Subgroups — C₁₃×#34228 #15720567

Order 3328.

2726 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2364	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2358	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2357	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2353	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2343	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2339	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2333	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×#123	C₂	1	4	yes	maximal, complemented
13	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#525	C₄	1	16	yes	complemented
19	C₂×C₁₃×#123	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#120	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
33	C₁₃×#391	C₂²	1	4	yes	complemented
34	C₁₃×#390	C₂²	1	4	yes	—
35	C₁₃×#388	C₂²	1	4	yes	—
36	C₁₃×#388	C₂²	1	4	yes	—
37	C₁₃×#388	C₂²	1	4	yes	complemented
38	C₁₃×#388	C₂²	1	4	yes	complemented
39	C₁₃×#387	C₂²	1	4	yes	complemented
40	C₁₃×#387	C₂²	1	4	yes	complemented
41	C₁₃×#387	C₂²	1	4	yes	complemented
42	C₁₃×#387	C₂²	1	4	yes	complemented
43	C₁₃×#386	C₂²	1	4	yes	—
44	C₁₃×#386	C₂²	1	4	yes	—
45	C₁₃×#386	C₂²	1	4	yes	—
46	C₁₃×#386	C₂²	1	4	yes	complemented
47	C₁₃×#385	C₂²	1	4	yes	—
48	C₁₃×#385	C₂²	1	4	yes	—
49	C₁₃×#383	C₂²	1	2	yes	complemented
50	C₁₃×#382	C₂²	1	2	yes	complemented
51	C₁₃×#381	C₂²	1	2	yes	—
52	C₁₃×#381	C₂²	1	2	yes	—
53	C₁₃×#381	C₂²	1	2	yes	—
54	C₁₃×#381	C₂²	1	1	yes	characteristic
55	C₁₃×#381	C₂²	1	1	yes	characteristic
56	C₁₃×#381	C₂²	1	2	yes	complemented
57	C₁₃×#380	C₂²	1	2	yes	complemented
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
61	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
67	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
68	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
69	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
71	C₁₃×#376	C₂²	1	2	yes	complemented
72	C₂×C₁₃×#95	C₂²	1	2	yes	—
73	C₂×C₁₃×#95	C₂²	1	2	yes	—
74	C₂×C₁₃×#95	C₂²	1	2	yes	—
75	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
76	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×#41	—	4	4	no	—
78	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	—	4	4	no	—
85	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	complemented
86	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
96	C₁₃×#123	C₂×C₄	1	16	yes	complemented
97	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
98	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
99	C₁₃×#121	C₂×C₄	1	8	yes	complemented
100	C₁₃×#121	C₂×C₄	1	8	yes	complemented
101	C₁₃×#120	C₂×C₄	1	16	yes	complemented
102	C₄×D₄×C₁₃	—	2	16	no	—
103	C₄×D₄×C₁₃	—	4	8	no	—
104	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
105	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
106	C₁₃×#117	C₂×C₄	1	8	yes	complemented
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	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃	—	4	4	no	—
131	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	2	yes	—
139	C₁₃×#95	C₂³	1	2	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	4	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	2	yes	—
146	C₁₃×#95	C₂³	1	2	yes	—
147	C₁₃×#95	C₂³	1	4	yes	—
148	C₁₃×#95	C₂³	1	4	yes	—
149	C₁₃×#95	C₂³	1	2	yes	—
150	C₁₃×#95	C₂³	1	4	yes	—
151	C₁₃×#95	C₂³	1	2	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	#34228	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂⁴×C₁₃	—	2	4	no	—
155	C₂⁴×C₁₃	—	2	4	no	—
156	C₂⁴×C₁₃	—	4	2	no	—
157	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
158	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
160	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₁₃×#41	—	4	16	no	—
163	C₂×Q₈×C₁₃	—	4	2	no	—
164	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
165	C₂×D₄×C₁₃	—	2	8	no	—
