Subgroups — C₁₃×#60814 #15747153

Order 3328.

2026 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3223	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3209	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3156	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3044	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3002	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#137	C₂²	1	2	yes	—
21	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#135	C₂²	1	2	yes	—
23	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
24	C₁₃×#556	—	2	1	no	—
25	C₁₃×#554	—	2	1	no	—
26	C₁₃×#552	—	2	2	no	—
27	C₁₃×#552	—	2	1	no	—
28	C₁₃×#552	—	2	1	no	—
29	C₁₃×#551	—	2	2	no	—
30	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#542	C₂²	1	2	yes	complemented
32	C₁₃×#541	C₂²	1	2	yes	complemented
33	C₁₃×#536	—	2	1	no	—
34	C₁₃×#536	—	2	2	no	—
35	C₁₃×#536	—	2	1	no	—
36	C₁₃×#536	C₂²	1	2	yes	—
37	C₁₃×#536	C₂²	1	2	yes	—
38	C₁₃×#536	C₂²	1	4	yes	—
39	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#533	C₂²	1	2	yes	—
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
42	C₁₃×#529	C₂²	1	2	yes	—
43	C₂×C₁₃×#124	C₂²	1	2	yes	—
44	C₁₃×#525	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#123	—	2	2	no	—
46	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
47	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
48	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
52	C₁₃×#497	C₂²	1	4	yes	complemented
53	C₁₃×#497	C₂²	1	4	yes	complemented
54	C₁₃×#495	C₂²	1	4	yes	complemented
55	C₁₃×#494	C₂²	1	4	yes	complemented
56	C₁₃×#491	C₂²	1	4	yes	complemented
57	C₁₃×#489	C₂²	1	4	yes	complemented
58	C₁₃×#488	C₂²	1	4	yes	complemented
59	C₁₃×#487	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#464	C₂²	1	4	yes	complemented
62	C₁₃×#464	C₂²	1	4	yes	complemented
63	C₁₃×#463	C₂²	1	4	yes	complemented
64	C₁₃×#462	C₂²	1	4	yes	complemented
65	C₁₃×#462	C₂²	1	4	yes	complemented
66	C₁₃×#462	C₂²	1	4	yes	complemented
67	C₁₃×#461	C₂²	1	4	yes	complemented
68	C₁₃×#452	C₂²	1	4	yes	—
69	C₁₃×#452	C₂²	1	2	yes	—
70	C₁₃×#451	C₂²	1	2	yes	—
71	C₁₃×#451	C₂²	1	1	yes	characteristic
72	C₁₃×#451	C₂²	1	2	yes	—
73	C₁₃×#451	C₂²	1	2	yes	—
74	C₁₃×#451	C₂²	1	2	yes	—
75	C₁₃×#451	C₂²	1	2	yes	complemented
76	C₁₃×#451	C₂²	1	4	yes	complemented
77	C₁₃×#450	C₂²	1	2	yes	—
78	C₁₃×#450	C₂²	1	1	yes	characteristic
79	C₁₃×#449	C₂²	1	2	yes	—
80	C₁₃×#448	C₂²	1	2	yes	—
81	C₁₃×#448	C₂²	1	1	yes	characteristic
82	C₁₃×#448	C₂²	1	2	yes	complemented
83	C₁₃×#447	C₂²	1	1	yes	characteristic
84	C₁₃×#433	C₂²	1	4	yes	complemented
85	C₁₃×#432	C₂²	1	2	yes	—
86	C₁₃×#431	C₂²	1	2	yes	—
87	C₁₃×#424	C₂²	1	2	yes	complemented
88	C₁₃×#419	C₂²	1	2	yes	complemented
89	C₁₃×#417	C₂²	1	2	yes	—
90	C₁₃×#416	C₂²	1	2	yes	—
91	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
92	C₁₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₁₃×#405	C₂²	1	2	yes	complemented
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	—	4	4	no	—
98	C₂×C₁₃×#41	C₂³	1	2	yes	—
99	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×#41	C₂³	1	2	yes	—
101	C₂²×Q₈×C₁₃	—	2	1	no	—
102	C₂²×Q₈×C₁₃	—	2	1	no	—
103	C₂²×Q₈×C₁₃	—	2	1	no	—
104	C₂²×Q₈×C₁₃	—	4	4	no	—
105	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
106	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	—	2	1	no	—
111	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	—	2	1	no	—
113	C₂³×C₄×C₁₃	—	2	1	no	—
114	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₁₃×#137	—	4	4	no	—
116	C₁₃×#137	—	4	4	no	—
117	C₁₃×#135	—	4	4	no	—
118	C₂×C₁₃×Q₁₆	—	4	4	no	—
119	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
