Subgroups — C₁₃×#61002 #15747341

Order 3328.

1682 conjugacy classes of subgroups.

The subgroup lattice has 938 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	2	yes	maximal, complemented
2	C₁₃×#3250	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3248	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3242	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3191	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3181	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3127	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3124	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3121	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
19	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#556	—	2	2	no	—
21	C₁₃×#554	—	2	2	no	—
22	C₁₃×#552	—	2	2	no	—
23	C₁₃×#552	—	2	2	no	—
24	C₁₃×#552	—	2	2	no	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#551	—	2	2	no	—
27	C₁₃×#551	—	2	2	no	—
28	C₁₃×#544	C₂²	1	2	yes	—
29	C₁₃×#542	C₂²	1	2	yes	—
30	C₁₃×#542	C₂²	1	2	yes	—
31	C₁₃×#541	C₂²	1	2	yes	—
32	C₁₃×#541	C₂²	1	2	yes	—
33	C₁₃×#536	C₂²	1	2	yes	—
34	C₁₃×#533	C₂²	1	2	yes	—
35	C₁₃×#533	C₂²	1	2	yes	—
36	C₁₃×#529	C₂²	1	2	yes	—
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₁₃×#525	C₂²	1	2	yes	—
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₁₃×#520	C₂²	1	2	yes	—
41	C₁₃×#519	C₂²	1	2	yes	—
42	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
43	C₁₃×#501	C₂²	1	2	yes	complemented
44	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#497	C₂²	1	2	yes	complemented
47	C₁₃×#495	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#491	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	2	yes	complemented
51	C₁₃×#488	C₂²	1	2	yes	complemented
52	C₁₃×#487	C₂²	1	2	yes	complemented
53	C₁₃×#485	C₂²	1	2	yes	—
54	C₁₃×#485	C₂²	1	2	yes	—
55	C₁₃×#485	C₂²	1	2	yes	—
56	C₁₃×#484	C₂²	1	2	yes	—
57	C₁₃×#484	C₂²	1	2	yes	—
58	C₁₃×#483	C₂²	1	2	yes	—
59	C₁₃×#482	C₂²	1	2	yes	—
60	C₁₃×#480	C₂²	1	2	yes	—
61	C₁₃×#479	C₂²	1	2	yes	complemented
62	C₁₃×#479	C₂²	1	2	yes	complemented
63	C₁₃×#479	C₂²	1	2	yes	complemented
64	C₁₃×#478	C₂²	1	2	yes	complemented
65	C₁₃×#477	C₂²	1	2	yes	complemented
66	C₁₃×#477	C₂²	1	2	yes	complemented
67	C₁₃×#475	C₂²	1	2	yes	complemented
68	C₁₃×#474	C₂²	1	2	yes	complemented
69	C₁₃×#467	C₂²	1	1	yes	characteristic
70	C₁₃×#467	C₂²	1	1	yes	characteristic
71	C₁₃×#467	C₂²	1	2	yes	—
72	C₁₃×#467	C₂²	1	1	yes	characteristic
73	C₁₃×#467	C₂²	1	2	yes	—
74	C₁₃×#467	C₂²	1	2	yes	—
75	C₁₃×#466	C₂²	1	1	yes	characteristic
76	C₁₃×#465	C₂²	1	2	yes	—
77	C₁₃×#465	C₂²	1	2	yes	—
78	C₁₃×#465	C₂²	1	2	yes	—
79	C₁₃×#464	C₂²	1	2	yes	complemented
80	C₁₃×#464	C₂²	1	2	yes	complemented
81	C₁₃×#464	C₂²	1	2	yes	complemented
82	C₁₃×#463	C₂²	1	2	yes	complemented
83	C₁₃×#462	C₂²	1	2	yes	complemented
84	C₁₃×#462	C₂²	1	2	yes	complemented
85	C₁₃×#462	C₂²	1	2	yes	complemented
86	C₁₃×#461	C₂²	1	2	yes	complemented
87	C₁₃×#452	C₂²	1	2	yes	—
88	C₁₃×#452	C₂²	1	2	yes	—
89	C₁₃×#452	C₂²	1	2	yes	—
90	C₁₃×#451	C₂²	1	2	yes	—
91	C₁₃×#451	C₂²	1	2	yes	—
92	C₁₃×#451	C₂²	1	2	yes	—
93	C₁₃×#449	C₂²	1	2	yes	—
94	C₁₃×#448	C₂²	1	2	yes	—
95	C₁₃×#441	C₂²	1	2	yes	complemented
96	C₁₃×#441	C₂²	1	2	yes	complemented
97	C₁₃×#440	C₂²	1	2	yes	complemented
98	C₁₃×#440	C₂²	1	2	yes	complemented
99	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
102	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
