Subgroups — C₁₃×#36704 #15723043

Order 3328.

3018 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2849	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2688	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2686	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2673	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2671	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2613	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2484	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2482	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2412	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2410	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2406	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2404	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2308	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#535	—	2	8	no	—
22	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#121	—	2	8	no	—
27	C₂×C₁₃×#121	C₂²	1	4	yes	—
28	C₂×C₁₃×#121	C₂²	1	4	yes	—
29	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#120	C₂²	1	2	yes	—
33	C₂×C₁₃×#120	C₂²	1	2	yes	—
34	C₂×C₁₃×#120	C₂²	1	2	yes	—
35	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₁₃×#400	C₂²	1	2	yes	complemented
41	C₁₃×#399	C₂²	1	2	yes	complemented
42	C₁₃×#398	C₂²	1	2	yes	complemented
43	C₁₃×#397	C₂²	1	4	yes	complemented
44	C₁₃×#397	C₂²	1	2	yes	complemented
45	C₁₃×#395	C₂²	1	2	yes	complemented
46	C₁₃×#394	C₂²	1	4	yes	complemented
47	C₁₃×#394	C₂²	1	4	yes	complemented
48	C₁₃×#394	C₂²	1	2	yes	complemented
49	C₁₃×#394	C₂²	1	4	yes	complemented
50	C₁₃×#394	C₂²	1	4	yes	complemented
51	C₁₃×#393	C₂²	1	2	yes	complemented
52	C₁₃×#392	C₂²	1	4	yes	complemented
53	C₁₃×#392	C₂²	1	4	yes	complemented
54	C₁₃×#392	C₂²	1	2	yes	complemented
55	C₁₃×#392	C₂²	1	4	yes	complemented
56	C₁₃×#388	C₂²	1	4	yes	complemented
57	C₁₃×#387	C₂²	1	4	yes	complemented
58	C₁₃×#386	C₂²	1	2	yes	—
59	C₁₃×#386	C₂²	1	2	yes	—
60	C₁₃×#386	C₂²	1	4	yes	complemented
61	C₁₃×#386	C₂²	1	4	yes	complemented
62	C₁₃×#386	C₂²	1	4	yes	complemented
63	C₁₃×#386	C₂²	1	4	yes	complemented
64	C₁₃×#386	C₂²	1	4	yes	complemented
65	C₁₃×#386	C₂²	1	4	yes	complemented
66	C₁₃×#385	C₂²	1	2	yes	—
67	C₁₃×#385	C₂²	1	2	yes	—
68	C₁₃×#385	C₂²	1	4	yes	complemented
69	C₁₃×#385	C₂²	1	4	yes	complemented
70	C₁₃×#381	C₂²	1	1	yes	characteristic
71	C₁₃×#381	C₂²	1	1	yes	characteristic
72	C₁₃×#381	C₂²	1	2	yes	—
73	C₁₃×#381	C₂²	1	4	yes	complemented
74	C₁₃×#380	C₂²	1	4	yes	complemented
75	C₁₃×#379	C₂²	1	2	yes	—
76	C₁₃×#379	C₂²	1	2	yes	—
77	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
78	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
79	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×#41	—	2	4	no	—
81	C₂×C₁₃×#41	—	4	4	no	—
82	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	—	2	4	no	—
84	C₂²×D₄×C₁₃	—	2	4	no	—
85	C₂²×D₄×C₁₃	—	4	4	no	—
86	C₂²×D₄×C₁₃	—	4	4	no	—
87	C₂²×D₄×C₁₃	—	4	4	no	—
88	C₂²×D₄×C₁₃	D₄	1	8	yes	complemented
89	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₃	—	2	4	no	—
101	C₂³×C₄×C₁₃	—	4	4	no	—
102	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
109	C₁₃×#127	—	2	8	no	—
110	C₁₃×#124	—	2	8	no	—
111	C₁₃×#123	—	4	8	no	—
112	C₁₃×#123	—	4	4	no	—
113	C₁₃×#121	—	2	16	no	—
114	C₁₃×#121	—	2	16	no	—
115	C₁₃×#121	—	2	8	no	—
