Subgroups — C₁₃×#63066 #15749405

Order 3328.

7352 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3558	C₂	1	6	yes	maximal, complemented
2	C₁₃×#3551	C₂	1	6	yes	maximal, complemented
3	C₁₃×#3549	C₂	1	3	yes	maximal, complemented
4	C₁₃×#3543	C₂	1	12	yes	maximal, complemented
5	C₁₃×#3542	C₂	1	12	yes	maximal, complemented
6	C₁₃×#3537	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3529	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3524	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3517	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3498	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3488	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3487	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
18	C₁₃×#563	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#563	C₂²	1	6	yes	complemented
20	C₁₃×#562	C₂²	1	12	yes	complemented
21	C₁₃×#562	C₂²	1	6	yes	complemented
22	C₁₃×H(3,𝔽₄)	C₂²	1	3	yes	complemented
23	C₁₃×H(3,𝔽₄)	C₂²	1	6	yes	complemented
24	C₁₃×#560	C₂²	1	6	yes	complemented
25	C₁₃×#560	C₂²	1	12	yes	complemented
26	C₁₃×#560	C₂²	1	12	yes	complemented
27	C₁₃×#560	C₂²	1	12	yes	complemented
28	C₁₃×#559	C₂²	1	12	yes	complemented
29	C₁₃×#557	C₂²	1	2	yes	complemented
30	C₁₃×#555	C₂²	1	12	yes	complemented
31	C₁₃×#555	C₂²	1	6	yes	complemented
32	C₁₃×#553	C₂²	1	12	yes	complemented
33	C₁₃×#553	C₂²	1	12	yes	complemented
34	C₁₃×#552	C₂²	1	12	yes	complemented
35	C₁₃×#551	C₂²	1	12	yes	complemented
36	C₁₃×#550	C₂²	1	4	yes	complemented
37	C₁₃×#550	C₂²	1	12	yes	complemented
38	C₁₃×#550	C₂²	1	6	yes	complemented
39	C₁₃×#550	C₂²	1	4	yes	complemented
40	C₁₃×#550	C₂²	1	2	yes	complemented
41	C₁₃×#548	C₂²	1	4	yes	complemented
42	C₁₃×#548	C₂²	1	4	yes	complemented
43	C₁₃×#548	C₂²	1	12	yes	complemented
44	C₁₃×#547	C₂²	1	6	yes	complemented
45	C₁₃×#546	C₂²	1	24	yes	complemented
46	C₁₃×#546	C₂²	1	12	yes	complemented
47	C₁₃×#546	C₂²	1	12	yes	complemented
48	C₁₃×#546	C₂²	1	12	yes	complemented
49	D₄²×C₁₃	C₂²	1	6	yes	complemented
50	D₄²×C₁₃	C₂²	1	12	yes	complemented
51	D₄²×C₁₃	C₂²	1	12	yes	complemented
52	D₄²×C₁₃	C₂²	1	12	yes	complemented
53	D₄²×C₁₃	C₂²	1	12	yes	complemented
54	D₄²×C₁₃	C₂²	1	12	yes	complemented
55	C₁₃×#542	C₂²	1	12	yes	complemented
56	C₁₃×#540	C₂²	1	12	yes	complemented
57	C₁₃×#540	C₂²	1	24	yes	complemented
58	C₁₃×#540	C₂²	1	12	yes	complemented
59	C₁₃×#538	C₂²	1	24	yes	complemented
60	C₁₃×#538	C₂²	1	12	yes	complemented
61	C₁₃×#537	C₂²	1	12	yes	complemented
62	C₁₃×#536	C₂²	1	3	yes	complemented
63	C₁₃×#535	C₂²	1	3	yes	complemented
64	C₁₃×#535	C₂²	1	6	yes	complemented
65	C₁₃×#535	C₂²	1	6	yes	complemented
66	C₁₃×#535	C₂²	1	24	yes	complemented
67	C₁₃×#535	C₂²	1	6	yes	complemented
68	C₁₃×#535	C₂²	1	12	yes	complemented
69	C₁₃×#535	C₂²	1	6	yes	complemented
70	C₁₃×#534	C₂²	1	24	yes	complemented
71	C₁₃×#534	C₂²	1	12	yes	complemented
72	C₁₃×#532	C₂²	1	3	yes	complemented
73	C₁₃×#532	C₂²	1	6	yes	complemented
74	C₁₃×#532	C₂²	1	6	yes	complemented
75	C₂×C₁₃×#127	C₂²	1	6	yes	complemented
76	C₁₃×#529	C₂²	1	12	yes	complemented
77	C₁₃×#529	C₂²	1	12	yes	complemented
78	C₁₃×#529	C₂²	1	6	yes	complemented
79	C₂×C₁₃×#124	C₂²	1	3	yes	complemented
80	C₁₃×#525	C₂²	1	6	yes	complemented
81	C₁₃×#525	C₂²	1	12	yes	complemented
82	C₁₃×#525	C₂²	1	6	yes	complemented
83	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
84	C₁₃×#520	C₂²	1	4	yes	complemented
85	C₁₃×#519	C₂²	1	2	yes	complemented
86	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
87	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×2₋¹⁺⁴	—	4	4	no	—
89	C₁₃×H(5,𝔽₂)	—	4	8	no	—
90	C₁₃×H(5,𝔽₂)	—	4	4	no	—
91	C₂×C₁₃×#41	—	4	8	no	—
92	C₂×C₁₃×#41	C₂³	1	2	yes	—
93	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×#41	C₂³	1	4	yes	—
95	C₂×C₁₃×#41	C₂³	1	3	yes	—
96	C₂×C₁₃×#41	C₂³	1	6	yes	—
97	C₂×C₁₃×#41	C₂³	1	6	yes	—
98	C₂×C₁₃×#41	C₂³	1	3	yes	—
99	C₂×C₁₃×#41	C₂³	1	12	yes	—
100	C₂×C₁₃×#41	C₂³	1	12	yes	—
101	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
103	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
104	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
105	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
106	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