104	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
105	C₁₃×#433	C₂²	1	2	yes	—
106	C₁₃×#433	C₂²	1	2	yes	—
107	C₁₃×#433	C₂²	1	2	yes	—
108	C₁₃×#433	C₂²	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
111	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
112	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
113	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
114	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
115	C₂×C₁₃×#41	C₂³	1	2	yes	—
116	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
121	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₁₃×C₄⋊Q₈	—	2	2	no	—
133	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×#126	—	2	2	no	—
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×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#125	—	2	2	no	—
146	C₁₃×#125	—	2	2	no	—
147	C₁₃×#125	—	2	2	no	—
148	C₁₃×#125	—	2	2	no	—
149	C₁₃×#125	—	2	2	no	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	—	2	2	no	—
152	C₁₃×#125	C₂³	1	2	yes	—
153	C₁₃×#125	C₂³	1	2	yes	—
154	C₁₃×#124	—	2	2	no	—
155	C₁₃×#124	—	2	2	no	—
156	C₁₃×#124	C₂³	1	2	yes	—
157	C₁₃×#124	C₂³	1	2	yes	—
158	C₁₃×#123	—	2	2	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×#123	—	2	2	no	—
162	C₁₃×#123	—	2	2	no	—
163	C₁₃×#123	—	2	2	no	—
164	C₁₃×#123	—	2	2	no	—
165	C₁₃×C₂²⋊Q₈	—	2	2	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	—	2	2	no	—
169	C₁₃×C₂²⋊Q₈	—	2	2	no	—
170	C₁₃×C₂²⋊Q₈	—	2	2	no	—
171	C₁₃×C₂²⋊Q₈	—	2	2	no	—
172	C₁₃×C₂²⋊Q₈	—	2	2	no	—
173	C₁₃×C₂²⋊Q₈	—	2	2	no	—
174	C₁₃×C₂²⋊Q₈	—	2	2	no	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
181	C₁₃×#121	C₂³	1	2	yes	—
182	C₁₃×#121	C₂³	1	2	yes	—
183	C₁₃×#120	—	2	2	no	—
184	C₄×Q₈×C₁₃	—	2	2	no	—
185	C₄×Q₈×C₁₃	—	2	2	no	—
186	C₄×Q₈×C₁₃	—	2	2	no	—
187	C₄×Q₈×C₁₃	—	2	2	no	—
188	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
189	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
190	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
191	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
192	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
193	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
194	C₄×D₄×C₁₃	—	2	2	no	—
195	C₄×D₄×C₁₃	—	2	2	no	—
196	C₄×D₄×C₁₃	—	2	2	no	—
197	C₄×D₄×C₁₃	—	2	2	no	—
198	C₄×D₄×C₁₃	—	2	2	no	—
199	C₄×D₄×C₁₃	—	2	2	no	—
200	C₄×D₄×C₁₃	C₂³	1	2	yes	—
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₁₃×#117	—	2	2	no	—
203	C₁₃×#117	—	2	2	no	—
204	C₁₃×#117	—	2	2	no	—
205	C₁₃×#117	—	2	2	no	—
206	C₁₃×#117	—	2	2	no	—
207	C₁₃×#117	—	2	2	no	—
208	C₁₃×#117	—	2	2	no	—
209	C₁₃×#117	D₄	1	2	yes	—
210	C₁₃×#117	D₄	1	2	yes	—
211	C₁₃×#117	C₂³	1	2	yes	—
212	C₁₃×#117	C₂³	1	2	yes	—
213	C₁₃×#117	C₂³	1	2	yes	—
214	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
217	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
218	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
221	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
224	C₁₃×#107	C₂³	1	1	yes	characteristic
225	C₁₃×#107	C₂³	1	1	yes	characteristic
226	C₁₃×#107	C₂³	1	2	yes	—
227	C₁₃×#107	C₂³	1	1	yes	characteristic
228	C₁₃×#107	C₂³	1	1	yes	characteristic
229	C₁₃×#107	C₂³	1	2	yes	—
230	C₁₃×#107	C₂³	1	2	yes	—
231	C₁₃×#106	C₂³	1	2	yes	—
232	C₁₃×#106	C₂³	1	2	yes	—
233	C₁₃×#106	C₂³	1	2	yes	—
234	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₁₃×#103	C₂³	1	2	yes	—
239	C₁₃×#103	C₂³	1	2	yes	—
240	C₁₃×#103	C₂³	1	2	yes	—
241	C₁₃×#103	C₂³	1	2	yes	—
