2	yes	—
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
36	C₁₃×#400	C₂²	1	4	yes	—
37	C₁₃×#399	C₂²	1	4	yes	—
38	C₁₃×#398	C₂²	1	4	yes	—
39	C₁₃×#398	C₂²	1	4	yes	—
40	C₁₃×#396	C₂²	1	4	yes	—
41	C₁₃×#396	C₂²	1	4	yes	—
42	C₁₃×#395	C₂²	1	4	yes	—
43	C₁₃×#393	C₂²	1	4	yes	—
44	C₁₃×#391	C₂²	1	1	yes	characteristic
45	C₁₃×#391	C₂²	1	2	yes	—
46	C₁₃×#391	C₂²	1	1	yes	characteristic
47	C₁₃×#391	C₂²	1	4	yes	—
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#390	C₂²	1	2	yes	—
50	C₁₃×#390	C₂²	1	1	yes	characteristic
51	C₁₃×#389	C₂²	1	2	yes	—
52	C₁₃×#389	C₂²	1	2	yes	—
53	C₁₃×#389	C₂²	1	2	yes	—
54	C₁₃×#389	C₂²	1	2	yes	—
55	C₁₃×#389	C₂²	1	4	yes	—
56	C₁₃×#387	C₂²	1	4	yes	—
57	C₁₃×#387	C₂²	1	4	yes	—
58	C₁₃×#386	C₂²	1	2	yes	—
59	C₁₃×#386	C₂²	1	4	yes	—
60	C₁₃×#386	C₂²	1	2	yes	—
61	C₁₃×#385	C₂²	1	2	yes	—
62	C₁₃×#385	C₂²	1	4	yes	—
63	C₁₃×#385	C₂²	1	2	yes	—
64	C₁₃×#385	C₂²	1	4	yes	—
65	C₁₃×#385	C₂²	1	4	yes	—
66	C₁₃×#380	C₂²	1	4	yes	—
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
76	C₂×C₁₃×#95	C₂²	1	2	yes	—
77	C₂×C₁₃×#41	—	2	4	no	—
78	C₂×C₁₃×#41	—	2	4	no	—
79	C₂×C₁₃×#41	Q₈	1	8	yes	complemented
80	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
81	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊Q₈	—	2	8	no	—
92	C₁₃×#125	—	2	8	no	—
93	C₁₃×C₂²⋊Q₈	—	2	16	no	—
94	C₁₃×C₂²⋊Q₈	—	2	16	no	—
95	C₄×Q₈×C₁₃	—	2	8	no	—
96	C₄×Q₈×C₁₃	—	2	16	no	—
97	C₄×D₄×C₁₃	—	2	8	no	—
98	C₄×D₄×C₁₃	—	2	16	no	—
99	C₁₃×#117	—	2	4	no	—
100	C₁₃×#117	—	2	4	no	—
101	C₁₃×#117	—	2	8	no	—
102	C₁₃×#117	D₄	1	8	yes	—
103	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	4	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃	—	2	4	no	—
129	C₂×C₄²×C₁₃	—	2	4	no	—
130	C₂×C₄²×C₁₃	—	2	4	no	—
131	C₂×C₄²×C₁₃	—	2	8	no	—
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	4	yes	—
148	C₁₃×#95	C₂³	1	2	yes	—
149	C₁₃×#95	C₂³	1	2	yes	—
150	C₁₃×#95	C₂³	1	2	yes	—
151	C₁₃×#95	C₂³	1	2	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	#34745	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
158	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₁₃×#41	—	2	32	no	—
160	C₂×Q₈×C₁₃	—	2	2	no	—
161	C₂×Q₈×C₁₃	—	2	8	no	—
162	C₂×Q₈×C₁₃	—	2	2	no	—
163	C₂×Q₈×C₁₃	—	2	8	no	—
164	C₂×Q₈×C₁₃	—	4	4	no	—
165	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
166	C₂×D₄×C₁₃	—	2	4	no	—
167	C₂×D₄×C₁₃	—	2	4	no	—
168	C₂×D₄×C₁₃	—	2	2	no	—
169	C₂×D₄×C₁₃	—	2	2	no	—
170	C₂×D₄×C₁₃	C₂×Q₈	1	8	yes	—
171	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
172	C₂²×C₄×C₁₃	—	2	2	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	2	4	no	—
177	C₂²×C₄×C₁₃	—	2	4	no	—
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	8	no	—
180	C₂²×C₄×C₁₃	—	2	4	no	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	—	2	8	no	—
183	C₂²×C₄×C₁₃	—	4	4	no	—
184	C₂²×C₄×C₁₃	—	4	2	no	—
185	C₂²×C₄×C₁₃	—	4	2	no	—
186	C₂²×C₄×C₁₃	—	4	2	no	—
187	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
188	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
189	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
190	C₂²×C₄×C₁₃	#41	1	4	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₁₃×C₄⋊C₄	—	2	8	no	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	8	no	—
207	C₁₃×C₄⋊C₄	—	2	8	no	—
208	C₁₃×C₄⋊C₄	—	2	8	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	4	no	—
211	C₁₃×C₄⋊C₄	—	2	4	no	—
