Subgroups — C₁₃×#60758 #15747097

Order 3328.

2186 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3488	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3201	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3200	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3196	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3193	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3187	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3091	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3063	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3057	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3009	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
24	C₁₃×#550	—	2	1	no	—
25	C₁₃×#548	—	2	1	no	—
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#546	—	2	1	no	—
28	D₄²×C₁₃	—	2	2	no	—
29	D₄²×C₁₃	—	2	1	no	—
30	C₁₃×#537	C₂²	1	1	yes	characteristic
31	C₁₃×#537	C₂²	1	2	yes	—
32	C₁₃×#536	—	2	2	no	—
33	C₁₃×#536	—	2	1	no	—
34	C₁₃×#536	—	2	1	no	—
35	C₁₃×#536	C₂²	1	2	yes	—
36	C₁₃×#536	C₂²	1	2	yes	complemented
37	C₁₃×#536	C₂²	1	4	yes	complemented
38	C₁₃×#535	C₂²	1	1	yes	characteristic
39	C₁₃×#535	C₂²	1	2	yes	—
40	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₁₃×#124	—	2	1	no	—
42	C₁₃×#525	C₂²	1	1	yes	characteristic
43	C₁₃×#525	C₂²	1	2	yes	—
44	C₂×C₁₃×#123	—	2	2	no	—
45	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
46	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
47	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#121	C₂²	1	2	yes	—
49	C₁₃×#520	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#485	C₂²	1	2	yes	complemented
52	C₁₃×#485	C₂²	1	4	yes	complemented
53	C₁₃×#485	C₂²	1	4	yes	complemented
54	C₁₃×#484	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#484	C₂²	1	4	yes	complemented
56	C₁₃×#483	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#483	C₂²	1	4	yes	complemented
58	C₁₃×#482	C₂²	1	2	yes	complemented
59	C₁₃×#482	C₂²	1	4	yes	complemented
60	C₁₃×#481	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#481	C₂²	1	2	yes	complemented
62	C₁₃×#480	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#480	C₂²	1	2	yes	complemented
64	C₁₃×#470	C₂²	1	4	yes	complemented
65	C₁₃×#468	C₂²	1	4	yes	complemented
66	C₁₃×#468	C₂²	1	4	yes	complemented
67	C₁₃×#468	C₂²	1	4	yes	complemented
68	C₁₃×#467	C₂²	1	4	yes	complemented
69	C₁₃×#465	C₂²	1	4	yes	complemented
70	C₁₃×#465	C₂²	1	4	yes	complemented
71	C₁₃×#465	C₂²	1	4	yes	complemented
72	C₁₃×#452	C₂²	1	4	yes	complemented
73	C₁₃×#452	C₂²	1	4	yes	complemented
74	C₁₃×#451	C₂²	1	2	yes	complemented
75	C₁₃×#451	C₂²	1	2	yes	complemented
76	C₁₃×#450	C₂²	1	4	yes	complemented
77	C₁₃×#450	C₂²	1	4	yes	complemented
78	C₁₃×#448	C₂²	1	2	yes	complemented
79	C₁₃×#448	C₂²	1	2	yes	complemented
80	C₁₃×#448	C₂²	1	2	yes	complemented
81	C₁₃×#448	C₂²	1	2	yes	complemented
82	C₁₃×#448	C₂²	1	4	yes	complemented
83	C₁₃×#428	C₂²	1	2	yes	complemented
84	C₁₃×#427	C₂²	1	2	yes	complemented
85	C₁₃×#419	C₂²	1	2	yes	complemented
86	C₁₃×#418	C₂²	1	2	yes	complemented
87	C₁₃×#416	C₂²	1	2	yes	complemented
88	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
89	C₁₃×#408	C₂²	1	2	yes	—
90	C₁₃×#408	C₂²	1	4	yes	complemented
91	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#407	C₂²	1	2	yes	complemented
93	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
95	C₁₃×H(5,𝔽₂)	—	4	4	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	—	4	4	no	—
98	C₂×C₁₃×#41	D₄	1	2	yes	—
99	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
100	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
101	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×#41	C₂³	1	2	yes	—
103	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×#41	C₂³	1	2	yes	—
106	C₂²×Q₈×C₁₃	—	2	1	no	—
107	C₂²×Q₈×C₁₃	—	2	1	no	—
108	C₂²×Q₈×C₁₃	—	2	1	no	—
109	C₂²×Q₈×C₁₃	—	4	4	no	—
110	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
111	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
112	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
