Subgroups — C₁₃×#34223 #15720562

Order 3328.

2698 conjugacy classes of subgroups.

The subgroup lattice has 766 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×#2374	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2363	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2362	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2357	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2353	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×#2321	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	C₁₃×#2280	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	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#117	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	2	yes	complemented
37	C₁₃×#390	C₂²	1	4	yes	—
38	C₁₃×#390	C₂²	1	4	yes	—
39	C₁₃×#390	C₂²	1	2	yes	complemented
40	C₁₃×#389	C₂²	1	2	yes	complemented
41	C₁₃×#389	C₂²	1	2	yes	complemented
42	C₁₃×#388	C₂²	1	4	yes	—
43	C₁₃×#388	C₂²	1	4	yes	—
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×#383	C₂²	1	2	yes	complemented
55	C₁₃×#382	C₂²	1	2	yes	complemented
56	C₁₃×#381	C₂²	1	2	yes	—
57	C₁₃×#381	C₂²	1	2	yes	complemented
58	C₁₃×#380	C₂²	1	2	yes	—
59	C₁₃×#380	C₂²	1	1	yes	characteristic
60	C₁₃×#380	C₂²	1	1	yes	characteristic
61	C₁₃×#380	C₂²	1	2	yes	complemented
62	C₁₃×#379	C₂²	1	2	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
68	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
80	C₁₃×#376	C₂²	1	2	yes	complemented
81	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
82	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
90	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	C₂³	1	4	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	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
104	C₁₃×#123	C₂×C₄	1	16	yes	complemented
105	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
106	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
107	C₁₃×#121	C₂×C₄	1	8	yes	—
108	C₁₃×#121	C₂×C₄	1	8	yes	complemented
109	C₁₃×#120	C₂×C₄	1	16	yes	complemented
110	C₄×Q₈×C₁₃	—	4	4	no	—
111	C₄×D₄×C₁₃	—	2	16	no	—
112	C₄×D₄×C₁₃	—	4	4	no	—
113	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
114	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
115	C₁₃×#117	—	4	4	no	—
116	C₁₃×#117	C₂×C₄	1	8	yes	complemented
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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×C₄²×C₁₃	—	4	4	no	—
144	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
147	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
152	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
153	C₁₃×#95	C₂³	1	1	yes	characteristic
154	C₁₃×#95	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	2	yes	—
158	C₁₃×#95	C₂³	1	1	yes	characteristic
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	2	yes	—
161	C₁₃×#95	C₂³	1	4	yes	—
162	C₁₃×#95	C₂³	1	2	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
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	#34223	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂⁴×C₁₃	—	2	4	no	—
170	C₂⁴×C₁₃	—	4	2	no	—
171	C₂⁴×C₁₃	—	4	1	no	—
172	C₂⁴×C₁₃	—	4	1	no	—
173	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
174	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
177	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₁₃×#41	—	4	16	no	—
179	C₂×Q₈×C₁₃	—	2	4	no	—
180	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
181	C₂×D₄×C₁₃	—	2	8	no	—
182	C₂×D₄×C₁₃	—	2	4	no	—
183	C₂×D₄×C₁₃	—	4	2	no	—
184	C₂×D₄×C₁₃	—	4	2	no	—
185	C₂×D₄×C₁₃	—	4	4	no	—
186	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
187	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
188	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
189	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
190	C₂²×C₄×C₁₃	—	2	4	no	—
191	C₂²×C₄×C₁₃	—	2	4	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	2	4	no	—
194	C₂²×C₄×C₁₃	—	2	8	no	—
195	C₂²×C₄×C₁₃	—	4	16	no	—
196	C₂²×C₄×C₁₃	—	4	2	no	—
197	C₂²×C₄×C₁₃	—	4	2	no	—
198	C₂²×C₄×C₁₃	—	4	2	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	4	no	—
204	C₂²×C₄×C₁₃	—	4	4	no	—
205	C₂²×C₄×C₁₃	—	4	4	no	—
206	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
207	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
208	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
209	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
210	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
211	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
212	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
213	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
214	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	2	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	1	yes	characteristic
227	C₁₃×C₄⋊C₄	—	2	8	no	—
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	4	4	no	—
231	C₁₃×C₄⋊C₄	—	4	4	no	—
