Subgroups — C₁₃×#34233 #15720572

Order 3328.

2826 conjugacy classes of subgroups.

The subgroup lattice has 776 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×#2361	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2360	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2358	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×#2347	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2335	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#121	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2275	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#525	C₄	1	16	yes	complemented
21	C₂×C₁₃×#123	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊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×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#120	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
28	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
38	C₁₃×#391	C₂²	1	2	yes	complemented
39	C₁₃×#390	C₂²	1	4	yes	—
40	C₁₃×#390	C₂²	1	2	yes	complemented
41	C₁₃×#389	C₂²	1	2	yes	complemented
42	C₁₃×#389	C₂²	1	2	yes	complemented
43	C₁₃×#389	C₂²	1	4	yes	complemented
44	C₁₃×#388	C₂²	1	4	yes	—
45	C₁₃×#388	C₂²	1	4	yes	—
46	C₁₃×#388	C₂²	1	4	yes	complemented
47	C₁₃×#388	C₂²	1	4	yes	complemented
48	C₁₃×#387	C₂²	1	4	yes	complemented
49	C₁₃×#387	C₂²	1	4	yes	complemented
50	C₁₃×#386	C₂²	1	4	yes	—
51	C₁₃×#386	C₂²	1	4	yes	—
52	C₁₃×#386	C₂²	1	4	yes	—
53	C₁₃×#385	C₂²	1	4	yes	—
54	C₁₃×#385	C₂²	1	4	yes	—
55	C₁₃×#385	C₂²	1	4	yes	complemented
56	C₁₃×#383	C₂²	1	2	yes	complemented
57	C₁₃×#382	C₂²	1	2	yes	complemented
58	C₁₃×#381	C₂²	1	2	yes	complemented
59	C₁₃×#380	C₂²	1	2	yes	—
60	C₁₃×#380	C₂²	1	2	yes	—
61	C₁₃×#380	C₂²	1	1	yes	characteristic
62	C₁₃×#380	C₂²	1	1	yes	characteristic
63	C₁₃×#380	C₂²	1	2	yes	—
64	C₁₃×#380	C₂²	1	2	yes	complemented
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
69	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
73	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
74	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
76	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
79	C₁₃×#376	C₂²	1	2	yes	complemented
80	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
81	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
82	C₂×C₁₃×#95	C₂²	1	2	yes	—
83	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
84	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×#41	—	4	4	no	—
86	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	—	4	4	no	—
93	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	complemented
94	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
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	4	yes	—
100	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#123	C₂×C₄	1	16	yes	complemented
106	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
107	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
108	C₁₃×#121	C₂×C₄	1	8	yes	complemented
109	C₁₃×#121	C₂×C₄	1	8	yes	complemented
110	C₁₃×#120	C₂×C₄	1	16	yes	complemented
111	C₄×Q₈×C₁₃	—	4	4	no	—
112	C₄×D₄×C₁₃	—	2	16	no	—
113	C₄×D₄×C₁₃	—	4	4	no	—
114	C₄×D₄×C₁₃	—	4	8	no	—
115	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
116	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
117	C₁₃×#117	C₂×C₄	1	8	yes	complemented
118	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
130	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
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	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	—	4	4	no	—
147	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
152	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
154	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
155	C₁₃×#95	C₂³	1	1	yes	characteristic
156	C₁₃×#95	C₂³	1	1	yes	characteristic
157	C₁₃×#95	C₂³	1	1	yes	characteristic
158	C₁₃×#95	C₂³	1	1	yes	characteristic
159	C₁₃×#95	C₂³	1	2	yes	—
160	C₁₃×#95	C₂³	1	2	yes	—
161	C₁₃×#95	C₂³	1	4	yes	—
162	C₁₃×#95	C₂³	1	4	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
164	C₁₃×#95	C₂³	1	4	yes	—
165	C₁₃×#95	C₂³	1	2	yes	—
166	C₁₃×#95	C₂³	1	4	yes	—
167	C₁₃×#95	C₂³	1	4	yes	—
168	C₁₃×#95	C₂³	1	4	yes	—
169	C₁₃×#95	C₂³	1	2	yes	—
170	#34233	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂⁴×C₁₃	—	2	4	no	—
172	C₂⁴×C₁₃	—	2	2	no	—
173	C₂⁴×C₁₃	—	2	2	no	—