113	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₁₃	—	2	1	no	—
115	C₂²×D₄×C₁₃	—	2	2	no	—
116	C₂²×D₄×C₁₃	—	2	2	no	—
117	C₂²×D₄×C₁₃	—	2	1	no	—
118	C₂²×D₄×C₁₃	D₄	1	2	yes	—
119	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
120	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₁₃	—	2	1	no	—
123	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₁₃×#137	—	4	4	no	—
126	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
127	C₂×C₁₃×SD₁₆	—	4	4	no	—
128	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
131	C₁₃×#131	—	4	4	no	—
132	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
133	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
134	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
135	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
136	C₁₃×C₄⋊Q₈	—	2	2	no	—
137	C₁₃×C₄⋊Q₈	—	2	2	no	—
138	C₁₃×C₄⋊Q₈	—	2	4	no	—
139	C₁₃×#127	—	2	1	no	—
140	C₁₃×#127	—	2	2	no	—
141	C₁₃×#124	—	2	1	no	—
142	C₁₃×#124	—	2	2	no	—
143	C₁₃×#124	—	2	2	no	—
144	C₁₃×#124	—	2	2	no	—
145	C₁₃×#124	—	2	4	no	—
146	C₁₃×#123	—	2	4	no	—
147	C₁₃×#123	—	2	4	no	—
148	C₁₃×#123	—	2	4	no	—
149	C₁₃×#123	—	2	4	no	—
150	C₁₃×#123	—	2	1	no	—
151	C₁₃×#123	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	—	2	1	no	—
153	C₁₃×C₂²⋊Q₈	—	2	2	no	—
154	C₁₃×C₂²⋊Q₈	—	2	2	no	—
155	C₁₃×C₂²⋊Q₈	—	2	2	no	—
156	C₁₃×C₂²⋊Q₈	—	2	2	no	—
157	C₁₃×C₂²⋊Q₈	—	2	2	no	—
158	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
159	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
160	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
163	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
164	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
165	C₁₃×#121	—	2	2	no	—
166	C₁₃×#121	—	2	2	no	—
167	C₁₃×#121	—	2	2	no	—
168	C₁₃×#121	—	2	1	no	—
169	C₁₃×#121	—	2	2	no	—
170	C₁₃×#121	—	2	1	no	—
171	C₁₃×#121	—	2	2	no	—
172	C₁₃×#121	—	2	1	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	C₂³	1	2	yes	—
175	C₁₃×#121	C₂³	1	1	yes	characteristic
176	C₁₃×#121	C₂³	1	2	yes	—
177	C₁₃×#121	C₂³	1	1	yes	characteristic
178	C₁₃×#121	C₂³	1	2	yes	—
179	C₁₃×#121	C₂³	1	2	yes	—
180	C₁₃×#121	C₂³	1	2	yes	—
181	C₁₃×#120	—	2	1	no	—
182	C₁₃×#120	—	2	2	no	—
183	C₁₃×#120	—	2	2	no	—
184	C₁₃×#120	—	2	2	no	—
185	C₁₃×#120	—	2	2	no	—
186	C₄×Q₈×C₁₃	—	2	1	no	—
187	C₄×D₄×C₁₃	—	2	2	no	—
188	C₄×D₄×C₁₃	—	2	1	no	—
189	C₄×D₄×C₁₃	—	2	1	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	1	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₁₃×#117	—	2	1	no	—
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	C₂³	1	2	yes	—
196	C₁₃×#117	C₂³	1	1	yes	characteristic
197	C₁₃×#117	C₂³	1	2	yes	—
198	C₁₃×#117	C₂³	1	2	yes	—
199	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
208	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
209	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₄²×C₁₃	—	2	1	no	—
211	C₁₃×#107	C₂³	1	2	yes	—
212	C₁₃×#107	C₂³	1	2	yes	—
213	C₁₃×#107	C₂³	1	4	yes	—
214	C₁₃×#106	C₂³	1	2	yes	—
215	C₁₃×#106	C₂³	1	2	yes	—
216	C₁₃×#106	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
233	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
234	#60758	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	2	no	—
236	C₂⁴×C₁₃	—	2	1	no	—
237	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	2	4	no	—
242	C₁₃×#41	—	4	4	no	—
243	C₁₃×#41	—	4	4	no	—
244	C₁₃×#41	—	4	2	no	—
245	C₁₃×#41	—	4	2	no	—
246	C₁₃×#41	—	4	4	no	—
247	C₁₃×#41	—	4	4	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	—	2	2	no	—
250	C₂×Q₈×C₁₃	—	2	2	no	—
251	C₂×Q₈×C₁₃	—	2	4	no	—
252	C₂×Q₈×C₁₃	—	2	4	no	—
253	C₂×Q₈×C₁₃	—	4	4	no	—
254	C₂×Q₈×C₁₃	—	4	4	no	—
255	C₂×Q₈×C₁₃	—	4	2	no	—
256	C₂×Q₈×C₁₃	—	4	4	no	—
257	C₂×Q₈×C₁₃	—	4	4	no	—
258	C₂×Q₈×C₁₃	—	4	4	no	—
259	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
262	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
263	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×D₄×C₁₃	—	2	1	no	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	1	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	1	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	2	no	—