232	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
233	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
234	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
235	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
236	C₁₃×C₂²⋊C₄	—	2	8	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	2	4	no	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	8	no	—
242	C₁₃×C₂²⋊C₄	—	4	2	no	—
243	C₁₃×C₂²⋊C₄	—	4	2	no	—
244	C₁₃×C₂²⋊C₄	—	4	4	no	—
245	C₁₃×C₂²⋊C₄	—	4	4	no	—
246	C₁₃×C₂²⋊C₄	—	4	4	no	—
247	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
248	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
249	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
250	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
251	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
252	C₄²×C₁₃	—	2	8	no	—
253	C₄²×C₁₃	—	2	4	no	—
254	C₄²×C₁₃	—	2	4	no	—
255	C₄²×C₁₃	—	4	2	no	—
256	C₄²×C₁₃	—	4	2	no	—
257	C₄²×C₁₃	—	4	4	no	—
258	C₄²×C₁₃	—	4	4	no	—
259	C₄²×C₁₃	—	4	4	no	—
260	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
261	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
262	#2374	C₂×C₁₃	1	4	yes	complemented
263	#2363	C₂×C₁₃	1	2	yes	complemented
264	#2362	C₂×C₁₃	1	2	yes	complemented
265	#2357	C₂×C₁₃	1	2	yes	complemented
266	#2353	C₂×C₁₃	1	2	yes	complemented
267	#2347	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#2346	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#2341	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#2339	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#2321	C₂×C₁₃	1	4	yes	complemented
272	#2318	C₂×C₁₃	1	2	yes	complemented
273	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
274	C₄×#121	C₂×C₁₃	1	2	yes	complemented
275	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#2275	C₂×C₁₃	1	2	yes	complemented
277	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂³×C₁₃	—	2	2	no	—
279	C₂³×C₁₃	—	2	1	no	—
280	C₂³×C₁₃	—	2	1	no	—
281	C₂³×C₁₃	—	2	8	no	—
282	C₂³×C₁₃	—	2	2	no	—
283	C₂³×C₁₃	—	2	2	no	—
284	C₂³×C₁₃	—	2	4	no	—
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	—	2	4	no	—
287	C₂³×C₁₃	—	2	2	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	1	no	—
290	C₂³×C₁₃	—	2	1	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	1	no	—
293	C₂³×C₁₃	—	2	1	no	—
294	C₂³×C₁₃	—	4	4	no	—
295	C₂³×C₁₃	—	4	4	no	—
296	C₂³×C₁₃	—	4	8	no	—
297	C₂³×C₁₃	—	4	8	no	—
298	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
299	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
300	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
301	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
302	C₂³×C₁₃	C₂×#41	1	4	yes	—
303	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
304	Q₈×C₁₃	—	2	8	no	—
305	D₄×C₁₃	—	2	16	no	—
306	D₄×C₁₃	—	2	8	no	—
307	D₄×C₁₃	—	4	8	no	—
308	D₄×C₁₃	—	4	8	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	4	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	2	no	—
320	C₂×C₄×C₁₃	—	2	8	no	—
321	C₂×C₄×C₁₃	—	2	8	no	—
322	C₂×C₄×C₁₃	—	2	8	no	—
323	C₂×C₄×C₁₃	—	2	4	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	4	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	4	no	—
330	C₂×C₄×C₁₃	—	2	4	no	—
331	C₂×C₄×C₁₃	—	2	4	no	—
332	C₂×C₄×C₁₃	—	2	4	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	4	4	no	—
336	C₂×C₄×C₁₃	—	4	4	no	—
337	C₂×C₄×C₁₃	—	4	4	no	—
338	C₂×C₄×C₁₃	—	4	8	no	—
339	C₂×C₄×C₁₃	—	4	8	no	—
340	C₂×C₄×C₁₃	—	4	8	no	—
341	C₂×C₄×C₁₃	—	8	8	no	—
342	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
343	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
344	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
345	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
346	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
347	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
348	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
349	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
350	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
351	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
352	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
353	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
354	#525	C₄×C₁₃	1	16	yes	complemented
355	C₂×#123	C₂²×C₁₃	1	2	yes	—
356	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#120	C₂²×C₁₃	1	2	yes	—
361	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
362	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
363	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
364	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
365	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
366	C₂×#117	C₂²×C₁₃	1	2	yes	—
367	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
368	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
369	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
370	#391	C₂²×C₁₃	1	2	yes	complemented