166	C₂×D₄×C₁₃	—	2	8	no	—
167	C₂×D₄×C₁₃	—	4	2	no	—
168	C₂×D₄×C₁₃	—	4	2	no	—
169	C₂×D₄×C₁₃	—	4	2	no	—
170	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
171	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
172	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
173	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	2	8	no	—
177	C₂²×C₄×C₁₃	—	2	8	no	—
178	C₂²×C₄×C₁₃	—	2	8	no	—
179	C₂²×C₄×C₁₃	—	2	8	no	—
180	C₂²×C₄×C₁₃	—	4	16	no	—
181	C₂²×C₄×C₁₃	—	4	2	no	—
182	C₂²×C₄×C₁₃	—	4	2	no	—
183	C₂²×C₄×C₁₃	—	4	2	no	—
184	C₂²×C₄×C₁₃	—	4	2	no	—
185	C₂²×C₄×C₁₃	—	4	4	no	—
186	C₂²×C₄×C₁₃	—	4	4	no	—
187	C₂²×C₄×C₁₃	—	4	4	no	—
188	C₂²×C₄×C₁₃	—	4	4	no	—
189	C₂²×C₄×C₁₃	—	4	4	no	—
190	C₂²×C₄×C₁₃	—	4	4	no	—
191	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
196	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
209	C₁₃×C₄⋊C₄	—	2	8	no	—
210	C₁₃×C₄⋊C₄	—	4	4	no	—
211	C₁₃×C₄⋊C₄	—	4	4	no	—
212	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
213	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
214	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
215	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
216	C₁₃×C₂²⋊C₄	—	2	4	no	—
217	C₁₃×C₂²⋊C₄	—	2	8	no	—
218	C₁₃×C₂²⋊C₄	—	2	8	no	—
219	C₁₃×C₂²⋊C₄	—	2	8	no	—
220	C₁₃×C₂²⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	4	2	no	—
222	C₁₃×C₂²⋊C₄	—	4	4	no	—
223	C₁₃×C₂²⋊C₄	—	4	4	no	—
224	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
225	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
226	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
227	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
228	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
229	C₁₃×C₂²⋊C₄	#41	1	8	yes	complemented
230	C₄²×C₁₃	—	2	8	no	—
231	C₄²×C₁₃	—	4	2	no	—
232	C₄²×C₁₃	—	4	4	no	—
233	C₄²×C₁₃	—	4	2	no	—
234	C₄²×C₁₃	—	4	4	no	—
235	C₄²×C₁₃	—	4	4	no	—
236	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
237	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
238	#2368	C₂×C₁₃	1	2	yes	complemented
239	#2364	C₂×C₁₃	1	2	yes	complemented
240	#2358	C₂×C₁₃	1	4	yes	complemented
241	#2357	C₂×C₁₃	1	2	yes	complemented
242	#2353	C₂×C₁₃	1	2	yes	complemented
243	#2343	C₂×C₁₃	1	2	yes	complemented
244	#2339	C₂×C₁₃	1	2	yes	complemented
245	#2333	C₂×C₁₃	1	2	yes	complemented
246	#2332	C₂×C₁₃	1	2	yes	complemented
247	#2318	C₂×C₁₃	1	2	yes	complemented
248	C₄×#123	C₂×C₁₃	1	4	yes	complemented
249	C₂×#381	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#2275	C₂×C₁₃	1	2	yes	complemented
251	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
252	C₂³×C₁₃	—	2	2	no	—
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	8	no	—
257	C₂³×C₁₃	—	2	8	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	4	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	4	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	2	2	no	—
265	C₂³×C₁₃	—	4	4	no	—
266	C₂³×C₁₃	—	4	16	no	—
267	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
268	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
269	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
270	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
271	C₂³×C₁₃	C₂×#41	1	4	yes	—
272	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
273	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
274	Q₈×C₁₃	—	4	4	no	—
275	D₄×C₁₃	—	2	16	no	—
276	D₄×C₁₃	—	2	16	no	—
277	D₄×C₁₃	—	4	8	no	—
278	D₄×C₁₃	—	4	4	no	—
279	C₂×C₄×C₁₃	—	2	8	no	—
280	C₂×C₄×C₁₃	—	2	8	no	—
281	C₂×C₄×C₁₃	—	2	4	no	—
282	C₂×C₄×C₁₃	—	2	4	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	4	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	4	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	4	no	—
293	C₂×C₄×C₁₃	—	2	4	no	—
294	C₂×C₄×C₁₃	—	2	4	no	—
295	C₂×C₄×C₁₃	—	2	4	no	—
296	C₂×C₄×C₁₃	—	2	4	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	4	no	—