107	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
108	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
111	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
114	C₁₃×#127	C₂³	1	6	yes	—
115	C₁₃×#127	C₂³	1	12	yes	—
116	C₁₃×#127	C₂³	1	12	yes	—
117	C₁₃×#127	C₂³	1	12	yes	—
118	C₁₃×#127	C₂³	1	6	yes	—
119	C₁₃×#127	C₂³	1	3	yes	—
120	C₁₃×#127	C₂³	1	12	yes	—
121	C₁₃×#126	C₂³	1	4	yes	—
122	C₁₃×#126	C₂³	1	12	yes	—
123	C₁₃×#126	C₂³	1	12	yes	—
124	C₁₃×#126	C₂³	1	24	yes	—
125	C₁₃×#125	C₂³	1	2	yes	—
126	C₁₃×#125	C₂³	1	12	yes	—
127	C₁₃×#125	C₂³	1	12	yes	—
128	C₁₃×#124	C₂³	1	3	yes	—
129	C₁₃×#124	C₂³	1	6	yes	—
130	C₁₃×#124	C₂³	1	12	yes	—
131	C₁₃×#124	C₂³	1	6	yes	—
132	C₁₃×#124	C₂³	1	12	yes	—
133	C₁₃×#124	C₂³	1	12	yes	—
134	C₁₃×#124	C₂³	1	1	yes	characteristic
135	C₁₃×#124	C₂³	1	6	yes	—
136	C₁₃×#124	C₂³	1	6	yes	—
137	C₁₃×#124	C₂³	1	12	yes	—
138	C₁₃×#124	C₂³	1	24	yes	—
139	C₁₃×#123	C₂³	1	2	yes	—
140	C₁₃×#123	C₂³	1	6	yes	—
141	C₁₃×#123	C₂³	1	12	yes	—
142	C₁₃×#123	C₂³	1	12	yes	—
143	C₁₃×#123	C₂³	1	24	yes	—
144	C₁₃×#123	C₂³	1	12	yes	—
145	C₁₃×#123	C₂³	1	12	yes	—
146	C₁₃×#123	C₂³	1	12	yes	—
147	C₁₃×#123	C₂³	1	24	yes	—
148	C₁₃×#123	C₂³	1	24	yes	—
149	C₁₃×#123	C₂³	1	12	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
157	C₁₃×#121	C₂³	1	12	yes	—
158	C₁₃×#121	C₂³	1	24	yes	—
159	C₁₃×#121	C₂³	1	12	yes	—
160	C₁₃×#121	C₂³	1	12	yes	—
161	C₁₃×#121	C₂³	1	12	yes	—
162	C₁₃×#121	C₂³	1	12	yes	—
163	C₁₃×#121	C₂³	1	12	yes	—
164	C₁₃×#121	C₂³	1	12	yes	—
165	C₁₃×#121	C₂³	1	12	yes	—
166	C₁₃×#121	C₂³	1	6	yes	—
167	C₁₃×#121	C₂³	1	12	yes	—
168	C₁₃×#121	C₂³	1	12	yes	—
169	C₁₃×#121	C₂³	1	12	yes	—
170	C₁₃×#121	C₂³	1	12	yes	—
171	C₁₃×#121	C₂³	1	12	yes	—
172	C₁₃×#121	C₂³	1	12	yes	—
173	C₁₃×#121	C₂³	1	12	yes	—
174	C₁₃×#121	C₂³	1	24	yes	—
175	C₁₃×#121	C₂³	1	24	yes	—
176	C₁₃×#121	C₂³	1	24	yes	—
177	C₁₃×#121	C₂³	1	24	yes	—
178	C₁₃×#121	C₂³	1	24	yes	—
179	C₁₃×#120	C₂³	1	12	yes	—
180	C₁₃×#120	C₂³	1	12	yes	—
181	C₁₃×#120	C₂³	1	6	yes	—
182	C₁₃×#120	C₂³	1	6	yes	—
183	C₁₃×#120	C₂³	1	12	yes	—
184	C₁₃×#120	C₂³	1	12	yes	—
185	C₁₃×#120	C₂³	1	24	yes	—
186	C₁₃×#120	C₂³	1	24	yes	—
187	C₁₃×#120	C₂³	1	24	yes	—
188	C₁₃×#120	C₂³	1	12	yes	—
189	C₁₃×#120	C₂³	1	12	yes	—
190	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
191	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
192	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
193	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
194	C₄×D₄×C₁₃	C₂³	1	6	yes	—
195	C₄×D₄×C₁₃	C₂³	1	12	yes	—
196	C₄×D₄×C₁₃	C₂³	1	12	yes	—
197	C₄×D₄×C₁₃	C₂³	1	12	yes	—
198	C₄×D₄×C₁₃	C₂³	1	12	yes	—
199	C₄×D₄×C₁₃	C₂³	1	6	yes	—
200	C₄×D₄×C₁₃	C₂³	1	12	yes	—
201	C₄×D₄×C₁₃	C₂³	1	12	yes	—
202	C₄×D₄×C₁₃	C₂³	1	12	yes	—
203	C₄×D₄×C₁₃	C₂³	1	24	yes	—
204	C₄×D₄×C₁₃	C₂³	1	24	yes	—
205	C₄×D₄×C₁₃	C₂³	1	12	yes	—
206	C₁₃×#117	C₂³	1	6	yes	—
207	C₁₃×#117	C₂³	1	3	yes	—
208	C₁₃×#117	C₂³	1	6	yes	—
209	C₁₃×#117	C₂³	1	6	yes	—
210	C₁₃×#117	C₂³	1	12	yes	—
211	C₁₃×#117	C₂³	1	24	yes	—
212	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
213	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
214	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
215	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
216	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
217	#63066	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
219	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
220	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
221	C₁₃×#41	—	2	16	no	—
222	C₁₃×#41	—	2	8	no	—
223	C₁₃×#41	—	2	4	no	—
224	C₁₃×#41	—	4	12	no	—
225	C₁₃×#41	—	4	6	no	—
226	C₁₃×#41	—	4	6	no	—
227	C₁₃×#41	—	4	24	no	—
228	C₁₃×#41	—	4	12	no	—
229	C₁₃×#41	—	8	12	no	—
230	C₂×Q₈×C₁₃	—	2	8	no	—
231	C₂×Q₈×C₁₃	—	4	6	no	—
232	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
233	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
234	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
236	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×D₄×C₁₃	—	4	12	no	—
239	C₂×D₄×C₁₃	—	4	24	no	—
240	C₂×D₄×C₁₃	—	4	12	no	—
241	C₂×D₄×C₁₃	—	4	12	no	—
242	C₂×D₄×C₁₃	—	4	6	no	—
243	C₂×D₄×C₁₃	—	8	24	no	—
244	C₂×D₄×C₁₃	—	8	24	no	—
245	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