371	#390	C₂²×C₁₃	1	4	yes	—
372	#390	C₂²×C₁₃	1	4	yes	—
373	#390	C₂²×C₁₃	1	2	yes	complemented
374	#389	C₂²×C₁₃	1	2	yes	complemented
375	#389	C₂²×C₁₃	1	2	yes	complemented
376	#388	C₂²×C₁₃	1	4	yes	—
377	#388	C₂²×C₁₃	1	4	yes	—
378	#388	C₂²×C₁₃	1	4	yes	—
379	#388	C₂²×C₁₃	1	4	yes	—
380	#388	C₂²×C₁₃	1	4	yes	complemented
381	#388	C₂²×C₁₃	1	4	yes	complemented
382	#387	C₂²×C₁₃	1	4	yes	complemented
383	#387	C₂²×C₁₃	1	4	yes	complemented
384	#386	C₂²×C₁₃	1	4	yes	—
385	#386	C₂²×C₁₃	1	4	yes	—
386	#386	C₂²×C₁₃	1	4	yes	—
387	#385	C₂²×C₁₃	1	4	yes	—
388	#383	C₂²×C₁₃	1	2	yes	complemented
389	#382	C₂²×C₁₃	1	2	yes	complemented
390	#381	C₂²×C₁₃	1	2	yes	—
391	#381	C₂²×C₁₃	1	2	yes	complemented
392	#380	C₂²×C₁₃	1	1	yes	characteristic
393	#380	C₂²×C₁₃	1	1	yes	characteristic
394	#380	C₂²×C₁₃	1	2	yes	—
395	#380	C₂²×C₁₃	1	2	yes	complemented
396	#379	C₂²×C₁₃	1	2	yes	—
397	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
398	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
399	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
400	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
401	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
402	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
403	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
404	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
405	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
406	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
407	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
410	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
412	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
413	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
414	#376	C₂²×C₁₃	1	2	yes	complemented
415	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	4	no	—
421	C₂²×C₁₃	—	2	4	no	—
422	C₂²×C₁₃	—	2	4	no	—
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	2	no	—
429	C₂²×C₁₃	—	2	4	no	—
430	C₂²×C₁₃	—	2	2	no	—
431	C₂²×C₁₃	—	4	16	no	—
432	C₂²×C₁₃	—	4	4	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	2	no	—
435	C₂²×C₁₃	—	4	4	no	—
436	C₂²×C₁₃	—	4	2	no	—
437	C₂²×C₁₃	—	4	2	no	—
438	C₂²×C₁₃	C₄×#41	1	4	yes	—
439	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
440	C₂²×C₁₃	C₂²×#41	1	2	yes	—
441	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
442	C₂²×C₁₃	#585	1	1	yes	characteristic
443	C₂²×C₁₃	#585	1	1	yes	characteristic
444	C₄×C₁₃	—	2	4	no	—
445	C₄×C₁₃	—	2	2	no	—
446	C₄×C₁₃	—	2	2	no	—
447	C₄×C₁₃	—	2	2	no	—
448	C₄×C₁₃	—	2	4	no	—
449	C₄×C₁₃	—	2	4	no	—
450	C₄×C₁₃	—	2	4	no	—
451	C₄×C₁₃	—	2	4	no	—
452	C₄×C₁₃	—	4	4	no	—
453	C₄×C₁₃	—	4	4	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	4	2	no	—
456	C₄×C₁₃	#518	1	4	yes	—
457	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×#41	—	4	4	no	—
459	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
460	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
462	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
464	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
465	C₂³×C₄	—	4	4	no	—
466	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
467	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
471	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
472	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
475	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
477	#123	C₂×C₄×C₁₃	1	16	yes	complemented
478	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
479	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
480	#121	C₂×C₄×C₁₃	1	8	yes	—
481	#121	C₂×C₄×C₁₃	1	8	yes	complemented
482	#120	C₂×C₄×C₁₃	1	16	yes	complemented
483	C₄×Q₈	—	4	4	no	—
484	C₄×D₄	—	2	16	no	—
485	C₄×D₄	—	4	4	no	—
486	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
487	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
488	#117	—	4	4	no	—
489	#117	C₂×C₄×C₁₃	1	8	yes	complemented
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	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
499	C₂×C₂²⋊C₄	—	2	8	no	—
500	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	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	4	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	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂×C₄²	—	4	4	no	—
517	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
518	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
519	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
520	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
521	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
522	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
523	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
525	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
526	#95	C₂³×C₁₃	1	1	yes	characteristic
527	#95	C₂³×C₁₃	1	1	yes	characteristic
528	#95	C₂³×C₁₃	1	2	yes	—