299	C₂×C₄×C₁₃	—	2	4	no	—
300	C₂×C₄×C₁₃	—	4	4	no	—
301	C₂×C₄×C₁₃	—	4	4	no	—
302	C₂×C₄×C₁₃	—	4	4	no	—
303	C₂×C₄×C₁₃	—	4	4	no	—
304	C₂×C₄×C₁₃	—	4	8	no	—
305	C₂×C₄×C₁₃	—	4	16	no	—
306	C₂×C₄×C₁₃	—	8	8	no	—
307	C₂×C₄×C₁₃	—	8	8	no	—
308	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
309	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
310	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
311	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
313	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
314	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
315	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
316	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
317	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
318	#525	C₄×C₁₃	1	16	yes	complemented
319	C₂×#123	C₂²×C₁₃	1	2	yes	—
320	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#120	C₂²×C₁₃	1	2	yes	—
325	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
326	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
327	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
328	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
329	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
331	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
332	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
333	#391	C₂²×C₁₃	1	4	yes	complemented
334	#390	C₂²×C₁₃	1	4	yes	—
335	#388	C₂²×C₁₃	1	4	yes	—
336	#388	C₂²×C₁₃	1	4	yes	—
337	#388	C₂²×C₁₃	1	4	yes	complemented
338	#388	C₂²×C₁₃	1	4	yes	complemented
339	#387	C₂²×C₁₃	1	4	yes	complemented
340	#387	C₂²×C₁₃	1	4	yes	complemented
341	#387	C₂²×C₁₃	1	4	yes	complemented
342	#387	C₂²×C₁₃	1	4	yes	complemented
343	#386	C₂²×C₁₃	1	4	yes	—
344	#386	C₂²×C₁₃	1	4	yes	—
345	#386	C₂²×C₁₃	1	4	yes	—
346	#386	C₂²×C₁₃	1	4	yes	complemented
347	#385	C₂²×C₁₃	1	4	yes	—
348	#385	C₂²×C₁₃	1	4	yes	—
349	#383	C₂²×C₁₃	1	2	yes	complemented
350	#382	C₂²×C₁₃	1	2	yes	complemented
351	#381	C₂²×C₁₃	1	2	yes	—
352	#381	C₂²×C₁₃	1	2	yes	—
353	#381	C₂²×C₁₃	1	1	yes	characteristic
354	#381	C₂²×C₁₃	1	1	yes	characteristic
355	#381	C₂²×C₁₃	1	2	yes	—
356	#381	C₂²×C₁₃	1	2	yes	complemented
357	#380	C₂²×C₁₃	1	2	yes	complemented
358	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
359	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
360	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
361	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
362	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
363	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
364	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
365	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
366	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
367	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
368	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
369	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
370	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
371	#376	C₂²×C₁₃	1	2	yes	complemented
372	C₂×#95	C₂²×C₁₃	1	2	yes	—
373	C₂×#95	C₂²×C₁₃	1	2	yes	—
374	C₂×#95	C₂²×C₁₃	1	2	yes	—
375	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
376	C₂²×C₁₃	—	2	2	no	—
377	C₂²×C₁₃	—	2	2	no	—
378	C₂²×C₁₃	—	2	2	no	—
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	8	no	—
381	C₂²×C₁₃	—	2	8	no	—
382	C₂²×C₁₃	—	2	4	no	—
383	C₂²×C₁₃	—	2	2	no	—
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	2	4	no	—
386	C₂²×C₁₃	—	2	2	no	—
387	C₂²×C₁₃	—	2	4	no	—
388	C₂²×C₁₃	—	4	16	no	—
389	C₂²×C₁₃	—	4	4	no	—
390	C₂²×C₁₃	—	4	4	no	—
391	C₂²×C₁₃	—	4	4	no	—
392	C₂²×C₁₃	C₄×#41	1	4	yes	—
393	C₂²×C₁₃	#518	1	4	yes	—
394	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
395	C₂²×C₁₃	C₂²×#41	1	2	yes	—
396	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
397	C₂²×C₁₃	#585	1	2	yes	—
