Subgroups — C₁₃×#34123 #15720462

Order 3328.

2598 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2356	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2353	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2349	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2346	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2343	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2339	C₂	1	2	yes	maximal
8	C₁₃×#2295	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2290	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2283	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄²×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#376	C₂	1	2	yes	maximal, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×#41	C₄	1	16	yes	complemented
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
24	C₂×C₁₃×#117	C₂²	1	2	yes	—
25	C₂×C₁₃×#117	C₂²	1	2	yes	—
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
28	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#391	C₂²	1	4	yes	—
31	C₁₃×#389	C₂²	1	4	yes	—
32	C₁₃×#388	C₂²	1	8	yes	—
33	C₁₃×#387	C₂²	1	8	yes	—
34	C₁₃×#387	C₂²	1	8	yes	—
35	C₁₃×#386	C₂²	1	8	yes	—
36	C₁₃×#385	C₂²	1	8	yes	—
37	C₁₃×#383	C₂²	1	2	yes	—
38	C₁₃×#383	C₂²	1	4	yes	—
39	C₁₃×#382	C₂²	1	4	yes	—
40	C₁₃×#382	C₂²	1	2	yes	—
41	C₁₃×#381	C₂²	1	4	yes	—
42	C₁₃×#381	C₂²	1	2	yes	—
43	C₁₃×#380	C₂²	1	2	yes	—
44	C₁₃×#380	C₂²	1	4	yes	—
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
51	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
53	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
55	C₁₃×#376	C₂²	1	1	yes	characteristic
56	C₁₃×#376	C₂²	1	2	yes	—
57	C₁₃×#376	C₂²	1	4	yes	—
58	C₁₃×#376	C₂²	1	4	yes	—
59	C₁₃×#376	C₂²	1	4	yes	—
60	C₁₃×#376	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#95	C₂²	1	4	yes	—
62	C₂×C₁₃×#95	C₂²	1	4	yes	—
63	C₄³×C₁₃	C₂²	1	2	yes	—
64	C₂×C₁₃×#41	—	2	8	no	—
65	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
77	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
78	C₄×D₄×C₁₃	—	2	16	no	—
79	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
80	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
81	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
82	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
83	C₁₃×#117	—	2	8	no	—
84	C₁₃×#117	C₂×C₄	1	16	yes	complemented
85	C₁₃×#117	C₂×C₄	1	8	yes	complemented
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₃	—	2	16	no	—
100	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
101	C₂×C₄²×C₁₃	C₂×C₄	1	16	yes	complemented
102	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
103	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
104	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
105	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
115	C₁₃×#95	C₂³	1	4	yes	—
116	C₁₃×#95	C₂³	1	8	yes	—
117	C₁₃×#95	C₂³	1	2	yes	—
118	C₁₃×#95	C₂³	1	2	yes	—
119	C₁₃×#95	C₂³	1	2	yes	—
120	C₁₃×#95	C₂³	1	2	yes	—
121	C₁₃×#95	C₂³	1	4	yes	—
122	C₁₃×#95	C₂³	1	8	yes	—
123	C₁₃×#95	C₂³	1	4	yes	—
124	C₁₃×#95	C₂³	1	4	yes	—
125	C₁₃×#95	C₂³	1	8	yes	—
126	C₁₃×#95	C₂³	1	8	yes	—
127	#34123	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
130	C₁₃×#41	—	2	32	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
133	C₂×D₄×C₁₃	—	2	8	no	—
134	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
135	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
136	C₂×D₄×C₁₃	#41	1	8	yes	—
137	C₂²×C₄×C₁₃	—	2	8	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	16	no	—
142	C₂²×C₄×C₁₃	—	2	16	no	—
143	C₂²×C₄×C₁₃	—	4	2	no	—
144	C₂²×C₄×C₁₃	—	4	8	no	—
145	C₂²×C₄×C₁₃	—	4	4	no	—
146	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
147	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
149	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
151	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₁₃×C₄⋊C₄	—	2	8	no	—
165	C₁₃×C₄⋊C₄	—	2	8	no	—
166	C₁₃×C₄⋊C₄	—	4	8	no	—
167	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
168	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
169	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
170	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
171	C₁₃×C₂²⋊C₄	—	2	16	no	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	4	4	no	—
174	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
