Subgroups — C₁₃×#25078 #15711417

Order 3328.

1166 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2361	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1927	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃	—	2	1	no	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₁₃×#465	—	2	4	no	—
29	C₁₃×#461	—	2	4	no	—
30	C₁₃×#448	—	2	4	no	—
31	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	—	2	4	no	—
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₃×#395	—	2	1	no	—
47	C₁₃×#395	—	2	1	no	—
48	C₁₃×#391	C₂²	1	1	yes	characteristic
49	C₁₃×#391	C₂²	1	1	yes	characteristic
50	C₁₃×#390	C₂²	1	1	yes	characteristic
51	C₁₃×#389	C₂²	1	1	yes	characteristic
52	C₁₃×#388	—	2	1	no	—
53	C₁₃×#386	—	2	1	no	—
54	C₁₃×#385	—	2	1	no	—
55	C₁₃×#385	—	2	1	no	—
56	C₁₃×#385	—	2	1	no	—
57	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	—	2	1	no	—
64	C₂²×Q₈×C₁₃	—	2	2	no	—
65	C₂²×Q₈×C₁₃	—	2	2	no	—
66	C₂²×Q₈×C₁₃	—	2	2	no	—
67	C₂²×Q₈×C₁₃	—	2	2	no	—
68	C₂²×Q₈×C₁₃	—	4	1	no	—
69	C₂²×Q₈×C₁₃	—	4	1	no	—
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	—	2	1	no	—
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₂³×C₄×C₁₃	—	2	1	no	—
77	C₂³×C₄×C₁₃	—	2	1	no	—
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×SD₁₆	—	2	2	no	—
80	C₂×C₁₃×SD₁₆	—	2	2	no	—
81	C₂×C₁₃×SD₁₆	—	2	2	no	—
82	C₂×C₁₃×SD₁₆	—	2	2	no	—
83	C₂×C₁₃×SD₁₆	—	2	2	no	—
84	C₂×C₁₃×SD₁₆	—	2	2	no	—
85	C₂×C₁₃×SD₁₆	—	4	1	no	—
86	C₂×C₁₃×SD₁₆	—	4	1	no	—
87	C₂×C₁₃×SD₁₆	—	4	1	no	—
88	C₂²×C₈×C₁₃	—	2	2	no	—
89	C₂²×C₈×C₁₃	—	2	2	no	—
90	C₂²×C₈×C₁₃	—	4	1	no	—
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×C₄⋊Q₈	—	2	2	no	—
96	C₁₃×C₄⋊Q₈	—	2	2	no	—
97	C₁₃×C₄⋊Q₈	—	4	1	no	—
98	C₁₃×C₄⋊Q₈	—	4	1	no	—
99	C₁₃×C₂²⋊Q₈	—	2	2	no	—
100	C₁₃×C₂²⋊Q₈	—	2	2	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	D₄	1	4	yes	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	—	4	1	no	—
105	C₄×D₄×C₁₃	—	4	4	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
125	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	—	2	1	no	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₁₃×#106	—	2	2	no	—
130	C₁₃×C₄⋊C₈	—	2	2	no	—
131	C₁₃×C₄⋊C₈	—	4	1	no	—
132	C₁₃×#103	—	2	2	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	—	2	2	no	—
138	C₁₃×#103	—	2	2	no	—
139	C₁₃×#103	—	4	1	no	—
140	C₁₃×#103	D₄	1	4	yes	complemented
141	C₁₃×#102	—	2	2	no	—
142	C₁₃×C₂²⋊C₈	—	2	2	no	—
143	C₁₃×#95	—	2	1	no	—
144	C₁₃×#95	—	2	1	no	—
145	C₁₃×#95	—	2	1	no	—
146	C₁₃×#95	—	2	1	no	—
147	C₁₃×#95	—	2	1	no	—
148	C₁₃×#95	—	2	1	no	—
149	C₁₃×#95	D₄	1	1	yes	characteristic
150	C₁₃×#95	D₄	1	1	yes	characteristic
151	#25078	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	8	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	1	no	—
165	C₂×Q₈×C₁₃	—	2	1	no	—
166	C₂×Q₈×C₁₃	—	2	1	no	—
167	C₂×Q₈×C₁₃	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	4	2	no	—
172	C₂×Q₈×C₁₃	—	4	2	no	—
173	C₂×Q₈×C₁₃	—	4	4	no	—
174	C₂×Q₈×C₁₃	—	4	4	no	—
175	C₂×Q₈×C₁₃	—	4	4	no	—
176	C₂×Q₈×C₁₃	—	4	2	no	—
177	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
178	C₂×Q₈×C₁₃	#41	1	2	yes	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	4	2	no	—
186	C₂×D₄×C₁₃	—	4	2	no	—
187	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₃	—	2	1	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	4	2	no	—