120	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
121	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×D₈	C₂³	1	2	yes	—
129	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
130	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
131	C₁₃×C₄⋊Q₈	—	2	1	no	—
132	C₁₃×C₄⋊Q₈	—	2	2	no	—
133	C₁₃×C₄⋊Q₈	—	2	2	no	—
134	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
135	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×#126	—	2	2	no	—
139	C₁₃×#126	—	2	2	no	—
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#125	—	2	2	no	—
143	C₁₃×#125	—	2	2	no	—
144	C₁₃×#125	—	2	1	no	—
145	C₁₃×#125	—	2	2	no	—
146	C₁₃×#125	C₂³	1	2	yes	—
147	C₁₃×#124	—	2	2	no	—
148	C₁₃×#124	—	2	2	no	—
149	C₁₃×#124	—	2	2	no	—
150	C₁₃×#124	C₂³	1	4	yes	—
151	C₁₃×#124	C₂³	1	4	yes	—
152	C₁₃×#124	C₂³	1	2	yes	—
153	C₁₃×#123	—	2	1	no	—
154	C₁₃×#123	—	2	2	no	—
155	C₁₃×#123	—	2	4	no	—
156	C₁₃×#123	—	2	4	no	—
157	C₁₃×#123	—	2	4	no	—
158	C₁₃×#123	—	2	4	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×C₂²⋊Q₈	—	2	1	no	—
162	C₁₃×C₂²⋊Q₈	—	2	1	no	—
163	C₁₃×C₂²⋊Q₈	—	2	2	no	—
164	C₁₃×C₂²⋊Q₈	—	2	2	no	—
165	C₁₃×C₂²⋊Q₈	—	2	2	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	4	no	—
168	C₁₃×C₂²⋊Q₈	—	2	2	no	—
169	C₁₃×C₂²⋊Q₈	—	2	4	no	—
170	C₁₃×C₂²⋊Q₈	—	2	1	no	—
171	C₁₃×C₂²⋊Q₈	—	2	1	no	—
172	C₁₃×C₂²⋊Q₈	—	2	2	no	—
173	C₁₃×C₂²⋊Q₈	—	2	2	no	—
174	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
176	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
178	C₁₃×#121	C₂³	1	1	yes	characteristic
179	C₁₃×#121	C₂³	1	1	yes	characteristic
180	C₁₃×#120	—	2	1	no	—
181	C₄×Q₈×C₁₃	—	2	1	no	—
182	C₄×Q₈×C₁₃	—	2	1	no	—
183	C₄×Q₈×C₁₃	—	2	2	no	—
184	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
185	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
186	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
187	C₄×D₄×C₁₃	—	2	1	no	—
188	C₄×D₄×C₁₃	—	2	1	no	—
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	C₂³	1	2	yes	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	—	2	1	no	—
194	C₁₃×#117	—	2	2	no	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	D₄	1	1	yes	characteristic
197	C₁₃×#117	D₄	1	2	yes	—
198	C₁₃×#117	D₄	1	1	yes	characteristic
199	C₁₃×#117	C₂³	1	1	yes	characteristic
200	C₁₃×#117	C₂³	1	1	yes	characteristic
201	C₁₃×#117	C₂³	1	1	yes	characteristic
202	C₁₃×#117	C₂³	1	2	yes	—
203	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
205	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
208	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
209	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
211	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
212	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
213	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
214	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
216	C₁₃×C₄⋊C₈	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×#103	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	2	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	2	yes	—
231	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₁₃×#97	C₂³	1	4	yes	—
233	C₄×C₈×C₁₃	C₂³	1	4	yes	—
234	#60814	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	1	no	—
236	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₁₃×#41	—	2	4	no	—
238	C₁₃×#41	—	2	4	no	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	4	2	no	—
241	C₁₃×#41	—	4	2	no	—
242	C₁₃×#41	—	4	4	no	—
243	C₁₃×#41	—	4	4	no	—
244	C₂×Q₈×C₁₃	—	2	1	no	—
245	C₂×Q₈×C₁₃	—	2	2	no	—
246	C₂×Q₈×C₁₃	—	2	2	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	2	1	no	—