212	C₁₃×C₄⋊C₄	—	2	2	no	—
213	C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₁₃×C₄⋊C₄	—	2	8	no	—
215	C₁₃×C₄⋊C₄	—	2	8	no	—
216	C₁₃×C₄⋊C₄	—	4	4	no	—
217	C₁₃×C₄⋊C₄	—	4	4	no	—
218	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
219	C₁₃×C₄⋊C₄	#41	1	8	yes	complemented
220	C₁₃×C₂²⋊C₄	—	2	4	no	—
221	C₁₃×C₂²⋊C₄	—	2	4	no	—
222	C₁₃×C₂²⋊C₄	—	2	8	no	—
223	C₁₃×C₂²⋊C₄	—	2	8	no	—
224	C₁₃×C₂²⋊C₄	—	2	8	no	—
225	C₁₃×C₂²⋊C₄	—	4	4	no	—
226	C₁₃×C₂²⋊C₄	—	4	4	no	—
227	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
228	C₄²×C₁₃	—	2	2	no	—
229	C₄²×C₁₃	—	2	2	no	—
230	C₄²×C₁₃	—	2	8	no	—
231	C₄²×C₁₃	—	2	4	no	—
232	C₄²×C₁₃	—	2	4	no	—
233	C₄²×C₁₃	—	2	2	no	—
234	C₄²×C₁₃	—	2	2	no	—
235	C₄²×C₁₃	—	2	4	no	—
236	C₄²×C₁₃	—	2	4	no	—
237	C₄²×C₁₃	—	2	4	no	—
238	C₄²×C₁₃	—	2	4	no	—
239	C₄²×C₁₃	C₂×D₄	1	8	yes	—
240	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic
242	#2454	C₂×C₁₃	1	2	yes	complemented
243	#2453	C₂×C₁₃	1	2	yes	complemented
244	#2452	C₂×C₁₃	1	2	yes	complemented
245	#2451	C₂×C₁₃	1	2	yes	complemented
246	#2450	C₂×C₁₃	1	4	yes	complemented
247	#2449	C₂×C₁₃	1	4	yes	complemented
248	#2396	C₂×C₁₃	1	4	yes	complemented
249	C₄×C₂²⋊Q₈	C₂×C₁₃	1	4	yes	complemented
250	#2297	C₂×C₁₃	1	1	yes	characteristic
251	#2297	C₂×C₁₃	1	1	yes	characteristic
252	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
254	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	4	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	4	no	—
261	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
262	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
263	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
264	C₂³×C₁₃	C₂×#41	1	2	yes	—
265	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
266	Q₈×C₁₃	—	2	8	no	—
267	Q₈×C₁₃	—	4	16	no	—
268	D₄×C₁₃	—	2	16	no	—
269	D₄×C₁₃	—	2	8	no	—
270	C₂×C₄×C₁₃	—	2	8	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	16	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	4	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	4	no	—
289	C₂×C₄×C₁₃	—	2	4	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	4	no	—
295	C₂×C₄×C₁₃	—	2	4	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	4	16	no	—
299	C₂×C₄×C₁₃	—	4	8	no	—
300	C₂×C₄×C₁₃	—	4	8	no	—
301	C₂×C₄×C₁₃	—	4	4	no	—
302	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	complemented
303	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
304	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
307	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
308	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
309	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
310	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
311	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
312	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
313	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
314	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
315	#533	—	2	8	no	—
316	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
317	C₂×#125	C₂²×C₁₃	1	2	yes	—
318	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
319	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
320	C₄×#41	—	2	8	no	—
321	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
322	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
323	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