200	C₂²×C₄×C₁₃	—	4	2	no	—
201	C₂²×C₄×C₁₃	—	4	2	no	—
202	C₂²×C₄×C₁₃	—	4	2	no	—
203	C₂²×C₄×C₁₃	—	4	2	no	—
204	C₂²×C₄×C₁₃	—	4	2	no	—
205	C₂²×C₄×C₁₃	—	4	2	no	—
206	C₂²×C₄×C₁₃	—	8	1	no	—
207	C₂²×C₄×C₁₃	—	8	1	no	—
208	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	#41	1	2	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₁₃×SD₁₆	—	4	4	no	—
217	C₁₃×SD₁₆	—	4	4	no	—
218	C₁₃×SD₁₆	—	4	4	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	2	1	no	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	2	1	no	—
226	C₂×C₈×C₁₃	—	2	1	no	—
227	C₂×C₈×C₁₃	—	2	1	no	—
228	C₂×C₈×C₁₃	—	2	1	no	—
229	C₂×C₈×C₁₃	—	2	1	no	—
230	C₂×C₈×C₁₃	—	4	4	no	—
231	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	4	2	no	—
239	C₁₃×C₄⋊C₄	—	4	2	no	—
240	C₁₃×C₄⋊C₄	—	4	2	no	—
241	C₁₃×C₄⋊C₄	—	4	2	no	—
242	C₁₃×C₄⋊C₄	—	4	2	no	—
243	C₁₃×C₄⋊C₄	—	4	2	no	—
244	C₁₃×C₄⋊C₄	—	4	2	no	—
245	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
246	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
247	C₁₃×C₂²⋊C₄	—	2	2	no	—
248	C₁₃×C₂²⋊C₄	—	2	4	no	—
249	C₁₃×C₂²⋊C₄	—	4	2	no	—
250	C₁₃×C₂²⋊C₄	—	4	2	no	—
251	C₁₃×C₂²⋊C₄	—	4	2	no	—
252	C₁₃×C₂²⋊C₄	—	8	1	no	—
253	C₁₃×C₂²⋊C₄	SD₁₆	1	4	yes	complemented
254	C₄²×C₁₃	—	2	1	no	—
255	C₄²×C₁₃	—	2	1	no	—
256	C₄²×C₁₃	—	2	1	no	—
257	C₄²×C₁₃	—	2	1	no	—
258	C₄²×C₁₃	—	4	2	no	—
259	C₂×#465	C₂×C₁₃	1	1	yes	characteristic
260	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
261	C₂×#448	C₂×C₁₃	1	1	yes	characteristic
262	C₂²×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2434	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#2361	C₂×C₁₃	1	1	yes	characteristic
265	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#2043	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#2013	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1927	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1850	C₂×C₁₃	1	1	yes	characteristic, complemented
274	C₂³×C₁₃	—	2	1	no	—
275	C₂³×C₁₃	—	2	1	no	—
276	C₂³×C₁₃	—	2	1	no	—
277	C₂³×C₁₃	—	2	1	no	—
278	C₂³×C₁₃	—	2	2	no	—
279	C₂³×C₁₃	—	4	1	no	—
280	C₂³×C₁₃	—	4	1	no	—
281	C₂³×C₁₃	—	4	1	no	—
282	C₂³×C₁₃	—	4	1	no	—
283	C₂³×C₁₃	—	4	1	no	—
284	C₂³×C₁₃	—	4	1	no	—
285	C₂³×C₁₃	#121	1	2	yes	—
286	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
287	C₂³×C₁₃	#137	1	2	yes	—
288	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₁₃	—	2	2	no	—
290	Q₈×C₁₃	—	2	2	no	—
291	Q₈×C₁₃	—	2	2	no	—
292	Q₈×C₁₃	—	2	2	no	—
293	Q₈×C₁₃	—	4	8	no	—
294	Q₈×C₁₃	—	4	1	no	—
295	Q₈×C₁₃	—	4	1	no	—
296	Q₈×C₁₃	—	4	1	no	—
297	Q₈×C₁₃	—	4	1	no	—
298	Q₈×C₁₃	—	4	1	no	—
299	Q₈×C₁₃	—	4	1	no	—
300	Q₈×C₁₃	—	4	1	no	—
301	Q₈×C₁₃	—	4	1	no	—
302	D₄×C₁₃	—	2	2	no	—
303	D₄×C₁₃	—	2	2	no	—
304	D₄×C₁₃	—	4	8	no	—
305	D₄×C₁₃	—	4	1	no	—
306	D₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	2	1	no	—
308	C₂×C₄×C₁₃	—	2	1	no	—
309	C₂×C₄×C₁₃	—	2	1	no	—
310	C₂×C₄×C₁₃	—	2	1	no	—
311	C₂×C₄×C₁₃	—	2	1	no	—
312	C₂×C₄×C₁₃	—	2	1	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	4	8	no	—
328	C₂×C₄×C₁₃	—	4	1	no	—
329	C₂×C₄×C₁₃	—	4	1	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	4	1	no	—
332	C₂×C₄×C₁₃	—	4	1	no	—
333	C₂×C₄×C₁₃	—	4	1	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	4	1	no	—