242	C₁₃×#103	C₂³	1	2	yes	—
243	C₁₃×#103	C₂³	1	2	yes	—
244	C₁₃×#103	C₂³	1	2	yes	—
245	C₁₃×#103	C₂³	1	2	yes	—
246	C₁₃×#103	C₂³	1	2	yes	—
247	C₁₃×#103	C₂³	1	2	yes	—
248	C₁₃×#103	C₂³	1	2	yes	—
249	C₁₃×#103	C₂³	1	2	yes	—
250	C₁₃×#102	C₂³	1	2	yes	—
251	C₁₃×#102	C₂³	1	2	yes	—
252	C₁₃×#102	C₂³	1	2	yes	—
253	C₁₃×#102	C₂³	1	2	yes	—
254	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₁₃×#97	C₂³	1	2	yes	—
259	C₁₃×#97	C₂³	1	2	yes	—
260	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
264	#61002	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₁₃×#41	—	4	2	no	—
267	C₁₃×#41	—	4	2	no	—
268	C₂×Q₈×C₁₃	—	2	2	no	—
269	C₂×Q₈×C₁₃	—	2	2	no	—
270	C₂×Q₈×C₁₃	—	2	2	no	—
271	C₂×Q₈×C₁₃	—	4	2	no	—
272	C₂×Q₈×C₁₃	—	4	2	no	—
273	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×D₄×C₁₃	—	2	2	no	—
277	C₂×D₄×C₁₃	—	2	2	no	—
278	C₂×D₄×C₁₃	—	2	2	no	—
279	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₁₃	—	2	2	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	—	2	2	no	—
285	C₂²×C₄×C₁₃	—	4	1	no	—
286	C₂²×C₄×C₁₃	—	4	1	no	—
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	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₁₃×Q₁₆	—	4	1	no	—
296	C₁₃×Q₁₆	—	4	2	no	—
297	C₁₃×Q₁₆	—	4	2	no	—
298	C₁₃×Q₁₆	—	4	1	no	—
299	C₁₃×Q₁₆	—	4	2	no	—
300	C₁₃×Q₁₆	—	4	1	no	—
301	C₁₃×SD₁₆	—	4	2	no	—
302	C₁₃×SD₁₆	—	4	2	no	—
303	C₁₃×SD₁₆	—	4	2	no	—
304	C₁₃×D₈	—	4	1	no	—
305	C₂×C₈×C₁₃	—	4	1	no	—
306	C₂×C₈×C₁₃	—	4	1	no	—
307	C₂×C₈×C₁₃	—	4	1	no	—
308	C₂×C₈×C₁₃	—	4	1	no	—
309	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
312	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
313	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
314	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
339	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
340	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
341	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
342	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
343	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
344	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
345	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	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	2	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
363	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
364	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
365	C₄²×C₁₃	—	2	2	no	—
366	C₄²×C₁₃	—	2	2	no	—
367	C₄²×C₁₃	—	2	2	no	—
368	C₄²×C₁₃	—	2	2	no	—
369	C₄²×C₁₃	—	2	2	no	—
370	C₄²×C₁₃	—	2	2	no	—
371	C₄²×C₁₃	—	2	2	no	—
372	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₁₃	C₂×D₄	1	2	yes	—
374	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₄²×C₁₃	C₂⁴	1	2	yes	—
378	#3495	C₂×C₁₃	1	2	yes	complemented
379	#3250	C₂×C₁₃	1	1	yes	characteristic, complemented
380	#3249	C₂×C₁₃	1	1	yes	characteristic, complemented
381	#3248	C₂×C₁₃	1	2	yes	complemented
382	#3243	C₂×C₁₃	1	2	yes	complemented
383	#3242	C₂×C₁₃	1	2	yes	complemented
384	#3225	C₂×C₁₃	1	2	yes	complemented
385	#3223	C₂×C₁₃	1	2	yes	complemented
386	#3191	C₂×C₁₃	1	1	yes	characteristic
387	#3190	C₂×C₁₃	1	2	yes	complemented
388	#3189	C₂×C₁₃	1	1	yes	characteristic, complemented
389	#3181	C₂×C₁₃	1	2	yes	complemented
390	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
391	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
392	#3127	C₂×C₁₃	1	2	yes	complemented
393	#3124	C₂×C₁₃	1	2	yes	complemented
