Subgroups — C₁₃×#34218 #15720557

Order 3328.

3014 conjugacy classes of subgroups.

The subgroup lattice has 722 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×#2359	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2353	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2349	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×#2329	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2325	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×#120	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
15	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#525	C₄	1	16	yes	complemented
20	C₂×C₁₃×#123	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#120	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
33	C₁₃×#391	C₂²	1	4	yes	complemented
34	C₁₃×#389	C₂²	1	4	yes	complemented
35	C₁₃×#388	C₂²	1	4	yes	complemented
36	C₁₃×#388	C₂²	1	4	yes	complemented
37	C₁₃×#387	C₂²	1	4	yes	complemented
38	C₁₃×#387	C₂²	1	4	yes	complemented
39	C₁₃×#387	C₂²	1	4	yes	complemented
40	C₁₃×#387	C₂²	1	4	yes	complemented
41	C₁₃×#386	C₂²	1	4	yes	—
42	C₁₃×#386	C₂²	1	4	yes	—
43	C₁₃×#386	C₂²	1	4	yes	—
44	C₁₃×#386	C₂²	1	4	yes	complemented
45	C₁₃×#385	C₂²	1	4	yes	—
46	C₁₃×#385	C₂²	1	4	yes	—
47	C₁₃×#385	C₂²	1	4	yes	—
48	C₁₃×#385	C₂²	1	4	yes	complemented
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	complemented
53	C₁₃×#380	C₂²	1	2	yes	—
54	C₁₃×#380	C₂²	1	1	yes	characteristic
55	C₁₃×#380	C₂²	1	1	yes	characteristic
56	C₁₃×#380	C₂²	1	2	yes	complemented
57	C₁₃×#379	C₂²	1	2	yes	—
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
60	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
67	C₁₃×#376	C₂²	1	2	yes	complemented
68	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#95	C₂²	1	2	yes	—
71	C₂×C₁₃×#95	C₂²	1	2	yes	—
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	—	2	8	no	—
85	C₂³×C₄×C₁₃	—	4	4	no	—
86	C₂³×C₄×C₁₃	—	4	4	no	—
87	C₂³×C₄×C₁₃	—	4	4	no	—
88	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	complemented
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	4	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
101	C₁₃×#123	C₂×C₄	1	16	yes	complemented
102	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
103	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
104	C₁₃×#121	C₂×C₄	1	8	yes	complemented
105	C₁₃×#121	C₂×C₄	1	8	yes	complemented
106	C₁₃×#120	C₂×C₄	1	16	yes	complemented
107	C₄×D₄×C₁₃	—	2	16	no	—
108	C₄×D₄×C₁₃	—	4	8	no	—
109	C₄×D₄×C₁₃	—	4	8	no	—
110	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
111	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
112	C₁₃×#117	—	4	4	no	—
113	C₁₃×#117	C₂×C₄	1	8	yes	complemented
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×C₄⋊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	2	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
138	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
140	C₁₃×#95	C₂³	1	2	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	2	yes	—
143	C₁₃×#95	C₂³	1	4	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	4	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	2	yes	—
155	#34218	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂⁴×C₁₃	—	2	4	no	—
157	C₂⁴×C₁₃	—	2	2	no	—
158	C₂⁴×C₁₃	—	2	4	no	—
159	C₂⁴×C₁₃	—	2	2	no	—
160	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
161	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
162	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₁₃×#41	—	4	16	no	—
166	C₂×Q₈×C₁₃	—	4	2	no	—
167	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	complemented
168	C₂×D₄×C₁₃	—	2	8	no	—
169	C₂×D₄×C₁₃	—	2	4	no	—
170	C₂×D₄×C₁₃	—	2	8	no	—
171	C₂×D₄×C₁₃	—	2	4	no	—
172	C₂×D₄×C₁₃	—	4	2	no	—
173	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
174	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
175	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
176	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	complemented
177	C₂²×C₄×C₁₃	—	2	4	no	—
178	C₂²×C₄×C₁₃	—	2	4	no	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	—	2	8	no	—