338	C₂×C₄×C₁₃	—	4	1	no	—
339	C₂×C₄×C₁₃	—	4	1	no	—
340	C₂×C₄×C₁₃	—	4	1	no	—
341	C₂×C₄×C₁₃	—	4	1	no	—
342	C₂×C₄×C₁₃	—	4	1	no	—
343	C₂×C₄×C₁₃	—	4	1	no	—
344	C₂×C₄×C₁₃	—	4	1	no	—
345	C₂×C₄×C₁₃	—	8	4	no	—
346	C₂×C₄×C₁₃	—	8	4	no	—
347	C₂×C₄×C₁₃	#121	1	2	yes	—
348	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
349	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
353	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
354	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
356	C₈×C₁₃	—	2	2	no	—
357	C₈×C₁₃	—	4	1	no	—
358	C₈×C₁₃	—	4	1	no	—
359	C₈×C₁₃	—	4	1	no	—
360	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
361	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
362	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
363	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
364	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
366	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×C₄×D₄	—	2	1	no	—
370	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
371	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
372	#465	—	2	4	no	—
373	#461	—	2	4	no	—
374	#448	—	2	4	no	—
375	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
376	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×#103	—	2	4	no	—
379	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
390	#395	—	2	1	no	—
391	#395	—	2	1	no	—
392	#391	C₂²×C₁₃	1	1	yes	characteristic
393	#391	C₂²×C₁₃	1	1	yes	characteristic
394	#390	C₂²×C₁₃	1	1	yes	characteristic
395	#389	C₂²×C₁₃	1	1	yes	characteristic
396	#388	—	2	1	no	—
397	#386	—	2	1	no	—
398	#385	—	2	1	no	—
399	#385	—	2	1	no	—
400	#385	—	2	1	no	—
401	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
402	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
403	#340	C₂²×C₁₃	1	1	yes	characteristic
404	#340	C₂²×C₁₃	1	1	yes	characteristic
405	#336	C₂²×C₁₃	1	1	yes	characteristic
406	#336	C₂²×C₁₃	1	1	yes	characteristic
407	C₂²×C₁₃	—	2	2	no	—
408	C₂²×C₁₃	—	2	2	no	—
409	C₂²×C₁₃	—	2	2	no	—
410	C₂²×C₁₃	—	2	2	no	—
411	C₂²×C₁₃	—	2	2	no	—
412	C₂²×C₁₃	—	2	2	no	—
413	C₂²×C₁₃	—	4	2	no	—
414	C₂²×C₁₃	—	4	2	no	—
415	C₂²×C₁₃	—	4	2	no	—
416	C₂²×C₁₃	—	8	1	no	—
417	C₂²×C₁₃	—	8	1	no	—
418	C₂²×C₁₃	—	8	1	no	—
419	C₂²×C₁₃	—	8	1	no	—
420	C₂²×C₁₃	#461	1	4	yes	complemented
421	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
422	C₂²×C₁₃	D₄²	1	1	yes	characteristic
423	C₂²×C₁₃	#546	1	1	yes	characteristic
424	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
425	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
426	C₂²×C₁₃	#577	1	1	yes	characteristic
427	C₂²×C₁₃	#578	1	1	yes	characteristic
428	C₄×C₁₃	—	2	2	no	—
429	C₄×C₁₃	—	2	2	no	—
430	C₄×C₁₃	—	2	2	no	—
431	C₄×C₁₃	—	4	2	no	—
432	C₄×C₁₃	—	4	2	no	—
433	C₄×C₁₃	—	4	1	no	—
434	C₄×C₁₃	—	4	2	no	—
435	C₄×C₁₃	—	4	2	no	—
436	C₄×C₁₃	—	4	1	no	—
437	C₄×C₁₃	—	8	1	no	—
438	C₄×C₁₃	—	8	1	no	—
439	C₄×C₁₃	—	8	1	no	—
440	C₄×C₁₃	#525	1	1	yes	characteristic
441	C₄×C₁₃	#538	1	1	yes	characteristic
442	C₄×C₁₃	D₄²	1	1	yes	characteristic
443	C₄×C₁₃	#546	1	1	yes	characteristic
444	C₂²×Q₈	—	2	1	no	—
445	C₂²×Q₈	—	2	2	no	—
446	C₂²×Q₈	—	2	2	no	—
447	C₂²×Q₈	—	2	2	no	—
448	C₂²×Q₈	—	2	2	no	—
449	C₂²×Q₈	—	4	1	no	—
450	C₂²×Q₈	—	4	1	no	—
451	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