274	C₂×D₄×C₁₃	—	2	1	no	—
275	C₂×D₄×C₁₃	—	2	4	no	—
276	C₂×D₄×C₁₃	—	4	2	no	—
277	C₂×D₄×C₁₃	—	4	4	no	—
278	C₂×D₄×C₁₃	—	4	4	no	—
279	C₂×D₄×C₁₃	—	4	8	no	—
280	C₂×D₄×C₁₃	—	4	4	no	—
281	C₂×D₄×C₁₃	—	8	2	no	—
282	C₂×D₄×C₁₃	—	8	4	no	—
283	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
286	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
288	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
289	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
290	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	—	2	4	no	—
293	C₂²×C₄×C₁₃	—	2	1	no	—
294	C₂²×C₄×C₁₃	—	2	1	no	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	—	2	2	no	—
297	C₂²×C₄×C₁₃	—	2	2	no	—
298	C₂²×C₄×C₁₃	—	2	2	no	—
299	C₂²×C₄×C₁₃	—	2	1	no	—
300	C₂²×C₄×C₁₃	—	2	2	no	—
301	C₂²×C₄×C₁₃	—	2	1	no	—
302	C₂²×C₄×C₁₃	—	4	4	no	—
303	C₂²×C₄×C₁₃	—	4	4	no	—
304	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
308	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
309	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
310	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
315	C₁₃×Q₁₆	—	4	4	no	—
316	C₁₃×SD₁₆	—	4	4	no	—
317	C₁₃×SD₁₆	—	4	4	no	—
318	C₁₃×SD₁₆	—	4	4	no	—
319	C₁₃×M₁₆	—	2	4	no	—
320	C₁₃×M₁₆	—	4	4	no	—
321	C₂×C₈×C₁₃	—	2	4	no	—
322	C₂×C₈×C₁₃	—	4	4	no	—
323	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
324	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
325	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
326	C₁₃×C₄⋊C₄	—	2	4	no	—
327	C₁₃×C₄⋊C₄	—	2	4	no	—
328	C₁₃×C₄⋊C₄	—	2	4	no	—
329	C₁₃×C₄⋊C₄	—	2	4	no	—
330	C₁₃×C₄⋊C₄	—	2	1	no	—
331	C₁₃×C₄⋊C₄	—	2	1	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	1	no	—
334	C₁₃×C₄⋊C₄	—	2	1	no	—
335	C₁₃×C₄⋊C₄	—	2	1	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
338	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
339	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
340	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
341	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	2	no	—
344	C₁₃×C₂²⋊C₄	—	2	4	no	—
345	C₁₃×C₂²⋊C₄	—	2	4	no	—
346	C₁₃×C₂²⋊C₄	—	2	4	no	—
347	C₁₃×C₂²⋊C₄	—	2	4	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	1	no	—
350	C₁₃×C₂²⋊C₄	—	2	1	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	1	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	1	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	1	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₄²×C₁₃	—	2	2	no	—
361	C₄²×C₁₃	—	2	2	no	—
362	C₄²×C₁₃	—	2	2	no	—
363	C₄²×C₁₃	—	2	1	no	—
364	#3488	C₂×C₁₃	1	1	yes	characteristic
365	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#3201	C₂×C₁₃	1	4	yes	complemented
367	#3200	C₂×C₁₃	1	4	yes	complemented
368	#3196	C₂×C₁₃	1	2	yes	complemented
369	#3193	C₂×C₁₃	1	2	yes	complemented
370	#3190	C₂×C₁₃	1	2	yes	complemented
371	#3187	C₂×C₁₃	1	2	yes	complemented
372	#3097	C₂×C₁₃	1	2	yes	complemented
373	#3094	C₂×C₁₃	1	1	yes	characteristic, complemented
374	#3091	C₂×C₁₃	1	1	yes	characteristic, complemented
375	#3063	C₂×C₁₃	1	2	yes	complemented
376	#3057	C₂×C₁₃	1	2	yes	complemented
377	#3009	C₂×C₁₃	1	2	yes	complemented
378	#3004	C₂×C₁₃	1	1	yes	characteristic, complemented
379	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
380	#2880	C₂×C₁₃	1	1	yes	characteristic, complemented
381	C₂³×C₁₃	—	2	2	no	—
382	C₂³×C₁₃	—	2	2	no	—
383	C₂³×C₁₃	—	2	4	no	—
384	C₂³×C₁₃	—	2	2	no	—
385	C₂³×C₁₃	—	2	1	no	—
386	C₂³×C₁₃	—	4	1	no	—
387	C₂³×C₁₃	—	4	2	no	—
388	C₂³×C₁₃	—	4	2	no	—
389	C₂³×C₁₃	—	4	4	no	—
390	C₂³×C₁₃	—	4	2	no	—
391	C₂³×C₁₃	—	8	1	no	—
392	C₂³×C₁₃	—	8	2	no	—
393	C₂³×C₁₃	—	8	1	no	—
394	C₂³×C₁₃	—	8	2	no	—
395	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
396	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	Q₈×C₁₃	—	2	2	no	—
401	Q₈×C₁₃	—	2	2	no	—
402	Q₈×C₁₃	—	2	4	no	—
403	Q₈×C₁₃	—	2	4	no	—
404	Q₈×C₁₃	—	2	2	no	—
405	Q₈×C₁₃	—	4	2	no	—
406	Q₈×C₁₃	—	4	4	no	—
407	Q₈×C₁₃	—	4	4	no	—
408	Q₈×C₁₃	—	4	4	no	—
409	D₄×C₁₃	—	2	4	no	—
410	D₄×C₁₃	—	2	4	no	—
411	D₄×C₁₃	—	2	2	no	—
412	D₄×C₁₃	—	2	2	no	—