398	C₄×C₁₃	—	2	4	no	—
399	C₄×C₁₃	—	2	2	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	2	2	no	—
402	C₄×C₁₃	—	2	2	no	—
403	C₄×C₁₃	—	2	4	no	—
404	C₄×C₁₃	—	2	4	no	—
405	C₄×C₁₃	—	2	8	no	—
406	C₄×C₁₃	—	4	4	no	—
407	C₄×C₁₃	—	4	4	no	—
408	C₄×C₁₃	—	4	4	no	—
409	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×#41	—	4	4	no	—
411	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
412	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
414	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
415	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
416	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂³×C₄	—	4	4	no	—
418	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
419	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
420	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
423	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
424	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
427	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
429	#123	C₂×C₄×C₁₃	1	16	yes	complemented
430	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
431	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
432	#121	C₂×C₄×C₁₃	1	8	yes	complemented
433	#121	C₂×C₄×C₁₃	1	8	yes	complemented
434	#120	C₂×C₄×C₁₃	1	16	yes	complemented
435	C₄×D₄	—	2	16	no	—
436	C₄×D₄	—	4	8	no	—
437	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
438	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
439	#117	C₂×C₄×C₁₃	1	8	yes	complemented
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	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
447	C₂×C₂²⋊C₄	—	2	8	no	—
448	C₂×C₂²⋊C₄	—	4	4	no	—
449	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	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×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
463	C₂×C₄²	—	4	4	no	—
464	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
465	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
466	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
467	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
468	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
469	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
470	C₂×C₄²	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	2	yes	—
476	#95	C₂³×C₁₃	1	2	yes	—
477	#95	C₂³×C₁₃	1	4	yes	—
478	#95	C₂³×C₁₃	1	2	yes	—
479	#95	C₂³×C₁₃	1	4	yes	—
480	#95	C₂³×C₁₃	1	4	yes	—
481	#95	C₂³×C₁₃	1	4	yes	—
482	#95	C₂³×C₁₃	1	4	yes	—
483	#95	C₂³×C₁₃	1	4	yes	—
484	#95	C₂³×C₁₃	1	4	yes	—
485	#95	C₂³×C₁₃	1	4	yes	—
486	C₂×C₁₃	—	2	4	no	—
487	C₂×C₁₃	—	2	4	no	—
488	C₂×C₁₃	—	4	4	no	—
489	C₂×C₁₃	—	4	2	no	—
490	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
491	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
492	C₂×C₁₃	#3428	1	1	yes	characteristic
493	C₂×C₁₃	#3513	1	4	yes	—
494	C₂⁴	—	2	4	no	—
495	C₂⁴	—	2	4	no	—
496	C₂⁴	—	4	2	no	—
497	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
498	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
499	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
500	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
501	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
502	#41	—	4	16	no	—
503	C₂×Q₈	—	4	2	no	—
504	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
505	C₂×D₄	—	2	8	no	—
506	C₂×D₄	—	2	8	no	—
507	C₂×D₄	—	4	2	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
511	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
512	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
513	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	8	no	—
517	C₂²×C₄	—	2	8	no	—
518	C₂²×C₄	—	2	8	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	4	16	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	4	no	—
526	C₂²×C₄	—	4	4	no	—
527	C₂²×C₄	—	4	4	no	—
528	C₂²×C₄	—	4	4	no	—