394	#3121	C₂×C₁₃	1	2	yes	complemented
395	#3120	C₂×C₁₃	1	2	yes	complemented
396	C₂×#433	C₂×C₁₃	1	1	yes	characteristic, complemented
397	C₂³×C₁₃	—	2	2	no	—
398	C₂³×C₁₃	—	2	2	no	—
399	C₂³×C₁₃	—	4	1	no	—
400	C₂³×C₁₃	—	4	1	no	—
401	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
402	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	Q₈×C₁₃	—	2	2	no	—
404	Q₈×C₁₃	—	2	2	no	—
405	Q₈×C₁₃	—	2	2	no	—
406	Q₈×C₁₃	—	2	2	no	—
407	Q₈×C₁₃	—	2	2	no	—
408	Q₈×C₁₃	—	2	2	no	—
409	Q₈×C₁₃	—	4	4	no	—
410	Q₈×C₁₃	—	8	2	no	—
411	Q₈×C₁₃	—	8	2	no	—
412	D₄×C₁₃	—	2	2	no	—
413	D₄×C₁₃	—	2	2	no	—
414	D₄×C₁₃	—	4	4	no	—
415	D₄×C₁₃	—	4	4	no	—
416	D₄×C₁₃	—	8	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	4	1	no	—
431	C₂×C₄×C₁₃	—	4	2	no	—
432	C₂×C₄×C₁₃	—	4	1	no	—
433	C₂×C₄×C₁₃	—	4	1	no	—
434	C₂×C₄×C₁₃	—	4	4	no	—
435	C₂×C₄×C₁₃	—	4	4	no	—
436	C₂×C₄×C₁₃	—	8	2	no	—
437	C₂×C₄×C₁₃	—	8	2	no	—
438	C₂×C₄×C₁₃	—	8	2	no	—
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
448	C₈×C₁₃	—	2	1	no	—
449	C₈×C₁₃	—	2	1	no	—
450	C₈×C₁₃	—	2	2	no	—
451	C₈×C₁₃	—	2	2	no	—
452	C₈×C₁₃	—	2	1	no	—
453	C₈×C₁₃	—	2	1	no	—
454	#556	—	2	2	no	—
455	#554	—	2	2	no	—
456	#552	—	2	2	no	—
457	#552	—	2	2	no	—
458	#552	—	2	2	no	—
459	#552	—	2	2	no	—
460	#551	—	2	2	no	—
461	#551	—	2	2	no	—
462	#544	C₂²×C₁₃	1	2	yes	—
463	#542	C₂²×C₁₃	1	2	yes	—
464	#542	C₂²×C₁₃	1	2	yes	—
465	#541	C₂²×C₁₃	1	2	yes	—
466	#541	C₂²×C₁₃	1	2	yes	—
467	#536	C₂²×C₁₃	1	2	yes	—
468	#533	C₂²×C₁₃	1	2	yes	—
469	#533	C₂²×C₁₃	1	2	yes	—
470	#529	C₂²×C₁₃	1	2	yes	—
471	#529	C₂²×C₁₃	1	2	yes	—
472	#525	C₂²×C₁₃	1	2	yes	—
473	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
474	#520	C₂²×C₁₃	1	2	yes	—
475	#519	C₂²×C₁₃	1	2	yes	—
476	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
477	#501	C₂²×C₁₃	1	2	yes	complemented
478	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
479	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
480	#497	C₂²×C₁₃	1	2	yes	complemented
481	#495	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
483	#491	C₂²×C₁₃	1	2	yes	complemented
484	#489	C₂²×C₁₃	1	2	yes	complemented
485	#488	C₂²×C₁₃	1	2	yes	complemented
486	#487	C₂²×C₁₃	1	2	yes	complemented
487	#485	C₂²×C₁₃	1	2	yes	—
488	#485	C₂²×C₁₃	1	2	yes	—
489	#485	C₂²×C₁₃	1	2	yes	—
490	#484	C₂²×C₁₃	1	2	yes	—
491	#484	C₂²×C₁₃	1	2	yes	—
492	#483	C₂²×C₁₃	1	2	yes	—
493	#482	C₂²×C₁₃	1	2	yes	—
494	#480	C₂²×C₁₃	1	2	yes	—
495	#479	C₂²×C₁₃	1	2	yes	complemented
496	#479	C₂²×C₁₃	1	2	yes	complemented
497	#479	C₂²×C₁₃	1	2	yes	complemented
498	#478	C₂²×C₁₃	1	2	yes	complemented
499	#477	C₂²×C₁₃	1	2	yes	complemented
500	#477	C₂²×C₁₃	1	2	yes	complemented
501	#475	C₂²×C₁₃	1	2	yes	complemented
502	#474	C₂²×C₁₃	1	2	yes	complemented
503	#467	C₂²×C₁₃	1	1	yes	characteristic
504	#467	C₂²×C₁₃	1	1	yes	characteristic
505	#467	C₂²×C₁₃	1	2	yes	—
506	#467	C₂²×C₁₃	1	1	yes	characteristic
507	#467	C₂²×C₁₃	1	2	yes	—
508	#467	C₂²×C₁₃	1	2	yes	—
509	#466	C₂²×C₁₃	1	1	yes	characteristic
510	#465	C₂²×C₁₃	1	2	yes	—
511	#465	C₂²×C₁₃	1	2	yes	—
512	#465	C₂²×C₁₃	1	2	yes	—
513	#464	C₂²×C₁₃	1	2	yes	complemented
514	#464	C₂²×C₁₃	1	2	yes	complemented
515	#464	C₂²×C₁₃	1	2	yes	complemented
516	#463	C₂²×C₁₃	1	2	yes	complemented
517	#462	C₂²×C₁₃	1	2	yes	complemented
518	#462	C₂²×C₁₃	1	2	yes	complemented
519	#462	C₂²×C₁₃	1	2	yes	complemented
520	#461	C₂²×C₁₃	1	2	yes	complemented
521	#452	C₂²×C₁₃	1	2	yes	—
522	#452	C₂²×C₁₃	1	2	yes	—
