Subgroups — C₁₃×#34875 #15721214

Order 3328.

2802 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2609	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2599	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2598	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2579	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2534	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2484	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2482	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2406	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2404	C₂	1	1	yes	maximal, characteristic
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×#2290	C₂	1	4	yes	maximal, complemented
17	C₁₃×#2283	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	C₂×C₁₃×#123	C₂²	1	2	yes	—
21	C₂×C₁₃×#120	C₂²	1	2	yes	—
22	C₄×C₁₃×#41	—	2	8	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#117	—	2	8	no	—
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂×C₁₃×#117	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	2	yes	—
34	C₂×C₁₃×#117	C₂²	1	2	yes	—
35	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
44	C₁₃×#400	C₂²	1	2	yes	complemented
45	C₁₃×#399	C₂²	1	2	yes	—
46	C₁₃×#398	C₂²	1	4	yes	complemented
47	C₁₃×#398	C₂²	1	2	yes	complemented
48	C₁₃×#397	C₂²	1	2	yes	—
49	C₁₃×#396	C₂²	1	4	yes	—
50	C₁₃×#396	C₂²	1	4	yes	complemented
51	C₁₃×#395	C₂²	1	2	yes	complemented
52	C₁₃×#394	C₂²	1	4	yes	—
53	C₁₃×#394	C₂²	1	2	yes	complemented
54	C₁₃×#393	C₂²	1	2	yes	—
55	C₁₃×#392	C₂²	1	2	yes	—
56	C₁₃×#388	C₂²	1	4	yes	—
57	C₁₃×#388	C₂²	1	4	yes	—
58	C₁₃×#388	C₂²	1	4	yes	complemented
59	C₁₃×#387	C₂²	1	4	yes	complemented
60	C₁₃×#387	C₂²	1	4	yes	complemented
61	C₁₃×#387	C₂²	1	4	yes	complemented
62	C₁₃×#386	C₂²	1	4	yes	—
63	C₁₃×#386	C₂²	1	4	yes	—
64	C₁₃×#386	C₂²	1	2	yes	—
65	C₁₃×#386	C₂²	1	4	yes	—
66	C₁₃×#386	C₂²	1	2	yes	—
67	C₁₃×#385	C₂²	1	2	yes	—
68	C₁₃×#385	C₂²	1	4	yes	—
69	C₁₃×#385	C₂²	1	2	yes	—
70	C₁₃×#385	C₂²	1	4	yes	complemented
71	C₁₃×#385	C₂²	1	4	yes	complemented
72	C₁₃×#383	C₂²	1	2	yes	complemented
73	C₁₃×#382	C₂²	1	2	yes	complemented
74	C₁₃×#381	C₂²	1	2	yes	—
75	C₁₃×#381	C₂²	1	1	yes	characteristic
76	C₁₃×#381	C₂²	1	1	yes	characteristic
77	C₁₃×#380	C₂²	1	2	yes	—
78	C₁₃×#379	C₂²	1	2	yes	—
79	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
81	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
84	C₁₃×#376	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×#41	—	2	8	no	—
87	C₂×C₁₃×#41	—	2	4	no	—
88	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	—	2	4	no	—
93	C₂³×C₄×C₁₃	—	2	8	no	—
94	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
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	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
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	—	2	8	no	—
106	C₁₃×#120	—	2	8	no	—
107	C₄×Q₈×C₁₃	—	2	4	no	—
108	C₄×Q₈×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	8	no	—
110	C₄×D₄×C₁₃	—	2	8	no	—
111	C₄×D₄×C₁₃	—	2	16	no	—
112	C₄×D₄×C₁₃	—	2	4	no	—
113	C₄×D₄×C₁₃	—	2	4	no	—
114	C₁₃×#117	—	2	4	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	C₁₃×#117	—	2	8	no	—
120	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
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	2	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	1	yes	characteristic
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
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	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	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₃	—	2	4	no	—
152	C₂×C₄²×C₁₃	—	2	8	no	—
153	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
154	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
158	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₁₃×#95	C₂³	1	4	yes	—
165	C₁₃×#95	C₂³	1	4	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	C₁₃×#95	C₂³	1	2	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	2	yes	—