413	D₄×C₁₃	—	2	4	no	—
414	D₄×C₁₃	—	2	2	no	—
415	D₄×C₁₃	—	4	2	no	—
416	D₄×C₁₃	—	4	2	no	—
417	D₄×C₁₃	—	4	2	no	—
418	D₄×C₁₃	—	4	4	no	—
419	D₄×C₁₃	—	4	4	no	—
420	D₄×C₁₃	—	4	2	no	—
421	D₄×C₁₃	—	4	4	no	—
422	D₄×C₁₃	—	4	2	no	—
423	D₄×C₁₃	—	4	2	no	—
424	D₄×C₁₃	—	8	1	no	—
425	D₄×C₁₃	—	8	2	no	—
426	D₄×C₁₃	—	8	2	no	—
427	D₄×C₁₃	—	8	2	no	—
428	D₄×C₁₃	—	8	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	4	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	4	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	1	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	4	no	—
443	C₂×C₄×C₁₃	—	4	2	no	—
444	C₂×C₄×C₁₃	—	4	2	no	—
445	C₂×C₄×C₁₃	—	4	2	no	—
446	C₂×C₄×C₁₃	—	4	4	no	—
447	C₂×C₄×C₁₃	—	4	2	no	—
448	C₂×C₄×C₁₃	—	4	4	no	—
449	C₂×C₄×C₁₃	—	4	4	no	—
450	C₂×C₄×C₁₃	—	4	4	no	—
451	C₂×C₄×C₁₃	—	4	2	no	—
452	C₂×C₄×C₁₃	—	4	2	no	—
453	C₂×C₄×C₁₃	—	8	1	no	—
454	C₂×C₄×C₁₃	—	8	2	no	—
455	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
461	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
462	C₈×C₁₃	—	2	2	no	—
463	C₈×C₁₃	—	2	2	no	—
464	C₈×C₁₃	—	2	4	no	—
465	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
466	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
467	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
469	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
470	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
471	#550	—	2	1	no	—
472	#548	—	2	1	no	—
473	#546	—	2	2	no	—
474	#546	—	2	1	no	—
475	D₄²	—	2	2	no	—
476	D₄²	—	2	1	no	—
477	#537	C₂²×C₁₃	1	2	yes	—
478	#537	C₂²×C₁₃	1	1	yes	characteristic
479	#536	—	2	2	no	—
480	#536	—	2	1	no	—
481	#536	—	2	1	no	—
482	#536	C₂²×C₁₃	1	2	yes	—
483	#536	C₂²×C₁₃	1	4	yes	complemented
484	#536	C₂²×C₁₃	1	2	yes	complemented
485	#535	C₂²×C₁₃	1	2	yes	—
486	#535	C₂²×C₁₃	1	1	yes	characteristic
487	C₂×C₄⋊Q₈	—	2	1	no	—
488	C₂×#124	—	2	1	no	—
489	#525	C₂²×C₁₃	1	1	yes	characteristic
490	#525	C₂²×C₁₃	1	2	yes	—
491	C₂×#123	—	2	2	no	—
492	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
493	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
494	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
495	C₂×#121	C₂²×C₁₃	1	2	yes	—
496	#520	C₂²×C₁₃	1	1	yes	characteristic
497	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	#485	C₂²×C₁₃	1	2	yes	complemented
499	#485	C₂²×C₁₃	1	4	yes	complemented
500	#485	C₂²×C₁₃	1	4	yes	complemented
501	#484	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	#484	C₂²×C₁₃	1	4	yes	complemented
503	#483	C₂²×C₁₃	1	1	yes	characteristic, complemented
504	#483	C₂²×C₁₃	1	4	yes	complemented
505	#482	C₂²×C₁₃	1	2	yes	complemented
506	#482	C₂²×C₁₃	1	4	yes	complemented
507	#481	C₂²×C₁₃	1	1	yes	characteristic, complemented
508	#481	C₂²×C₁₃	1	2	yes	complemented
509	#480	C₂²×C₁₃	1	1	yes	characteristic, complemented
510	#480	C₂²×C₁₃	1	2	yes	complemented
511	#470	C₂²×C₁₃	1	4	yes	complemented
512	#468	C₂²×C₁₃	1	4	yes	complemented
513	#468	C₂²×C₁₃	1	4	yes	complemented
514	#468	C₂²×C₁₃	1	4	yes	complemented
515	#467	C₂²×C₁₃	1	4	yes	complemented
516	#465	C₂²×C₁₃	1	4	yes	complemented
517	#465	C₂²×C₁₃	1	4	yes	complemented
518	#465	C₂²×C₁₃	1	4	yes	complemented
519	#452	C₂²×C₁₃	1	4	yes	complemented
520	#452	C₂²×C₁₃	1	4	yes	complemented
521	#451	C₂²×C₁₃	1	2	yes	complemented
522	#451	C₂²×C₁₃	1	2	yes	complemented
523	#450	C₂²×C₁₃	1	4	yes	complemented
524	#450	C₂²×C₁₃	1	4	yes	complemented
525	#448	C₂²×C₁₃	1	2	yes	complemented
526	#448	C₂²×C₁₃	1	2	yes	complemented
527	#448	C₂²×C₁₃	1	2	yes	complemented
528	#448	C₂²×C₁₃	1	2	yes	complemented
529	#448	C₂²×C₁₃	1	4	yes	complemented
530	#428	C₂²×C₁₃	1	2	yes	complemented
531	#427	C₂²×C₁₃	1	2	yes	complemented
532	#419	C₂²×C₁₃	1	2	yes	complemented
533	#418	C₂²×C₁₃	1	2	yes	complemented
534	#416	C₂²×C₁₃	1	2	yes	complemented
535	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
536	#408	C₂²×C₁₃	1	2	yes	—
537	#408	C₂²×C₁₃	1	4	yes	complemented
538	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
539	#407	C₂²×C₁₃	1	2	yes	complemented
540	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