523	#452	C₂²×C₁₃	1	2	yes	—
524	#451	C₂²×C₁₃	1	2	yes	—
525	#451	C₂²×C₁₃	1	2	yes	—
526	#451	C₂²×C₁₃	1	2	yes	—
527	#449	C₂²×C₁₃	1	2	yes	—
528	#448	C₂²×C₁₃	1	2	yes	—
529	#441	C₂²×C₁₃	1	2	yes	complemented
530	#441	C₂²×C₁₃	1	2	yes	complemented
531	#440	C₂²×C₁₃	1	2	yes	complemented
532	#440	C₂²×C₁₃	1	2	yes	complemented
533	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
534	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
535	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
536	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
537	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
538	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
539	#433	C₂²×C₁₃	1	2	yes	—
540	#433	C₂²×C₁₃	1	2	yes	—
541	#433	C₂²×C₁₃	1	2	yes	—
542	#433	C₂²×C₁₃	1	2	yes	—
543	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
544	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
545	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
547	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
548	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
549	C₂²×C₁₃	—	2	1	no	—
550	C₂²×C₁₃	—	2	1	no	—
551	C₂²×C₁₃	—	2	2	no	—
552	C₂²×C₁₃	—	2	2	no	—
553	C₂²×C₁₃	—	2	2	no	—
554	C₂²×C₁₃	—	4	2	no	—
555	C₂²×C₁₃	—	4	2	no	—
556	C₂²×C₁₃	—	4	2	no	—
557	C₂²×C₁₃	—	8	2	no	—
558	C₂²×C₁₃	#578	1	2	yes	—
559	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
560	C₄×C₁₃	—	2	1	no	—
561	C₄×C₁₃	—	2	2	no	—
562	C₄×C₁₃	—	2	1	no	—
563	C₄×C₁₃	—	2	2	no	—
564	C₄×C₁₃	—	2	1	no	—
565	C₄×C₁₃	—	2	1	no	—
566	C₄×C₁₃	—	2	2	no	—
567	C₄×C₁₃	—	2	1	no	—
568	C₄×C₁₃	—	4	2	no	—
569	C₄×C₁₃	—	4	2	no	—
570	C₄×C₁₃	—	4	2	no	—
571	C₄×C₁₃	—	4	2	no	—
572	C₄×C₁₃	—	4	2	no	—
573	C₄×C₁₃	—	4	2	no	—
574	C₄×C₁₃	—	4	2	no	—
575	C₄×C₁₃	#585	1	1	yes	characteristic
576	C₄×C₁₃	#585	1	1	yes	characteristic
577	C₂×#41	C₂³×C₁₃	1	2	yes	—
578	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
579	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
583	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
584	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
585	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
586	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
587	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
588	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
589	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
590	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
592	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄⋊Q₈	—	2	2	no	—
595	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
596	C₄⋊Q₈	C₂³×C₁₃	1	2	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	#126	—	2	2	no	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	—	2	2	no	—
609	#125	—	2	2	no	—
610	#125	—	2	2	no	—
611	#125	—	2	2	no	—
612	#125	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	C₂³×C₁₃	1	2	yes	—
615	#125	C₂³×C₁₃	1	2	yes	—
616	#124	—	2	2	no	—
617	#124	—	2	2	no	—
618	#124	C₂³×C₁₃	1	2	yes	—
619	#124	C₂³×C₁₃	1	2	yes	—
620	#123	—	2	2	no	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	#123	—	2	2	no	—
626	#123	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
638	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
639	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
640	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
641	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