324	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
325	C₂×#117	C₂²×C₁₃	1	2	yes	—
326	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
330	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
331	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
332	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
333	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
334	#400	C₂²×C₁₃	1	4	yes	—
335	#399	C₂²×C₁₃	1	4	yes	—
336	#398	C₂²×C₁₃	1	4	yes	—
337	#398	C₂²×C₁₃	1	4	yes	—
338	#396	C₂²×C₁₃	1	4	yes	—
339	#396	C₂²×C₁₃	1	4	yes	—
340	#395	C₂²×C₁₃	1	4	yes	—
341	#393	C₂²×C₁₃	1	4	yes	—
342	#391	C₂²×C₁₃	1	4	yes	—
343	#391	C₂²×C₁₃	1	1	yes	characteristic
344	#391	C₂²×C₁₃	1	2	yes	—
345	#391	C₂²×C₁₃	1	1	yes	characteristic
346	#390	C₂²×C₁₃	1	1	yes	characteristic
347	#390	C₂²×C₁₃	1	2	yes	—
348	#390	C₂²×C₁₃	1	1	yes	characteristic
349	#389	C₂²×C₁₃	1	4	yes	—
350	#389	C₂²×C₁₃	1	2	yes	—
351	#389	C₂²×C₁₃	1	2	yes	—
352	#389	C₂²×C₁₃	1	2	yes	—
353	#389	C₂²×C₁₃	1	2	yes	—
354	#387	C₂²×C₁₃	1	4	yes	—
355	#387	C₂²×C₁₃	1	4	yes	—
356	#386	C₂²×C₁₃	1	2	yes	—
357	#386	C₂²×C₁₃	1	4	yes	—
358	#386	C₂²×C₁₃	1	2	yes	—
359	#385	C₂²×C₁₃	1	2	yes	—
360	#385	C₂²×C₁₃	1	4	yes	—
361	#385	C₂²×C₁₃	1	4	yes	—
362	#385	C₂²×C₁₃	1	2	yes	—
363	#385	C₂²×C₁₃	1	4	yes	—
364	#380	C₂²×C₁₃	1	4	yes	—
365	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
366	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
367	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
368	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
369	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
370	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
371	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
372	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
373	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
374	C₂×#95	C₂²×C₁₃	1	2	yes	—
375	C₂²×C₁₃	—	2	2	no	—
376	C₂²×C₁₃	—	2	2	no	—
377	C₂²×C₁₃	—	2	4	no	—
378	C₂²×C₁₃	—	2	4	no	—
379	C₂²×C₁₃	—	2	4	no	—
380	C₂²×C₁₃	—	2	8	no	—
381	C₂²×C₁₃	—	4	2	no	—
382	C₂²×C₁₃	—	4	2	no	—
383	C₂²×C₁₃	—	4	4	no	—
384	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
385	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
386	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
387	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
388	C₂²×C₁₃	C₂²×#41	1	2	yes	—
389	C₂²×C₁₃	#585	1	2	yes	—
390	C₄×C₁₃	—	2	4	no	—
391	C₄×C₁₃	—	2	4	no	—
392	C₄×C₁₃	—	2	4	no	—
393	C₄×C₁₃	—	2	8	no	—
394	C₄×C₁₃	—	2	4	no	—
395	C₄×C₁₃	—	4	2	no	—
396	C₄×C₁₃	—	4	2	no	—
397	C₄×C₁₃	—	4	2	no	—
398	C₄×C₁₃	—	4	2	no	—
399	C₄×C₁₃	—	4	2	no	—
400	C₄×C₁₃	—	4	4	no	—
401	C₄×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
402	C₄×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
403	C₂×#41	—	2	4	no	—
404	C₂×#41	—	2	4	no	—
405	C₂×#41	Q₈×C₁₃	1	8	yes	complemented
406	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
407	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
409	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
412	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
413	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
414	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
415	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₄⋊Q₈	—	2	8	no	—
418	#125	—	2	8	no	—
419	C₂²⋊Q₈	—	2	16	no	—
420	C₂²⋊Q₈	—	2	16	no	—