541	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
542	C₂²×C₁₃	—	2	1	no	—
543	C₂²×C₁₃	—	2	1	no	—
544	C₂²×C₁₃	—	2	1	no	—
545	C₂²×C₁₃	—	2	1	no	—
546	C₂²×C₁₃	—	2	1	no	—
547	C₂²×C₁₃	—	2	2	no	—
548	C₂²×C₁₃	—	2	2	no	—
549	C₂²×C₁₃	—	2	1	no	—
550	C₂²×C₁₃	—	2	2	no	—
551	C₂²×C₁₃	—	2	2	no	—
552	C₂²×C₁₃	—	2	2	no	—
553	C₂²×C₁₃	—	2	1	no	—
554	C₂²×C₁₃	—	2	2	no	—
555	C₂²×C₁₃	—	4	4	no	—
556	C₂²×C₁₃	—	4	2	no	—
557	C₂²×C₁₃	—	4	1	no	—
558	C₂²×C₁₃	—	4	2	no	—
559	C₂²×C₁₃	—	4	1	no	—
560	C₂²×C₁₃	—	4	2	no	—
561	C₂²×C₁₃	—	4	1	no	—
562	C₂²×C₁₃	—	8	4	no	—
563	C₂²×C₁₃	—	16	2	no	—
564	C₂²×C₁₃	—	16	4	no	—
565	C₂²×C₁₃	#534	1	2	yes	—
566	C₂²×C₁₃	#577	1	2	yes	—
567	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
568	C₄×C₁₃	—	2	1	no	—
569	C₄×C₁₃	—	2	1	no	—
570	C₄×C₁₃	—	2	2	no	—
571	C₄×C₁₃	—	2	2	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	—	4	1	no	—
574	C₄×C₁₃	—	4	1	no	—
575	C₄×C₁₃	—	4	4	no	—
576	C₄×C₁₃	—	4	2	no	—
577	C₄×C₁₃	—	4	2	no	—
578	C₄×C₁₃	—	4	1	no	—
579	C₄×C₁₃	#534	1	2	yes	—
580	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
581	H(5,𝔽₂)	—	4	4	no	—
582	C₂×#41	—	2	1	no	—
583	C₂×#41	—	4	4	no	—
584	C₂×#41	D₄×C₁₃	1	2	yes	—
585	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
586	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
587	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
588	C₂×#41	C₂³×C₁₃	1	2	yes	—
589	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
590	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×#41	C₂³×C₁₃	1	2	yes	—
592	C₂²×Q₈	—	2	1	no	—
593	C₂²×Q₈	—	2	1	no	—
594	C₂²×Q₈	—	2	1	no	—
595	C₂²×Q₈	—	4	4	no	—
596	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
597	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
598	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
599	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
600	C₂²×D₄	—	2	1	no	—
601	C₂²×D₄	—	2	2	no	—
602	C₂²×D₄	—	2	2	no	—
603	C₂²×D₄	—	2	1	no	—
604	C₂²×D₄	D₄×C₁₃	1	2	yes	—
605	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
606	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
608	C₂³×C₄	—	2	1	no	—
609	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
611	#137	—	4	4	no	—
612	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
613	C₂×SD₁₆	—	4	4	no	—
614	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
615	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
616	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
617	#131	—	4	4	no	—
618	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
619	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
620	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
621	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
622	C₄⋊Q₈	—	2	2	no	—
623	C₄⋊Q₈	—	2	2	no	—
624	C₄⋊Q₈	—	2	4	no	—
625	#127	—	2	1	no	—
626	#127	—	2	2	no	—
627	#124	—	2	1	no	—
628	#124	—	2	2	no	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	—	2	4	no	—
632	#123	—	2	4	no	—
633	#123	—	2	4	no	—
634	#123	—	2	4	no	—
635	#123	—	2	4	no	—
636	#123	—	2	1	no	—
637	#123	—	2	2	no	—
638	C₂²⋊Q₈	—	2	1	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
645	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
646	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
647	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
648	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
649	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
650	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	1	no	—
655	#121	—	2	2	no	—
656	#121	—	2	1	no	—
657	#121	—	2	2	no	—
658	#121	—	2	1	no	—
659	#121	—	2	2	no	—
660	#121	C₂³×C₁₃	1	2	yes	—
661	#121	C₂³×C₁₃	1	1	yes	characteristic
662	#121	C₂³×C₁₃	1	2	yes	—
663	#121	C₂³×C₁₃	1	2	yes	—
664	#121	C₂³×C₁₃	1	2	yes	—
665	#121	C₂³×C₁₃	1	1	yes	characteristic
666	#121	C₂³×C₁₃	1	2	yes	—
667	#120	—	2	1	no	—
668	#120	—	2	2	no	—
669	#120	—	2	2	no	—
670	#120	—	2	2	no	—
671	#120	—	2	2	no	—
672	C₄×Q₈	—	2	1	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	1	no	—
675	C₄×D₄	—	2	1	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	1	no	—