246	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
247	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
248	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
249	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
250	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
251	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
252	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
253	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
254	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
259	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
260	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
261	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
262	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
263	C₂²×C₄×C₁₃	—	4	12	no	—
264	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
266	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
268	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
274	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
275	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
276	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
288	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
289	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
290	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
291	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
292	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
293	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
294	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
295	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
296	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
297	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
298	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
299	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
300	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
301	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
302	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
303	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
304	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
305	C₄²×C₁₃	C₂⁴	1	2	yes	—
306	C₄²×C₁₃	C₂⁴	1	6	yes	—
307	C₄²×C₁₃	C₂⁴	1	6	yes	—
308	C₄²×C₁₃	C₂⁴	1	12	yes	—
309	C₄²×C₁₃	C₂⁴	1	3	yes	—
310	C₄²×C₁₃	C₂⁴	1	12	yes	—
311	#3558	C₂×C₁₃	1	6	yes	complemented
312	#3551	C₂×C₁₃	1	6	yes	complemented
313	#3549	C₂×C₁₃	1	3	yes	complemented
314	#3543	C₂×C₁₃	1	12	yes	complemented
315	#3542	C₂×C₁₃	1	12	yes	complemented
316	#3537	C₂×C₁₃	1	6	yes	complemented
317	#3529	C₂×C₁₃	1	3	yes	complemented
318	#3524	C₂×C₁₃	1	4	yes	complemented
319	#3517	C₂×C₁₃	1	2	yes	complemented
320	#3500	C₂×C₁₃	1	1	yes	characteristic, complemented
321	#3498	C₂×C₁₃	1	2	yes	complemented
322	#3488	C₂×C₁₃	1	4	yes	complemented
323	#3487	C₂×C₁₃	1	2	yes	complemented
324	C₂³×C₁₃	—	4	6	no	—
325	C₂³×C₁₃	—	4	12	no	—
326	C₂³×C₁₃	—	4	6	no	—
327	C₂³×C₁₃	—	4	12	no	—
328	C₂³×C₁₃	—	4	24	no	—
329	C₂³×C₁₃	—	4	12	no	—
330	C₂³×C₁₃	C₂⁵	1	6	yes	—
331	C₂³×C₁₃	C₂⁵	1	2	yes	—
332	C₂³×C₁₃	C₂⁵	1	12	yes	—
333	C₂³×C₁₃	C₂⁵	1	3	yes	—
334	Q₈×C₁₃	—	2	12	no	—
335	Q₈×C₁₃	—	4	3	no	—
336	Q₈×C₁₃	—	4	2	no	—
337	Q₈×C₁₃	—	4	1	no	—
338	Q₈×C₁₃	—	4	6	no	—
339	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
340	D₄×C₁₃	—	2	12	no	—
341	D₄×C₁₃	—	2	24	no	—
342	D₄×C₁₃	—	2	6	no	—
343	D₄×C₁₃	—	4	12	no	—
344	D₄×C₁₃	—	4	6	no	—
345	D₄×C₁₃	—	4	6	no	—
346	D₄×C₁₃	—	4	3	no	—
347	D₄×C₁₃	—	4	12	no	—
348	D₄×C₁₃	—	4	12	no	—
349	D₄×C₁₃	—	4	12	no	—
350	D₄×C₁₃	—	4	12	no	—
351	D₄×C₁₃	—	4	12	no	—
352	D₄×C₁₃	—	4	24	no	—
353	D₄×C₁₃	—	4	12	no	—
354	D₄×C₁₃	—	4	24	no	—
355	D₄×C₁₃	—	4	1	no	—
356	D₄×C₁₃	—	4	6	no	—
357	D₄×C₁₃	—	4	6	no	—
358	C₂×C₄×C₁₃	—	2	12	no	—
359	C₂×C₄×C₁₃	—	2	24	no	—
360	C₂×C₄×C₁₃	—	2	12	no	—
361	C₂×C₄×C₁₃	—	2	6	no	—
362	C₂×C₄×C₁₃	—	4	2	no	—
363	C₂×C₄×C₁₃	—	4	12	no	—
364	C₂×C₄×C₁₃	—	4	12	no	—
365	C₂×C₄×C₁₃	—	4	24	no	—
366	C₂×C₄×C₁₃	—	4	6	no	—
367	C₂×C₄×C₁₃	—	4	6	no	—
368	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
369	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
371	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
372	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