529	#95	C₂³×C₁₃	1	1	yes	characteristic
530	#95	C₂³×C₁₃	1	1	yes	characteristic
531	#95	C₂³×C₁₃	1	2	yes	—
532	#95	C₂³×C₁₃	1	2	yes	—
533	#95	C₂³×C₁₃	1	4	yes	—
534	#95	C₂³×C₁₃	1	2	yes	—
535	#95	C₂³×C₁₃	1	4	yes	—
536	#95	C₂³×C₁₃	1	4	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	C₂×C₁₃	—	2	4	no	—
542	C₂×C₁₃	—	4	4	no	—
543	C₂×C₁₃	—	4	2	no	—
544	C₂×C₁₃	—	4	2	no	—
545	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
546	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
547	C₂×C₁₃	#3428	1	1	yes	characteristic
548	C₂×C₁₃	#3505	1	2	yes	—
549	C₂×C₁₃	#3506	1	2	yes	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	4	2	no	—
552	C₂⁴	—	4	1	no	—
553	C₂⁴	—	4	1	no	—
554	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
555	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
556	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
557	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
558	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
559	#41	—	4	16	no	—
560	C₂×Q₈	—	2	4	no	—
561	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
562	C₂×D₄	—	2	8	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	4	4	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
568	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
569	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
570	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
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	8	no	—
576	C₂²×C₄	—	4	16	no	—
577	C₂²×C₄	—	4	2	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	4	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
588	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
589	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
590	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
591	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
592	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
593	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
594	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
595	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
598	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
608	C₄⋊C₄	—	2	8	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	4	4	no	—
612	C₄⋊C₄	—	4	4	no	—
613	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
614	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
615	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
616	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
629	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
630	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
631	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
632	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
633	C₄²	—	2	8	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	4	2	no	—
637	C₄²	—	4	2	no	—
638	C₄²	—	4	4	no	—
639	C₄²	—	4	4	no	—
640	C₄²	—	4	4	no	—
641	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
642	C₁₃	#34223	1	1	yes	characteristic, direct product factor, Sylow
643	C₂³	—	2	2	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	8	no	—
647	C₂³	—	2	2	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	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	4	no	—
661	C₂³	—	4	8	no	—
662	C₂³	—	4	8	no	—
663	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
664	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
665	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
666	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
667	C₂³	C₂×C₁₃×#41	1	4	yes	—
668	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
669	Q₈	—	2	8	no	—
670	D₄	—	2	16	no	—
671	D₄	—	2	8	no	—
672	D₄	—	4	8	no	—
673	D₄	—	4	8	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	4	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	8	no	—
687	C₂×C₄	—	2	8	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	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	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	4	4	no	—
703	C₂×C₄	—	4	8	no	—
704	C₂×C₄	—	4	8	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	—	8	8	no	—
707	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
708	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
709	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
710	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
711	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
712	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
713	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
714	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
715	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
716	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	4	16	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	C₄×C₁₃×#41	1	4	yes	—
738	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
739	C₂²	C₂²×C₁₃×#41	1	2	yes	—