249	C₂×Q₈×C₁₃	—	2	2	no	—
250	C₂×Q₈×C₁₃	—	2	4	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	C₂⁴	1	4	yes	—
260	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
261	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
262	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₁₃	—	2	1	no	—
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	1	no	—
269	C₂×D₄×C₁₃	—	4	2	no	—
270	C₂×D₄×C₁₃	—	4	4	no	—
271	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	2	1	no	—
276	C₂²×C₄×C₁₃	—	2	1	no	—
277	C₂²×C₄×C₁₃	—	2	2	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	2	1	no	—
280	C₂²×C₄×C₁₃	—	2	1	no	—
281	C₂²×C₄×C₁₃	—	2	2	no	—
282	C₂²×C₄×C₁₃	—	2	2	no	—
283	C₂²×C₄×C₁₃	—	2	2	no	—
284	C₂²×C₄×C₁₃	—	4	4	no	—
285	C₂²×C₄×C₁₃	—	4	4	no	—
286	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₁₃×Q₁₆	—	4	4	no	—
295	C₁₃×Q₁₆	—	4	4	no	—
296	C₁₃×Q₁₆	—	4	2	no	—
297	C₁₃×Q₁₆	—	4	4	no	—
298	C₁₃×Q₁₆	—	4	4	no	—
299	C₁₃×SD₁₆	—	4	2	no	—
300	C₁₃×SD₁₆	—	4	2	no	—
301	C₁₃×SD₁₆	—	4	4	no	—
302	C₁₃×SD₁₆	—	4	4	no	—
303	C₁₃×D₈	—	4	2	no	—
304	C₁₃×M₁₆	—	2	4	no	—
305	C₂×C₈×C₁₃	—	2	4	no	—
306	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
307	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
308	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
309	C₁₃×C₄⋊C₄	—	2	1	no	—
310	C₁₃×C₄⋊C₄	—	2	2	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	2	no	—
313	C₁₃×C₄⋊C₄	—	2	4	no	—
314	C₁₃×C₄⋊C₄	—	2	4	no	—
315	C₁₃×C₄⋊C₄	—	2	4	no	—
316	C₁₃×C₄⋊C₄	—	2	4	no	—
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	1	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	1	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
327	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
328	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
330	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
331	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
332	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
333	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
334	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
335	C₁₃×C₂²⋊C₄	—	2	2	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	1	no	—
338	C₁₃×C₂²⋊C₄	—	2	1	no	—
339	C₁₃×C₂²⋊C₄	—	2	1	no	—
340	C₁₃×C₂²⋊C₄	—	2	4	no	—
341	C₁₃×C₂²⋊C₄	—	2	4	no	—
342	C₁₃×C₂²⋊C₄	—	2	4	no	—
343	C₁₃×C₂²⋊C₄	—	2	4	no	—
344	C₁₃×C₂²⋊C₄	—	2	1	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	1	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
350	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
351	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
352	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
353	C₄²×C₁₃	—	2	2	no	—
354	C₄²×C₁₃	—	2	2	no	—
355	C₄²×C₁₃	—	2	2	no	—
356	C₄²×C₁₃	—	2	1	no	—
357	C₄²×C₁₃	C₂×D₄	1	2	yes	—
358	C₄²×C₁₃	C₂×D₄	1	2	yes	—
359	C₄²×C₁₃	C₂⁴	1	2	yes	—
360	C₄²×C₁₃	C₂⁴	1	2	yes	—
361	#3495	C₂×C₁₃	1	1	yes	characteristic, complemented
362	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3225	C₂×C₁₃	1	4	yes	complemented
364	#3223	C₂×C₁₃	1	4	yes	complemented
365	#3218	C₂×C₁₃	1	2	yes	complemented
366	#3215	C₂×C₁₃	1	2	yes	complemented
367	#3211	C₂×C₁₃	1	2	yes	complemented
368	#3209	C₂×C₁₃	1	2	yes	complemented
369	#3156	C₂×C₁₃	1	2	yes	complemented
370	#3137	C₂×C₁₃	1	2	yes	complemented
371	#3046	C₂×C₁₃	1	2	yes	complemented
372	#3044	C₂×C₁₃	1	2	yes	complemented
373	#3007	C₂×C₁₃	1	1	yes	characteristic, complemented
374	#3004	C₂×C₁₃	1	1	yes	characteristic, complemented
375	#3002	C₂×C₁₃	1	1	yes	characteristic
376	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
377	#2924	C₂×C₁₃	1	1	yes	characteristic, complemented