642	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
643	#121	C₂³×C₁₃	1	2	yes	—
644	#121	C₂³×C₁₃	1	2	yes	—
645	#120	—	2	2	no	—
646	C₄×Q₈	—	2	2	no	—
647	C₄×Q₈	—	2	2	no	—
648	C₄×Q₈	—	2	2	no	—
649	C₄×Q₈	—	2	2	no	—
650	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
651	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
652	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
653	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
654	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
655	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	—	2	2	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	2	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	C₂³×C₁₃	1	2	yes	—
663	C₄×D₄	C₂³×C₁₃	1	2	yes	—
664	#117	—	2	2	no	—
665	#117	—	2	2	no	—
666	#117	—	2	2	no	—
667	#117	—	2	2	no	—
668	#117	—	2	2	no	—
669	#117	—	2	2	no	—
670	#117	—	2	2	no	—
671	#117	D₄×C₁₃	1	2	yes	—
672	#117	D₄×C₁₃	1	2	yes	—
673	#117	C₂³×C₁₃	1	2	yes	—
674	#117	C₂³×C₁₃	1	2	yes	—
675	#117	C₂³×C₁₃	1	2	yes	—
676	C₂×C₄⋊C₄	—	2	2	no	—
677	C₂×C₄⋊C₄	—	2	2	no	—
678	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
679	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
681	C₂×C₂²⋊C₄	—	2	2	no	—
682	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
686	#107	C₂³×C₁₃	1	1	yes	characteristic
687	#107	C₂³×C₁₃	1	1	yes	characteristic
688	#107	C₂³×C₁₃	1	2	yes	—
689	#107	C₂³×C₁₃	1	1	yes	characteristic
690	#107	C₂³×C₁₃	1	1	yes	characteristic
691	#107	C₂³×C₁₃	1	2	yes	—
692	#107	C₂³×C₁₃	1	2	yes	—
693	#106	C₂³×C₁₃	1	2	yes	—
694	#106	C₂³×C₁₃	1	2	yes	—
695	#106	C₂³×C₁₃	1	2	yes	—
696	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
697	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
698	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
699	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
700	#103	C₂³×C₁₃	1	2	yes	—
701	#103	C₂³×C₁₃	1	2	yes	—
702	#103	C₂³×C₁₃	1	2	yes	—
703	#103	C₂³×C₁₃	1	2	yes	—
704	#103	C₂³×C₁₃	1	2	yes	—
705	#103	C₂³×C₁₃	1	2	yes	—
706	#103	C₂³×C₁₃	1	2	yes	—
707	#103	C₂³×C₁₃	1	2	yes	—
708	#103	C₂³×C₁₃	1	2	yes	—
709	#103	C₂³×C₁₃	1	2	yes	—
710	#103	C₂³×C₁₃	1	2	yes	—
711	#103	C₂³×C₁₃	1	2	yes	—
712	#102	C₂³×C₁₃	1	2	yes	—
713	#102	C₂³×C₁₃	1	2	yes	—
714	#102	C₂³×C₁₃	1	2	yes	—
715	#102	C₂³×C₁₃	1	2	yes	—
716	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
717	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
718	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
719	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
720	#97	C₂³×C₁₃	1	2	yes	—
721	#97	C₂³×C₁₃	1	2	yes	—
722	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
723	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
724	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
725	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
726	C₂×C₁₃	—	2	2	no	—
727	C₂×C₁₃	—	4	2	no	—
728	C₂×C₁₃	—	8	2	no	—
729	C₂×C₁₃	#3449	1	1	yes	characteristic
730	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
731	C₂×C₁₃	#3584	1	1	yes	characteristic
732	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
733	#41	—	4	2	no	—
734	#41	—	4	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	2	no	—
738	C₂×Q₈	—	4	2	no	—
739	C₂×Q₈	—	4	2	no	—
740	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
741	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
742	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	4	1	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