116	C₁₃×#121	—	2	8	no	—
117	C₁₃×#121	—	4	8	no	—
118	C₁₃×#120	—	2	8	no	—
119	C₁₃×#120	—	2	8	no	—
120	C₁₃×#120	—	4	4	no	—
121	C₁₃×#117	—	2	4	no	—
122	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
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	1	yes	characteristic
127	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
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	2	yes	—
136	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	4	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	4	yes	—
145	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	2	yes	—
156	C₁₃×#95	C₂³	1	2	yes	—
157	C₁₃×#95	C₂³	1	2	yes	—
158	C₁₃×#95	C₂³	1	2	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	C₁₃×#95	C₂³	1	4	yes	—
161	C₁₃×#95	C₂³	1	4	yes	—
162	C₁₃×#95	C₂³	1	4	yes	—
163	#36704	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	—	2	4	no	—
165	C₂⁴×C₁₃	—	2	4	no	—
166	C₂⁴×C₁₃	—	2	2	no	—
167	C₂⁴×C₁₃	—	2	4	no	—
168	C₂⁴×C₁₃	—	4	2	no	—
169	C₂⁴×C₁₃	—	4	2	no	—
170	C₂⁴×C₁₃	—	4	2	no	—
171	C₂⁴×C₁₃	—	4	2	no	—
172	C₂⁴×C₁₃	—	4	2	no	—
173	C₂⁴×C₁₃	—	4	2	no	—
174	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
175	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
176	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
177	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
178	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
179	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
180	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₁₃×#41	—	4	16	no	—
182	C₂×Q₈×C₁₃	—	2	2	no	—
183	C₂×Q₈×C₁₃	—	4	2	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	8	no	—
186	C₂×D₄×C₁₃	—	2	8	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	4	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	2	4	no	—
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	8	no	—
195	C₂×D₄×C₁₃	—	4	16	no	—
196	C₂×D₄×C₁₃	—	4	2	no	—
197	C₂×D₄×C₁₃	—	4	2	no	—
198	C₂×D₄×C₁₃	—	4	4	no	—
199	C₂×D₄×C₁₃	—	4	2	no	—
200	C₂×D₄×C₁₃	—	4	2	no	—
201	C₂×D₄×C₁₃	—	4	4	no	—
202	C₂×D₄×C₁₃	—	4	4	no	—
203	C₂×D₄×C₁₃	—	4	2	no	—
204	C₂×D₄×C₁₃	—	4	16	no	—
205	C₂×D₄×C₁₃	—	4	4	no	—
206	C₂×D₄×C₁₃	—	4	4	no	—
207	C₂×D₄×C₁₃	—	4	4	no	—
208	C₂×D₄×C₁₃	—	4	4	no	—
209	C₂×D₄×C₁₃	—	4	4	no	—
210	C₂×D₄×C₁₃	—	4	4	no	—
211	C₂×D₄×C₁₃	—	4	4	no	—
212	C₂×D₄×C₁₃	—	4	16	no	—
213	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
214	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	—	2	4	no	—
218	C₂²×C₄×C₁₃	—	2	2	no	—
219	C₂²×C₄×C₁₃	—	2	2	no	—
220	C₂²×C₄×C₁₃	—	2	8	no	—
221	C₂²×C₄×C₁₃	—	2	4	no	—
222	C₂²×C₄×C₁₃	—	2	4	no	—
223	C₂²×C₄×C₁₃	—	2	8	no	—
224	C₂²×C₄×C₁₃	—	4	4	no	—
225	C₂²×C₄×C₁₃	—	4	2	no	—
226	C₂²×C₄×C₁₃	—	4	2	no	—
227	C₂²×C₄×C₁₃	—	4	2	no	—
228	C₂²×C₄×C₁₃	—	4	4	no	—
229	C₂²×C₄×C₁₃	—	4	4	no	—
230	C₂²×C₄×C₁₃	—	4	4	no	—
231	C₂²×C₄×C₁₃	—	4	16	no	—
232	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	8	no	—
248	C₁₃×C₄⋊C₄	—	4	4	no	—
249	C₁₃×C₄⋊C₄	—	4	4	no	—
250	C₁₃×C₂²⋊C₄	—	2	8	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	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	4	no	—
259	C₁₃×C₂²⋊C₄	—	2	4	no	—
260	C₁₃×C₂²⋊C₄	—	2	8	no	—
261	C₁₃×C₂²⋊C₄	—	4	4	no	—
262	C₁₃×C₂²⋊C₄	—	4	4	no	—
263	C₁₃×C₂²⋊C₄	—	4	4	no	—
264	C₁₃×C₂²⋊C₄	—	4	4	no	—
265	C₁₃×C₂²⋊C₄	—	4	4	no	—
266	C₁₃×C₂²⋊C₄	—	4	4	no	—
267	C₁₃×C₂²⋊C₄	—	4	4	no	—