175	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
176	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
177	C₄²×C₁₃	—	2	16	no	—
178	C₄²×C₁₃	—	2	8	no	—
179	C₄²×C₁₃	—	2	4	no	—
180	C₄²×C₁₃	—	2	8	no	—
181	C₄²×C₁₃	—	4	4	no	—
182	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
183	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
184	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
185	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
186	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
187	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
188	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
189	C₄²×C₁₃	#41	1	8	yes	complemented
190	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic
191	#2356	C₂×C₁₃	1	2	yes	complemented
192	#2353	C₂×C₁₃	1	4	yes	complemented
193	#2349	C₂×C₁₃	1	2	yes	complemented
194	#2346	C₂×C₁₃	1	2	yes	complemented
195	#2343	C₂×C₁₃	1	4	yes	complemented
196	#2339	C₂×C₁₃	1	2	yes	—
197	#2295	C₂×C₁₃	1	2	yes	complemented
198	#2290	C₂×C₁₃	1	4	yes	complemented
199	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#2283	C₂×C₁₃	1	2	yes	complemented
201	C₄²×D₄	C₂×C₁₃	1	2	yes	complemented
202	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×#376	C₂×C₁₃	1	2	yes	complemented
204	C₂³×C₁₃	—	2	4	no	—
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
210	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
211	C₂³×C₁₃	C₂×#41	1	8	yes	—
212	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
213	Q₈×C₁₃	—	2	8	no	—
214	D₄×C₁₃	—	2	16	no	—
215	D₄×C₁₃	#117	1	16	yes	complemented
216	C₂×C₄×C₁₃	—	2	16	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	8	no	—
227	C₂×C₄×C₁₃	—	2	16	no	—
228	C₂×C₄×C₁₃	—	2	8	no	—
229	C₂×C₄×C₁₃	—	2	8	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	8	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	8	no	—
235	C₂×C₄×C₁₃	—	4	8	no	—
236	C₂×C₄×C₁₃	—	4	4	no	—
237	C₂×C₄×C₁₃	—	4	32	no	—
238	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
239	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
241	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
242	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
243	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
244	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
245	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
246	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
247	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
248	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
249	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
250	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
251	C₄×#41	C₄×C₁₃	1	16	yes	complemented
252	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
255	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
258	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
259	C₂×#117	C₂²×C₁₃	1	2	yes	—
260	C₂×#117	C₂²×C₁₃	1	2	yes	—
261	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
263	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
264	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
265	#391	C₂²×C₁₃	1	4	yes	—
266	#389	C₂²×C₁₃	1	4	yes	—
267	#388	C₂²×C₁₃	1	8	yes	—
268	#387	C₂²×C₁₃	1	8	yes	—
269	#387	C₂²×C₁₃	1	8	yes	—
270	#386	C₂²×C₁₃	1	8	yes	—
271	#385	C₂²×C₁₃	1	8	yes	—
272	#383	C₂²×C₁₃	1	2	yes	—
273	#383	C₂²×C₁₃	1	4	yes	—
274	#382	C₂²×C₁₃	1	4	yes	—
275	#382	C₂²×C₁₃	1	2	yes	—
276	#381	C₂²×C₁₃	1	4	yes	—
277	#381	C₂²×C₁₃	1	2	yes	—
278	#380	C₂²×C₁₃	1	2	yes	—
279	#380	C₂²×C₁₃	1	4	yes	—
280	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
281	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
282	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
283	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
284	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
285	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
286	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
287	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
288	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
289	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
290	#376	C₂²×C₁₃	1	4	yes	—
291	#376	C₂²×C₁₃	1	4	yes	—
292	#376	C₂²×C₁₃	1	1	yes	characteristic
293	#376	C₂²×C₁₃	1	2	yes	—
294	#376	C₂²×C₁₃	1	4	yes	—