181	C₂²×C₄×C₁₃	—	2	8	no	—
182	C₂²×C₄×C₁₃	—	2	8	no	—
183	C₂²×C₄×C₁₃	—	2	8	no	—
184	C₂²×C₄×C₁₃	—	2	8	no	—
185	C₂²×C₄×C₁₃	—	4	16	no	—
186	C₂²×C₄×C₁₃	—	4	2	no	—
187	C₂²×C₄×C₁₃	—	4	2	no	—
188	C₂²×C₄×C₁₃	—	4	2	no	—
189	C₂²×C₄×C₁₃	—	4	2	no	—
190	C₂²×C₄×C₁₃	—	4	4	no	—
191	C₂²×C₄×C₁₃	—	4	4	no	—
192	C₂²×C₄×C₁₃	—	4	2	no	—
193	C₂²×C₄×C₁₃	—	4	2	no	—
194	C₂²×C₄×C₁₃	—	4	2	no	—
195	C₂²×C₄×C₁₃	—	4	2	no	—
196	C₂²×C₄×C₁₃	—	4	4	no	—
197	C₂²×C₄×C₁₃	—	4	4	no	—
198	C₂²×C₄×C₁₃	—	4	4	no	—
199	C₂²×C₄×C₁₃	—	4	32	no	—
200	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
202	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
203	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
204	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
205	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
206	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	complemented
207	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
208	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
219	C₁₃×C₄⋊C₄	—	2	8	no	—
220	C₁₃×C₄⋊C₄	—	4	2	no	—
221	C₁₃×C₄⋊C₄	—	4	2	no	—
222	C₁₃×C₄⋊C₄	—	4	4	no	—
223	C₁₃×C₄⋊C₄	—	4	4	no	—
224	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
225	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	complemented
226	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
227	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	complemented
228	C₁₃×C₂²⋊C₄	—	2	8	no	—
229	C₁₃×C₂²⋊C₄	—	2	8	no	—
230	C₁₃×C₂²⋊C₄	—	2	4	no	—
231	C₁₃×C₂²⋊C₄	—	2	4	no	—
232	C₁₃×C₂²⋊C₄	—	2	8	no	—
233	C₁₃×C₂²⋊C₄	—	4	4	no	—
234	C₁₃×C₂²⋊C₄	—	4	4	no	—
235	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
236	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
237	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
238	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
239	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	complemented
240	C₄²×C₁₃	—	2	8	no	—
241	C₄²×C₁₃	—	4	4	no	—
242	C₄²×C₁₃	—	4	4	no	—
243	C₄²×C₁₃	—	4	4	no	—
244	C₄²×C₁₃	C₂²×C₄	1	8	yes	complemented
245	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
246	#2368	C₂×C₁₃	1	2	yes	complemented
247	#2364	C₂×C₁₃	1	2	yes	complemented
248	#2359	C₂×C₁₃	1	4	yes	complemented
249	#2353	C₂×C₁₃	1	2	yes	complemented
250	#2349	C₂×C₁₃	1	2	yes	complemented
251	#2343	C₂×C₁₃	1	2	yes	complemented
252	#2339	C₂×C₁₃	1	2	yes	complemented
253	#2329	C₂×C₁₃	1	2	yes	complemented
254	#2325	C₂×C₁₃	1	2	yes	complemented
255	#2318	C₂×C₁₃	1	2	yes	complemented
256	C₄×#120	C₂×C₁₃	1	4	yes	complemented
257	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#2275	C₂×C₁₃	1	2	yes	complemented
259	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂³×C₁₃	—	2	16	no	—
261	C₂³×C₁₃	—	2	16	no	—
262	C₂³×C₁₃	—	2	8	no	—
263	C₂³×C₁₃	—	2	8	no	—
264	C₂³×C₁₃	—	2	8	no	—
265	C₂³×C₁₃	—	2	2	no	—
266	C₂³×C₁₃	—	2	2	no	—
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	—	2	2	no	—
269	C₂³×C₁₃	—	2	1	no	—
270	C₂³×C₁₃	—	2	1	no	—
271	C₂³×C₁₃	—	2	1	no	—
272	C₂³×C₁₃	—	2	1	no	—
273	C₂³×C₁₃	—	2	4	no	—
274	C₂³×C₁₃	—	2	2	no	—
275	C₂³×C₁₃	—	2	4	no	—
276	C₂³×C₁₃	—	2	2	no	—
277	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
278	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
279	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
280	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
281	C₂³×C₁₃	C₂×#41	1	4	yes	—
282	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
283	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
284	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
285	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
286	Q₈×C₁₃	—	4	4	no	—
287	D₄×C₁₃	—	2	16	no	—
288	D₄×C₁₃	—	2	16	no	—
289	D₄×C₁₃	—	2	16	no	—
290	D₄×C₁₃	—	4	4	no	—
291	C₂×C₄×C₁₃	—	2	8	no	—
292	C₂×C₄×C₁₃	—	2	8	no	—
293	C₂×C₄×C₁₃	—	2	4	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	2	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	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	4	no	—
304	C₂×C₄×C₁₃	—	2	4	no	—
305	C₂×C₄×C₁₃	—	2	4	no	—
306	C₂×C₄×C₁₃	—	2	4	no	—
307	C₂×C₄×C₁₃	—	2	4	no	—