678	C₄×D₄	—	2	2	no	—
679	#117	—	2	1	no	—
680	#117	—	2	1	no	—
681	#117	C₂³×C₁₃	1	2	yes	—
682	#117	C₂³×C₁₃	1	2	yes	—
683	#117	C₂³×C₁₃	1	1	yes	characteristic
684	#117	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄⋊C₄	—	2	2	no	—
686	C₂×C₄⋊C₄	—	2	2	no	—
687	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
691	C₂×C₂²⋊C₄	—	2	1	no	—
692	C₂×C₂²⋊C₄	—	2	2	no	—
693	C₂×C₂²⋊C₄	—	2	2	no	—
694	C₂×C₂²⋊C₄	—	2	1	no	—
695	C₂×C₂²⋊C₄	—	2	2	no	—
696	C₂×C₄²	—	2	1	no	—
697	#107	C₂³×C₁₃	1	2	yes	—
698	#107	C₂³×C₁₃	1	2	yes	—
699	#107	C₂³×C₁₃	1	4	yes	—
700	#106	C₂³×C₁₃	1	2	yes	—
701	#106	C₂³×C₁₃	1	2	yes	—
702	#106	C₂³×C₁₃	1	4	yes	—
703	#103	C₂³×C₁₃	1	4	yes	—
704	#103	C₂³×C₁₃	1	4	yes	—
705	#103	C₂³×C₁₃	1	2	yes	—
706	#103	C₂³×C₁₃	1	2	yes	—
707	#103	C₂³×C₁₃	1	4	yes	—
708	#103	C₂³×C₁₃	1	4	yes	—
709	#102	C₂³×C₁₃	1	2	yes	—
710	#102	C₂³×C₁₃	1	2	yes	—
711	#102	C₂³×C₁₃	1	4	yes	—
712	#102	C₂³×C₁₃	1	4	yes	—
713	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
714	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
715	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
716	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
717	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
718	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
719	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
720	C₂×C₁₃	—	2	2	no	—
721	C₂×C₁₃	—	2	2	no	—
722	C₂×C₁₃	—	4	1	no	—
723	C₂×C₁₃	—	4	2	no	—
724	C₂×C₁₃	—	4	2	no	—
725	C₂×C₁₃	—	8	2	no	—
726	C₂×C₁₃	—	8	1	no	—
727	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
728	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
729	C₂×C₁₃	#3586	1	1	yes	characteristic
730	C₂⁴	—	2	2	no	—
731	C₂⁴	—	2	1	no	—
732	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
734	#41	—	2	4	no	—
735	#41	—	2	4	no	—
736	#41	—	2	4	no	—
737	#41	—	4	4	no	—
738	#41	—	4	4	no	—
739	#41	—	4	2	no	—
740	#41	—	4	2	no	—
741	#41	—	4	4	no	—
742	#41	—	4	4	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	2	4	no	—
747	C₂×Q₈	—	2	4	no	—
748	C₂×Q₈	—	4	4	no	—
749	C₂×Q₈	—	4	4	no	—
750	C₂×Q₈	—	4	2	no	—
751	C₂×Q₈	—	4	4	no	—
752	C₂×Q₈	—	4	4	no	—
753	C₂×Q₈	—	4	4	no	—
754	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
755	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
756	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
757	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
758	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₂×D₄	—	2	1	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	1	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	1	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	1	no	—
770	C₂×D₄	—	2	4	no	—
771	C₂×D₄	—	4	2	no	—
772	C₂×D₄	—	4	4	no	—
773	C₂×D₄	—	4	4	no	—
774	C₂×D₄	—	4	8	no	—
775	C₂×D₄	—	4	4	no	—
776	C₂×D₄	—	8	2	no	—
777	C₂×D₄	—	8	4	no	—
778	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
779	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
781	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
782	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
783	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
784	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
785	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
786	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
787	C₂²×C₄	—	2	4	no	—
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	4	4	no	—
798	C₂²×C₄	—	4	4	no	—
799	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
800	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
801	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
802	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
803	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
804	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
809	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
810	Q₁₆	—	4	4	no	—
811	SD₁₆	—	4	4	no	—
812	SD₁₆	—	4	4	no	—
813	SD₁₆	—	4	4	no	—
814	M₁₆	—	2	4	no	—
815	M₁₆	—	4	4	no	—
816	C₂×C₈	—	2	4	no	—
817	C₂×C₈	—	4	4	no	—
818	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