295	#376	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#95	C₂²×C₁₃	1	4	yes	—
297	C₂×#95	C₂²×C₁₃	1	4	yes	—
298	C₄³	C₂²×C₁₃	1	2	yes	—
299	C₂²×C₁₃	—	2	4	no	—
300	C₂²×C₁₃	—	2	4	no	—
301	C₂²×C₁₃	—	2	16	no	—
302	C₂²×C₁₃	—	2	2	no	—
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	4	4	no	—
306	C₂²×C₁₃	C₂×#117	1	8	yes	—
307	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
308	C₂²×C₁₃	C₂²×#41	1	2	yes	—
309	C₂²×C₁₃	C₂²×#41	1	2	yes	—
310	C₂²×C₁₃	#585	1	2	yes	—
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	2	4	no	—
313	C₄×C₁₃	—	2	4	no	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	2	2	no	—
316	C₄×C₁₃	—	2	2	no	—
317	C₄×C₁₃	—	2	4	no	—
318	C₄×C₁₃	—	2	8	no	—
319	C₄×C₁₃	—	4	4	no	—
320	C₄×C₁₃	—	4	8	no	—
321	C₄×C₁₃	C₂×#117	1	4	yes	—
322	C₄×C₁₃	C₄×#41	1	4	yes	—
323	C₂×#41	—	2	8	no	—
324	C₂×#41	C₂×C₄×C₁₃	1	8	yes	—
325	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
326	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
327	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
329	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
331	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
333	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
334	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
336	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
337	C₄×D₄	—	2	16	no	—
338	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
339	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
340	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
341	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
342	#117	—	2	8	no	—
343	#117	C₂×C₄×C₁₃	1	16	yes	complemented
344	#117	C₂×C₄×C₁₃	1	8	yes	complemented
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
358	C₂×C₄²	—	2	16	no	—
359	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
360	C₂×C₄²	C₂×C₄×C₁₃	1	16	yes	complemented
361	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
362	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
363	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
364	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
365	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
366	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
367	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
370	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
371	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
374	#95	C₂³×C₁₃	1	2	yes	—
375	#95	C₂³×C₁₃	1	2	yes	—
376	#95	C₂³×C₁₃	1	4	yes	—
377	#95	C₂³×C₁₃	1	4	yes	—
378	#95	C₂³×C₁₃	1	8	yes	—
379	#95	C₂³×C₁₃	1	8	yes	—
380	#95	C₂³×C₁₃	1	2	yes	—
381	#95	C₂³×C₁₃	1	2	yes	—
382	#95	C₂³×C₁₃	1	4	yes	—
383	#95	C₂³×C₁₃	1	8	yes	—
384	#95	C₂³×C₁₃	1	4	yes	—
385	#95	C₂³×C₁₃	1	8	yes	—
386	C₂×C₁₃	—	2	8	no	—
387	C₂×C₁₃	—	4	2	no	—
388	C₂×C₁₃	C₂²×#117	1	1	yes	characteristic
389	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
390	C₂×C₁₃	#3428	1	1	yes	characteristic
391	C₂×C₁₃	#3475	1	4	yes	—
392	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
393	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
394	#41	—	2	32	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
399	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
400	C₂×D₄	C₁₃×#41	1	8	yes	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	16	no	—
406	C₂²×C₄	—	2	16	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	—	4	8	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
411	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
412	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
413	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
414	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
415	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
419	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	4	8	no	—
431	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
432	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
433	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
434	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
435	C₂²⋊C₄	—	2	16	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	4	4	no	—
438	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
439	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
440	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
441	C₄²	—	2	16	no	—