175	C₁₃×#95	C₂³	1	2	yes	—
176	#34875	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	C₁₃×#41	—	2	32	no	—
185	C₂×Q₈×C₁₃	—	2	2	no	—
186	C₂×Q₈×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	4	no	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	4	no	—
190	C₂×D₄×C₁₃	—	2	8	no	—
191	C₂×D₄×C₁₃	—	2	8	no	—
192	C₂×D₄×C₁₃	—	2	2	no	—
193	C₂×D₄×C₁₃	—	4	4	no	—
194	C₂×D₄×C₁₃	#41	1	8	yes	—
195	C₂²×C₄×C₁₃	—	2	32	no	—
196	C₂²×C₄×C₁₃	—	2	2	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	4	no	—
205	C₂²×C₄×C₁₃	—	2	4	no	—
206	C₂²×C₄×C₁₃	—	2	4	no	—
207	C₂²×C₄×C₁₃	—	2	4	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	4	no	—
211	C₂²×C₄×C₁₃	—	2	4	no	—
212	C₂²×C₄×C₁₃	—	2	4	no	—
213	C₂²×C₄×C₁₃	—	2	8	no	—
214	C₂²×C₄×C₁₃	—	4	2	no	—
215	C₂²×C₄×C₁₃	—	4	4	no	—
216	C₂²×C₄×C₁₃	—	4	2	no	—
217	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
218	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
219	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
220	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
221	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
223	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	4	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	4	no	—
241	C₁₃×C₄⋊C₄	—	2	2	no	—
242	C₁₃×C₄⋊C₄	—	2	2	no	—
243	C₁₃×C₄⋊C₄	—	2	8	no	—
244	C₁₃×C₄⋊C₄	—	2	8	no	—
245	C₁₃×C₄⋊C₄	—	4	4	no	—
246	C₁₃×C₄⋊C₄	—	4	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	8	no	—
249	C₁₃×C₂²⋊C₄	—	2	4	no	—
250	C₁₃×C₂²⋊C₄	—	2	4	no	—
251	C₁₃×C₂²⋊C₄	—	2	8	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	—	2	4	no	—
256	C₁₃×C₂²⋊C₄	—	2	4	no	—
257	C₁₃×C₂²⋊C₄	—	2	4	no	—
258	C₁₃×C₂²⋊C₄	—	2	8	no	—
259	C₁₃×C₂²⋊C₄	—	2	8	no	—
260	C₁₃×C₂²⋊C₄	—	4	4	no	—
261	C₁₃×C₂²⋊C₄	—	4	4	no	—
262	C₄²×C₁₃	—	2	4	no	—
263	C₄²×C₁₃	—	2	4	no	—
264	C₄²×C₁₃	—	2	4	no	—
265	C₄²×C₁₃	—	2	4	no	—
266	C₄²×C₁₃	—	2	4	no	—
267	C₄²×C₁₃	—	2	8	no	—
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	C₄²×C₁₃	C₂×D₄	1	4	yes	—
272	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2609	C₂×C₁₃	1	4	yes	complemented
275	#2599	C₂×C₁₃	1	2	yes	complemented
276	#2598	C₂×C₁₃	1	2	yes	complemented
277	#2579	C₂×C₁₃	1	2	yes	complemented
278	#2534	C₂×C₁₃	1	2	yes	complemented
279	#2484	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2482	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#2406	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#2404	C₂×C₁₃	1	1	yes	characteristic
283	#2396	C₂×C₁₃	1	2	yes	complemented
284	#2392	C₂×C₁₃	1	2	yes	complemented
285	C₄×#123	C₂×C₁₃	1	2	yes	complemented
286	C₄×#120	C₂×C₁₃	1	2	yes	complemented
287	#2290	C₂×C₁₃	1	4	yes	complemented
288	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂³×C₁₃	—	2	2	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	8	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	4	no	—
295	C₂³×C₁₃	—	2	4	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	4	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	C₂×#41	1	4	yes	—
307	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
308	Q₈×C₁₃	—	2	8	no	—
309	D₄×C₁₃	—	2	8	no	—
310	D₄×C₁₃	—	2	16	no	—
311	D₄×C₁₃	—	4	16	no	—
312	C₂×C₄×C₁₃	—	2	16	no	—
313	C₂×C₄×C₁₃	—	2	8	no	—
314	C₂×C₄×C₁₃	—	2	16	no	—
315	C₂×C₄×C₁₃	—	2	8	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	2	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	2	no	—
325	C₂×C₄×C₁₃	—	2	8	no	—
326	C₂×C₄×C₁₃	—	2	16	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	2	no	—
331	C₂×C₄×C₁₃	—	2	4	no	—
332	C₂×C₄×C₁₃	—	2	4	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	4	no	—
337	C₂×C₄×C₁₃	—	2	4	no	—
338	C₂×C₄×C₁₃	—	2	4	no	—
339	C₂×C₄×C₁₃	—	2	4	no	—
340	C₂×C₄×C₁₃	—	2	4	no	—
341	C₂×C₄×C₁₃	—	4	4	no	—
342	C₂×C₄×C₁₃	—	4	8	no	—
343	C₂×C₄×C₁₃	—	4	4	no	—
344	C₂×C₄×C₁₃	—	4	4	no	—
345	C₂×C₄×C₁₃	—	4	8	no	—
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	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