373	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
374	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
375	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
376	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
377	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic, complemented
378	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
379	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic, complemented
380	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
381	#563	C₂²×C₁₃	1	1	yes	characteristic, complemented
382	#563	C₂²×C₁₃	1	6	yes	complemented
383	#562	C₂²×C₁₃	1	12	yes	complemented
384	#562	C₂²×C₁₃	1	6	yes	complemented
385	H(3,𝔽₄)	C₂²×C₁₃	1	3	yes	complemented
386	H(3,𝔽₄)	C₂²×C₁₃	1	6	yes	complemented
387	#560	C₂²×C₁₃	1	6	yes	complemented
388	#560	C₂²×C₁₃	1	12	yes	complemented
389	#560	C₂²×C₁₃	1	12	yes	complemented
390	#560	C₂²×C₁₃	1	12	yes	complemented
391	#559	C₂²×C₁₃	1	12	yes	complemented
392	#557	C₂²×C₁₃	1	2	yes	complemented
393	#555	C₂²×C₁₃	1	12	yes	complemented
394	#555	C₂²×C₁₃	1	6	yes	complemented
395	#553	C₂²×C₁₃	1	12	yes	complemented
396	#553	C₂²×C₁₃	1	12	yes	complemented
397	#552	C₂²×C₁₃	1	12	yes	complemented
398	#551	C₂²×C₁₃	1	12	yes	complemented
399	#550	C₂²×C₁₃	1	4	yes	complemented
400	#550	C₂²×C₁₃	1	12	yes	complemented
401	#550	C₂²×C₁₃	1	2	yes	complemented
402	#550	C₂²×C₁₃	1	4	yes	complemented
403	#550	C₂²×C₁₃	1	6	yes	complemented
404	#548	C₂²×C₁₃	1	4	yes	complemented
405	#548	C₂²×C₁₃	1	12	yes	complemented
406	#548	C₂²×C₁₃	1	4	yes	complemented
407	#547	C₂²×C₁₃	1	6	yes	complemented
408	#546	C₂²×C₁₃	1	12	yes	complemented
409	#546	C₂²×C₁₃	1	12	yes	complemented
410	#546	C₂²×C₁₃	1	12	yes	complemented
411	#546	C₂²×C₁₃	1	24	yes	complemented
412	D₄²	C₂²×C₁₃	1	12	yes	complemented
413	D₄²	C₂²×C₁₃	1	12	yes	complemented
414	D₄²	C₂²×C₁₃	1	12	yes	complemented
415	D₄²	C₂²×C₁₃	1	12	yes	complemented
416	D₄²	C₂²×C₁₃	1	6	yes	complemented
417	D₄²	C₂²×C₁₃	1	12	yes	complemented
418	#542	C₂²×C₁₃	1	12	yes	complemented
419	#540	C₂²×C₁₃	1	12	yes	complemented
420	#540	C₂²×C₁₃	1	12	yes	complemented
421	#540	C₂²×C₁₃	1	24	yes	complemented
422	#538	C₂²×C₁₃	1	24	yes	complemented
423	#538	C₂²×C₁₃	1	12	yes	complemented
424	#537	C₂²×C₁₃	1	12	yes	complemented
425	#536	C₂²×C₁₃	1	3	yes	complemented
426	#535	C₂²×C₁₃	1	6	yes	complemented
427	#535	C₂²×C₁₃	1	6	yes	complemented
428	#535	C₂²×C₁₃	1	12	yes	complemented
429	#535	C₂²×C₁₃	1	6	yes	complemented
430	#535	C₂²×C₁₃	1	6	yes	complemented
431	#535	C₂²×C₁₃	1	3	yes	complemented
432	#535	C₂²×C₁₃	1	24	yes	complemented
433	#534	C₂²×C₁₃	1	24	yes	complemented
434	#534	C₂²×C₁₃	1	12	yes	complemented
435	#532	C₂²×C₁₃	1	6	yes	complemented
436	#532	C₂²×C₁₃	1	3	yes	complemented
437	#532	C₂²×C₁₃	1	6	yes	complemented
438	C₂×#127	C₂²×C₁₃	1	6	yes	complemented
439	#529	C₂²×C₁₃	1	6	yes	complemented
440	#529	C₂²×C₁₃	1	12	yes	complemented
441	#529	C₂²×C₁₃	1	12	yes	complemented
442	C₂×#124	C₂²×C₁₃	1	3	yes	complemented
443	#525	C₂²×C₁₃	1	6	yes	complemented
444	#525	C₂²×C₁₃	1	6	yes	complemented
445	#525	C₂²×C₁₃	1	12	yes	complemented
446	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
447	#520	C₂²×C₁₃	1	4	yes	complemented
448	#519	C₂²×C₁₃	1	2	yes	complemented
449	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
450	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	C₂²×C₁₃	—	2	2	no	—
452	C₂²×C₁₃	—	2	3	no	—
453	C₂²×C₁₃	—	2	12	no	—
454	C₂²×C₁₃	—	2	6	no	—
455	C₂²×C₁₃	—	2	12	no	—
456	C₂²×C₁₃	—	2	6	no	—
457	C₂²×C₁₃	—	2	12	no	—
458	C₂²×C₁₃	—	2	4	no	—
459	C₂²×C₁₃	—	2	12	no	—
460	C₂²×C₁₃	—	8	12	no	—
461	C₂²×C₁₃	—	16	12	no	—
462	C₂²×C₁₃	—	16	6	no	—
463	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
464	C₄×C₁₃	—	2	4	no	—
465	C₄×C₁₃	—	2	2	no	—
466	C₄×C₁₃	—	2	1	no	—
467	C₄×C₁₃	—	2	6	no	—
468	C₄×C₁₃	—	2	6	no	—
469	C₄×C₁₃	—	2	4	no	—
470	C₄×C₁₃	—	2	12	no	—
471	C₄×C₁₃	—	2	2	no	—
472	C₄×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
473	2₋¹⁺⁴	—	4	4	no	—
474	H(5,𝔽₂)	—	4	8	no	—
475	H(5,𝔽₂)	—	4	4	no	—
476	C₂×#41	—	4	8	no	—
477	C₂×#41	C₂³×C₁₃	1	2	yes	—
478	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×#41	C₂³×C₁₃	1	4	yes	—
480	C₂×#41	C₂³×C₁₃	1	3	yes	—