268	C₁₃×C₂²⋊C₄	—	4	4	no	—
269	C₄²×C₁₃	—	2	4	no	—
270	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
271	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#2849	C₂×C₁₃	1	2	yes	complemented
273	#2688	C₂×C₁₃	1	4	yes	complemented
274	#2686	C₂×C₁₃	1	4	yes	complemented
275	#2673	C₂×C₁₃	1	4	yes	complemented
276	#2671	C₂×C₁₃	1	4	yes	complemented
277	#2613	C₂×C₁₃	1	2	yes	complemented
278	#2484	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2482	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2412	C₂×C₁₃	1	2	yes	complemented
281	#2410	C₂×C₁₃	1	2	yes	complemented
282	#2406	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#2404	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#2308	C₂×C₁₃	1	1	yes	characteristic, complemented
285	C₂³×C₁₃	—	2	2	no	—
286	C₂³×C₁₃	—	2	2	no	—
287	C₂³×C₁₃	—	2	8	no	—
288	C₂³×C₁₃	—	2	2	no	—
289	C₂³×C₁₃	—	2	4	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	4	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	8	no	—
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	2	4	no	—
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	2	4	no	—
302	C₂³×C₁₃	—	2	4	no	—
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	—	2	2	no	—
305	C₂³×C₁₃	—	2	4	no	—
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	4	4	no	—
308	C₂³×C₁₃	—	4	4	no	—
309	C₂³×C₁₃	—	4	4	no	—
310	C₂³×C₁₃	—	4	4	no	—
311	C₂³×C₁₃	—	4	16	no	—
312	C₂³×C₁₃	—	4	4	no	—
313	C₂³×C₁₃	—	4	4	no	—
314	C₂³×C₁₃	—	4	4	no	—
315	C₂³×C₁₃	—	8	8	no	—
316	C₂³×C₁₃	—	8	8	no	—
317	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
318	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
319	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
320	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
321	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
322	Q₈×C₁₃	—	4	4	no	—
323	D₄×C₁₃	—	4	8	no	—
324	D₄×C₁₃	—	4	8	no	—
325	D₄×C₁₃	—	4	16	no	—
326	D₄×C₁₃	—	4	4	no	—
327	D₄×C₁₃	—	4	16	no	—
328	D₄×C₁₃	—	4	8	no	—
329	D₄×C₁₃	—	8	4	no	—
330	D₄×C₁₃	—	8	4	no	—
331	D₄×C₁₃	—	8	4	no	—
332	D₄×C₁₃	—	8	4	no	—
333	D₄×C₁₃	—	8	8	no	—
334	C₂×C₄×C₁₃	—	2	8	no	—
335	C₂×C₄×C₁₃	—	2	8	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	4	no	—
346	C₂×C₄×C₁₃	—	2	4	no	—
347	C₂×C₄×C₁₃	—	2	4	no	—
348	C₂×C₄×C₁₃	—	2	4	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	4	no	—
351	C₂×C₄×C₁₃	—	2	4	no	—
352	C₂×C₄×C₁₃	—	2	4	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	4	no	—
355	C₂×C₄×C₁₃	—	2	4	no	—
356	C₂×C₄×C₁₃	—	2	4	no	—
357	C₂×C₄×C₁₃	—	4	16	no	—
358	C₂×C₄×C₁₃	—	4	8	no	—
359	C₂×C₄×C₁₃	—	4	4	no	—
360	C₂×C₄×C₁₃	—	4	4	no	—
361	C₂×C₄×C₁₃	—	8	8	no	—
362	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
365	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
366	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
367	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
368	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
369	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
370	#535	—	2	8	no	—
371	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
372	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
373	C₂×#123	C₂²×C₁₃	1	2	yes	—
374	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
375	C₂×#121	—	2	8	no	—
376	C₂×#121	C₂²×C₁₃	1	4	yes	—
377	C₂×#121	C₂²×C₁₃	1	4	yes	—