452	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₂³×C₄	—	2	1	no	—
457	C₂³×C₄	—	2	1	no	—
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×SD₁₆	—	2	2	no	—
461	C₂×SD₁₆	—	2	2	no	—
462	C₂×SD₁₆	—	2	2	no	—
463	C₂×SD₁₆	—	2	2	no	—
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×SD₁₆	—	2	2	no	—
466	C₂×SD₁₆	—	4	1	no	—
467	C₂×SD₁₆	—	4	1	no	—
468	C₂×SD₁₆	—	4	1	no	—
469	C₂²×C₈	—	2	2	no	—
470	C₂²×C₈	—	2	2	no	—
471	C₂²×C₈	—	4	1	no	—
472	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	—	2	2	no	—
478	C₄⋊Q₈	—	4	1	no	—
479	C₄⋊Q₈	—	4	1	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	#121	—	2	2	no	—
483	#121	D₄×C₁₃	1	4	yes	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	4	1	no	—
486	C₄×D₄	—	4	4	no	—
487	C₂×C₄⋊C₄	—	2	2	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	4	1	no	—
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
507	C₂×C₄²	—	2	1	no	—
508	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
510	#106	—	2	2	no	—
511	C₄⋊C₈	—	2	2	no	—
512	C₄⋊C₈	—	4	1	no	—
513	#103	—	2	2	no	—
514	#103	—	2	2	no	—
515	#103	—	2	2	no	—
516	#103	—	2	2	no	—
517	#103	—	2	2	no	—
518	#103	—	2	2	no	—
519	#103	—	2	2	no	—
520	#103	—	4	1	no	—
521	#103	D₄×C₁₃	1	4	yes	complemented
522	#102	—	2	2	no	—
523	C₂²⋊C₈	—	2	2	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	#95	—	2	1	no	—
527	#95	—	2	1	no	—
528	#95	—	2	1	no	—
529	#95	—	2	1	no	—
530	#95	D₄×C₁₃	1	1	yes	characteristic
531	#95	D₄×C₁₃	1	1	yes	characteristic
532	C₂×C₁₃	—	2	4	no	—
533	C₂×C₁₃	—	8	2	no	—
534	C₂×C₁₃	#2424	1	1	yes	characteristic
535	C₂×C₁₃	C₂×#461	1	1	yes	characteristic
536	C₂×C₁₃	#3046	1	1	yes	characteristic
537	C₂×C₁₃	#3270	1	1	yes	characteristic
538	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
539	C₂×C₁₃	#3298	1	1	yes	characteristic
540	C₂×C₁₃	#3320	1	1	yes	characteristic
541	C₂⁴	—	2	1	no	—
542	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	8	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	4	2	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×Q₈	—	4	4	no	—
563	C₂×Q₈	—	4	4	no	—
564	C₂×Q₈	—	4	4	no	—
565	C₂×Q₈	—	4	2	no	—
566	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
567	C₂×Q₈	C₁₃×#41	1	2	yes	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	2	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	8	1	no	—
596	C₂²×C₄	—	8	1	no	—
597	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
601	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₂²×C₄	C₁₃×#41	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
605	SD₁₆	—	4	4	no	—
606	SD₁₆	—	4	4	no	—
607	SD₁₆	—	4	4	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	4	4	no	—
620	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₄⋊C₄	—	4	2	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
635	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	8	1	no	—
642	C₂²⋊C₄	C₁₃×SD₁₆	1	4	yes	complemented
643	C₄²	—	2	1	no	—
644	C₄²	—	2	1	no	—
645	C₄²	—	2	1	no	—
646	C₄²	—	2	1	no	—
647	C₄²	—	4	2	no	—
648	C₁₃	#25078	1	1	yes	characteristic, direct product factor, Sylow
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	C₁₃×#121	1	2	yes	—
661	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
662	C₂³	C₁₃×#137	1	2	yes	—
663	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