174	C₂⁴×C₁₃	—	4	2	no	—
175	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
176	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
178	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₁₃×#41	—	4	16	no	—
181	C₂×Q₈×C₁₃	—	2	4	no	—
182	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
183	C₂×D₄×C₁₃	—	2	8	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	4	no	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	4	4	no	—
188	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
189	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
190	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
191	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	2	4	no	—
194	C₂²×C₄×C₁₃	—	2	4	no	—
195	C₂²×C₄×C₁₃	—	2	4	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	2	8	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	2	8	no	—
201	C₂²×C₄×C₁₃	—	4	16	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	—	4	2	no	—
207	C₂²×C₄×C₁₃	—	4	4	no	—
208	C₂²×C₄×C₁₃	—	4	4	no	—
209	C₂²×C₄×C₁₃	—	4	4	no	—
210	C₂²×C₄×C₁₃	—	4	4	no	—
211	C₂²×C₄×C₁₃	—	4	4	no	—
212	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
213	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
214	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
215	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
216	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
217	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
218	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₁₃×C₄⋊C₄	—	2	8	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	4	4	no	—
236	C₁₃×C₄⋊C₄	—	4	4	no	—
237	C₁₃×C₄⋊C₄	—	4	4	no	—
238	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
239	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
240	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
241	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	8	no	—
244	C₁₃×C₂²⋊C₄	—	2	4	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	8	no	—
247	C₁₃×C₂²⋊C₄	—	4	2	no	—
248	C₁₃×C₂²⋊C₄	—	4	2	no	—
249	C₁₃×C₂²⋊C₄	—	4	4	no	—
250	C₁₃×C₂²⋊C₄	—	4	4	no	—
251	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
252	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
253	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
254	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
255	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
256	C₁₃×C₂²⋊C₄	#41	1	8	yes	complemented
257	C₄²×C₁₃	—	2	8	no	—
258	C₄²×C₁₃	—	2	4	no	—
259	C₄²×C₁₃	—	2	4	no	—
260	C₄²×C₁₃	—	4	2	no	—
261	C₄²×C₁₃	—	4	2	no	—
262	C₄²×C₁₃	—	4	4	no	—
263	C₄²×C₁₃	—	4	4	no	—
264	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
265	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
266	#2361	C₂×C₁₃	1	2	yes	complemented
267	#2360	C₂×C₁₃	1	2	yes	complemented
268	#2358	C₂×C₁₃	1	4	yes	complemented
269	#2353	C₂×C₁₃	1	2	yes	complemented
270	#2349	C₂×C₁₃	1	2	yes	complemented
271	#2347	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#2346	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#2341	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2339	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#2335	C₂×C₁₃	1	4	yes	complemented
276	#2318	C₂×C₁₃	1	2	yes	complemented
277	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
278	C₄×#121	C₂×C₁₃	1	2	yes	complemented
279	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2275	C₂×C₁₃	1	2	yes	complemented
281	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂³×C₁₃	—	2	2	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	2	1	no	—
286	C₂³×C₁₃	—	2	1	no	—
287	C₂³×C₁₃	—	2	8	no	—
288	C₂³×C₁₃	—	2	8	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	4	no	—
291	C₂³×C₁₃	—	2	1	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	4	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	1	no	—
297	C₂³×C₁₃	—	4	4	no	—
298	C₂³×C₁₃	—	4	8	no	—
299	C₂³×C₁₃	—	4	8	no	—
300	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
301	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
302	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
303	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
304	C₂³×C₁₃	C₂×#41	1	4	yes	—
305	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
306	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
307	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