378	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
379	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
380	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
381	C₂×#120	C₂²×C₁₃	1	2	yes	—
382	C₂×#120	C₂²×C₁₃	1	2	yes	—
383	C₂×#120	C₂²×C₁₃	1	2	yes	—
384	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
385	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
386	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
387	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
388	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
389	#400	C₂²×C₁₃	1	2	yes	complemented
390	#399	C₂²×C₁₃	1	2	yes	complemented
391	#398	C₂²×C₁₃	1	2	yes	complemented
392	#397	C₂²×C₁₃	1	4	yes	complemented
393	#397	C₂²×C₁₃	1	2	yes	complemented
394	#395	C₂²×C₁₃	1	2	yes	complemented
395	#394	C₂²×C₁₃	1	4	yes	complemented
396	#394	C₂²×C₁₃	1	4	yes	complemented
397	#394	C₂²×C₁₃	1	2	yes	complemented
398	#394	C₂²×C₁₃	1	4	yes	complemented
399	#394	C₂²×C₁₃	1	4	yes	complemented
400	#393	C₂²×C₁₃	1	2	yes	complemented
401	#392	C₂²×C₁₃	1	4	yes	complemented
402	#392	C₂²×C₁₃	1	4	yes	complemented
403	#392	C₂²×C₁₃	1	2	yes	complemented
404	#392	C₂²×C₁₃	1	4	yes	complemented
405	#388	C₂²×C₁₃	1	4	yes	complemented
406	#387	C₂²×C₁₃	1	4	yes	complemented
407	#386	C₂²×C₁₃	1	2	yes	—
408	#386	C₂²×C₁₃	1	2	yes	—
409	#386	C₂²×C₁₃	1	4	yes	complemented
410	#386	C₂²×C₁₃	1	4	yes	complemented
411	#386	C₂²×C₁₃	1	4	yes	complemented
412	#386	C₂²×C₁₃	1	4	yes	complemented
413	#386	C₂²×C₁₃	1	4	yes	complemented
414	#386	C₂²×C₁₃	1	4	yes	complemented
415	#385	C₂²×C₁₃	1	2	yes	—
416	#385	C₂²×C₁₃	1	2	yes	—
417	#385	C₂²×C₁₃	1	4	yes	complemented
418	#385	C₂²×C₁₃	1	4	yes	complemented
419	#381	C₂²×C₁₃	1	1	yes	characteristic
420	#381	C₂²×C₁₃	1	1	yes	characteristic
421	#381	C₂²×C₁₃	1	2	yes	—
422	#381	C₂²×C₁₃	1	4	yes	complemented
423	#380	C₂²×C₁₃	1	4	yes	complemented
424	#379	C₂²×C₁₃	1	2	yes	—
425	#379	C₂²×C₁₃	1	2	yes	—
426	C₂²×C₁₃	—	2	2	no	—
427	C₂²×C₁₃	—	2	2	no	—
428	C₂²×C₁₃	—	2	8	no	—
429	C₂²×C₁₃	—	2	4	no	—
430	C₂²×C₁₃	—	2	4	no	—
431	C₂²×C₁₃	—	2	4	no	—
432	C₂²×C₁₃	—	2	4	no	—
433	C₂²×C₁₃	—	2	4	no	—
434	C₂²×C₁₃	—	2	4	no	—
435	C₂²×C₁₃	—	4	16	no	—
436	C₂²×C₁₃	—	4	4	no	—
437	C₂²×C₁₃	—	4	4	no	—
438	C₂²×C₁₃	—	4	4	no	—
439	C₂²×C₁₃	—	4	4	no	—
440	C₂²×C₁₃	—	4	2	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	4	2	no	—
443	C₂²×C₁₃	—	4	2	no	—
444	C₂²×C₁₃	—	4	2	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	4	4	no	—
447	C₂²×C₁₃	—	4	4	no	—
448	C₂²×C₁₃	—	4	4	no	—
449	C₂²×C₁₃	—	4	4	no	—
450	C₂²×C₁₃	—	8	8	no	—
451	C₂²×C₁₃	—	8	8	no	—
452	C₂²×C₁₃	#534	1	4	yes	—
453	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
454	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
455	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
456	C₂²×C₁₃	#585	1	2	yes	—
457	C₄×C₁₃	—	2	2	no	—
458	C₄×C₁₃	—	2	2	no	—
459	C₄×C₁₃	—	2	4	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	—	4	2	no	—
462	C₄×C₁₃	—	4	2	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	—	4	4	no	—
466	C₄×C₁₃	—	4	4	no	—
467	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
468	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
469	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×#41	—	2	4	no	—
471	C₂×#41	—	4	4	no	—
472	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
473	C₂²×D₄	—	2	4	no	—