762	Q₁₆	—	4	1	no	—
763	Q₁₆	—	4	2	no	—
764	Q₁₆	—	4	2	no	—
765	Q₁₆	—	4	1	no	—
766	Q₁₆	—	4	2	no	—
767	Q₁₆	—	4	1	no	—
768	SD₁₆	—	4	2	no	—
769	SD₁₆	—	4	2	no	—
770	SD₁₆	—	4	2	no	—
771	D₈	—	4	1	no	—
772	C₂×C₈	—	4	1	no	—
773	C₂×C₈	—	4	1	no	—
774	C₂×C₈	—	4	1	no	—
775	C₂×C₈	—	4	1	no	—
776	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
777	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
778	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
779	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
780	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
781	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	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	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
806	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
807	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
808	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
809	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
811	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
812	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
829	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
830	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
831	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
840	C₄²	C₂×D₄×C₁₃	1	2	yes	—
841	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
842	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
843	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
844	C₄²	C₂⁴×C₁₃	1	2	yes	—
845	C₁₃	#61002	1	1	yes	characteristic, direct product factor, Sylow
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	4	1	no	—
849	C₂³	—	4	1	no	—
850	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
851	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
852	Q₈	—	2	2	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	4	4	no	—
859	Q₈	—	8	2	no	—
860	Q₈	—	8	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	4	no	—
865	D₄	—	8	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	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	2	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	8	2	no	—
886	C₂×C₄	—	8	2	no	—
887	C₂×C₄	—	8	2	no	—
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	1	yes	characteristic
891	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
892	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
894	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
896	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
897	C₈	—	2	1	no	—
898	C₈	—	2	1	no	—
899	C₈	—	2	2	no	—
900	C₈	—	2	2	no	—
901	C₈	—	2	1	no	—
902	C₈	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	8	2	no	—
912	C₂²	C₁₃×#578	1	2	yes	—
913	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
914	C₄	—	2	1	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	C₁₃×#585	1	1	yes	characteristic
930	C₄	C₁₃×#585	1	1	yes	characteristic
931	C₂	—	2	2	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₁₃×#3449	1	1	yes	characteristic
935	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
936	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3191	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. C₁₃×#3250	C₂	semidirect
3. C₁₃×#3249	C₂	semidirect
4. C₁₃×#3248	C₂	semidirect
5. C₁₃×#3243	C₂	semidirect
6. C₁₃×#3242	C₂	semidirect
7. C₁₃×#3225	C₂	semidirect
8. C₁₃×#3223	C₂	semidirect