378	C₂³×C₁₃	—	2	2	no	—
379	C₂³×C₁₃	—	2	2	no	—
380	C₂³×C₁₃	—	2	1	no	—
381	C₂³×C₁₃	—	2	2	no	—
382	C₂³×C₁₃	—	4	1	no	—
383	C₂³×C₁₃	—	4	2	no	—
384	C₂³×C₁₃	—	4	2	no	—
385	C₂³×C₁₃	—	4	2	no	—
386	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
387	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
388	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	Q₈×C₁₃	—	2	4	no	—
390	Q₈×C₁₃	—	2	2	no	—
391	Q₈×C₁₃	—	2	4	no	—
392	Q₈×C₁₃	—	2	2	no	—
393	Q₈×C₁₃	—	2	4	no	—
394	Q₈×C₁₃	—	2	2	no	—
395	Q₈×C₁₃	—	4	4	no	—
396	Q₈×C₁₃	—	4	4	no	—
397	Q₈×C₁₃	—	4	2	no	—
398	Q₈×C₁₃	—	4	2	no	—
399	Q₈×C₁₃	—	4	4	no	—
400	Q₈×C₁₃	—	8	2	no	—
401	D₄×C₁₃	—	2	2	no	—
402	D₄×C₁₃	—	2	2	no	—
403	D₄×C₁₃	—	2	2	no	—
404	D₄×C₁₃	—	4	2	no	—
405	D₄×C₁₃	—	4	4	no	—
406	D₄×C₁₃	—	4	4	no	—
407	D₄×C₁₃	—	4	2	no	—
408	D₄×C₁₃	—	4	2	no	—
409	D₄×C₁₃	—	8	1	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	4	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	4	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	4	2	no	—
424	C₂×C₄×C₁₃	—	4	4	no	—
425	C₂×C₄×C₁₃	—	4	2	no	—
426	C₂×C₄×C₁₃	—	4	4	no	—
427	C₂×C₄×C₁₃	—	4	4	no	—
428	C₂×C₄×C₁₃	—	4	4	no	—
429	C₂×C₄×C₁₃	—	4	2	no	—
430	C₂×C₄×C₁₃	—	4	4	no	—
431	C₂×C₄×C₁₃	—	4	2	no	—
432	C₂×C₄×C₁₃	—	8	2	no	—
433	C₂×C₄×C₁₃	—	8	1	no	—
434	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
442	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
443	C₈×C₁₃	—	2	2	no	—
444	C₈×C₁₃	—	2	2	no	—
445	C₈×C₁₃	—	2	4	no	—
446	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
447	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×#137	C₂²×C₁₃	1	2	yes	—
449	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
450	C₂×#135	C₂²×C₁₃	1	2	yes	—
451	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
452	#556	—	2	1	no	—
453	#554	—	2	1	no	—
454	#552	—	2	2	no	—
455	#552	—	2	1	no	—
456	#552	—	2	1	no	—
457	#551	—	2	2	no	—
458	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
459	#542	C₂²×C₁₃	1	2	yes	complemented
460	#541	C₂²×C₁₃	1	2	yes	complemented
461	#536	—	2	1	no	—
462	#536	—	2	2	no	—
463	#536	—	2	1	no	—
464	#536	C₂²×C₁₃	1	2	yes	—
465	#536	C₂²×C₁₃	1	4	yes	—
466	#536	C₂²×C₁₃	1	2	yes	—
467	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	#533	C₂²×C₁₃	1	2	yes	—
469	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
470	#529	C₂²×C₁₃	1	2	yes	—
471	C₂×#124	C₂²×C₁₃	1	2	yes	—
472	#525	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×#123	—	2	2	no	—
474	C₂×C₂²⋊Q₈	—	2	1	no	—
475	C₂×C₂²⋊Q₈	—	2	1	no	—
476	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
477	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
478	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
480	#497	C₂²×C₁₃	1	4	yes	complemented
481	#497	C₂²×C₁₃	1	4	yes	complemented
482	#495	C₂²×C₁₃	1	4	yes	complemented
483	#494	C₂²×C₁₃	1	4	yes	complemented
484	#491	C₂²×C₁₃	1	4	yes	complemented
485	#489	C₂²×C₁₃	1	4	yes	complemented
486	#488	C₂²×C₁₃	1	4	yes	complemented
487	#487	C₂²×C₁₃	1	4	yes	complemented
488	#464	C₂²×C₁₃	1	4	yes	complemented
489	#464	C₂²×C₁₃	1	4	yes	complemented
490	#464	C₂²×C₁₃	1	4	yes	complemented
491	#463	C₂²×C₁₃	1	4	yes	complemented
492	#462	C₂²×C₁₃	1	4	yes	complemented
493	#462	C₂²×C₁₃	1	4	yes	complemented
494	#462	C₂²×C₁₃	1	4	yes	complemented
495	#461	C₂²×C₁₃	1	4	yes	complemented
496	#452	C₂²×C₁₃	1	2	yes	—
497	#452	C₂²×C₁₃	1	4	yes	—
498	#451	C₂²×C₁₃	1	1	yes	characteristic
499	#451	C₂²×C₁₃	1	2	yes	—
500	#451	C₂²×C₁₃	1	2	yes	—
501	#451	C₂²×C₁₃	1	2	yes	—
502	#451	C₂²×C₁₃	1	2	yes	—
503	#451	C₂²×C₁₃	1	2	yes	complemented
504	#451	C₂²×C₁₃	1	4	yes	complemented
505	#450	C₂²×C₁₃	1	2	yes	—