474	C₂²×D₄	—	2	4	no	—
475	C₂²×D₄	—	4	4	no	—
476	C₂²×D₄	—	4	4	no	—
477	C₂²×D₄	—	4	4	no	—
478	C₂²×D₄	D₄×C₁₃	1	8	yes	complemented
479	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
480	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
481	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
482	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
483	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
484	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
485	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
486	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
487	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
488	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
489	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
490	C₂³×C₄	—	2	4	no	—
491	C₂³×C₄	—	4	4	no	—
492	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
495	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
498	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
499	#127	—	2	8	no	—
500	#124	—	2	8	no	—
501	#123	—	4	8	no	—
502	#123	—	4	4	no	—
503	#121	—	2	16	no	—
504	#121	—	2	16	no	—
505	#121	—	2	8	no	—
506	#121	—	2	8	no	—
507	#121	—	4	8	no	—
508	#120	—	2	8	no	—
509	#120	—	2	8	no	—
510	#120	—	4	4	no	—
511	#117	—	2	4	no	—
512	C₂×C₄⋊C₄	—	2	4	no	—
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
520	C₂×C₂²⋊C₄	—	2	4	no	—
521	C₂×C₂²⋊C₄	—	2	4	no	—
522	C₂×C₂²⋊C₄	—	4	4	no	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
542	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
543	#95	C₂³×C₁₃	1	4	yes	—
544	#95	C₂³×C₁₃	1	4	yes	—
545	#95	C₂³×C₁₃	1	2	yes	—
546	#95	C₂³×C₁₃	1	2	yes	—
547	#95	C₂³×C₁₃	1	2	yes	—
548	#95	C₂³×C₁₃	1	2	yes	—
549	#95	C₂³×C₁₃	1	4	yes	—
550	#95	C₂³×C₁₃	1	4	yes	—
551	#95	C₂³×C₁₃	1	4	yes	—
552	#95	C₂³×C₁₃	1	4	yes	—
553	C₂×C₁₃	—	2	4	no	—
554	C₂×C₁₃	—	4	4	no	—
555	C₂×C₁₃	—	4	4	no	—
556	C₂×C₁₃	—	8	2	no	—
557	C₂×C₁₃	—	8	2	no	—
558	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
559	C₂×C₁₃	#3484	1	1	yes	characteristic
560	C₂×C₁₃	#3485	1	1	yes	characteristic
561	C₂×C₁₃	#3542	1	4	yes	—
562	C₂⁴	—	2	4	no	—
563	C₂⁴	—	2	4	no	—
564	C₂⁴	—	2	2	no	—
565	C₂⁴	—	2	4	no	—
566	C₂⁴	—	4	2	no	—
567	C₂⁴	—	4	2	no	—
568	C₂⁴	—	4	2	no	—
569	C₂⁴	—	4	2	no	—
570	C₂⁴	—	4	2	no	—
571	C₂⁴	—	4	2	no	—
572	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
573	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
574	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
575	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
576	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
577	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
578	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
579	#41	—	4	16	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	4	2	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	8	no	—
584	C₂×D₄	—	2	8	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	8	no	—
593	C₂×D₄	—	4	16	no	—
594	C₂×D₄	—	4	2	no	—
595	C₂×D₄	—	4	2	no	—
596	C₂×D₄	—	4	4	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	4	2	no	—
599	C₂×D₄	—	4	4	no	—
600	C₂×D₄	—	4	4	no	—
601	C₂×D₄	—	4	2	no	—
602	C₂×D₄	—	4	16	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	—	4	16	no	—
611	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
