Subgroups — C₁₃×#34877 #15721216

Order 3328.

2646 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2611	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2610	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2601	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2591	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2583	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2539	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#2413	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2411	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2396	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2392	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#123	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#120	C₂	1	2	yes	maximal, complemented
16	C₁₃×#2293	C₂	1	4	yes	maximal, complemented
17	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#529	—	2	8	no	—
20	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#123	C₂²	1	2	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#120	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
32	C₂×C₁₃×#117	—	2	8	no	—
33	C₂×C₁₃×#117	C₂²	1	2	yes	—
34	C₂×C₁₃×#117	C₂²	1	2	yes	—
35	C₂×C₁₃×#117	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	C₂²	1	2	yes	—
37	C₂×C₁₃×#117	C₂²	1	2	yes	—
38	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
39	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#400	C₂²	1	2	yes	complemented
46	C₁₃×#399	C₂²	1	2	yes	—
47	C₁₃×#398	C₂²	1	2	yes	complemented
48	C₁₃×#398	C₂²	1	4	yes	complemented
49	C₁₃×#397	C₂²	1	2	yes	—
50	C₁₃×#396	C₂²	1	4	yes	—
51	C₁₃×#396	C₂²	1	4	yes	complemented
52	C₁₃×#395	C₂²	1	2	yes	complemented
53	C₁₃×#394	C₂²	1	4	yes	—
54	C₁₃×#394	C₂²	1	2	yes	complemented
55	C₁₃×#393	C₂²	1	2	yes	—
56	C₁₃×#392	C₂²	1	2	yes	—
57	C₁₃×#390	C₂²	1	4	yes	—
58	C₁₃×#390	C₂²	1	4	yes	—
59	C₁₃×#389	C₂²	1	4	yes	complemented
60	C₁₃×#389	C₂²	1	4	yes	complemented
61	C₁₃×#388	C₂²	1	4	yes	—
62	C₁₃×#388	C₂²	1	4	yes	—
63	C₁₃×#388	C₂²	1	4	yes	complemented
64	C₁₃×#388	C₂²	1	4	yes	complemented
65	C₁₃×#388	C₂²	1	4	yes	complemented
66	C₁₃×#387	C₂²	1	4	yes	complemented
67	C₁₃×#386	C₂²	1	2	yes	—
68	C₁₃×#386	C₂²	1	4	yes	—
69	C₁₃×#386	C₂²	1	2	yes	—
70	C₁₃×#385	C₂²	1	2	yes	—
71	C₁₃×#385	C₂²	1	4	yes	—
72	C₁₃×#385	C₂²	1	2	yes	—
73	C₁₃×#381	C₂²	1	2	yes	—
74	C₁₃×#379	C₂²	1	2	yes	—
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
77	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
82	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
83	C₁₃×#376	C₂²	1	2	yes	complemented
84	C₄³×C₁₃	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	—	2	4	no	—
91	C₂³×C₄×C₁₃	—	2	8	no	—
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
99	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#126	—	2	8	no	—
102	C₁₃×#125	—	2	4	no	—
103	C₁₃×#124	—	2	4	no	—
104	C₁₃×#123	—	2	8	no	—
105	C₁₃×#123	—	2	8	no	—
106	C₁₃×C₂²⋊Q₈	—	2	4	no	—
107	C₁₃×#121	—	2	4	no	—
108	C₁₃×#120	—	2	8	no	—
109	C₄×Q₈×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	—	2	8	no	—
111	C₄×D₄×C₁₃	—	2	16	no	—
112	C₄×D₄×C₁₃	—	2	4	no	—
113	C₁₃×#117	—	2	8	no	—
114	C₁₃×#117	—	2	8	no	—
115	C₁₃×#117	—	2	8	no	—
116	C₁₃×#117	—	2	8	no	—
117	C₁₃×#117	—	2	8	no	—
118	C₁₃×#117	—	2	8	no	—
119	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	2	yes	—