506	#450	C₂²×C₁₃	1	1	yes	characteristic
507	#449	C₂²×C₁₃	1	2	yes	—
508	#448	C₂²×C₁₃	1	2	yes	—
509	#448	C₂²×C₁₃	1	1	yes	characteristic
510	#448	C₂²×C₁₃	1	2	yes	complemented
511	#447	C₂²×C₁₃	1	1	yes	characteristic
512	#433	C₂²×C₁₃	1	4	yes	complemented
513	#432	C₂²×C₁₃	1	2	yes	—
514	#431	C₂²×C₁₃	1	2	yes	—
515	#424	C₂²×C₁₃	1	2	yes	complemented
516	#419	C₂²×C₁₃	1	2	yes	complemented
517	#417	C₂²×C₁₃	1	2	yes	—
518	#416	C₂²×C₁₃	1	2	yes	—
519	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
520	#407	C₂²×C₁₃	1	1	yes	characteristic
521	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
522	#405	C₂²×C₁₃	1	2	yes	complemented
523	C₂²×C₁₃	—	2	1	no	—
524	C₂²×C₁₃	—	2	1	no	—
525	C₂²×C₁₃	—	2	1	no	—
526	C₂²×C₁₃	—	2	1	no	—
527	C₂²×C₁₃	—	2	1	no	—
528	C₂²×C₁₃	—	2	1	no	—
529	C₂²×C₁₃	—	2	1	no	—
530	C₂²×C₁₃	—	4	4	no	—
531	C₂²×C₁₃	—	4	1	no	—
532	C₂²×C₁₃	—	4	2	no	—
533	C₂²×C₁₃	—	4	2	no	—
534	C₂²×C₁₃	—	4	1	no	—
535	C₂²×C₁₃	—	4	1	no	—
536	C₂²×C₁₃	—	4	2	no	—
537	C₂²×C₁₃	—	8	4	no	—
538	C₂²×C₁₃	#535	1	2	yes	—
539	C₂²×C₁₃	#578	1	2	yes	—
540	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
541	C₄×C₁₃	—	2	2	no	—
542	C₄×C₁₃	—	2	2	no	—
543	C₄×C₁₃	—	2	1	no	—
544	C₄×C₁₃	—	2	1	no	—
545	C₄×C₁₃	—	2	2	no	—
546	C₄×C₁₃	—	2	2	no	—
547	C₄×C₁₃	—	4	2	no	—
548	C₄×C₁₃	—	4	1	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	—	4	4	no	—
551	C₄×C₁₃	—	4	1	no	—
552	C₄×C₁₃	—	4	2	no	—
553	C₄×C₁₃	—	4	1	no	—
554	C₄×C₁₃	#535	1	2	yes	—
555	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
556	C₂×#41	—	2	1	no	—
557	C₂×#41	—	2	1	no	—
558	C₂×#41	—	4	4	no	—
559	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
560	C₂×#41	C₂³×C₁₃	1	2	yes	—
561	C₂×#41	C₂³×C₁₃	1	2	yes	—
562	C₂²×Q₈	—	2	1	no	—
563	C₂²×Q₈	—	2	1	no	—
564	C₂²×Q₈	—	2	1	no	—
565	C₂²×Q₈	—	4	4	no	—
566	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
567	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
568	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
569	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
570	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
571	C₂²×D₄	—	2	1	no	—
572	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
573	C₂³×C₄	—	2	1	no	—
574	C₂³×C₄	—	2	1	no	—
575	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
576	#137	—	4	4	no	—
577	#137	—	4	4	no	—
578	#135	—	4	4	no	—
579	C₂×Q₁₆	—	4	4	no	—
580	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
581	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
582	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
583	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
584	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
585	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
586	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
587	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
588	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
589	C₂×D₈	C₂³×C₁₃	1	2	yes	—
590	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
591	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
592	C₄⋊Q₈	—	2	1	no	—
593	C₄⋊Q₈	—	2	2	no	—
594	C₄⋊Q₈	—	2	2	no	—
595	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
596	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
597	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
599	#126	—	2	2	no	—
600	#126	—	2	2	no	—
601	#126	—	2	2	no	—
602	#126	—	2	2	no	—
603	#125	—	2	2	no	—
604	#125	—	2	2	no	—
605	#125	—	2	1	no	—
606	#125	—	2	2	no	—
607	#125	C₂³×C₁₃	1	2	yes	—
608	#124	—	2	2	no	—
609	#124	—	2	2	no	—
610	#124	—	2	2	no	—
611	#124	C₂³×C₁₃	1	4	yes	—
612	#124	C₂³×C₁₃	1	4	yes	—
613	#124	C₂³×C₁₃	1	2	yes	—