529	C₂²×C₄	—	4	4	no	—
530	C₂²×C₄	—	4	4	no	—
531	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
532	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
533	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
534	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
535	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
536	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
537	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
538	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
540	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
543	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
544	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
547	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
548	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
549	C₄⋊C₄	—	2	8	no	—
550	C₄⋊C₄	—	4	4	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
553	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
555	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	8	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	2	8	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	4	no	—
563	C₂²⋊C₄	—	4	4	no	—
564	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
565	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
569	C₂²⋊C₄	C₁₃×#41	1	8	yes	complemented
570	C₄²	—	2	8	no	—
571	C₄²	—	4	2	no	—
572	C₄²	—	4	4	no	—
573	C₄²	—	4	2	no	—
574	C₄²	—	4	4	no	—
575	C₄²	—	4	4	no	—
576	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
577	C₁₃	#34228	1	1	yes	characteristic, direct product factor, Sylow
578	C₂³	—	2	2	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	8	no	—
583	C₂³	—	2	8	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	4	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	4	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	4	4	no	—
592	C₂³	—	4	16	no	—
593	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
594	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
595	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
596	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
597	C₂³	C₂×C₁₃×#41	1	4	yes	—
598	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
599	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
600	Q₈	—	4	4	no	—
601	D₄	—	2	16	no	—
602	D₄	—	2	16	no	—
603	D₄	—	4	8	no	—
604	D₄	—	4	4	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	8	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	4	8	no	—
631	C₂×C₄	—	4	16	no	—
632	C₂×C₄	—	8	8	no	—
633	C₂×C₄	—	8	8	no	—
634	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
635	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
636	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
637	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
638	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
639	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
640	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
641	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	8	no	—
647	C₂²	—	2	8	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	4	no	—
654	C₂²	—	4	16	no	—
655	C₂²	—	4	4	no	—
656	C₂²	—	4	4	no	—
657	C₂²	—	4	4	no	—
658	C₂²	C₄×C₁₃×#41	1	4	yes	—
659	C₂²	C₁₃×#518	1	4	yes	—
660	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
661	C₂²	C₂²×C₁₃×#41	1	2	yes	—
662	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
663	C₂²	C₁₃×#585	1	2	yes	—
664	C₄	—	2	4	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	4	no	—
670	C₄	—	2	4	no	—
671	C₄	—	2	8	no	—
672	C₄	—	4	4	no	—
673	C₄	—	4	4	no	—
674	C₄	—	4	4	no	—
675	C₂	—	2	4	no	—
676	C₂	—	2	4	no	—
677	C₂	—	4	2	no	—
678	C₂	—	4	4	no	—
679	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
680	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
681	C₂	C₁₃×#3428	1	1	yes	characteristic