421	C₄×Q₈	—	2	8	no	—
422	C₄×Q₈	—	2	16	no	—
423	C₄×D₄	—	2	8	no	—
424	C₄×D₄	—	2	16	no	—
425	#117	—	2	4	no	—
426	#117	—	2	4	no	—
427	#117	—	2	8	no	—
428	#117	D₄×C₁₃	1	8	yes	—
429	C₂×C₄⋊C₄	—	2	8	no	—
430	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
454	C₂×C₄²	—	2	4	no	—
455	C₂×C₄²	—	2	4	no	—
456	C₂×C₄²	—	2	4	no	—
457	C₂×C₄²	—	2	8	no	—
458	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
460	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
461	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
462	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
463	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
464	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
467	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
469	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
470	#95	C₂³×C₁₃	1	2	yes	—
471	#95	C₂³×C₁₃	1	2	yes	—
472	#95	C₂³×C₁₃	1	2	yes	—
473	#95	C₂³×C₁₃	1	2	yes	—
474	#95	C₂³×C₁₃	1	4	yes	—
475	#95	C₂³×C₁₃	1	4	yes	—
476	#95	C₂³×C₁₃	1	4	yes	—
477	#95	C₂³×C₁₃	1	4	yes	—
478	#95	C₂³×C₁₃	1	4	yes	—
479	#95	C₂³×C₁₃	1	4	yes	—
480	#95	C₂³×C₁₃	1	4	yes	—
481	#95	C₂³×C₁₃	1	4	yes	—
482	C₂×C₁₃	—	2	4	no	—
483	C₂×C₁₃	—	4	4	no	—
484	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
485	C₂×C₁₃	#3444	1	1	yes	characteristic
486	C₂×C₁₃	#3455	1	1	yes	characteristic
487	C₂×C₁₃	D₄×#41	1	2	yes	—
488	C₂×C₁₃	Q₈×#41	1	2	yes	—
489	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
490	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
491	#41	—	2	32	no	—
492	C₂×Q₈	—	2	2	no	—
493	C₂×Q₈	—	2	8	no	—
494	C₂×Q₈	—	2	2	no	—
495	C₂×Q₈	—	2	8	no	—
496	C₂×Q₈	—	4	4	no	—
497	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	C₂×Q₈×C₁₃	1	8	yes	—
503	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	8	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	8	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
520	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
521	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
522	C₂²×C₄	C₁₃×#41	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
536	C₄⋊C₄	—	2	8	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	8	no	—
539	C₄⋊C₄	—	2	8	no	—
540	C₄⋊C₄	—	2	8	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	8	no	—
547	C₄⋊C₄	—	2	8	no	—
548	C₄⋊C₄	—	4	4	no	—
549	C₄⋊C₄	—	4	4	no	—
550	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
551	C₄⋊C₄	C₁₃×#41	1	8	yes	complemented
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	4	no	—
554	C₂²⋊C₄	—	2	8	no	—
555	C₂²⋊C₄	—	2	8	no	—
556	C₂²⋊C₄	—	2	8	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	—	4	4	no	—
559	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
560	C₄²	—	2	2	no	—
561	C₄²	—	2	2	no	—
562	C₄²	—	2	8	no	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	4	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	4	no	—
571	C₄²	C₂×D₄×C₁₃	1	8	yes	—
572	C₁₃	#34745	1	1	yes	characteristic, direct product factor, Sylow
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	4	no	—
579	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
580	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
581	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
582	C₂³	C₂×C₁₃×#41	1	2	yes	—
583	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
584	Q₈	—	2	8	no	—
585	Q₈	—	4	16	no	—