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
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	4	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₄²×C₁₃	—	2	4	no	—
155	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
156	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
158	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
159	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₁₃×#95	C₂³	1	4	yes	—
168	C₁₃×#95	C₂³	1	2	yes	—
169	C₁₃×#95	C₂³	1	2	yes	—
170	C₁₃×#95	C₂³	1	4	yes	—
171	C₁₃×#95	C₂³	1	4	yes	—
172	C₁₃×#95	C₂³	1	4	yes	—
173	C₁₃×#95	C₂³	1	4	yes	—
174	C₁₃×#95	C₂³	1	4	yes	—
175	C₁₃×#95	C₂³	1	4	yes	—
176	#34877	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂⁴×C₁₃	—	2	2	no	—
178	C₂⁴×C₁₃	—	2	4	no	—
179	C₂⁴×C₁₃	—	2	4	no	—
180	C₂⁴×C₁₃	—	4	2	no	—
181	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
182	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
183	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂×Q₈×C₁₃	—	2	2	no	—
185	C₂×Q₈×C₁₃	—	4	2	no	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	8	no	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	4	no	—
190	C₂×D₄×C₁₃	—	2	2	no	—
191	C₂×D₄×C₁₃	—	2	8	no	—
192	C₂×D₄×C₁₃	—	4	4	no	—
193	C₂×D₄×C₁₃	—	4	2	no	—
194	C₂²×C₄×C₁₃	—	2	32	no	—
195	C₂²×C₄×C₁₃	—	2	2	no	—
196	C₂²×C₄×C₁₃	—	2	4	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	2	4	no	—
201	C₂²×C₄×C₁₃	—	2	4	no	—
202	C₂²×C₄×C₁₃	—	2	4	no	—
203	C₂²×C₄×C₁₃	—	2	4	no	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	4	no	—
207	C₂²×C₄×C₁₃	—	2	4	no	—
208	C₂²×C₄×C₁₃	—	2	8	no	—
209	C₂²×C₄×C₁₃	—	4	2	no	—
210	C₂²×C₄×C₁₃	—	4	2	no	—
211	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₁₃	#41	1	8	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	4	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	2	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	8	no	—
240	C₁₃×C₄⋊C₄	—	2	8	no	—
241	C₁₃×C₄⋊C₄	—	2	8	no	—
242	C₁₃×C₄⋊C₄	—	4	4	no	—
243	C₁₃×C₂²⋊C₄	—	2	4	no	—
244	C₁₃×C₂²⋊C₄	—	2	4	no	—
245	C₁₃×C₂²⋊C₄	—	2	8	no	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	4	no	—
249	C₁₃×C₂²⋊C₄	—	2	4	no	—
250	C₁₃×C₂²⋊C₄	—	2	4	no	—
251	C₁₃×C₂²⋊C₄	—	2	4	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	8	no	—
255	C₁₃×C₂²⋊C₄	—	2	8	no	—
256	C₁₃×C₂²⋊C₄	—	2	8	no	—
257	C₁₃×C₂²⋊C₄	—	4	4	no	—
258	C₁₃×C₂²⋊C₄	—	4	4	no	—
259	C₁₃×C₂²⋊C₄	#41	1	8	yes	—
260	C₄²×C₁₃	—	2	4	no	—
261	C₄²×C₁₃	—	2	4	no	—
262	C₄²×C₁₃	—	2	4	no	—
263	C₄²×C₁₃	—	2	8	no	—
264	C₄²×C₁₃	—	2	8	no	—
265	C₄²×C₁₃	—	4	2	no	—
266	C₄²×C₁₃	—	4	2	no	—
267	C₄²×C₁₃	C₂×D₄	1	4	yes	—
268	C₄²×C₁₃	C₂×D₄	1	4	yes	—
269	C₄²×C₁₃	C₂×D₄	1	4	yes	—
270	C₄²×C₁₃	C₂×D₄	1	4	yes	—
271	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
272	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#2611	C₂×C₁₃	1	2	yes	complemented
274	#2610	C₂×C₁₃	1	2	yes	complemented
275	#2601	C₂×C₁₃	1	4	yes	complemented
276	#2591	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2583	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2561	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2539	C₂×C₁₃	1	1	yes	characteristic
280	#2413	C₂×C₁₃	1	2	yes	complemented
281	#2411	C₂×C₁₃	1	2	yes	complemented
282	#2396	C₂×C₁₃	1	2	yes	complemented
283	#2392	C₂×C₁₃	1	2	yes	complemented
284	C₄×#123	C₂×C₁₃	1	2	yes	complemented