614	#123	—	2	1	no	—
615	#123	—	2	2	no	—
616	#123	—	2	4	no	—
617	#123	—	2	4	no	—
618	#123	—	2	4	no	—
619	#123	—	2	4	no	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	C₂²⋊Q₈	—	2	1	no	—
623	C₂²⋊Q₈	—	2	1	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	4	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	4	no	—
631	C₂²⋊Q₈	—	2	1	no	—
632	C₂²⋊Q₈	—	2	1	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
636	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
637	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
638	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
639	#121	C₂³×C₁₃	1	1	yes	characteristic
640	#121	C₂³×C₁₃	1	1	yes	characteristic
641	#120	—	2	1	no	—
642	C₄×Q₈	—	2	1	no	—
643	C₄×Q₈	—	2	1	no	—
644	C₄×Q₈	—	2	2	no	—
645	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
646	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
647	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	C₂³×C₁₃	1	2	yes	—
653	#117	—	2	2	no	—
654	#117	—	2	1	no	—
655	#117	—	2	2	no	—
656	#117	—	2	2	no	—
657	#117	D₄×C₁₃	1	1	yes	characteristic
658	#117	D₄×C₁₃	1	2	yes	—
659	#117	D₄×C₁₃	1	1	yes	characteristic
660	#117	C₂³×C₁₃	1	1	yes	characteristic
661	#117	C₂³×C₁₃	1	1	yes	characteristic
662	#117	C₂³×C₁₃	1	1	yes	characteristic
663	#117	C₂³×C₁₃	1	2	yes	—
664	C₂×C₄⋊C₄	—	2	2	no	—
665	C₂×C₄⋊C₄	—	2	2	no	—
666	C₂×C₄⋊C₄	—	2	1	no	—
667	C₂×C₄⋊C₄	—	2	1	no	—
668	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
669	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	2	no	—
673	C₂×C₂²⋊C₄	—	2	2	no	—
674	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
675	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
676	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
677	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
678	#103	C₂³×C₁₃	1	4	yes	—
679	#103	C₂³×C₁₃	1	4	yes	—
680	#103	C₂³×C₁₃	1	2	yes	—
681	#103	C₂³×C₁₃	1	2	yes	—
682	#103	C₂³×C₁₃	1	4	yes	—
683	#103	C₂³×C₁₃	1	4	yes	—
684	#103	C₂³×C₁₃	1	4	yes	—
685	#102	C₂³×C₁₃	1	2	yes	—
686	#102	C₂³×C₁₃	1	2	yes	—
687	#102	C₂³×C₁₃	1	4	yes	—
688	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
689	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
690	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
691	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
692	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
693	#97	C₂³×C₁₃	1	4	yes	—
694	C₄×C₈	C₂³×C₁₃	1	4	yes	—
695	C₂×C₁₃	—	2	2	no	—
696	C₂×C₁₃	—	2	2	no	—
697	C₂×C₁₃	—	4	1	no	—
698	C₂×C₁₃	—	8	1	no	—
699	C₂×C₁₃	—	8	2	no	—
700	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
701	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
702	C₂×C₁₃	#3586	1	1	yes	characteristic
703	C₂⁴	—	2	1	no	—
704	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
705	#41	—	2	4	no	—
706	#41	—	2	4	no	—
707	#41	—	2	4	no	—
708	#41	—	4	2	no	—
709	#41	—	4	2	no	—
710	#41	—	4	4	no	—
711	#41	—	4	4	no	—
712	C₂×Q₈	—	2	1	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	2	2	no	—
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	1	no	—
717	C₂×Q₈	—	2	2	no	—
718	C₂×Q₈	—	2	4	no	—
719	C₂×Q₈	—	2	4	no	—
720	C₂×Q₈	—	2	4	no	—
721	C₂×Q₈	—	4	4	no	—
722	C₂×Q₈	—	4	4	no	—
723	C₂×Q₈	—	4	2	no	—
724	C₂×Q₈	—	4	4	no	—
725	C₂×Q₈	—	4	4	no	—
726	C₂×Q₈	—	4	4	no	—
727	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
728	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
729	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
730	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
731	C₂×D₄	—	2	1	no	—
732	C₂×D₄	—	2	1	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	1	no	—