308	Q₈×C₁₃	—	2	8	no	—
309	D₄×C₁₃	—	2	16	no	—
310	D₄×C₁₃	—	2	16	no	—
311	D₄×C₁₃	—	2	8	no	—
312	D₄×C₁₃	—	4	8	no	—
313	C₂×C₄×C₁₃	—	2	4	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	2	no	—
319	C₂×C₄×C₁₃	—	2	4	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	8	no	—
325	C₂×C₄×C₁₃	—	2	8	no	—
326	C₂×C₄×C₁₃	—	2	8	no	—
327	C₂×C₄×C₁₃	—	2	4	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	4	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	4	no	—
334	C₂×C₄×C₁₃	—	2	4	no	—
335	C₂×C₄×C₁₃	—	2	4	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	4	4	no	—
340	C₂×C₄×C₁₃	—	4	4	no	—
341	C₂×C₄×C₁₃	—	4	4	no	—
342	C₂×C₄×C₁₃	—	4	8	no	—
343	C₂×C₄×C₁₃	—	4	8	no	—
344	C₂×C₄×C₁₃	—	4	8	no	—
345	C₂×C₄×C₁₃	—	8	8	no	—
346	C₂×C₄×C₁₃	—	8	8	no	—
347	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
348	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
349	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
350	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
352	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
353	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
354	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
355	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
356	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
357	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
358	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
359	#525	C₄×C₁₃	1	16	yes	complemented
360	C₂×#123	C₂²×C₁₃	1	2	yes	—
361	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
362	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
363	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
364	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
365	C₂×#120	C₂²×C₁₃	1	2	yes	—
366	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
367	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
368	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
369	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
370	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
371	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
372	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
373	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
374	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
375	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
376	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
377	#391	C₂²×C₁₃	1	2	yes	complemented
378	#390	C₂²×C₁₃	1	4	yes	—
379	#390	C₂²×C₁₃	1	2	yes	complemented
380	#389	C₂²×C₁₃	1	4	yes	complemented
381	#389	C₂²×C₁₃	1	2	yes	complemented
382	#389	C₂²×C₁₃	1	2	yes	complemented
383	#388	C₂²×C₁₃	1	4	yes	—
384	#388	C₂²×C₁₃	1	4	yes	—
385	#388	C₂²×C₁₃	1	4	yes	complemented
386	#388	C₂²×C₁₃	1	4	yes	complemented
387	#387	C₂²×C₁₃	1	4	yes	complemented
388	#387	C₂²×C₁₃	1	4	yes	complemented
389	#386	C₂²×C₁₃	1	4	yes	—
390	#386	C₂²×C₁₃	1	4	yes	—
391	#386	C₂²×C₁₃	1	4	yes	—
392	#385	C₂²×C₁₃	1	4	yes	—
393	#385	C₂²×C₁₃	1	4	yes	—
394	#385	C₂²×C₁₃	1	4	yes	complemented
395	#383	C₂²×C₁₃	1	2	yes	complemented
396	#382	C₂²×C₁₃	1	2	yes	complemented
397	#381	C₂²×C₁₃	1	2	yes	complemented
398	#380	C₂²×C₁₃	1	2	yes	—
399	#380	C₂²×C₁₃	1	1	yes	characteristic
400	#380	C₂²×C₁₃	1	1	yes	characteristic
401	#380	C₂²×C₁₃	1	2	yes	—
402	#380	C₂²×C₁₃	1	2	yes	—
403	#380	C₂²×C₁₃	1	2	yes	complemented
404	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
405	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
406	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
407	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
408	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
410	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
411	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
415	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
416	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
417	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
418	#376	C₂²×C₁₃	1	2	yes	complemented
419	C₂×#95	C₂²×C₁₃	1	2	yes	—
420	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
423	C₂²×C₁₃	—	2	2	no	—
424	C₂²×C₁₃	—	2	2	no	—
425	C₂²×C₁₃	—	2	2	no	—
426	C₂²×C₁₃	—	2	2	no	—
427	C₂²×C₁₃	—	2	4	no	—
428	C₂²×C₁₃	—	2	4	no	—
429	C₂²×C₁₃	—	2	4	no	—
430	C₂²×C₁₃	—	2	4	no	—
431	C₂²×C₁₃	—	2	4	no	—