285	C₄×#120	C₂×C₁₃	1	2	yes	complemented
286	#2293	C₂×C₁₃	1	4	yes	complemented
287	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	8	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	4	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	4	no	—
295	C₂³×C₁₃	—	2	2	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	2	4	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	2	4	no	—
300	C₂³×C₁₃	—	4	16	no	—
301	C₂³×C₁₃	—	4	4	no	—
302	C₂³×C₁₃	—	4	4	no	—
303	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
304	C₂³×C₁₃	C₂×#41	1	4	yes	—
305	C₂³×C₁₃	C₂×#41	1	4	yes	—
306	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
307	Q₈×C₁₃	—	4	4	no	—
308	D₄×C₁₃	—	4	16	no	—
309	D₄×C₁₃	—	4	4	no	—
310	D₄×C₁₃	—	4	8	no	—
311	C₂×C₄×C₁₃	—	2	16	no	—
312	C₂×C₄×C₁₃	—	2	8	no	—
313	C₂×C₄×C₁₃	—	2	8	no	—
314	C₂×C₄×C₁₃	—	2	2	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	4	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	4	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	8	no	—
324	C₂×C₄×C₁₃	—	2	16	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	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	4	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	2	no	—
336	C₂×C₄×C₁₃	—	2	4	no	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	2	4	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	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
350	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
351	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
352	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
353	#529	—	2	8	no	—
354	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
355	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
356	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
357	C₂×#123	C₂²×C₁₃	1	2	yes	—
358	C₂×#123	C₂²×C₁₃	1	2	yes	—
359	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×#120	C₂²×C₁₃	1	2	yes	—
362	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
363	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
364	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
365	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
366	C₂×#117	—	2	8	no	—
367	C₂×#117	C₂²×C₁₃	1	2	yes	—
368	C₂×#117	C₂²×C₁₃	1	2	yes	—
369	C₂×#117	C₂²×C₁₃	1	2	yes	—
370	C₂×#117	C₂²×C₁₃	1	2	yes	—
371	C₂×#117	C₂²×C₁₃	1	2	yes	—
372	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
373	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
374	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
379	#400	C₂²×C₁₃	1	2	yes	complemented
380	#399	C₂²×C₁₃	1	2	yes	—
381	#398	C₂²×C₁₃	1	2	yes	complemented
382	#398	C₂²×C₁₃	1	4	yes	complemented
383	#397	C₂²×C₁₃	1	2	yes	—
384	#396	C₂²×C₁₃	1	4	yes	—
385	#396	C₂²×C₁₃	1	4	yes	complemented
386	#395	C₂²×C₁₃	1	2	yes	complemented
387	#394	C₂²×C₁₃	1	4	yes	—
388	#394	C₂²×C₁₃	1	2	yes	complemented
389	#393	C₂²×C₁₃	1	2	yes	—
390	#392	C₂²×C₁₃	1	2	yes	—
391	#390	C₂²×C₁₃	1	4	yes	—
392	#390	C₂²×C₁₃	1	4	yes	—
393	#389	C₂²×C₁₃	1	4	yes	complemented
394	#389	C₂²×C₁₃	1	4	yes	complemented
395	#388	C₂²×C₁₃	1	4	yes	—
396	#388	C₂²×C₁₃	1	4	yes	—
397	#388	C₂²×C₁₃	1	4	yes	complemented
398	#388	C₂²×C₁₃	1	4	yes	complemented
399	#388	C₂²×C₁₃	1	4	yes	complemented
400	#387	C₂²×C₁₃	1	4	yes	complemented
401	#386	C₂²×C₁₃	1	2	yes	—