442	C₄²	—	2	8	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	8	no	—
445	C₄²	—	4	4	no	—
446	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
447	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
448	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
449	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
450	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
451	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
452	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
453	C₄²	C₁₃×#41	1	8	yes	complemented
454	C₁₃	#34123	1	1	yes	characteristic, direct product factor, Sylow
455	C₂³	—	2	4	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
461	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
462	C₂³	C₂×C₁₃×#41	1	8	yes	—
463	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
464	Q₈	—	2	8	no	—
465	D₄	—	2	16	no	—
466	D₄	C₁₃×#117	1	16	yes	complemented
467	C₂×C₄	—	2	16	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	16	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	4	8	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	32	no	—
489	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
490	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
491	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
492	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
493	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
494	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
495	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
496	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
497	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
498	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
499	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
500	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	16	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	4	no	—
508	C₂²	C₂×C₁₃×#117	1	8	yes	—
509	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
510	C₂²	C₂²×C₁₃×#41	1	2	yes	—
511	C₂²	C₂²×C₁₃×#41	1	2	yes	—
512	C₂²	C₁₃×#585	1	2	yes	—
513	C₄	—	2	2	no	—
514	C₄	—	2	4	no	—
515	C₄	—	2	4	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	4	no	—
520	C₄	—	2	8	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	8	no	—
523	C₄	C₂×C₁₃×#117	1	4	yes	—
524	C₄	C₄×C₁₃×#41	1	4	yes	—
525	C₂	—	2	8	no	—
526	C₂	—	4	2	no	—
527	C₂	C₂²×C₁₃×#117	1	1	yes	characteristic
528	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
529	C₂	C₁₃×#3428	1	1	yes	characteristic
530	C₂	C₁₃×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2356	C₂	semidirect
3. C₁₃×#2353	C₂	semidirect
4. C₁₃×#2349	C₂	semidirect
5. C₁₃×#2346	C₂	semidirect
6. C₁₃×#2343	C₂	semidirect
8. C₁₃×#2295	C₂	semidirect
9. C₁₃×#2290	C₂	semidirect
10. C₁₃×#2283	C₂	semidirect
11. C₁₃×#2283	C₂	semidirect
12. C₄²×D₄×C₁₃	C₂	semidirect
13. C₄×C₁₃×#117	C₂	semidirect
14. C₂×C₁₃×#376	C₂	semidirect
16. C₄×C₁₃×#41	C₄	semidirect
76. C₄×Q₈×C₁₃	C₂×C₄	semidirect
77. C₄×Q₈×C₁₃	C₂×C₄	semidirect
81. C₄×D₄×C₁₃	C₂×C₄	semidirect
82. C₄×D₄×C₁₃	C₂×C₄	semidirect
84. C₁₃×#117	C₂×C₄	semidirect
85. C₁₃×#117	C₂×C₄	semidirect
100. C₂×C₄²×C₁₃	C₂×C₄	semidirect
101. C₂×C₄²×C₁₃	C₂×C₄	semidirect
127. #34123	C₁₃	direct (N × H)
189. C₄²×C₁₃	#41	semidirect
191. #2356	C₂×C₁₃	semidirect
192. #2353	C₂×C₁₃	semidirect
193. #2349	C₂×C₁₃	semidirect
194. #2346	C₂×C₁₃	semidirect
195. #2343	C₂×C₁₃	semidirect
197. #2295	C₂×C₁₃	semidirect
198. #2290	C₂×C₁₃	semidirect
199. #2283	C₂×C₁₃	semidirect
200. #2283	C₂×C₁₃	semidirect
201. C₄²×D₄	C₂×C₁₃	semidirect
202. C₄×#117	C₂×C₁₃	semidirect
203. C₂×#376	C₂×C₁₃	semidirect
215. D₄×C₁₃	#117	semidirect
251. C₄×#41	C₄×C₁₃	semidirect
335. C₄×Q₈	C₂×C₄×C₁₃	semidirect
336. C₄×Q₈	C₂×C₄×C₁₃	semidirect
340. C₄×D₄	C₂×C₄×C₁₃	semidirect
341. C₄×D₄	C₂×C₄×C₁₃	semidirect
343. #117	C₂×C₄×C₁₃	semidirect
344. #117	C₂×C₄×C₁₃	semidirect
359. C₂×C₄²	C₂×C₄×C₁₃	semidirect
360. C₂×C₄²	C₂×C₄×C₁₃	semidirect
453. C₄²	C₁₃×#41	semidirect
454. C₁₃	#34123	direct (N × H)
466. D₄	C₁₃×#117	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×C₁₃×#41	2
C₁₃×#2356	2
C₁₃×#2353	2
C₁₃×#2349	2
C₁₃×#2346	2
C₁₃×#2343	2
C₁₃×#2339	2
C₁₃×#2295	2
C₁₃×#2290	2
C₁₃×#2283	2
C₄²×D₄×C₁₃	2
C₄×C₁₃×#117	2
C₂×C₁₃×#376	2
#34123	13

Subgroups — C13×#34123 #15720462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34123 #15720462