612	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	8	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	—	4	2	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	—	4	16	no	—
630	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
631	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
633	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	8	no	—
646	C₄⋊C₄	—	4	4	no	—
647	C₄⋊C₄	—	4	4	no	—
648	C₂²⋊C₄	—	2	8	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	8	no	—
659	C₂²⋊C₄	—	4	4	no	—
660	C₂²⋊C₄	—	4	4	no	—
661	C₂²⋊C₄	—	4	4	no	—
662	C₂²⋊C₄	—	4	4	no	—
663	C₂²⋊C₄	—	4	4	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	—	4	4	no	—
666	C₂²⋊C₄	—	4	4	no	—
667	C₄²	—	2	4	no	—
668	C₁₃	#36704	1	1	yes	characteristic, direct product factor, Sylow
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	2	8	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	4	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	4	no	—
686	C₂³	—	2	4	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	4	4	no	—
692	C₂³	—	4	4	no	—
693	C₂³	—	4	4	no	—
694	C₂³	—	4	4	no	—
695	C₂³	—	4	16	no	—
696	C₂³	—	4	4	no	—
697	C₂³	—	4	4	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	8	8	no	—
700	C₂³	—	8	8	no	—
701	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
702	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
703	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
704	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
705	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
706	Q₈	—	4	4	no	—
707	D₄	—	4	8	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	16	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	16	no	—
712	D₄	—	4	8	no	—
713	D₄	—	8	4	no	—
714	D₄	—	8	4	no	—
715	D₄	—	8	4	no	—
716	D₄	—	8	4	no	—
717	D₄	—	8	8	no	—
718	C₂×C₄	—	2	8	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	4	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	4	16	no	—
742	C₂×C₄	—	4	8	no	—
743	C₂×C₄	—	4	4	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	8	8	no	—
746	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
747	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
748	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
749	C₂²	—	2	8	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	4	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	4	16	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	4	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	4	no	—
763	C₂²	—	4	4	no	—
764	C₂²	—	4	4	no	—
765	C₂²	—	4	4	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	8	8	no	—
774	C₂²	—	8	8	no	—
775	C₂²	C₁₃×#534	1	4	yes	—
776	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
777	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
778	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
779	C₂²	C₁₃×#585	1	2	yes	—
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	4	no	—
783	C₄	—	4	4	no	—
784	C₄	—	4	4	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₂	—	2	4	no	—
791	C₂	—	4	4	no	—
792	C₂	—	4	4	no	—
793	C₂	—	8	2	no	—
794	C₂	—	8	2	no	—
795	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
796	C₂	C₁₃×#3484	1	1	yes	characteristic
797	C₂	C₁₃×#3485	1	1	yes	characteristic
798	C₂	C₁₃×#3542	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#535	C₂	semidirect
2. C₂²×C₁₃×#121	C₂	semidirect