308	C₂×C₄×C₁₃	—	2	4	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	2	4	no	—
311	C₂×C₄×C₁₃	—	2	4	no	—
312	C₂×C₄×C₁₃	—	4	4	no	—
313	C₂×C₄×C₁₃	—	4	4	no	—
314	C₂×C₄×C₁₃	—	4	4	no	—
315	C₂×C₄×C₁₃	—	4	4	no	—
316	C₂×C₄×C₁₃	—	4	8	no	—
317	C₂×C₄×C₁₃	—	4	8	no	—
318	C₂×C₄×C₁₃	—	4	16	no	—
319	C₂×C₄×C₁₃	—	4	16	no	—
320	C₂×C₄×C₁₃	—	4	8	no	—
321	C₂×C₄×C₁₃	—	8	8	no	—
322	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
323	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
324	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
325	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
326	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
327	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
328	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
329	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
330	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
331	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
332	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
333	#525	C₄×C₁₃	1	16	yes	complemented
334	C₂×#123	C₂²×C₁₃	1	2	yes	—
335	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#120	C₂²×C₁₃	1	2	yes	—
340	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
341	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
342	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
343	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
344	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
345	C₂×#117	C₂²×C₁₃	1	2	yes	—
346	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
347	#391	C₂²×C₁₃	1	4	yes	complemented
348	#389	C₂²×C₁₃	1	4	yes	complemented
349	#388	C₂²×C₁₃	1	4	yes	complemented
350	#388	C₂²×C₁₃	1	4	yes	complemented
351	#387	C₂²×C₁₃	1	4	yes	complemented
352	#387	C₂²×C₁₃	1	4	yes	complemented
353	#387	C₂²×C₁₃	1	4	yes	complemented
354	#387	C₂²×C₁₃	1	4	yes	complemented
355	#386	C₂²×C₁₃	1	4	yes	—
356	#386	C₂²×C₁₃	1	4	yes	—
357	#386	C₂²×C₁₃	1	4	yes	—
358	#386	C₂²×C₁₃	1	4	yes	complemented
359	#385	C₂²×C₁₃	1	4	yes	—
360	#385	C₂²×C₁₃	1	4	yes	—
361	#385	C₂²×C₁₃	1	4	yes	—
362	#385	C₂²×C₁₃	1	4	yes	complemented
363	#383	C₂²×C₁₃	1	2	yes	complemented
364	#382	C₂²×C₁₃	1	2	yes	complemented
365	#381	C₂²×C₁₃	1	2	yes	—
366	#381	C₂²×C₁₃	1	2	yes	complemented
367	#380	C₂²×C₁₃	1	2	yes	—
368	#380	C₂²×C₁₃	1	1	yes	characteristic
369	#380	C₂²×C₁₃	1	1	yes	characteristic
370	#380	C₂²×C₁₃	1	2	yes	complemented
371	#379	C₂²×C₁₃	1	2	yes	—
372	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
373	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
374	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
375	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
377	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
378	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
379	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
380	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
381	#376	C₂²×C₁₃	1	2	yes	complemented
382	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#95	C₂²×C₁₃	1	2	yes	—
384	C₂×#95	C₂²×C₁₃	1	2	yes	—
385	C₂×#95	C₂²×C₁₃	1	2	yes	—
386	C₂×#95	C₂²×C₁₃	1	2	yes	—
387	C₂×#95	C₂²×C₁₃	1	2	yes	—
388	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
390	C₂²×C₁₃	—	2	32	no	—
391	C₂²×C₁₃	—	2	2	no	—
392	C₂²×C₁₃	—	2	2	no	—
393	C₂²×C₁₃	—	2	2	no	—
394	C₂²×C₁₃	—	2	2	no	—
395	C₂²×C₁₃	—	2	2	no	—
396	C₂²×C₁₃	—	2	2	no	—
397	C₂²×C₁₃	—	2	4	no	—
398	C₂²×C₁₃	—	2	4	no	—
399	C₂²×C₁₃	—	2	4	no	—
400	C₂²×C₁₃	—	2	4	no	—
401	C₂²×C₁₃	—	2	4	no	—
402	C₂²×C₁₃	—	2	4	no	—
403	C₂²×C₁₃	—	2	4	no	—
404	C₂²×C₁₃	—	2	4	no	—
405	C₂²×C₁₃	—	2	4	no	—
406	C₂²×C₁₃	—	4	4	no	—
407	C₂²×C₁₃	—	4	4	no	—
408	C₂²×C₁₃	C₄×#41	1	4	yes	—
409	C₂²×C₁₃	#518	1	4	yes	—
410	C₂²×C₁₃	#520	1	4	yes	—
411	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
412	C₂²×C₁₃	C₂²×#41	1	2	yes	—
413	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
414	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
416	C₄×C₁₃	—	2	4	no	—
417	C₄×C₁₃	—	2	2	no	—
418	C₄×C₁₃	—	2	2	no	—
419	C₄×C₁₃	—	2	2	no	—
420	C₄×C₁₃	—	2	2	no	—
421	C₄×C₁₃	—	2	4	no	—
422	C₄×C₁₃	—	2	4	no	—
423	C₄×C₁₃	—	2	8	no	—