353	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
354	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
355	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
356	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#123	C₂²×C₁₃	1	2	yes	—
358	C₂×#120	C₂²×C₁₃	1	2	yes	—
359	C₄×#41	—	2	8	no	—
360	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
361	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
362	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
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×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
367	C₂×#117	—	2	8	no	—
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	1	yes	characteristic
373	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
374	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
375	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
376	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
380	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
381	#400	C₂²×C₁₃	1	2	yes	complemented
382	#399	C₂²×C₁₃	1	2	yes	—
383	#398	C₂²×C₁₃	1	4	yes	complemented
384	#398	C₂²×C₁₃	1	2	yes	complemented
385	#397	C₂²×C₁₃	1	2	yes	—
386	#396	C₂²×C₁₃	1	4	yes	—
387	#396	C₂²×C₁₃	1	4	yes	complemented
388	#395	C₂²×C₁₃	1	2	yes	complemented
389	#394	C₂²×C₁₃	1	4	yes	—
390	#394	C₂²×C₁₃	1	2	yes	complemented
391	#393	C₂²×C₁₃	1	2	yes	—
392	#392	C₂²×C₁₃	1	2	yes	—
393	#388	C₂²×C₁₃	1	4	yes	—
394	#388	C₂²×C₁₃	1	4	yes	—
395	#388	C₂²×C₁₃	1	4	yes	complemented
396	#387	C₂²×C₁₃	1	4	yes	complemented
397	#387	C₂²×C₁₃	1	4	yes	complemented
398	#387	C₂²×C₁₃	1	4	yes	complemented
399	#386	C₂²×C₁₃	1	2	yes	—
400	#386	C₂²×C₁₃	1	2	yes	—
401	#386	C₂²×C₁₃	1	4	yes	—
402	#386	C₂²×C₁₃	1	4	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	#385	C₂²×C₁₃	1	4	yes	complemented
408	#385	C₂²×C₁₃	1	4	yes	complemented
409	#383	C₂²×C₁₃	1	2	yes	complemented
410	#382	C₂²×C₁₃	1	2	yes	complemented
411	#381	C₂²×C₁₃	1	1	yes	characteristic
412	#381	C₂²×C₁₃	1	1	yes	characteristic
413	#381	C₂²×C₁₃	1	2	yes	—
414	#380	C₂²×C₁₃	1	2	yes	—
415	#379	C₂²×C₁₃	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
417	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
418	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
421	#376	C₂²×C₁₃	1	2	yes	complemented
422	C₂²×C₁₃	—	2	2	no	—
423	C₂²×C₁₃	—	2	2	no	—
424	C₂²×C₁₃	—	2	8	no	—
425	C₂²×C₁₃	—	2	4	no	—
426	C₂²×C₁₃	—	2	4	no	—
427	C₂²×C₁₃	—	2	8	no	—
428	C₂²×C₁₃	—	2	8	no	—
429	C₂²×C₁₃	—	4	16	no	—
430	C₂²×C₁₃	—	4	2	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	2	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	4	no	—
435	C₂²×C₁₃	—	4	4	no	—
436	C₂²×C₁₃	#525	1	4	yes	—
437	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
438	C₂²×C₁₃	C₂²×#41	1	2	yes	—
439	C₂²×C₁₃	C₂²×#41	1	2	yes	—
440	C₂²×C₁₃	#585	1	2	yes	—
441	C₄×C₁₃	—	2	2	no	—
442	C₄×C₁₃	—	2	2	no	—
443	C₄×C₁₃	—	2	4	no	—
444	C₄×C₁₃	—	2	2	no	—
445	C₄×C₁₃	—	2	4	no	—
446	C₄×C₁₃	—	2	2	no	—
447	C₄×C₁₃	—	2	2	no	—
448	C₄×C₁₃	—	4	2	no	—
449	C₄×C₁₃	—	4	2	no	—
450	C₄×C₁₃	—	4	2	no	—
451	C₄×C₁₃	—	4	2	no	—
452	C₄×C₁₃	—	4	4	no	—
453	C₄×C₁₃	—	4	4	no	—
454	C₄×C₁₃	#525	1	4	yes	—
455	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×#41	—	2	8	no	—
457	C₂×#41	—	2	4	no	—
458	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
461	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
462	C₂³×C₄	—	2	4	no	—
463	C₂³×C₄	—	2	8	no	—
464	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
467	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
468	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
469	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
474	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
475	#123	—	2	8	no	—
476	#120	—	2	8	no	—
477	C₄×Q₈	—	2	4	no	—
478	C₄×Q₈	—	2	4	no	—
479	C₄×D₄	—	2	8	no	—
480	C₄×D₄	—	2	8	no	—
481	C₄×D₄	—	2	16	no	—