3. C₁₃×#2849	C₂	semidirect
4. C₁₃×#2688	C₂	semidirect
5. C₁₃×#2686	C₂	semidirect
6. C₁₃×#2673	C₂	semidirect
7. C₁₃×#2671	C₂	semidirect
8. C₁₃×#2613	C₂	semidirect
9. C₁₃×#2484	C₂	semidirect
10. C₁₃×#2482	C₂	semidirect
11. C₁₃×#2412	C₂	semidirect
12. C₁₃×#2410	C₂	semidirect
13. C₁₃×#2406	C₂	semidirect
14. C₁₃×#2404	C₂	semidirect
15. C₁₃×#2308	C₂	semidirect
22. C₂×C₁₃×#127	C₂²	semidirect
23. C₂×C₁₃×#124	C₂²	semidirect
25. C₂×C₁₃×#123	C₂²	semidirect
29. C₂×C₁₃×#121	C₂²	semidirect
30. C₂×C₁₃×#121	C₂²	semidirect
31. C₂×C₁₃×#121	C₂²	semidirect
40. C₁₃×#400	C₂²	semidirect
41. C₁₃×#399	C₂²	semidirect
42. C₁₃×#398	C₂²	semidirect
43. C₁₃×#397	C₂²	semidirect
44. C₁₃×#397	C₂²	semidirect
45. C₁₃×#395	C₂²	semidirect
46. C₁₃×#394	C₂²	semidirect
47. C₁₃×#394	C₂²	semidirect
48. C₁₃×#394	C₂²	semidirect
49. C₁₃×#394	C₂²	semidirect
50. C₁₃×#394	C₂²	semidirect
51. C₁₃×#393	C₂²	semidirect
52. C₁₃×#392	C₂²	semidirect
53. C₁₃×#392	C₂²	semidirect
54. C₁₃×#392	C₂²	semidirect
55. C₁₃×#392	C₂²	semidirect
56. C₁₃×#388	C₂²	semidirect
57. C₁₃×#387	C₂²	semidirect
60. C₁₃×#386	C₂²	semidirect
61. C₁₃×#386	C₂²	semidirect
62. C₁₃×#386	C₂²	semidirect
63. C₁₃×#386	C₂²	semidirect
64. C₁₃×#386	C₂²	semidirect
65. C₁₃×#386	C₂²	semidirect
68. C₁₃×#385	C₂²	semidirect
69. C₁₃×#385	C₂²	semidirect
73. C₁₃×#381	C₂²	semidirect
74. C₁₃×#380	C₂²	semidirect
88. C₂²×D₄×C₁₃	D₄	semidirect
163. #36704	C₁₃	direct (N × H)
270. C₂×#535	C₂×C₁₃	semidirect
271. C₂²×#121	C₂×C₁₃	semidirect
272. #2849	C₂×C₁₃	semidirect
273. #2688	C₂×C₁₃	semidirect
274. #2686	C₂×C₁₃	semidirect
275. #2673	C₂×C₁₃	semidirect
276. #2671	C₂×C₁₃	semidirect
277. #2613	C₂×C₁₃	semidirect
278. #2484	C₂×C₁₃	semidirect
279. #2482	C₂×C₁₃	semidirect
280. #2412	C₂×C₁₃	semidirect
281. #2410	C₂×C₁₃	semidirect
282. #2406	C₂×C₁₃	semidirect
283. #2404	C₂×C₁₃	semidirect
284. #2308	C₂×C₁₃	semidirect
371. C₂×#127	C₂²×C₁₃	semidirect
372. C₂×#124	C₂²×C₁₃	semidirect
374. C₂×#123	C₂²×C₁₃	semidirect
378. C₂×#121	C₂²×C₁₃	semidirect
379. C₂×#121	C₂²×C₁₃	semidirect
380. C₂×#121	C₂²×C₁₃	semidirect
389. #400	C₂²×C₁₃	semidirect
390. #399	C₂²×C₁₃	semidirect
391. #398	C₂²×C₁₃	semidirect
392. #397	C₂²×C₁₃	semidirect
393. #397	C₂²×C₁₃	semidirect
394. #395	C₂²×C₁₃	semidirect
395. #394	C₂²×C₁₃	semidirect
396. #394	C₂²×C₁₃	semidirect
397. #394	C₂²×C₁₃	semidirect
398. #394	C₂²×C₁₃	semidirect
399. #394	C₂²×C₁₃	semidirect
400. #393	C₂²×C₁₃	semidirect
401. #392	C₂²×C₁₃	semidirect
402. #392	C₂²×C₁₃	semidirect
403. #392	C₂²×C₁₃	semidirect
404. #392	C₂²×C₁₃	semidirect
405. #388	C₂²×C₁₃	semidirect
406. #387	C₂²×C₁₃	semidirect
409. #386	C₂²×C₁₃	semidirect
410. #386	C₂²×C₁₃	semidirect
411. #386	C₂²×C₁₃	semidirect
412. #386	C₂²×C₁₃	semidirect
413. #386	C₂²×C₁₃	semidirect
414. #386	C₂²×C₁₃	semidirect
417. #385	C₂²×C₁₃	semidirect
418. #385	C₂²×C₁₃	semidirect
422. #381	C₂²×C₁₃	semidirect
423. #380	C₂²×C₁₃	semidirect
478. C₂²×D₄	D₄×C₁₃	semidirect
668. C₁₃	#36704	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×#535	2
C₂²×C₁₃×#121	2
C₁₃×#2849	2
C₁₃×#2688	2
C₁₃×#2686	2
C₁₃×#2673	2
C₁₃×#2671	2
C₁₃×#2613	2
C₁₃×#2484	2
C₁₃×#2482	2
C₁₃×#2412	2
C₁₃×#2410	2
C₁₃×#2406	2
C₁₃×#2404	2
C₁₃×#2308	2
#36704	13

Subgroups — C13×#36704 #15723043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36704 #15723043