481	C₂×#41	C₂³×C₁₃	1	6	yes	—
482	C₂×#41	C₂³×C₁₃	1	6	yes	—
483	C₂×#41	C₂³×C₁₃	1	3	yes	—
484	C₂×#41	C₂³×C₁₃	1	12	yes	—
485	C₂×#41	C₂³×C₁₃	1	12	yes	—
486	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
487	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
488	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
489	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
490	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
491	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
492	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
493	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
494	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
495	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
496	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
497	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
498	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
499	#127	C₂³×C₁₃	1	6	yes	—
500	#127	C₂³×C₁₃	1	12	yes	—
501	#127	C₂³×C₁₃	1	12	yes	—
502	#127	C₂³×C₁₃	1	12	yes	—
503	#127	C₂³×C₁₃	1	6	yes	—
504	#127	C₂³×C₁₃	1	3	yes	—
505	#127	C₂³×C₁₃	1	12	yes	—
506	#126	C₂³×C₁₃	1	4	yes	—
507	#126	C₂³×C₁₃	1	12	yes	—
508	#126	C₂³×C₁₃	1	12	yes	—
509	#126	C₂³×C₁₃	1	24	yes	—
510	#125	C₂³×C₁₃	1	2	yes	—
511	#125	C₂³×C₁₃	1	12	yes	—
512	#125	C₂³×C₁₃	1	12	yes	—
513	#124	C₂³×C₁₃	1	3	yes	—
514	#124	C₂³×C₁₃	1	6	yes	—
515	#124	C₂³×C₁₃	1	12	yes	—
516	#124	C₂³×C₁₃	1	6	yes	—
517	#124	C₂³×C₁₃	1	12	yes	—
518	#124	C₂³×C₁₃	1	12	yes	—
519	#124	C₂³×C₁₃	1	1	yes	characteristic
520	#124	C₂³×C₁₃	1	6	yes	—
521	#124	C₂³×C₁₃	1	6	yes	—
522	#124	C₂³×C₁₃	1	12	yes	—
523	#124	C₂³×C₁₃	1	24	yes	—
524	#123	C₂³×C₁₃	1	2	yes	—
525	#123	C₂³×C₁₃	1	6	yes	—
526	#123	C₂³×C₁₃	1	12	yes	—
527	#123	C₂³×C₁₃	1	12	yes	—
528	#123	C₂³×C₁₃	1	24	yes	—
529	#123	C₂³×C₁₃	1	12	yes	—
530	#123	C₂³×C₁₃	1	12	yes	—
531	#123	C₂³×C₁₃	1	12	yes	—
532	#123	C₂³×C₁₃	1	24	yes	—
533	#123	C₂³×C₁₃	1	24	yes	—
534	#123	C₂³×C₁₃	1	12	yes	—
535	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
536	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
537	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
538	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
539	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
540	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
541	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
542	#121	C₂³×C₁₃	1	12	yes	—
543	#121	C₂³×C₁₃	1	24	yes	—
544	#121	C₂³×C₁₃	1	12	yes	—
545	#121	C₂³×C₁₃	1	12	yes	—
546	#121	C₂³×C₁₃	1	12	yes	—
547	#121	C₂³×C₁₃	1	12	yes	—
548	#121	C₂³×C₁₃	1	12	yes	—
549	#121	C₂³×C₁₃	1	12	yes	—
550	#121	C₂³×C₁₃	1	12	yes	—
551	#121	C₂³×C₁₃	1	6	yes	—
552	#121	C₂³×C₁₃	1	12	yes	—
553	#121	C₂³×C₁₃	1	12	yes	—
554	#121	C₂³×C₁₃	1	12	yes	—
555	#121	C₂³×C₁₃	1	12	yes	—
556	#121	C₂³×C₁₃	1	12	yes	—
557	#121	C₂³×C₁₃	1	12	yes	—
558	#121	C₂³×C₁₃	1	12	yes	—
559	#121	C₂³×C₁₃	1	24	yes	—
560	#121	C₂³×C₁₃	1	24	yes	—
561	#121	C₂³×C₁₃	1	24	yes	—
562	#121	C₂³×C₁₃	1	24	yes	—
563	#121	C₂³×C₁₃	1	24	yes	—
564	#120	C₂³×C₁₃	1	12	yes	—
565	#120	C₂³×C₁₃	1	12	yes	—
566	#120	C₂³×C₁₃	1	6	yes	—
567	#120	C₂³×C₁₃	1	6	yes	—
568	#120	C₂³×C₁₃	1	12	yes	—
569	#120	C₂³×C₁₃	1	12	yes	—
570	#120	C₂³×C₁₃	1	24	yes	—
571	#120	C₂³×C₁₃	1	24	yes	—
572	#120	C₂³×C₁₃	1	24	yes	—
573	#120	C₂³×C₁₃	1	12	yes	—
574	#120	C₂³×C₁₃	1	12	yes	—
575	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
576	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
577	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
578	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
579	C₄×D₄	C₂³×C₁₃	1	6	yes	—
580	C₄×D₄	C₂³×C₁₃	1	12	yes	—
581	C₄×D₄	C₂³×C₁₃	1	12	yes	—
582	C₄×D₄	C₂³×C₁₃	1	12	yes	—
583	C₄×D₄	C₂³×C₁₃	1	12	yes	—
584	C₄×D₄	C₂³×C₁₃	1	6	yes	—
585	C₄×D₄	C₂³×C₁₃	1	12	yes	—
586	C₄×D₄	C₂³×C₁₃	1	12	yes	—
587	C₄×D₄	C₂³×C₁₃	1	12	yes	—
588	C₄×D₄	C₂³×C₁₃	1	24	yes	—
589	C₄×D₄	C₂³×C₁₃	1	24	yes	—
590	C₄×D₄	C₂³×C₁₃	1	12	yes	—
591	#117	C₂³×C₁₃	1	6	yes	—
592	#117	C₂³×C₁₃	1	3	yes	—
593	#117	C₂³×C₁₃	1	6	yes	—
594	#117	C₂³×C₁₃	1	6	yes	—
595	#117	C₂³×C₁₃	1	12	yes	—
596	#117	C₂³×C₁₃	1	24	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
600	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