402	#386	C₂²×C₁₃	1	2	yes	—
403	#386	C₂²×C₁₃	1	4	yes	—
404	#385	C₂²×C₁₃	1	2	yes	—
405	#385	C₂²×C₁₃	1	2	yes	—
406	#385	C₂²×C₁₃	1	4	yes	—
407	#381	C₂²×C₁₃	1	2	yes	—
408	#379	C₂²×C₁₃	1	2	yes	—
409	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
410	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
411	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
412	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
413	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
414	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
415	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
416	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
417	#376	C₂²×C₁₃	1	2	yes	complemented
418	C₄³	C₂²×C₁₃	1	2	yes	complemented
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	2	no	—
421	C₂²×C₁₃	—	2	8	no	—
422	C₂²×C₁₃	—	2	4	no	—
423	C₂²×C₁₃	—	2	8	no	—
424	C₂²×C₁₃	—	4	16	no	—
425	C₂²×C₁₃	—	4	2	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	4	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	4	no	—
432	C₂²×C₁₃	—	4	4	no	—
433	C₂²×C₁₃	#532	1	4	yes	—
434	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
435	C₂²×C₁₃	C₂²×#41	1	2	yes	—
436	C₂²×C₁₃	C₂²×#41	1	2	yes	—
437	C₂²×C₁₃	#585	1	2	yes	—
438	C₄×C₁₃	—	2	2	no	—
439	C₄×C₁₃	—	2	4	no	—
440	C₄×C₁₃	—	2	2	no	—
441	C₄×C₁₃	—	2	2	no	—
442	C₄×C₁₃	—	2	2	no	—
443	C₄×C₁₃	—	2	2	no	—
444	C₄×C₁₃	—	2	8	no	—
445	C₄×C₁₃	—	4	2	no	—
446	C₄×C₁₃	—	4	2	no	—
447	C₄×C₁₃	—	4	2	no	—
448	C₄×C₁₃	—	4	2	no	—
449	C₄×C₁₃	—	4	2	no	—
450	C₄×C₁₃	—	4	4	no	—
451	C₄×C₁₃	#525	1	4	yes	—
452	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
453	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
455	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
456	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₂³×C₄	—	2	4	no	—
458	C₂³×C₄	—	2	8	no	—
459	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
462	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
463	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
466	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
468	#126	—	2	8	no	—
469	#125	—	2	4	no	—
470	#124	—	2	4	no	—
471	#123	—	2	8	no	—
472	#123	—	2	8	no	—
473	C₂²⋊Q₈	—	2	4	no	—
474	#121	—	2	4	no	—
475	#120	—	2	8	no	—
476	C₄×Q₈	—	2	4	no	—
477	C₄×D₄	—	2	8	no	—
478	C₄×D₄	—	2	16	no	—
479	C₄×D₄	—	2	4	no	—
480	#117	—	2	8	no	—
481	#117	—	2	8	no	—
482	#117	—	2	8	no	—
483	#117	—	2	8	no	—
484	#117	—	2	8	no	—
485	#117	—	2	8	no	—
486	C₂×C₄⋊C₄	—	2	4	no	—
487	C₂×C₄⋊C₄	—	2	4	no	—
488	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
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	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
502	C₂×C₂²⋊C₄	—	2	4	no	—
503	C₂×C₂²⋊C₄	—	2	4	no	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	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	4	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	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₂×C₄²	—	2	4	no	—
522	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
523	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
525	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
526	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
528	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
529	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