424	C₄×C₁₃	—	4	4	no	—
425	C₄×C₁₃	—	4	4	no	—
426	C₄×C₁₃	—	4	4	no	—
427	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×#41	—	4	4	no	—
429	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
430	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
432	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
433	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
434	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₂³×C₄	—	2	8	no	—
436	C₂³×C₄	—	4	4	no	—
437	C₂³×C₄	—	4	4	no	—
438	C₂³×C₄	—	4	4	no	—
439	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
440	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
441	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
442	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
445	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
446	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
451	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
452	#123	C₂×C₄×C₁₃	1	16	yes	complemented
453	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
454	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
455	#121	C₂×C₄×C₁₃	1	8	yes	complemented
456	#121	C₂×C₄×C₁₃	1	8	yes	complemented
457	#120	C₂×C₄×C₁₃	1	16	yes	complemented
458	C₄×D₄	—	2	16	no	—
459	C₄×D₄	—	4	8	no	—
460	C₄×D₄	—	4	8	no	—
461	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
462	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
463	#117	—	4	4	no	—
464	#117	C₂×C₄×C₁₃	1	8	yes	complemented
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
486	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
487	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
488	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
489	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
490	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
491	#95	C₂³×C₁₃	1	2	yes	—
492	#95	C₂³×C₁₃	1	2	yes	—
493	#95	C₂³×C₁₃	1	2	yes	—
494	#95	C₂³×C₁₃	1	4	yes	—
495	#95	C₂³×C₁₃	1	4	yes	—
496	#95	C₂³×C₁₃	1	2	yes	—
497	#95	C₂³×C₁₃	1	2	yes	—
498	#95	C₂³×C₁₃	1	4	yes	—
499	#95	C₂³×C₁₃	1	2	yes	—
500	#95	C₂³×C₁₃	1	4	yes	—
501	#95	C₂³×C₁₃	1	4	yes	—
502	#95	C₂³×C₁₃	1	4	yes	—
503	#95	C₂³×C₁₃	1	4	yes	—
504	#95	C₂³×C₁₃	1	4	yes	—
505	#95	C₂³×C₁₃	1	4	yes	—
506	C₂×C₁₃	—	2	4	no	—
507	C₂×C₁₃	—	2	4	no	—
508	C₂×C₁₃	—	2	4	no	—
509	C₂×C₁₃	—	4	4	no	—
510	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
511	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
512	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
513	C₂×C₁₃	#3490	1	2	yes	—
514	C₂×C₁₃	#3492	1	2	yes	—
515	C₂⁴	—	2	4	no	—
516	C₂⁴	—	2	2	no	—
517	C₂⁴	—	2	4	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
520	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
521	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
522	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
523	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
524	#41	—	4	16	no	—
525	C₂×Q₈	—	4	2	no	—
526	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	complemented
527	C₂×D₄	—	2	8	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	8	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	4	2	no	—
532	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
533	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
534	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
535	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	complemented
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	8	no	—
540	C₂²×C₄	—	2	8	no	—
541	C₂²×C₄	—	2	8	no	—
542	C₂²×C₄	—	2	8	no	—
543	C₂²×C₄	—	2	8	no	—
544	C₂²×C₄	—	4	16	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	—	4	2	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	4	no	—
556	C₂²×C₄	—	4	4	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	32	no	—
559	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
560	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
561	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
562	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
563	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