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	—	2	4	no	—
484	#117	—	2	4	no	—
485	#117	—	2	8	no	—
486	#117	—	2	8	no	—
487	#117	—	2	8	no	—
488	#117	—	2	8	no	—
489	#117	—	2	8	no	—
490	C₂×C₄⋊C₄	—	2	4	no	—
491	C₂×C₄⋊C₄	—	2	4	no	—
492	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	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	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
504	C₂×C₂²⋊C₄	—	2	4	no	—
505	C₂×C₂²⋊C₄	—	2	4	no	—
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	2	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	4	yes	—
521	C₂×C₄²	—	2	4	no	—
522	C₂×C₄²	—	2	8	no	—
523	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
524	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
525	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
526	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
527	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
529	C₂×C₄²	C₂³×C₁₃	1	4	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	2	yes	—
543	#95	C₂³×C₁₃	1	2	yes	—
544	#95	C₂³×C₁₃	1	4	yes	—
545	#95	C₂³×C₁₃	1	4	yes	—
546	C₂×C₁₃	—	2	4	no	—
547	C₂×C₁₃	—	4	4	no	—
548	C₂×C₁₃	—	4	4	no	—
549	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
550	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
551	C₂×C₁₃	#3449	1	1	yes	characteristic
552	C₂×C₁₃	#3475	1	4	yes	—
553	C₂⁴	—	2	2	no	—
554	C₂⁴	—	2	4	no	—
555	C₂⁴	—	2	4	no	—
556	C₂⁴	—	4	2	no	—
557	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
558	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
559	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
560	#41	—	2	32	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	8	no	—
567	C₂×D₄	—	2	8	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	C₁₃×#41	1	8	yes	—
571	C₂²×C₄	—	2	32	no	—
572	C₂²×C₄	—	2	2	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	4	no	—
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	4	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	8	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
594	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
595	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
596	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
597	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	8	no	—
620	C₄⋊C₄	—	2	8	no	—
621	C₄⋊C₄	—	4	4	no	—
622	C₄⋊C₄	—	4	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	8	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	8	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	8	no	—
635	C₂²⋊C₄	—	2	8	no	—
636	C₂²⋊C₄	—	4	4	no	—
637	C₂²⋊C₄	—	4	4	no	—
638	C₄²	—	2	4	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	8	no	—
644	C₄²	C₂×D₄×C₁₃	1	4	yes	—
645	C₄²	C₂×D₄×C₁₃	1	4	yes	—
646	C₄²	C₂×D₄×C₁₃	1	4	yes	—
647	C₄²	C₂×D₄×C₁₃	1	4	yes	—
648	C₁₃	#34875	1	1	yes	characteristic, direct product factor, Sylow
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	8	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	4	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	4	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	4	16	no	—
661	C₂³	—	4	4	no	—
662	C₂³	—	4	4	no	—
663	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
664	C₂³	C₂×C₁₃×#41	1	4	yes	—
665	C₂³	C₂×C₁₃×#41	1	4	yes	—
666	C₂³	C₂×C₁₃×#41	1	4	yes	—
667	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
668	Q₈	—	2	8	no	—
669	D₄	—	2	8	no	—
670	D₄	—	2	16	no	—
671	D₄	—	4	16	no	—
672	C₂×C₄	—	2	16	no	—
673	C₂×C₄	—	2	8	no	—
674	C₂×C₄	—	2	16	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	8	no	—
686	C₂×C₄	—	2	16	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
708	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
710	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
711	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
712	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
713	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