534	#95	C₂³×C₁₃	1	4	yes	—
535	#95	C₂³×C₁₃	1	2	yes	—
536	#95	C₂³×C₁₃	1	2	yes	—
537	#95	C₂³×C₁₃	1	4	yes	—
538	#95	C₂³×C₁₃	1	4	yes	—
539	#95	C₂³×C₁₃	1	4	yes	—
540	#95	C₂³×C₁₃	1	4	yes	—
541	#95	C₂³×C₁₃	1	4	yes	—
542	#95	C₂³×C₁₃	1	4	yes	—
543	C₂×C₁₃	—	2	4	no	—
544	C₂×C₁₃	—	4	4	no	—
545	C₂×C₁₃	—	8	2	no	—
546	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
547	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
548	C₂×C₁₃	#3449	1	1	yes	characteristic
549	C₂×C₁₃	#3475	1	4	yes	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	4	2	no	—
554	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
555	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
556	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	4	2	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	8	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂²×C₄	—	2	32	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
585	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
586	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
587	C₂²×C₄	C₁₃×#41	1	8	yes	—
588	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
589	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	8	no	—
613	C₄⋊C₄	—	2	8	no	—
614	C₄⋊C₄	—	2	8	no	—
615	C₄⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	8	no	—
628	C₂²⋊C₄	—	2	8	no	—
629	C₂²⋊C₄	—	2	8	no	—
630	C₂²⋊C₄	—	4	4	no	—
631	C₂²⋊C₄	—	4	4	no	—
632	C₂²⋊C₄	C₁₃×#41	1	8	yes	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	8	no	—
637	C₄²	—	2	8	no	—
638	C₄²	—	4	2	no	—
639	C₄²	—	4	2	no	—
640	C₄²	C₂×D₄×C₁₃	1	4	yes	—
641	C₄²	C₂×D₄×C₁₃	1	4	yes	—
642	C₄²	C₂×D₄×C₁₃	1	4	yes	—
643	C₄²	C₂×D₄×C₁₃	1	4	yes	—
644	C₁₃	#34877	1	1	yes	characteristic, direct product factor, Sylow
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	8	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	4	16	no	—
658	C₂³	—	4	4	no	—
659	C₂³	—	4	4	no	—
660	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
661	C₂³	C₂×C₁₃×#41	1	4	yes	—
662	C₂³	C₂×C₁₃×#41	1	4	yes	—
663	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
664	Q₈	—	4	4	no	—
665	D₄	—	4	16	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	8	no	—
668	C₂×C₄	—	2	16	no	—
669	C₂×C₄	—	2	8	no	—
670	C₂×C₄	—	2	8	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	8	no	—
681	C₂×C₄	—	2	16	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
701	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
706	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
707	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
708	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	8	no	—
712	C₂²	—	2	4	no	—
713	C₂²	—	2	8	no	—
714	C₂²	—	4	16	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	4	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	C₁₃×#532	1	4	yes	—
724	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
725	C₂²	C₂²×C₁₃×#41	1	2	yes	—
726	C₂²	C₂²×C₁₃×#41	1	2	yes	—
727	C₂²	C₁₃×#585	1	2	yes	—
728	C₄	—	2	2	no	—
729	C₄	—	2	4	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	2	8	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	4	no	—
741	C₄	C₁₃×#525	1	4	yes	—
742	C₂	—	2	4	no	—
743	C₂	—	4	4	no	—
744	C₂	—	8	2	no	—
745	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
746	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