564	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
565	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
566	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
567	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
568	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
569	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
578	C₄⋊C₄	—	2	8	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₄⋊C₄	—	4	4	no	—
582	C₄⋊C₄	—	4	4	no	—
583	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	complemented
584	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	complemented
585	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
586	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
587	C₂²⋊C₄	—	2	8	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	4	4	no	—
593	C₂²⋊C₄	—	4	4	no	—
594	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
595	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
598	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	complemented
599	C₄²	—	2	8	no	—
600	C₄²	—	4	4	no	—
601	C₄²	—	4	4	no	—
602	C₄²	—	4	4	no	—
603	C₄²	C₂²×C₄×C₁₃	1	8	yes	complemented
604	C₁₃	#34218	1	1	yes	characteristic, direct product factor, Sylow
605	C₂³	—	2	16	no	—
606	C₂³	—	2	16	no	—
607	C₂³	—	2	8	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	2	8	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	2	no	—
622	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
623	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
624	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
625	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
626	C₂³	C₂×C₁₃×#41	1	4	yes	—
627	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
628	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
629	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
630	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
631	Q₈	—	4	4	no	—
632	D₄	—	2	16	no	—
633	D₄	—	2	16	no	—
634	D₄	—	2	16	no	—
635	D₄	—	4	4	no	—
636	C₂×C₄	—	2	8	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	8	no	—
662	C₂×C₄	—	4	8	no	—
663	C₂×C₄	—	4	16	no	—
664	C₂×C₄	—	4	16	no	—
665	C₂×C₄	—	4	8	no	—
666	C₂×C₄	—	8	8	no	—
667	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
668	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
669	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
670	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
671	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
672	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
673	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
674	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
675	C₂²	—	2	32	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	2	4	no	—
685	C₂²	—	2	4	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	4	no	—
693	C₂²	C₄×C₁₃×#41	1	4	yes	—
694	C₂²	C₁₃×#518	1	4	yes	—
695	C₂²	C₁₃×#520	1	4	yes	—
696	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
697	C₂²	C₂²×C₁₃×#41	1	2	yes	—
698	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
699	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
700	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
701	C₄	—	2	4	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	8	no	—
709	C₄	—	4	4	no	—
710	C₄	—	4	4	no	—
711	C₄	—	4	4	no	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	2	4	no	—
715	C₂	—	4	4	no	—
716	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
717	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
718	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
719	C₂	C₁₃×#3490	1	2	yes	—
720	C₂	C₁₃×#3492	1	2	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×#2359	C₂	semidirect
5. C₁₃×#2353	C₂	semidirect
6. C₁₃×#2349	C₂	semidirect
7. C₁₃×#2343	C₂	semidirect
8. C₁₃×#2339	C₂	semidirect
9. C₁₃×#2329	C₂	semidirect
10. C₁₃×#2325	C₂	semidirect
11. C₁₃×#2318	C₂	semidirect
12. C₄×C₁₃×#120	C₂	semidirect
13. C₁₃×#2280	C₂	semidirect
14. C₁₃×#2275	C₂	semidirect
15. C₂²×C₁₃×#95	C₂	semidirect
19. C₁₃×#525	C₄	semidirect
33. C₁₃×#391	C₂²	semidirect
34. C₁₃×#389	C₂²	semidirect