740	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
741	C₂²	C₁₃×#585	1	1	yes	characteristic
742	C₂²	C₁₃×#585	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	4	no	—
750	C₄	—	2	4	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	4	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	C₁₃×#518	1	4	yes	—
756	C₂	—	2	4	no	—
757	C₂	—	4	2	no	—
758	C₂	—	4	2	no	—
759	C₂	—	4	4	no	—
760	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
761	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
762	C₂	C₁₃×#3428	1	1	yes	characteristic
763	C₂	C₁₃×#3505	1	2	yes	—
764	C₂	C₁₃×#3506	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×#2374	C₂	semidirect
3. C₁₃×#2363	C₂	semidirect
4. C₁₃×#2362	C₂	semidirect
5. C₁₃×#2357	C₂	semidirect
6. C₁₃×#2353	C₂	semidirect
7. C₁₃×#2347	C₂	semidirect
8. C₁₃×#2346	C₂	semidirect
9. C₁₃×#2341	C₂	semidirect
10. C₁₃×#2339	C₂	semidirect
11. C₁₃×#2321	C₂	semidirect
12. C₁₃×#2318	C₂	semidirect
13. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₄×C₁₃×#121	C₂	semidirect
15. C₁₃×#2280	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
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
36. C₁₃×#391	C₂²	semidirect
39. C₁₃×#390	C₂²	semidirect
40. C₁₃×#389	C₂²	semidirect
41. C₁₃×#389	C₂²	semidirect
46. C₁₃×#388	C₂²	semidirect
47. C₁₃×#388	C₂²	semidirect
48. C₁₃×#387	C₂²	semidirect
49. C₁₃×#387	C₂²	semidirect
54. C₁₃×#383	C₂²	semidirect
55. C₁₃×#382	C₂²	semidirect
57. C₁₃×#381	C₂²	semidirect
61. C₁₃×#380	C₂²	semidirect
63. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
64. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
65. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
66. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
67. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
77. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
78. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
79. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
80. C₁₃×#376	C₂²	semidirect
83. C₂×C₁₃×#95	C₂²	semidirect
86. C₂×C₁₃×#41	C₂×C₄	semidirect
93. C₂³×C₄×C₁₃	C₂×C₄	semidirect
104. C₁₃×#123	C₂×C₄	semidirect
105. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
106. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
108. C₁₃×#121	C₂×C₄	semidirect
109. C₁₃×#120	C₂×C₄	semidirect
113. C₄×D₄×C₁₃	C₂×C₄	semidirect
114. C₄×D₄×C₁₃	C₂×C₄	semidirect
116. C₁₃×#117	C₂×C₄	semidirect
168. #34223	C₁₃	direct (N × H)
213. C₂²×C₄×C₁₃	#41	semidirect
262. #2374	C₂×C₁₃	semidirect
263. #2363	C₂×C₁₃	semidirect
264. #2362	C₂×C₁₃	semidirect
265. #2357	C₂×C₁₃	semidirect
266. #2353	C₂×C₁₃	semidirect
267. #2347	C₂×C₁₃	semidirect
268. #2346	C₂×C₁₃	semidirect
269. #2341	C₂×C₁₃	semidirect
270. #2339	C₂×C₁₃	semidirect
271. #2321	C₂×C₁₃	semidirect
272. #2318	C₂×C₁₃	semidirect
273. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
274. C₄×#121	C₂×C₁₃	semidirect
275. #2280	C₂×C₁₃	semidirect
276. #2275	C₂×C₁₃	semidirect
277. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
354. #525	C₄×C₁₃	semidirect
361. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
365. C₂×C₄×D₄	C₂²×C₁₃	semidirect
370. #391	C₂²×C₁₃	semidirect
373. #390	C₂²×C₁₃	semidirect
374. #389	C₂²×C₁₃	semidirect
375. #389	C₂²×C₁₃	semidirect
380. #388	C₂²×C₁₃	semidirect
381. #388	C₂²×C₁₃	semidirect
382. #387	C₂²×C₁₃	semidirect
383. #387	C₂²×C₁₃	semidirect
388. #383	C₂²×C₁₃	semidirect
389. #382	C₂²×C₁₃	semidirect
391. #381	C₂²×C₁₃	semidirect
395. #380	C₂²×C₁₃	semidirect
397. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
398. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
399. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
400. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
401. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
411. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
412. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
413. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
414. #376	C₂²×C₁₃	semidirect
417. C₂×#95	C₂²×C₁₃	semidirect
459. C₂×#41	C₂×C₄×C₁₃	semidirect
466. C₂³×C₄	C₂×C₄×C₁₃	semidirect
477. #123	C₂×C₄×C₁₃	semidirect
478. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
479. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
481. #121	C₂×C₄×C₁₃	semidirect
482. #120	C₂×C₄×C₁₃	semidirect
486. C₄×D₄	C₂×C₄×C₁₃	semidirect
487. C₄×D₄	C₂×C₄×C₁₃	semidirect
489. #117	C₂×C₄×C₁₃	semidirect
594. C₂²×C₄	C₁₃×#41	semidirect
642. C₁₃	#34223	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×#2374	2
C₁₃×#2363	2
C₁₃×#2362	2
C₁₃×#2357	2
C₁₃×#2353	2
C₁₃×#2347	2
C₁₃×#2346	2
C₁₃×#2341	2
C₁₃×#2339	2
C₁₃×#2321	2
C₁₃×#2318	2
C₄×C₁₃×C₂²⋊Q₈	2
C₄×C₁₃×#121	2
C₁₃×#2280	2
C₁₃×#2275	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34223	13

Subgroups — C13×#34223 #15720562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34223 #15720562