747	C₂	C₁₃×#3449	1	1	yes	characteristic
748	C₂	C₁₃×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₁₃×#2539	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#529	C₂	semidirect
2. C₂²×C₁₃×#117	C₂	semidirect
3. C₁₃×#2611	C₂	semidirect
4. C₁₃×#2610	C₂	semidirect
5. C₁₃×#2601	C₂	semidirect
6. C₁₃×#2591	C₂	semidirect
7. C₁₃×#2583	C₂	semidirect
8. C₁₃×#2561	C₂	semidirect
10. C₁₃×#2413	C₂	semidirect
11. C₁₃×#2411	C₂	semidirect
12. C₁₃×#2396	C₂	semidirect
13. C₁₃×#2392	C₂	semidirect
14. C₄×C₁₃×#123	C₂	semidirect
15. C₄×C₁₃×#120	C₂	semidirect
16. C₁₃×#2293	C₂	semidirect
17. C₄×C₁₃×#117	C₂	semidirect
20. C₂×C₁₃×#126	C₂²	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
22. C₂×C₁₃×#124	C₂²	semidirect
28. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
38. C₂×C₁₃×#117	C₂²	semidirect
45. C₁₃×#400	C₂²	semidirect
47. C₁₃×#398	C₂²	semidirect
48. C₁₃×#398	C₂²	semidirect
51. C₁₃×#396	C₂²	semidirect
52. C₁₃×#395	C₂²	semidirect
54. C₁₃×#394	C₂²	semidirect
59. C₁₃×#389	C₂²	semidirect
60. C₁₃×#389	C₂²	semidirect
63. C₁₃×#388	C₂²	semidirect
64. C₁₃×#388	C₂²	semidirect
65. C₁₃×#388	C₂²	semidirect
66. C₁₃×#387	C₂²	semidirect
75. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
76. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
77. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
82. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
83. C₁₃×#376	C₂²	semidirect
84. C₄³×C₁₃	C₂²	semidirect
155. C₂×C₄²×C₁₃	D₄	semidirect
176. #34877	C₁₃	direct (N × H)
271. C₂×#529	C₂×C₁₃	semidirect
272. C₂²×#117	C₂×C₁₃	semidirect
273. #2611	C₂×C₁₃	semidirect
274. #2610	C₂×C₁₃	semidirect
275. #2601	C₂×C₁₃	semidirect
276. #2591	C₂×C₁₃	semidirect
277. #2583	C₂×C₁₃	semidirect
278. #2561	C₂×C₁₃	semidirect
280. #2413	C₂×C₁₃	semidirect
281. #2411	C₂×C₁₃	semidirect
282. #2396	C₂×C₁₃	semidirect
283. #2392	C₂×C₁₃	semidirect
284. C₄×#123	C₂×C₁₃	semidirect
285. C₄×#120	C₂×C₁₃	semidirect
286. #2293	C₂×C₁₃	semidirect
287. C₄×#117	C₂×C₁₃	semidirect
354. C₂×#126	C₂²×C₁₃	semidirect
355. C₂×#125	C₂²×C₁₃	semidirect
356. C₂×#124	C₂²×C₁₃	semidirect
362. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
365. C₂×C₄×D₄	C₂²×C₁₃	semidirect
372. C₂×#117	C₂²×C₁₃	semidirect
379. #400	C₂²×C₁₃	semidirect
381. #398	C₂²×C₁₃	semidirect
382. #398	C₂²×C₁₃	semidirect
385. #396	C₂²×C₁₃	semidirect
386. #395	C₂²×C₁₃	semidirect
388. #394	C₂²×C₁₃	semidirect
393. #389	C₂²×C₁₃	semidirect
394. #389	C₂²×C₁₃	semidirect
397. #388	C₂²×C₁₃	semidirect
398. #388	C₂²×C₁₃	semidirect
399. #388	C₂²×C₁₃	semidirect
400. #387	C₂²×C₁₃	semidirect
409. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
410. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
411. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
416. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
417. #376	C₂²×C₁₃	semidirect
418. C₄³	C₂²×C₁₃	semidirect
522. C₂×C₄²	D₄×C₁₃	semidirect
644. C₁₃	#34877	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×#529	2
C₂²×C₁₃×#117	2
C₁₃×#2611	2
C₁₃×#2610	2
C₁₃×#2601	2
C₁₃×#2591	2
C₁₃×#2583	2
C₁₃×#2561	2
C₁₃×#2539	2
C₁₃×#2413	2
C₁₃×#2411	2
C₁₃×#2396	2
C₁₃×#2392	2
C₄×C₁₃×#123	2
C₄×C₁₃×#120	2
C₁₃×#2293	2
C₄×C₁₃×#117	2
#34877	13

Subgroups — C13×#34877 #15721216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34877 #15721216