10. C₁₃×#3190	C₂	semidirect
11. C₁₃×#3189	C₂	semidirect
12. C₁₃×#3181	C₂	semidirect
13. C₁₃×#3170	C₂	semidirect
14. C₁₃×#3168	C₂	semidirect
15. C₁₃×#3127	C₂	semidirect
16. C₁₃×#3124	C₂	semidirect
17. C₁₃×#3121	C₂	semidirect
18. C₁₃×#3120	C₂	semidirect
19. C₂×C₁₃×#433	C₂	semidirect
43. C₁₃×#501	C₂²	semidirect
44. C₁₃×#500	C₂²	semidirect
45. C₁₃×#499	C₂²	semidirect
46. C₁₃×#497	C₂²	semidirect
47. C₁₃×#495	C₂²	semidirect
48. C₁₃×#494	C₂²	semidirect
49. C₁₃×#491	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#488	C₂²	semidirect
52. C₁₃×#487	C₂²	semidirect
61. C₁₃×#479	C₂²	semidirect
62. C₁₃×#479	C₂²	semidirect
63. C₁₃×#479	C₂²	semidirect
64. C₁₃×#478	C₂²	semidirect
65. C₁₃×#477	C₂²	semidirect
66. C₁₃×#477	C₂²	semidirect
67. C₁₃×#475	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
79. C₁₃×#464	C₂²	semidirect
80. C₁₃×#464	C₂²	semidirect
81. C₁₃×#464	C₂²	semidirect
82. C₁₃×#463	C₂²	semidirect
83. C₁₃×#462	C₂²	semidirect
84. C₁₃×#462	C₂²	semidirect
85. C₁₃×#462	C₂²	semidirect
86. C₁₃×#461	C₂²	semidirect
95. C₁₃×#441	C₂²	semidirect
96. C₁₃×#441	C₂²	semidirect
97. C₁₃×#440	C₂²	semidirect
98. C₁₃×#440	C₂²	semidirect
99. C₄×C₁₃×Q₁₆	C₂²	semidirect
100. C₄×C₁₃×Q₁₆	C₂²	semidirect
101. C₄×C₁₃×Q₁₆	C₂²	semidirect
102. C₄×C₁₃×Q₁₆	C₂²	semidirect
103. C₄×C₁₃×SD₁₆	C₂²	semidirect
104. C₄×C₁₃×D₈	C₂²	semidirect
264. #61002	C₁₃	direct (N × H)
378. #3495	C₂×C₁₃	semidirect
379. #3250	C₂×C₁₃	semidirect
380. #3249	C₂×C₁₃	semidirect
381. #3248	C₂×C₁₃	semidirect
382. #3243	C₂×C₁₃	semidirect
383. #3242	C₂×C₁₃	semidirect
384. #3225	C₂×C₁₃	semidirect
385. #3223	C₂×C₁₃	semidirect
387. #3190	C₂×C₁₃	semidirect
388. #3189	C₂×C₁₃	semidirect
389. #3181	C₂×C₁₃	semidirect
390. #3170	C₂×C₁₃	semidirect
391. #3168	C₂×C₁₃	semidirect
392. #3127	C₂×C₁₃	semidirect
393. #3124	C₂×C₁₃	semidirect
394. #3121	C₂×C₁₃	semidirect
395. #3120	C₂×C₁₃	semidirect
396. C₂×#433	C₂×C₁₃	semidirect
477. #501	C₂²×C₁₃	semidirect
478. #500	C₂²×C₁₃	semidirect
479. #499	C₂²×C₁₃	semidirect
480. #497	C₂²×C₁₃	semidirect
481. #495	C₂²×C₁₃	semidirect
482. #494	C₂²×C₁₃	semidirect
483. #491	C₂²×C₁₃	semidirect
484. #489	C₂²×C₁₃	semidirect
485. #488	C₂²×C₁₃	semidirect
486. #487	C₂²×C₁₃	semidirect
495. #479	C₂²×C₁₃	semidirect
496. #479	C₂²×C₁₃	semidirect
497. #479	C₂²×C₁₃	semidirect
498. #478	C₂²×C₁₃	semidirect
499. #477	C₂²×C₁₃	semidirect
500. #477	C₂²×C₁₃	semidirect
501. #475	C₂²×C₁₃	semidirect
502. #474	C₂²×C₁₃	semidirect
513. #464	C₂²×C₁₃	semidirect
514. #464	C₂²×C₁₃	semidirect
515. #464	C₂²×C₁₃	semidirect
516. #463	C₂²×C₁₃	semidirect
517. #462	C₂²×C₁₃	semidirect
518. #462	C₂²×C₁₃	semidirect
519. #462	C₂²×C₁₃	semidirect
520. #461	C₂²×C₁₃	semidirect
529. #441	C₂²×C₁₃	semidirect
530. #441	C₂²×C₁₃	semidirect
531. #440	C₂²×C₁₃	semidirect
532. #440	C₂²×C₁₃	semidirect
533. C₄×Q₁₆	C₂²×C₁₃	semidirect
534. C₄×Q₁₆	C₂²×C₁₃	semidirect
535. C₄×Q₁₆	C₂²×C₁₃	semidirect
536. C₄×Q₁₆	C₂²×C₁₃	semidirect
537. C₄×SD₁₆	C₂²×C₁₃	semidirect
538. C₄×D₈	C₂²×C₁₃	semidirect
845. C₁₃	#61002	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
C₁₃×#3250	2
C₁₃×#3249	2
C₁₃×#3248	2
C₁₃×#3243	2
C₁₃×#3242	2
C₁₃×#3225	2
C₁₃×#3223	2
C₁₃×#3191	2
C₁₃×#3190	2
C₁₃×#3189	2
C₁₃×#3181	2
C₁₃×#3170	2
C₁₃×#3168	2
C₁₃×#3127	2
C₁₃×#3124	2
C₁₃×#3121	2
C₁₃×#3120	2
C₂×C₁₃×#433	2
#61002	13

Subgroups — C13×#61002 #15747341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61002 #15747341