432	C₂²×C₁₃	—	2	2	no	—
433	C₂²×C₁₃	—	2	2	no	—
434	C₂²×C₁₃	—	2	4	no	—
435	C₂²×C₁₃	—	2	4	no	—
436	C₂²×C₁₃	—	2	2	no	—
437	C₂²×C₁₃	—	4	16	no	—
438	C₂²×C₁₃	—	4	4	no	—
439	C₂²×C₁₃	—	4	2	no	—
440	C₂²×C₁₃	—	4	4	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	C₄×#41	1	4	yes	—
443	C₂²×C₁₃	#520	1	4	yes	—
444	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
445	C₂²×C₁₃	C₂²×#41	1	2	yes	—
446	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
447	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	C₄×C₁₃	—	2	4	no	—
450	C₄×C₁₃	—	2	2	no	—
451	C₄×C₁₃	—	2	2	no	—
452	C₄×C₁₃	—	2	2	no	—
453	C₄×C₁₃	—	2	4	no	—
454	C₄×C₁₃	—	2	4	no	—
455	C₄×C₁₃	—	2	4	no	—
456	C₄×C₁₃	—	2	4	no	—
457	C₄×C₁₃	—	4	2	no	—
458	C₄×C₁₃	—	4	4	no	—
459	C₄×C₁₃	—	4	4	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	#518	1	4	yes	—
462	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
463	C₂×#41	—	4	4	no	—
464	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
465	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
467	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
468	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
470	C₂³×C₄	—	4	4	no	—
471	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
472	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
473	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
474	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
478	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
479	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
482	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
483	#123	C₂×C₄×C₁₃	1	16	yes	complemented
484	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
485	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
486	#121	C₂×C₄×C₁₃	1	8	yes	complemented
487	#121	C₂×C₄×C₁₃	1	8	yes	complemented
488	#120	C₂×C₄×C₁₃	1	16	yes	complemented
489	C₄×Q₈	—	4	4	no	—
490	C₄×D₄	—	2	16	no	—
491	C₄×D₄	—	4	4	no	—
492	C₄×D₄	—	4	8	no	—
493	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
494	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
495	#117	C₂×C₄×C₁₃	1	8	yes	complemented
496	C₂×C₄⋊C₄	—	4	4	no	—
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
507	C₂×C₂²⋊C₄	—	2	8	no	—
508	C₂×C₂²⋊C₄	—	4	4	no	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄²	—	4	4	no	—
525	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
526	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
529	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
530	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
531	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
532	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
533	#95	C₂³×C₁₃	1	1	yes	characteristic
534	#95	C₂³×C₁₃	1	2	yes	—
535	#95	C₂³×C₁₃	1	1	yes	characteristic
536	#95	C₂³×C₁₃	1	1	yes	characteristic
537	#95	C₂³×C₁₃	1	1	yes	characteristic
538	#95	C₂³×C₁₃	1	2	yes	—
539	#95	C₂³×C₁₃	1	2	yes	—
540	#95	C₂³×C₁₃	1	2	yes	—
541	#95	C₂³×C₁₃	1	4	yes	—
542	#95	C₂³×C₁₃	1	4	yes	—
543	#95	C₂³×C₁₃	1	4	yes	—
544	#95	C₂³×C₁₃	1	4	yes	—
545	#95	C₂³×C₁₃	1	4	yes	—
546	#95	C₂³×C₁₃	1	4	yes	—
547	#95	C₂³×C₁₃	1	4	yes	—
548	C₂×C₁₃	—	2	4	no	—
549	C₂×C₁₃	—	2	4	no	—
550	C₂×C₁₃	—	4	4	no	—
551	C₂×C₁₃	—	4	2	no	—
552	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
553	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
554	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
555	C₂×C₁₃	#3519	1	2	yes	—
556	C₂×C₁₃	#3520	1	2	yes	—
557	C₂⁴	—	2	4	no	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	2	2	no	—
560	C₂⁴	—	4	2	no	—
561	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
562	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
563	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
564	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
565	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
566	#41	—	4	16	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
569	C₂×D₄	—	2	8	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
575	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
576	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
577	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	8	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	8	no	—
587	C₂²×C₄	—	4	16	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	4	no	—