35. C₁₃×#388	C₂²	semidirect
36. C₁₃×#388	C₂²	semidirect
37. C₁₃×#387	C₂²	semidirect
38. C₁₃×#387	C₂²	semidirect
39. C₁₃×#387	C₂²	semidirect
40. C₁₃×#387	C₂²	semidirect
44. C₁₃×#386	C₂²	semidirect
48. C₁₃×#385	C₂²	semidirect
49. C₁₃×#383	C₂²	semidirect
50. C₁₃×#382	C₂²	semidirect
52. C₁₃×#381	C₂²	semidirect
56. C₁₃×#380	C₂²	semidirect
58. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
59. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
65. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
66. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
67. C₁₃×#376	C₂²	semidirect
75. C₂×C₁₃×#95	C₂²	semidirect
78. C₂×C₁₃×#41	C₂×C₄	semidirect
88. C₂³×C₄×C₁₃	C₂×C₄	semidirect
101. C₁₃×#123	C₂×C₄	semidirect
102. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
103. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
104. C₁₃×#121	C₂×C₄	semidirect
105. C₁₃×#121	C₂×C₄	semidirect
106. C₁₃×#120	C₂×C₄	semidirect
110. C₄×D₄×C₁₃	C₂×C₄	semidirect
111. C₄×D₄×C₁₃	C₂×C₄	semidirect
113. C₁₃×#117	C₂×C₄	semidirect
155. #34218	C₁₃	direct (N × H)
167. C₂×Q₈×C₁₃	C₂²×C₄	semidirect
176. C₂×D₄×C₁₃	C₂²×C₄	semidirect
206. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
207. C₂²×C₄×C₁₃	#41	semidirect
224. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
225. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
226. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
227. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
238. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
239. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
244. C₄²×C₁₃	C₂²×C₄	semidirect
246. #2368	C₂×C₁₃	semidirect
247. #2364	C₂×C₁₃	semidirect
248. #2359	C₂×C₁₃	semidirect
249. #2353	C₂×C₁₃	semidirect
250. #2349	C₂×C₁₃	semidirect
251. #2343	C₂×C₁₃	semidirect
252. #2339	C₂×C₁₃	semidirect
253. #2329	C₂×C₁₃	semidirect
254. #2325	C₂×C₁₃	semidirect
255. #2318	C₂×C₁₃	semidirect
256. C₄×#120	C₂×C₁₃	semidirect
257. #2280	C₂×C₁₃	semidirect
258. #2275	C₂×C₁₃	semidirect
259. C₂²×#95	C₂×C₁₃	semidirect
333. #525	C₄×C₁₃	semidirect
347. #391	C₂²×C₁₃	semidirect
348. #389	C₂²×C₁₃	semidirect
349. #388	C₂²×C₁₃	semidirect
350. #388	C₂²×C₁₃	semidirect
351. #387	C₂²×C₁₃	semidirect
352. #387	C₂²×C₁₃	semidirect
353. #387	C₂²×C₁₃	semidirect
354. #387	C₂²×C₁₃	semidirect
358. #386	C₂²×C₁₃	semidirect
362. #385	C₂²×C₁₃	semidirect
363. #383	C₂²×C₁₃	semidirect
364. #382	C₂²×C₁₃	semidirect
366. #381	C₂²×C₁₃	semidirect
370. #380	C₂²×C₁₃	semidirect
372. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
373. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
379. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
380. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
381. #376	C₂²×C₁₃	semidirect
389. C₂×#95	C₂²×C₁₃	semidirect
429. C₂×#41	C₂×C₄×C₁₃	semidirect
439. C₂³×C₄	C₂×C₄×C₁₃	semidirect
452. #123	C₂×C₄×C₁₃	semidirect
453. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
454. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
455. #121	C₂×C₄×C₁₃	semidirect
456. #121	C₂×C₄×C₁₃	semidirect
457. #120	C₂×C₄×C₁₃	semidirect
461. C₄×D₄	C₂×C₄×C₁₃	semidirect
462. C₄×D₄	C₂×C₄×C₁₃	semidirect
464. #117	C₂×C₄×C₁₃	semidirect
526. C₂×Q₈	C₂²×C₄×C₁₃	semidirect
535. C₂×D₄	C₂²×C₄×C₁₃	semidirect
565. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
566. C₂²×C₄	C₁₃×#41	semidirect
583. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
584. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
585. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
586. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
597. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
598. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
603. C₄²	C₂²×C₄×C₁₃	semidirect
604. C₁₃	#34218	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×#2359	2
C₁₃×#2353	2
C₁₃×#2349	2
C₁₃×#2343	2
C₁₃×#2339	2
C₁₃×#2329	2
C₁₃×#2325	2
C₁₃×#2318	2
C₄×C₁₃×#120	2
C₁₃×#2280	2
C₁₃×#2275	2
C₂²×C₁₃×#95	2
#34218	13

Subgroups — C13×#34218 #15720557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34218 #15720557