601	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
602	C₂×C₁₃	—	4	2	no	—
603	C₂×C₁₃	—	4	12	no	—
604	C₂×C₁₃	—	4	3	no	—
605	C₂×C₁₃	—	4	6	no	—
606	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
607	C₂×C₁₃	H(7,𝔽₂)	1	2	yes	—
608	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
609	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
610	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
611	#41	—	2	16	no	—
612	#41	—	2	8	no	—
613	#41	—	2	4	no	—
614	#41	—	4	12	no	—
615	#41	—	4	6	no	—
616	#41	—	4	6	no	—
617	#41	—	4	24	no	—
618	#41	—	4	12	no	—
619	#41	—	8	12	no	—
620	C₂×Q₈	—	2	8	no	—
621	C₂×Q₈	—	4	6	no	—
622	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
623	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
624	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
626	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
627	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
628	C₂×D₄	—	4	12	no	—
629	C₂×D₄	—	4	24	no	—
630	C₂×D₄	—	4	12	no	—
631	C₂×D₄	—	4	12	no	—
632	C₂×D₄	—	4	6	no	—
633	C₂×D₄	—	8	24	no	—
634	C₂×D₄	—	8	24	no	—
635	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
636	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
637	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
638	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
639	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
640	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
641	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
642	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
643	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
644	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
645	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
646	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
647	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
648	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
649	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
650	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
651	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
652	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
653	C₂²×C₄	—	4	12	no	—
654	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
655	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
656	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
657	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
658	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
659	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
660	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
661	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
662	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
663	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
664	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
665	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
666	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
667	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
668	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
669	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
670	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
671	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
672	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
673	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
674	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
676	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
677	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
678	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
679	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
680	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
681	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
682	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
683	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
684	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
685	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
686	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
687	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
688	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