714	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	8	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	8	no	—
721	C₂²	—	2	8	no	—
722	C₂²	—	4	16	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	4	no	—
729	C₂²	C₁₃×#525	1	4	yes	—
730	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
731	C₂²	C₂²×C₁₃×#41	1	2	yes	—
732	C₂²	C₂²×C₁₃×#41	1	2	yes	—
733	C₂²	C₁₃×#585	1	2	yes	—
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	4	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	4	no	—
746	C₄	—	4	4	no	—
747	C₄	C₁₃×#525	1	4	yes	—
748	C₂	—	2	4	no	—
749	C₂	—	4	4	no	—
750	C₂	—	4	4	no	—
751	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
752	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
753	C₂	C₁₃×#3449	1	1	yes	characteristic
754	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×#2404	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×C₄×C₁₃×#41	C₂	semidirect
2. C₂²×C₁₃×#117	C₂	semidirect
3. C₁₃×#2609	C₂	semidirect
4. C₁₃×#2599	C₂	semidirect
5. C₁₃×#2598	C₂	semidirect
6. C₁₃×#2579	C₂	semidirect
7. C₁₃×#2534	C₂	semidirect
8. C₁₃×#2484	C₂	semidirect
9. C₁₃×#2482	C₂	semidirect
10. C₁₃×#2406	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×#2290	C₂	semidirect
17. C₁₃×#2283	C₂	semidirect
23. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃	C₂²	semidirect
36. C₂×C₁₃×#117	C₂²	semidirect
43. C₂²×C₄²×C₁₃	C₂²	semidirect
44. C₁₃×#400	C₂²	semidirect
46. C₁₃×#398	C₂²	semidirect
47. C₁₃×#398	C₂²	semidirect
50. C₁₃×#396	C₂²	semidirect
51. C₁₃×#395	C₂²	semidirect
53. C₁₃×#394	C₂²	semidirect
58. C₁₃×#388	C₂²	semidirect
59. C₁₃×#387	C₂²	semidirect
60. C₁₃×#387	C₂²	semidirect
61. C₁₃×#387	C₂²	semidirect
70. C₁₃×#385	C₂²	semidirect
71. C₁₃×#385	C₂²	semidirect
72. C₁₃×#383	C₂²	semidirect
73. C₁₃×#382	C₂²	semidirect
79. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
80. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
83. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
84. C₁₃×#376	C₂²	semidirect
153. C₂×C₄²×C₁₃	D₄	semidirect
176. #34875	C₁₃	direct (N × H)
220. C₂²×C₄×C₁₃	#41	semidirect
272. C₂×C₄×#41	C₂×C₁₃	semidirect
273. C₂²×#117	C₂×C₁₃	semidirect
274. #2609	C₂×C₁₃	semidirect
275. #2599	C₂×C₁₃	semidirect
276. #2598	C₂×C₁₃	semidirect
277. #2579	C₂×C₁₃	semidirect
278. #2534	C₂×C₁₃	semidirect
279. #2484	C₂×C₁₃	semidirect
280. #2482	C₂×C₁₃	semidirect
281. #2406	C₂×C₁₃	semidirect
283. #2396	C₂×C₁₃	semidirect
284. #2392	C₂×C₁₃	semidirect
285. C₄×#123	C₂×C₁₃	semidirect
286. C₄×#120	C₂×C₁₃	semidirect
287. #2290	C₂×C₁₃	semidirect
288. #2283	C₂×C₁₃	semidirect
360. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
361. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
365. C₂×C₄×D₄	C₂²×C₁₃	semidirect
366. C₂×C₄×D₄	C₂²×C₁₃	semidirect
373. C₂×#117	C₂²×C₁₃	semidirect
380. C₂²×C₄²	C₂²×C₁₃	semidirect
381. #400	C₂²×C₁₃	semidirect
383. #398	C₂²×C₁₃	semidirect
384. #398	C₂²×C₁₃	semidirect
387. #396	C₂²×C₁₃	semidirect
388. #395	C₂²×C₁₃	semidirect
390. #394	C₂²×C₁₃	semidirect
395. #388	C₂²×C₁₃	semidirect
396. #387	C₂²×C₁₃	semidirect
397. #387	C₂²×C₁₃	semidirect
398. #387	C₂²×C₁₃	semidirect
407. #385	C₂²×C₁₃	semidirect
408. #385	C₂²×C₁₃	semidirect
409. #383	C₂²×C₁₃	semidirect
410. #382	C₂²×C₁₃	semidirect
416. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
417. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
420. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
421. #376	C₂²×C₁₃	semidirect
523. C₂×C₄²	D₄×C₁₃	semidirect
596. C₂²×C₄	C₁₃×#41	semidirect
648. C₁₃	#34875	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×C₄×C₁₃×#41	2
C₂²×C₁₃×#117	2
C₁₃×#2609	2
C₁₃×#2599	2
C₁₃×#2598	2
C₁₃×#2579	2
C₁₃×#2534	2
C₁₃×#2484	2
C₁₃×#2482	2
C₁₃×#2406	2
C₁₃×#2404	2
C₁₃×#2396	2
C₁₃×#2392	2
C₄×C₁₃×#123	2
C₄×C₁₃×#120	2
C₁₃×#2290	2
C₁₃×#2283	2
#34875	13

Subgroups — C13×#34875 #15721214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34875 #15721214