819	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
820	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
821	C₄⋊C₄	—	2	4	no	—
822	C₄⋊C₄	—	2	4	no	—
823	C₄⋊C₄	—	2	4	no	—
824	C₄⋊C₄	—	2	4	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
833	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
836	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	4	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	4	no	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	1	no	—
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	1	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	1	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₄²	—	2	2	no	—
856	C₄²	—	2	2	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	1	no	—
859	C₁₃	#60758	1	1	yes	characteristic, direct product factor, Sylow
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	4	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	4	1	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	2	no	—
868	C₂³	—	4	4	no	—
869	C₂³	—	4	2	no	—
870	C₂³	—	8	1	no	—
871	C₂³	—	8	2	no	—
872	C₂³	—	8	1	no	—
873	C₂³	—	8	2	no	—
874	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
875	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
876	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
877	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
878	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
879	Q₈	—	2	2	no	—
880	Q₈	—	2	2	no	—
881	Q₈	—	2	4	no	—
882	Q₈	—	2	4	no	—
883	Q₈	—	2	2	no	—
884	Q₈	—	4	2	no	—
885	Q₈	—	4	4	no	—
886	Q₈	—	4	4	no	—
887	Q₈	—	4	4	no	—
888	D₄	—	2	4	no	—
889	D₄	—	2	4	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	4	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	2	no	—
895	D₄	—	4	2	no	—
896	D₄	—	4	2	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	4	no	—
899	D₄	—	4	2	no	—
900	D₄	—	4	4	no	—
901	D₄	—	4	2	no	—
902	D₄	—	4	2	no	—
903	D₄	—	8	2	no	—
904	D₄	—	8	2	no	—
905	D₄	—	8	2	no	—
906	D₄	—	8	1	no	—
907	D₄	—	8	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	4	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	4	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	4	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	2	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	2	no	—
932	C₂×C₄	—	8	1	no	—
933	C₂×C₄	—	8	2	no	—
934	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
939	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
940	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
941	C₈	—	2	2	no	—
942	C₈	—	2	2	no	—
943	C₈	—	2	4	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	1	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	2	no	—
956	C₂²	—	2	2	no	—
957	C₂²	—	4	4	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	1	no	—
964	C₂²	—	8	4	no	—
965	C₂²	—	16	2	no	—
966	C₂²	—	16	4	no	—
967	C₂²	C₁₃×#534	1	2	yes	—
968	C₂²	C₁₃×#577	1	2	yes	—
969	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	4	no	—
981	C₄	C₁₃×#534	1	2	yes	—
982	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
983	C₂	—	2	2	no	—
984	C₂	—	2	2	no	—
985	C₂	—	4	1	no	—
986	C₂	—	4	2	no	—
987	C₂	—	4	2	no	—
988	C₂	—	8	2	no	—
989	C₂	—	8	1	no	—
990	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
991	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
992	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3488	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#536	C₂	semidirect
3. C₁₃×#3201	C₂	semidirect
4. C₁₃×#3200	C₂	semidirect
5. C₁₃×#3196	C₂	semidirect
6. C₁₃×#3193	C₂	semidirect
7. C₁₃×#3190	C₂	semidirect
8. C₁₃×#3187	C₂	semidirect
9. C₁₃×#3097	C₂	semidirect
10. C₁₃×#3094	C₂	semidirect
11. C₁₃×#3091	C₂	semidirect
12. C₁₃×#3063	C₂	semidirect
13. C₁₃×#3057	C₂	semidirect
14. C₁₃×#3009	C₂	semidirect
15. C₁₃×#3004	C₂	semidirect
16. C₂×C₁₃×#448	C₂	semidirect
17. C₁₃×#2880	C₂	semidirect
20. C₂³×Q₈×C₁₃	C₂²	semidirect
21. C₂×C₁₃×#137	C₂²	semidirect
22. C₂²×C₁₃×SD₁₆	C₂²	semidirect
23. C₂×C₁₃×#131	C₂²	semidirect
36. C₁₃×#536	C₂²	semidirect
37. C₁₃×#536	C₂²	semidirect
45. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
46. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
50. C₂×C₁₃×#117	C₂²	semidirect
51. C₁₃×#485	C₂²	semidirect
52. C₁₃×#485	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
54. C₁₃×#484	C₂²	semidirect
55. C₁₃×#484	C₂²	semidirect
56. C₁₃×#483	C₂²	semidirect
57. C₁₃×#483	C₂²	semidirect
58. C₁₃×#482	C₂²	semidirect
59. C₁₃×#482	C₂²	semidirect
60. C₁₃×#481	C₂²	semidirect
61. C₁₃×#481	C₂²	semidirect
62. C₁₃×#480	C₂²	semidirect
63. C₁₃×#480	C₂²	semidirect
64. C₁₃×#470	C₂²	semidirect
65. C₁₃×#468	C₂²	semidirect
66. C₁₃×#468	C₂²	semidirect
67. C₁₃×#468	C₂²	semidirect
68. C₁₃×#467	C₂²	semidirect
69. C₁₃×#465	C₂²	semidirect
70. C₁₃×#465	C₂²	semidirect
71. C₁₃×#465	C₂²	semidirect
72. C₁₃×#452	C₂²	semidirect
73. C₁₃×#452	C₂²	semidirect
74. C₁₃×#451	C₂²	semidirect
75. C₁₃×#451	C₂²	semidirect
76. C₁₃×#450	C₂²	semidirect
77. C₁₃×#450	C₂²	semidirect
78. C₁₃×#448	C₂²	semidirect
79. C₁₃×#448	C₂²	semidirect
80. C₁₃×#448	C₂²	semidirect
81. C₁₃×#448	C₂²	semidirect
82. C₁₃×#448	C₂²	semidirect
83. C₁₃×#428	C₂²	semidirect
84. C₁₃×#427	C₂²	semidirect
85. C₁₃×#419	C₂²	semidirect
86. C₁₃×#418	C₂²	semidirect
87. C₁₃×#416	C₂²	semidirect
88. C₂×C₁₃×#103	C₂²	semidirect
90. C₁₃×#408	C₂²	semidirect
91. C₁₃×#407	C₂²	semidirect
92. C₁₃×#407	C₂²	semidirect
93. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
94. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
234. #60758	C₁₃	direct (N × H)
365. C₂×#536	C₂×C₁₃	semidirect
366. #3201	C₂×C₁₃	semidirect
367. #3200	C₂×C₁₃	semidirect
368. #3196	C₂×C₁₃	semidirect
369. #3193	C₂×C₁₃	semidirect
370. #3190	C₂×C₁₃	semidirect
371. #3187	C₂×C₁₃	semidirect
372. #3097	C₂×C₁₃	semidirect
373. #3094	C₂×C₁₃	semidirect
374. #3091	C₂×C₁₃	semidirect
375. #3063	C₂×C₁₃	semidirect
376. #3057	C₂×C₁₃	semidirect
377. #3009	C₂×C₁₃	semidirect
378. #3004	C₂×C₁₃	semidirect
379. C₂×#448	C₂×C₁₃	semidirect
380. #2880	C₂×C₁₃	semidirect
467. C₂³×Q₈	C₂²×C₁₃	semidirect
468. C₂×#137	C₂²×C₁₃	semidirect
469. C₂²×SD₁₆	C₂²×C₁₃	semidirect
470. C₂×#131	C₂²×C₁₃	semidirect
483. #536	C₂²×C₁₃	semidirect
484. #536	C₂²×C₁₃	semidirect
492. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
493. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
497. C₂×#117	C₂²×C₁₃	semidirect
498. #485	C₂²×C₁₃	semidirect
499. #485	C₂²×C₁₃	semidirect
500. #485	C₂²×C₁₃	semidirect
501. #484	C₂²×C₁₃	semidirect
502. #484	C₂²×C₁₃	semidirect
503. #483	C₂²×C₁₃	semidirect
504. #483	C₂²×C₁₃	semidirect
505. #482	C₂²×C₁₃	semidirect
506. #482	C₂²×C₁₃	semidirect
507. #481	C₂²×C₁₃	semidirect
508. #481	C₂²×C₁₃	semidirect
509. #480	C₂²×C₁₃	semidirect
510. #480	C₂²×C₁₃	semidirect
511. #470	C₂²×C₁₃	semidirect
512. #468	C₂²×C₁₃	semidirect
513. #468	C₂²×C₁₃	semidirect
514. #468	C₂²×C₁₃	semidirect
515. #467	C₂²×C₁₃	semidirect
516. #465	C₂²×C₁₃	semidirect
517. #465	C₂²×C₁₃	semidirect
518. #465	C₂²×C₁₃	semidirect
519. #452	C₂²×C₁₃	semidirect
520. #452	C₂²×C₁₃	semidirect
521. #451	C₂²×C₁₃	semidirect
522. #451	C₂²×C₁₃	semidirect
523. #450	C₂²×C₁₃	semidirect
524. #450	C₂²×C₁₃	semidirect
525. #448	C₂²×C₁₃	semidirect
526. #448	C₂²×C₁₃	semidirect
527. #448	C₂²×C₁₃	semidirect
528. #448	C₂²×C₁₃	semidirect
529. #448	C₂²×C₁₃	semidirect
530. #428	C₂²×C₁₃	semidirect
531. #427	C₂²×C₁₃	semidirect
532. #419	C₂²×C₁₃	semidirect
533. #418	C₂²×C₁₃	semidirect
534. #416	C₂²×C₁₃	semidirect
535. C₂×#103	C₂²×C₁₃	semidirect
537. #408	C₂²×C₁₃	semidirect
538. #407	C₂²×C₁₃	semidirect
539. #407	C₂²×C₁₃	semidirect
540. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
541. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
859. C₁₃	#60758	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×#3488	2
C₂×C₁₃×#536	2
C₁₃×#3201	2
C₁₃×#3200	2
C₁₃×#3196	2
C₁₃×#3193	2
C₁₃×#3190	2
C₁₃×#3187	2
C₁₃×#3097	2
C₁₃×#3094	2
C₁₃×#3091	2
C₁₃×#3063	2
C₁₃×#3057	2
C₁₃×#3009	2
C₁₃×#3004	2
C₂×C₁₃×#448	2
C₁₃×#2880	2
#60758	13

Subgroups — C13×#60758 #15747097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60758 #15747097