736	C₂×D₄	—	2	1	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
740	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	4	4	no	—
753	C₂²×C₄	—	4	4	no	—
754	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
758	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
762	Q₁₆	—	4	4	no	—
763	Q₁₆	—	4	4	no	—
764	Q₁₆	—	4	2	no	—
765	Q₁₆	—	4	4	no	—
766	Q₁₆	—	4	4	no	—
767	SD₁₆	—	4	2	no	—
768	SD₁₆	—	4	2	no	—
769	SD₁₆	—	4	4	no	—
770	SD₁₆	—	4	4	no	—
771	D₈	—	4	2	no	—
772	M₁₆	—	2	4	no	—
773	C₂×C₈	—	2	4	no	—
774	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
775	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
776	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
777	C₄⋊C₄	—	2	1	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
795	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
796	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
797	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
798	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
799	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
800	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
801	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
802	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	1	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	1	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	1	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
818	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
819	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
820	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	1	no	—
825	C₄²	C₂×D₄×C₁₃	1	2	yes	—
826	C₄²	C₂×D₄×C₁₃	1	2	yes	—
827	C₄²	C₂⁴×C₁₃	1	2	yes	—
828	C₄²	C₂⁴×C₁₃	1	2	yes	—
829	C₁₃	#60814	1	1	yes	characteristic, direct product factor, Sylow
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	4	1	no	—
835	C₂³	—	4	2	no	—
836	C₂³	—	4	2	no	—
837	C₂³	—	4	2	no	—
838	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
840	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
841	Q₈	—	2	4	no	—
842	Q₈	—	2	2	no	—
843	Q₈	—	2	4	no	—
844	Q₈	—	2	2	no	—
845	Q₈	—	2	4	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	4	4	no	—
848	Q₈	—	4	4	no	—
849	Q₈	—	4	2	no	—
850	Q₈	—	4	4	no	—
851	Q₈	—	4	2	no	—
852	Q₈	—	8	2	no	—
853	D₄	—	2	2	no	—
854	D₄	—	2	2	no	—
855	D₄	—	2	2	no	—
856	D₄	—	4	2	no	—
857	D₄	—	4	4	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	2	no	—
861	D₄	—	8	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	4	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	4	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	4	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	4	2	no	—
884	C₂×C₄	—	8	2	no	—
885	C₂×C₄	—	8	1	no	—
886	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
887	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
888	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
890	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
891	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
892	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
893	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
894	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
895	C₈	—	2	2	no	—
896	C₈	—	2	2	no	—
897	C₈	—	2	4	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	4	4	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	8	4	no	—
913	C₂²	C₁₃×#535	1	2	yes	—
914	C₂²	C₁₃×#578	1	2	yes	—
915	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	4	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	C₁₃×#535	1	2	yes	—