594	C₂²×C₄	—	4	4	no	—
595	C₂²×C₄	—	4	4	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	4	4	no	—
598	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
599	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
600	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
601	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
602	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
603	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
604	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
605	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
607	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
609	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
618	C₄⋊C₄	—	2	8	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	4	4	no	—
622	C₄⋊C₄	—	4	4	no	—
623	C₄⋊C₄	—	4	4	no	—
624	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
625	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
626	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
627	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	8	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	8	no	—
633	C₂²⋊C₄	—	4	2	no	—
634	C₂²⋊C₄	—	4	2	no	—
635	C₂²⋊C₄	—	4	4	no	—
636	C₂²⋊C₄	—	4	4	no	—
637	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
638	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
639	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
640	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
641	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
642	C₂²⋊C₄	C₁₃×#41	1	8	yes	complemented
643	C₄²	—	2	8	no	—
644	C₄²	—	2	4	no	—
645	C₄²	—	2	4	no	—
646	C₄²	—	4	2	no	—
647	C₄²	—	4	2	no	—
648	C₄²	—	4	4	no	—
649	C₄²	—	4	4	no	—
650	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
651	C₁₃	#34233	1	1	yes	characteristic, direct product factor, Sylow
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	8	no	—
658	C₂³	—	2	8	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	4	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	4	4	no	—
668	C₂³	—	4	8	no	—
669	C₂³	—	4	8	no	—
670	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
671	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
672	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
673	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
674	C₂³	C₂×C₁₃×#41	1	4	yes	—
675	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
676	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
677	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
678	Q₈	—	2	8	no	—
679	D₄	—	2	16	no	—
680	D₄	—	2	16	no	—
681	D₄	—	2	8	no	—
682	D₄	—	4	8	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	8	no	—
695	C₂×C₄	—	2	8	no	—
696	C₂×C₄	—	2	8	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	—	8	8	no	—
716	C₂×C₄	—	8	8	no	—
717	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
718	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
719	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
720	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
721	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
722	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
723	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
724	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
725	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
726	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	2	no	—
741	C₂²	—	4	16	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	4	no	—
745	C₂²	—	4	2	no	—
746	C₂²	C₄×C₁₃×#41	1	4	yes	—
747	C₂²	C₁₃×#520	1	4	yes	—
748	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
749	C₂²	C₂²×C₁₃×#41	1	2	yes	—
750	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
751	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
752	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
753	C₄	—	2	4	no	—
754	C₄	—	2	4	no	—
755	C₄	—	2	4	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	4	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	2	no	—
765	C₄	C₁₃×#518	1	4	yes	—
766	C₂	—	2	4	no	—
767	C₂	—	2	4	no	—
768	C₂	—	4	2	no	—
769	C₂	—	4	4	no	—
770	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
771	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
772	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
773	C₂	C₁₃×#3519	1	2	yes	—