664	Q₈	—	2	2	no	—
665	Q₈	—	2	2	no	—
666	Q₈	—	2	2	no	—
667	Q₈	—	2	2	no	—
668	Q₈	—	4	8	no	—
669	Q₈	—	4	1	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	Q₈	—	4	1	no	—
674	Q₈	—	4	1	no	—
675	Q₈	—	4	1	no	—
676	Q₈	—	4	1	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	2	no	—
679	D₄	—	4	8	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₁₃×#121	1	2	yes	—
723	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
724	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
727	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
728	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
729	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
730	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
731	C₈	—	2	2	no	—
732	C₈	—	4	1	no	—
733	C₈	—	4	1	no	—
734	C₈	—	4	1	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	8	1	no	—
745	C₂²	—	8	1	no	—
746	C₂²	—	8	1	no	—
747	C₂²	—	8	1	no	—
748	C₂²	C₁₃×#461	1	4	yes	complemented
749	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
750	C₂²	D₄²×C₁₃	1	1	yes	characteristic
751	C₂²	C₁₃×#546	1	1	yes	characteristic
752	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
753	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
754	C₂²	C₁₃×#577	1	1	yes	characteristic
755	C₂²	C₁₃×#578	1	1	yes	characteristic
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	8	1	no	—
766	C₄	—	8	1	no	—
767	C₄	—	8	1	no	—
768	C₄	C₁₃×#525	1	1	yes	characteristic
769	C₄	C₁₃×#538	1	1	yes	characteristic
770	C₄	D₄²×C₁₃	1	1	yes	characteristic
771	C₄	C₁₃×#546	1	1	yes	characteristic
772	C₂	—	2	4	no	—
773	C₂	—	8	2	no	—
774	C₂	C₁₃×#2424	1	1	yes	characteristic
775	C₂	C₂×C₁₃×#461	1	1	yes	characteristic
776	C₂	C₁₃×#3046	1	1	yes	characteristic
777	C₂	C₁₃×#3270	1	1	yes	characteristic
778	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
779	C₂	C₁₃×#3298	1	1	yes	characteristic
780	C₂	C₁₃×#3320	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#461	C₂	semidirect
4. C₂²×C₁₃×#103	C₂	semidirect
5. C₁₃×#2434	C₂	semidirect
7. C₁₃×#2066	C₂	semidirect
8. C₁₃×#2055	C₂	semidirect
9. C₁₃×#2043	C₂	semidirect
10. C₁₃×#2013	C₂	semidirect
11. C₁₃×#1981	C₂	semidirect
12. C₁₃×#1927	C₂	semidirect
13. C₁₃×#1877	C₂	semidirect
14. C₁₃×#1872	C₂	semidirect
15. C₁₃×#1850	C₂	semidirect
140. C₁₃×#103	D₄	semidirect
151. #25078	C₁₃	direct (N × H)
253. C₁₃×C₂²⋊C₄	SD₁₆	semidirect
260. C₂×#461	C₂×C₁₃	semidirect
262. C₂²×#103	C₂×C₁₃	semidirect
263. #2434	C₂×C₁₃	semidirect
265. #2066	C₂×C₁₃	semidirect
266. #2055	C₂×C₁₃	semidirect
267. #2043	C₂×C₁₃	semidirect
268. #2013	C₂×C₁₃	semidirect
269. #1981	C₂×C₁₃	semidirect
270. #1927	C₂×C₁₃	semidirect
271. #1877	C₂×C₁₃	semidirect
272. #1872	C₂×C₁₃	semidirect
273. #1850	C₂×C₁₃	semidirect
420. C₂²×C₁₃	#461	semidirect
521. #103	D₄×C₁₃	semidirect
642. C₂²⋊C₄	C₁₃×SD₁₆	semidirect
648. C₁₃	#25078	direct (N × H)
748. C₂²	C₁₃×#461	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#465	2
C₂×C₁₃×#461	2
C₂×C₁₃×#448	2
C₂²×C₁₃×#103	2
C₁₃×#2434	2
C₁₃×#2361	2
C₁₃×#2066	2
C₁₃×#2055	2
C₁₃×#2043	2
C₁₃×#2013	2
C₁₃×#1981	2
C₁₃×#1927	2
C₁₃×#1877	2
C₁₃×#1872	2
C₁₃×#1850	2
#25078	13

Subgroups — C13×#25078 #15711417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25078 #15711417