586	D₄	—	2	16	no	—
587	D₄	—	2	8	no	—
588	C₂×C₄	—	2	8	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	16	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	4	16	no	—
617	C₂×C₄	—	4	8	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	complemented
621	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
622	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
623	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
624	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
625	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
626	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
627	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
628	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
629	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
630	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
631	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	8	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	4	no	—
641	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
642	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
643	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
644	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
645	C₂²	C₂²×C₁₃×#41	1	2	yes	—
646	C₂²	C₁₃×#585	1	2	yes	—
647	C₄	—	2	4	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	4	no	—
650	C₄	—	2	8	no	—
651	C₄	—	2	4	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	4	no	—
658	C₄	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
659	C₄	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
660	C₂	—	2	4	no	—
661	C₂	—	4	4	no	—
662	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
663	C₂	C₁₃×#3444	1	1	yes	characteristic
664	C₂	C₁₃×#3455	1	1	yes	characteristic
665	C₂	D₄×C₁₃×#41	1	2	yes	—
666	C₂	Q₈×C₁₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×C₁₃×#41	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×#2454	C₂	semidirect
4. C₁₃×#2453	C₂	semidirect
5. C₁₃×#2452	C₂	semidirect
6. C₁₃×#2451	C₂	semidirect
7. C₁₃×#2450	C₂	semidirect
8. C₁₃×#2449	C₂	semidirect
9. C₁₃×#2396	C₂	semidirect
10. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
13. C₁₃×#2296	C₂	semidirect
14. C₁₃×#2296	C₂	semidirect
15. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
79. C₂×C₁₃×#41	Q₈	semidirect
156. #34745	C₁₃	direct (N × H)
219. C₁₃×C₄⋊C₄	#41	semidirect
240. C₂×#533	C₂×C₁₃	semidirect
242. #2454	C₂×C₁₃	semidirect
243. #2453	C₂×C₁₃	semidirect
244. #2452	C₂×C₁₃	semidirect
245. #2451	C₂×C₁₃	semidirect
246. #2450	C₂×C₁₃	semidirect
247. #2449	C₂×C₁₃	semidirect
248. #2396	C₂×C₁₃	semidirect
249. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
252. #2296	C₂×C₁₃	semidirect
253. #2296	C₂×C₁₃	semidirect
254. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
302. C₂×C₄×C₁₃	C₂²⋊Q₈	semidirect
405. C₂×#41	Q₈×C₁₃	semidirect
551. C₄⋊C₄	C₁₃×#41	semidirect
572. C₁₃	#34745	direct (N × H)
620. C₂×C₄	C₁₃×C₂²⋊Q₈	semidirect

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×C₄×C₁₃×#41	2
C₁₃×#2454	2
C₁₃×#2453	2
C₁₃×#2452	2
C₁₃×#2451	2
C₁₃×#2450	2
C₁₃×#2449	2
C₁₃×#2396	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2297	2
C₁₃×#2296	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#34745	13

Subgroups — C13×#34745 #15721084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34745 #15721084