689	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
690	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
691	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
692	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
693	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
694	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
695	C₄²	C₂⁴×C₁₃	1	2	yes	—
696	C₄²	C₂⁴×C₁₃	1	6	yes	—
697	C₄²	C₂⁴×C₁₃	1	6	yes	—
698	C₄²	C₂⁴×C₁₃	1	12	yes	—
699	C₄²	C₂⁴×C₁₃	1	3	yes	—
700	C₄²	C₂⁴×C₁₃	1	12	yes	—
701	C₁₃	#63066	1	1	yes	characteristic, direct product factor, Sylow
702	C₂³	—	4	6	no	—
703	C₂³	—	4	12	no	—
704	C₂³	—	4	6	no	—
705	C₂³	—	4	12	no	—
706	C₂³	—	4	24	no	—
707	C₂³	—	4	12	no	—
708	C₂³	C₂⁵×C₁₃	1	6	yes	—
709	C₂³	C₂⁵×C₁₃	1	2	yes	—
710	C₂³	C₂⁵×C₁₃	1	12	yes	—
711	C₂³	C₂⁵×C₁₃	1	3	yes	—
712	Q₈	—	2	12	no	—
713	Q₈	—	4	3	no	—
714	Q₈	—	4	2	no	—
715	Q₈	—	4	1	no	—
716	Q₈	—	4	6	no	—
717	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
718	D₄	—	2	12	no	—
719	D₄	—	2	24	no	—
720	D₄	—	2	6	no	—
721	D₄	—	4	12	no	—
722	D₄	—	4	6	no	—
723	D₄	—	4	6	no	—
724	D₄	—	4	3	no	—
725	D₄	—	4	12	no	—
726	D₄	—	4	12	no	—
727	D₄	—	4	12	no	—
728	D₄	—	4	12	no	—
729	D₄	—	4	12	no	—
730	D₄	—	4	24	no	—
731	D₄	—	4	12	no	—
732	D₄	—	4	24	no	—
733	D₄	—	4	1	no	—
734	D₄	—	4	6	no	—
735	D₄	—	4	6	no	—
736	C₂×C₄	—	2	12	no	—
737	C₂×C₄	—	2	24	no	—
738	C₂×C₄	—	2	12	no	—
739	C₂×C₄	—	2	6	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	12	no	—
742	C₂×C₄	—	4	12	no	—
743	C₂×C₄	—	4	24	no	—
744	C₂×C₄	—	4	6	no	—
745	C₂×C₄	—	4	6	no	—
746	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
747	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
748	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
749	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
750	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
751	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
752	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
753	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
754	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	3	no	—
757	C₂²	—	2	12	no	—
758	C₂²	—	2	6	no	—
759	C₂²	—	2	12	no	—
760	C₂²	—	2	6	no	—
761	C₂²	—	2	12	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	2	12	no	—
764	C₂²	—	8	12	no	—
765	C₂²	—	16	12	no	—
766	C₂²	—	16	6	no	—
767	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
768	C₄	—	2	4	no	—
769	C₄	—	2	2	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	6	no	—
772	C₄	—	2	6	no	—
773	C₄	—	2	4	no	—
774	C₄	—	2	12	no	—
775	C₄	—	2	2	no	—
776	C₄	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
777	C₂	—	4	2	no	—
778	C₂	—	4	12	no	—
779	C₂	—	4	6	no	—
780	C₂	—	4	3	no	—
781	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
782	C₂	C₁₃×H(7,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3558	C₂	semidirect
2. C₁₃×#3551	C₂	semidirect
3. C₁₃×#3549	C₂	semidirect
4. C₁₃×#3543	C₂	semidirect
5. C₁₃×#3542	C₂	semidirect
6. C₁₃×#3537	C₂	semidirect
7. C₁₃×#3529	C₂	semidirect
8. C₁₃×#3524	C₂	semidirect
9. C₁₃×#3517	C₂	semidirect
10. C₁₃×#3500	C₂	semidirect
11. C₁₃×#3498	C₂	semidirect
12. C₁₃×#3488	C₂	semidirect
13. C₁₃×#3487	C₂	semidirect
14. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
15. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×C₁₃×#41	C₂²	semidirect
18. C₁₃×#563	C₂²	semidirect
19. C₁₃×#563	C₂²	semidirect
20. C₁₃×#562	C₂²	semidirect
21. C₁₃×#562	C₂²	semidirect
22. C₁₃×H(3,𝔽₄)	C₂²	semidirect
23. C₁₃×H(3,𝔽₄)	C₂²	semidirect
24. C₁₃×#560	C₂²	semidirect
25. C₁₃×#560	C₂²	semidirect
26. C₁₃×#560	C₂²	semidirect
27. C₁₃×#560	C₂²	semidirect
28. C₁₃×#559	C₂²	semidirect
29. C₁₃×#557	C₂²	semidirect
30. C₁₃×#555	C₂²	semidirect
31. C₁₃×#555	C₂²	semidirect
32. C₁₃×#553	C₂²	semidirect
33. C₁₃×#553	C₂²	semidirect
34. C₁₃×#552	C₂²	semidirect
35. C₁₃×#551	C₂²	semidirect
36. C₁₃×#550	C₂²	semidirect
37. C₁₃×#550	C₂²	semidirect
38. C₁₃×#550	C₂²	semidirect
39. C₁₃×#550	C₂²	semidirect
40. C₁₃×#550	C₂²	semidirect
41. C₁₃×#548	C₂²	semidirect
42. C₁₃×#548	C₂²	semidirect
43. C₁₃×#548	C₂²	semidirect
44. C₁₃×#547	C₂²	semidirect
45. C₁₃×#546	C₂²	semidirect
46. C₁₃×#546	C₂²	semidirect
47. C₁₃×#546	C₂²	semidirect
48. C₁₃×#546	C₂²	semidirect