682	C₂	C₁₃×#3513	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2368	C₂	semidirect
3. C₁₃×#2364	C₂	semidirect
4. C₁₃×#2358	C₂	semidirect
5. C₁₃×#2357	C₂	semidirect
6. C₁₃×#2353	C₂	semidirect
7. C₁₃×#2343	C₂	semidirect
8. C₁₃×#2339	C₂	semidirect
9. C₁₃×#2333	C₂	semidirect
10. C₁₃×#2332	C₂	semidirect
11. C₁₃×#2318	C₂	semidirect
12. C₄×C₁₃×#123	C₂	semidirect
13. C₂×C₁₃×#381	C₂	semidirect
14. C₁₃×#2275	C₂	semidirect
15. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
18. C₁₃×#525	C₄	semidirect
33. C₁₃×#391	C₂²	semidirect
37. C₁₃×#388	C₂²	semidirect
38. C₁₃×#388	C₂²	semidirect
39. C₁₃×#387	C₂²	semidirect
40. C₁₃×#387	C₂²	semidirect
41. C₁₃×#387	C₂²	semidirect
42. C₁₃×#387	C₂²	semidirect
46. C₁₃×#386	C₂²	semidirect
49. C₁₃×#383	C₂²	semidirect
50. C₁₃×#382	C₂²	semidirect
56. C₁₃×#381	C₂²	semidirect
57. C₁₃×#380	C₂²	semidirect
58. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
59. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
60. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
68. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
69. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
70. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
71. C₁₃×#376	C₂²	semidirect
75. C₂×C₁₃×#95	C₂²	semidirect
78. C₂×C₁₃×#41	C₂×C₄	semidirect
85. C₂³×C₄×C₁₃	C₂×C₄	semidirect
96. C₁₃×#123	C₂×C₄	semidirect
97. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
98. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₁₃×#121	C₂×C₄	semidirect
100. C₁₃×#121	C₂×C₄	semidirect
101. C₁₃×#120	C₂×C₄	semidirect
104. C₄×D₄×C₁₃	C₂×C₄	semidirect
105. C₄×D₄×C₁₃	C₂×C₄	semidirect
106. C₁₃×#117	C₂×C₄	semidirect
153. #34228	C₁₃	direct (N × H)
229. C₁₃×C₂²⋊C₄	#41	semidirect
238. #2368	C₂×C₁₃	semidirect
239. #2364	C₂×C₁₃	semidirect
240. #2358	C₂×C₁₃	semidirect
241. #2357	C₂×C₁₃	semidirect
242. #2353	C₂×C₁₃	semidirect
243. #2343	C₂×C₁₃	semidirect
244. #2339	C₂×C₁₃	semidirect
245. #2333	C₂×C₁₃	semidirect
246. #2332	C₂×C₁₃	semidirect
247. #2318	C₂×C₁₃	semidirect
248. C₄×#123	C₂×C₁₃	semidirect
249. C₂×#381	C₂×C₁₃	semidirect
250. #2275	C₂×C₁₃	semidirect
251. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
318. #525	C₄×C₁₃	semidirect
333. #391	C₂²×C₁₃	semidirect
337. #388	C₂²×C₁₃	semidirect
338. #388	C₂²×C₁₃	semidirect
339. #387	C₂²×C₁₃	semidirect
340. #387	C₂²×C₁₃	semidirect
341. #387	C₂²×C₁₃	semidirect
342. #387	C₂²×C₁₃	semidirect
346. #386	C₂²×C₁₃	semidirect
349. #383	C₂²×C₁₃	semidirect
350. #382	C₂²×C₁₃	semidirect
356. #381	C₂²×C₁₃	semidirect
357. #380	C₂²×C₁₃	semidirect
358. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
359. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
360. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
368. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
369. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
370. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
371. #376	C₂²×C₁₃	semidirect
375. C₂×#95	C₂²×C₁₃	semidirect
411. C₂×#41	C₂×C₄×C₁₃	semidirect
418. C₂³×C₄	C₂×C₄×C₁₃	semidirect
429. #123	C₂×C₄×C₁₃	semidirect
430. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
431. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
432. #121	C₂×C₄×C₁₃	semidirect
433. #121	C₂×C₄×C₁₃	semidirect
434. #120	C₂×C₄×C₁₃	semidirect
437. C₄×D₄	C₂×C₄×C₁₃	semidirect
438. C₄×D₄	C₂×C₄×C₁₃	semidirect
439. #117	C₂×C₄×C₁₃	semidirect
569. C₂²⋊C₄	C₁₃×#41	semidirect
577. C₁₃	#34228	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×#525	2
C₁₃×#2368	2
C₁₃×#2364	2
C₁₃×#2358	2
C₁₃×#2357	2
C₁₃×#2353	2
C₁₃×#2343	2
C₁₃×#2339	2
C₁₃×#2333	2
C₁₃×#2332	2
C₁₃×#2318	2
C₄×C₁₃×#123	2
C₂×C₁₃×#381	2
C₁₃×#2275	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34228	13

Subgroups — C13×#34228 #15720567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34228 #15720567