930	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
931	C₂	—	2	2	no	—
932	C₂	—	2	2	no	—
933	C₂	—	4	1	no	—
934	C₂	—	8	2	no	—
935	C₂	—	8	1	no	—
936	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
937	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
938	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×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3495	C₂	semidirect
2. C₂×C₁₃×#536	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3223	C₂	semidirect
5. C₁₃×#3218	C₂	semidirect
6. C₁₃×#3215	C₂	semidirect
7. C₁₃×#3211	C₂	semidirect
8. C₁₃×#3209	C₂	semidirect
9. C₁₃×#3156	C₂	semidirect
10. C₁₃×#3137	C₂	semidirect
11. C₁₃×#3046	C₂	semidirect
12. C₁₃×#3044	C₂	semidirect
13. C₁₃×#3007	C₂	semidirect
14. C₁₃×#3004	C₂	semidirect
16. C₂×C₁₃×#451	C₂	semidirect
17. C₁₃×#2924	C₂	semidirect
21. C₂×C₁₃×#137	C₂²	semidirect
23. C₂²×C₁₃×Q₁₆	C₂²	semidirect
30. C₁₃×#544	C₂²	semidirect
31. C₁₃×#542	C₂²	semidirect
32. C₁₃×#541	C₂²	semidirect
39. C₁₃×#536	C₂²	semidirect
49. C₁₃×#520	C₂²	semidirect
50. C₁₃×#519	C₂²	semidirect
52. C₁₃×#497	C₂²	semidirect
53. C₁₃×#497	C₂²	semidirect
54. C₁₃×#495	C₂²	semidirect
55. C₁₃×#494	C₂²	semidirect
56. C₁₃×#491	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
58. C₁₃×#488	C₂²	semidirect
59. C₁₃×#487	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#464	C₂²	semidirect
62. C₁₃×#464	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#462	C₂²	semidirect
65. C₁₃×#462	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
75. C₁₃×#451	C₂²	semidirect
76. C₁₃×#451	C₂²	semidirect
82. C₁₃×#448	C₂²	semidirect
84. C₁₃×#433	C₂²	semidirect
87. C₁₃×#424	C₂²	semidirect
88. C₁₃×#419	C₂²	semidirect
91. C₂×C₁₃×#103	C₂²	semidirect
94. C₁₃×#405	C₂²	semidirect
234. #60814	C₁₃	direct (N × H)
361. #3495	C₂×C₁₃	semidirect
362. C₂×#536	C₂×C₁₃	semidirect
363. #3225	C₂×C₁₃	semidirect
364. #3223	C₂×C₁₃	semidirect
365. #3218	C₂×C₁₃	semidirect
366. #3215	C₂×C₁₃	semidirect
367. #3211	C₂×C₁₃	semidirect
368. #3209	C₂×C₁₃	semidirect
369. #3156	C₂×C₁₃	semidirect
370. #3137	C₂×C₁₃	semidirect
371. #3046	C₂×C₁₃	semidirect
372. #3044	C₂×C₁₃	semidirect
373. #3007	C₂×C₁₃	semidirect
374. #3004	C₂×C₁₃	semidirect
376. C₂×#451	C₂×C₁₃	semidirect
377. #2924	C₂×C₁₃	semidirect
449. C₂×#137	C₂²×C₁₃	semidirect
451. C₂²×Q₁₆	C₂²×C₁₃	semidirect
458. #544	C₂²×C₁₃	semidirect
459. #542	C₂²×C₁₃	semidirect
460. #541	C₂²×C₁₃	semidirect
467. #536	C₂²×C₁₃	semidirect
477. #520	C₂²×C₁₃	semidirect
478. #519	C₂²×C₁₃	semidirect
480. #497	C₂²×C₁₃	semidirect
481. #497	C₂²×C₁₃	semidirect
482. #495	C₂²×C₁₃	semidirect
483. #494	C₂²×C₁₃	semidirect
484. #491	C₂²×C₁₃	semidirect
485. #489	C₂²×C₁₃	semidirect
486. #488	C₂²×C₁₃	semidirect
487. #487	C₂²×C₁₃	semidirect
488. #464	C₂²×C₁₃	semidirect
489. #464	C₂²×C₁₃	semidirect
490. #464	C₂²×C₁₃	semidirect
491. #463	C₂²×C₁₃	semidirect
492. #462	C₂²×C₁₃	semidirect
493. #462	C₂²×C₁₃	semidirect
494. #462	C₂²×C₁₃	semidirect
495. #461	C₂²×C₁₃	semidirect
503. #451	C₂²×C₁₃	semidirect
504. #451	C₂²×C₁₃	semidirect
510. #448	C₂²×C₁₃	semidirect
512. #433	C₂²×C₁₃	semidirect
515. #424	C₂²×C₁₃	semidirect
516. #419	C₂²×C₁₃	semidirect
519. C₂×#103	C₂²×C₁₃	semidirect
522. #405	C₂²×C₁₃	semidirect
829. C₁₃	#60814	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×#3495	2
C₂×C₁₃×#536	2
C₁₃×#3225	2
C₁₃×#3223	2
C₁₃×#3218	2
C₁₃×#3215	2
C₁₃×#3211	2
C₁₃×#3209	2
C₁₃×#3156	2
C₁₃×#3137	2
C₁₃×#3046	2
C₁₃×#3044	2
C₁₃×#3007	2
C₁₃×#3004	2
C₁₃×#3002	2
C₂×C₁₃×#451	2
C₁₃×#2924	2
#60814	13

Subgroups — C13×#60814 #15747153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60814 #15747153