49. D₄²×C₁₃	C₂²	semidirect
50. D₄²×C₁₃	C₂²	semidirect
51. D₄²×C₁₃	C₂²	semidirect
52. D₄²×C₁₃	C₂²	semidirect
53. D₄²×C₁₃	C₂²	semidirect
54. D₄²×C₁₃	C₂²	semidirect
55. C₁₃×#542	C₂²	semidirect
56. C₁₃×#540	C₂²	semidirect
57. C₁₃×#540	C₂²	semidirect
58. C₁₃×#540	C₂²	semidirect
59. C₁₃×#538	C₂²	semidirect
60. C₁₃×#538	C₂²	semidirect
61. C₁₃×#537	C₂²	semidirect
62. C₁₃×#536	C₂²	semidirect
63. C₁₃×#535	C₂²	semidirect
64. C₁₃×#535	C₂²	semidirect
65. C₁₃×#535	C₂²	semidirect
66. C₁₃×#535	C₂²	semidirect
67. C₁₃×#535	C₂²	semidirect
68. C₁₃×#535	C₂²	semidirect
69. C₁₃×#535	C₂²	semidirect
70. C₁₃×#534	C₂²	semidirect
71. C₁₃×#534	C₂²	semidirect
72. C₁₃×#532	C₂²	semidirect
73. C₁₃×#532	C₂²	semidirect
74. C₁₃×#532	C₂²	semidirect
75. C₂×C₁₃×#127	C₂²	semidirect
76. C₁₃×#529	C₂²	semidirect
77. C₁₃×#529	C₂²	semidirect
78. C₁₃×#529	C₂²	semidirect
79. C₂×C₁₃×#124	C₂²	semidirect
80. C₁₃×#525	C₂²	semidirect
81. C₁₃×#525	C₂²	semidirect
82. C₁₃×#525	C₂²	semidirect
83. C₂×C₁₃×#121	C₂²	semidirect
84. C₁₃×#520	C₂²	semidirect
85. C₁₃×#519	C₂²	semidirect
86. C₄×C₁₃×#41	C₂²	semidirect
87. C₄×C₁₃×#41	C₂²	semidirect
217. #63066	C₁₃	direct (N × H)
311. #3558	C₂×C₁₃	semidirect
312. #3551	C₂×C₁₃	semidirect
313. #3549	C₂×C₁₃	semidirect
314. #3543	C₂×C₁₃	semidirect
315. #3542	C₂×C₁₃	semidirect
316. #3537	C₂×C₁₃	semidirect
317. #3529	C₂×C₁₃	semidirect
318. #3524	C₂×C₁₃	semidirect
319. #3517	C₂×C₁₃	semidirect
320. #3500	C₂×C₁₃	semidirect
321. #3498	C₂×C₁₃	semidirect
322. #3488	C₂×C₁₃	semidirect
323. #3487	C₂×C₁₃	semidirect
377. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
378. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
379. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
380. C₂²×#41	C₂²×C₁₃	semidirect
381. #563	C₂²×C₁₃	semidirect
382. #563	C₂²×C₁₃	semidirect
383. #562	C₂²×C₁₃	semidirect
384. #562	C₂²×C₁₃	semidirect
385. H(3,𝔽₄)	C₂²×C₁₃	semidirect
386. H(3,𝔽₄)	C₂²×C₁₃	semidirect
387. #560	C₂²×C₁₃	semidirect
388. #560	C₂²×C₁₃	semidirect
389. #560	C₂²×C₁₃	semidirect
390. #560	C₂²×C₁₃	semidirect
391. #559	C₂²×C₁₃	semidirect
392. #557	C₂²×C₁₃	semidirect
393. #555	C₂²×C₁₃	semidirect
394. #555	C₂²×C₁₃	semidirect
395. #553	C₂²×C₁₃	semidirect
396. #553	C₂²×C₁₃	semidirect
397. #552	C₂²×C₁₃	semidirect
398. #551	C₂²×C₁₃	semidirect
399. #550	C₂²×C₁₃	semidirect
400. #550	C₂²×C₁₃	semidirect
401. #550	C₂²×C₁₃	semidirect
402. #550	C₂²×C₁₃	semidirect
403. #550	C₂²×C₁₃	semidirect
404. #548	C₂²×C₁₃	semidirect
405. #548	C₂²×C₁₃	semidirect
406. #548	C₂²×C₁₃	semidirect
407. #547	C₂²×C₁₃	semidirect
408. #546	C₂²×C₁₃	semidirect
409. #546	C₂²×C₁₃	semidirect
410. #546	C₂²×C₁₃	semidirect
411. #546	C₂²×C₁₃	semidirect
412. D₄²	C₂²×C₁₃	semidirect
413. D₄²	C₂²×C₁₃	semidirect
414. D₄²	C₂²×C₁₃	semidirect
415. D₄²	C₂²×C₁₃	semidirect
416. D₄²	C₂²×C₁₃	semidirect
417. D₄²	C₂²×C₁₃	semidirect
418. #542	C₂²×C₁₃	semidirect
419. #540	C₂²×C₁₃	semidirect
420. #540	C₂²×C₁₃	semidirect
421. #540	C₂²×C₁₃	semidirect
422. #538	C₂²×C₁₃	semidirect
423. #538	C₂²×C₁₃	semidirect
424. #537	C₂²×C₁₃	semidirect
425. #536	C₂²×C₁₃	semidirect
426. #535	C₂²×C₁₃	semidirect
427. #535	C₂²×C₁₃	semidirect
428. #535	C₂²×C₁₃	semidirect
429. #535	C₂²×C₁₃	semidirect
430. #535	C₂²×C₁₃	semidirect
431. #535	C₂²×C₁₃	semidirect
432. #535	C₂²×C₁₃	semidirect
433. #534	C₂²×C₁₃	semidirect
434. #534	C₂²×C₁₃	semidirect
435. #532	C₂²×C₁₃	semidirect
436. #532	C₂²×C₁₃	semidirect
437. #532	C₂²×C₁₃	semidirect
438. C₂×#127	C₂²×C₁₃	semidirect
439. #529	C₂²×C₁₃	semidirect
440. #529	C₂²×C₁₃	semidirect
441. #529	C₂²×C₁₃	semidirect
442. C₂×#124	C₂²×C₁₃	semidirect
443. #525	C₂²×C₁₃	semidirect
444. #525	C₂²×C₁₃	semidirect
445. #525	C₂²×C₁₃	semidirect
446. C₂×#121	C₂²×C₁₃	semidirect
447. #520	C₂²×C₁₃	semidirect
448. #519	C₂²×C₁₃	semidirect
449. C₄×#41	C₂²×C₁₃	semidirect
450. C₄×#41	C₂²×C₁₃	semidirect
701. C₁₃	#63066	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3558	2
C₁₃×#3551	2
C₁₃×#3549	2
C₁₃×#3543	2
C₁₃×#3542	2
C₁₃×#3537	2
C₁₃×#3529	2
C₁₃×#3524	2
C₁₃×#3517	2
C₁₃×#3500	2
C₁₃×#3498	2
C₁₃×#3488	2
C₁₃×#3487	2
#63066	13

Subgroups — C13×#63066 #15749405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#63066 #15749405