774	C₂	C₁₃×#3520	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×#2361	C₂	semidirect
3. C₁₃×#2360	C₂	semidirect
4. C₁₃×#2358	C₂	semidirect
5. C₁₃×#2353	C₂	semidirect
6. C₁₃×#2349	C₂	semidirect
7. C₁₃×#2347	C₂	semidirect
8. C₁₃×#2346	C₂	semidirect
9. C₁₃×#2341	C₂	semidirect
10. C₁₃×#2339	C₂	semidirect
11. C₁₃×#2335	C₂	semidirect
12. C₁₃×#2318	C₂	semidirect
13. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₄×C₁₃×#121	C₂	semidirect
15. C₂×C₁₃×#380	C₂	semidirect
16. C₁₃×#2275	C₂	semidirect
17. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
20. C₁₃×#525	C₄	semidirect
27. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
38. C₁₃×#391	C₂²	semidirect
40. C₁₃×#390	C₂²	semidirect
41. C₁₃×#389	C₂²	semidirect
42. C₁₃×#389	C₂²	semidirect
43. C₁₃×#389	C₂²	semidirect
46. C₁₃×#388	C₂²	semidirect
47. C₁₃×#388	C₂²	semidirect
48. C₁₃×#387	C₂²	semidirect
49. C₁₃×#387	C₂²	semidirect
55. C₁₃×#385	C₂²	semidirect
56. C₁₃×#383	C₂²	semidirect
57. C₁₃×#382	C₂²	semidirect
58. C₁₃×#381	C₂²	semidirect
64. C₁₃×#380	C₂²	semidirect
65. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
66. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
67. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
68. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
77. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
78. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
79. C₁₃×#376	C₂²	semidirect
83. C₂×C₁₃×#95	C₂²	semidirect
86. C₂×C₁₃×#41	C₂×C₄	semidirect
93. C₂³×C₄×C₁₃	C₂×C₄	semidirect
105. C₁₃×#123	C₂×C₄	semidirect
106. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
107. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
108. C₁₃×#121	C₂×C₄	semidirect
109. C₁₃×#121	C₂×C₄	semidirect
110. C₁₃×#120	C₂×C₄	semidirect
115. C₄×D₄×C₁₃	C₂×C₄	semidirect
116. C₄×D₄×C₁₃	C₂×C₄	semidirect
117. C₁₃×#117	C₂×C₄	semidirect
170. #34233	C₁₃	direct (N × H)
256. C₁₃×C₂²⋊C₄	#41	semidirect
266. #2361	C₂×C₁₃	semidirect
267. #2360	C₂×C₁₃	semidirect
268. #2358	C₂×C₁₃	semidirect
269. #2353	C₂×C₁₃	semidirect
270. #2349	C₂×C₁₃	semidirect
271. #2347	C₂×C₁₃	semidirect
272. #2346	C₂×C₁₃	semidirect
273. #2341	C₂×C₁₃	semidirect
274. #2339	C₂×C₁₃	semidirect
275. #2335	C₂×C₁₃	semidirect
276. #2318	C₂×C₁₃	semidirect
277. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
278. C₄×#121	C₂×C₁₃	semidirect
279. C₂×#380	C₂×C₁₃	semidirect
280. #2275	C₂×C₁₃	semidirect
281. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
359. #525	C₄×C₁₃	semidirect
366. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
371. C₂×C₄×D₄	C₂²×C₁₃	semidirect
377. #391	C₂²×C₁₃	semidirect
379. #390	C₂²×C₁₃	semidirect
380. #389	C₂²×C₁₃	semidirect
381. #389	C₂²×C₁₃	semidirect
382. #389	C₂²×C₁₃	semidirect
385. #388	C₂²×C₁₃	semidirect
386. #388	C₂²×C₁₃	semidirect
387. #387	C₂²×C₁₃	semidirect
388. #387	C₂²×C₁₃	semidirect
394. #385	C₂²×C₁₃	semidirect
395. #383	C₂²×C₁₃	semidirect
396. #382	C₂²×C₁₃	semidirect
397. #381	C₂²×C₁₃	semidirect
403. #380	C₂²×C₁₃	semidirect
404. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
405. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
406. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
407. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
416. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
417. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
418. #376	C₂²×C₁₃	semidirect
422. C₂×#95	C₂²×C₁₃	semidirect
464. C₂×#41	C₂×C₄×C₁₃	semidirect
471. C₂³×C₄	C₂×C₄×C₁₃	semidirect
483. #123	C₂×C₄×C₁₃	semidirect
484. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
485. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
486. #121	C₂×C₄×C₁₃	semidirect
487. #121	C₂×C₄×C₁₃	semidirect
488. #120	C₂×C₄×C₁₃	semidirect
493. C₄×D₄	C₂×C₄×C₁₃	semidirect
494. C₄×D₄	C₂×C₄×C₁₃	semidirect
495. #117	C₂×C₄×C₁₃	semidirect
642. C₂²⋊C₄	C₁₃×#41	semidirect
651. C₁₃	#34233	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×#2361	2
C₁₃×#2360	2
C₁₃×#2358	2
C₁₃×#2353	2
C₁₃×#2349	2
C₁₃×#2347	2
C₁₃×#2346	2
C₁₃×#2341	2
C₁₃×#2339	2
C₁₃×#2335	2
C₁₃×#2318	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₂×C₁₃×#380	2
C₁₃×#2275	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34233	13

Subgroups — C13×#34233 #15720572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34233 #15720572