Subgroups — C₁₃×#61003 #15747342

Order 3328.

1792 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3494	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3256	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3244	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3241	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3197	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3194	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3192	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3184	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3171	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3125	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3122	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3119	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3118	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#555	—	2	2	no	—
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#553	—	2	2	no	—
23	C₁₃×#551	—	2	2	no	—
24	C₁₃×#551	—	2	2	no	—
25	C₁₃×#547	—	2	2	no	—
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#546	—	2	2	no	—
28	C₁₃×#544	C₂²	1	2	yes	complemented
29	C₁₃×#542	C₂²	1	2	yes	—
30	C₁₃×#542	C₂²	1	2	yes	—
31	C₁₃×#540	C₂²	1	2	yes	—
32	C₁₃×#540	C₂²	1	2	yes	—
33	C₁₃×#535	C₂²	1	2	yes	complemented
34	C₁₃×#532	C₂²	1	2	yes	complemented
35	C₁₃×#532	C₂²	1	2	yes	complemented
36	C₁₃×#529	C₂²	1	2	yes	complemented
37	C₁₃×#529	C₂²	1	2	yes	complemented
38	C₁₃×#525	C₂²	1	2	yes	—
39	C₂×C₁₃×#121	C₂²	1	2	yes	—
40	C₁₃×#520	C₂²	1	2	yes	complemented
41	C₁₃×#518	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
43	C₁₃×#501	C₂²	1	2	yes	complemented
44	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#496	C₂²	1	2	yes	complemented
47	C₁₃×#495	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#490	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	2	yes	complemented
51	C₁₃×#488	C₂²	1	2	yes	complemented
52	C₁₃×#486	C₂²	1	2	yes	complemented
53	C₁₃×#485	C₂²	1	2	yes	complemented
54	C₁₃×#483	C₂²	1	2	yes	complemented
55	C₁₃×#482	C₂²	1	2	yes	—
56	C₁₃×#482	C₂²	1	2	yes	—
57	C₁₃×#482	C₂²	1	2	yes	complemented
58	C₁₃×#481	C₂²	1	2	yes	—
59	C₁₃×#481	C₂²	1	2	yes	—
60	C₁₃×#480	C₂²	1	2	yes	complemented
61	C₁₃×#479	C₂²	1	2	yes	complemented
62	C₁₃×#478	C₂²	1	2	yes	complemented
63	C₁₃×#478	C₂²	1	2	yes	complemented
64	C₁₃×#478	C₂²	1	2	yes	complemented
65	C₁₃×#476	C₂²	1	2	yes	complemented
66	C₁₃×#476	C₂²	1	2	yes	complemented
67	C₁₃×#475	C₂²	1	2	yes	complemented
68	C₁₃×#474	C₂²	1	2	yes	complemented
69	C₁₃×#470	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#469	C₂²	1	2	yes	—
71	C₁₃×#469	C₂²	1	1	yes	characteristic
72	C₁₃×#469	C₂²	1	1	yes	characteristic
73	C₁₃×#469	C₂²	1	2	yes	complemented
74	C₁₃×#469	C₂²	1	2	yes	complemented
75	C₁₃×#469	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#468	C₂²	1	2	yes	complemented
77	C₁₃×#468	C₂²	1	2	yes	complemented
78	C₁₃×#468	C₂²	1	2	yes	complemented
79	C₁₃×#464	C₂²	1	2	yes	complemented
80	C₁₃×#463	C₂²	1	2	yes	complemented
81	C₁₃×#463	C₂²	1	2	yes	complemented
82	C₁₃×#463	C₂²	1	2	yes	complemented
83	C₁₃×#460	C₂²	1	2	yes	complemented
84	C₁₃×#459	C₂²	1	2	yes	complemented
85	C₁₃×#459	C₂²	1	2	yes	complemented
86	C₁₃×#459	C₂²	1	2	yes	complemented
87	C₁₃×#452	C₂²	1	2	yes	complemented
88	C₁₃×#450	C₂²	1	2	yes	complemented
89	C₁₃×#449	C₂²	1	2	yes	—
90	C₁₃×#449	C₂²	1	2	yes	—
91	C₁₃×#449	C₂²	1	2	yes	complemented
92	C₁₃×#447	C₂²	1	2	yes	—
93	C₁₃×#447	C₂²	1	2	yes	—
94	C₁₃×#447	C₂²	1	2	yes	complemented
95	C₁₃×#442	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#442	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#442	C₂²	1	1	yes	characteristic, complemented
98	C₁₃×#442	C₂²	1	2	yes	complemented
99	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#440	C₂²	1	2	yes	complemented
101	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
102	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
103	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
104	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
105	C₁₃×#433	C₂²	1	2	yes	complemented
106	C₁₃×#433	C₂²	1	2	yes	complemented
107	C₁₃×#433	C₂²	1	2	yes	complemented
108	C₁₃×#433	C₂²	1	2	yes	complemented
109	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
110	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
111	C₁₃×#407	C₂²	1	1	yes	characteristic
112	C₁₃×#407	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₁₃×#41	—	2	2	no	—
116	C₂×C₁₃×#41	—	2	2	no	—
117	C₂×C₁₃×#41	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	—	2	2	no	—
119	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×D₈	C₂³	1	2	yes	—
126	C₂×C₁₃×D₈	C₂³	1	2	yes	—
127	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×D₈	C₂³	1	2	yes	—
130	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
133	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
134	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×#127	C₂³	1	2	yes	—
139	C₁₃×#127	C₂³	1	2	yes	—
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×#125	—	2	2	no	—
145	C₁₃×#125	C₂³	1	2	yes	—
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	—	2	2	no	—
151	C₁₃×#124	C₂³	1	2	yes	—
152	C₁₃×#124	C₂³	1	2	yes	—
153	C₁₃×#123	—	2	2	no	—
154	C₁₃×#123	—	2	2	no	—
155	C₁₃×#123	—	2	2	no	—
156	C₁₃×#123	—	2	2	no	—
157	C₁₃×#123	—	2	2	no	—
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×C₂²⋊Q₈	—	2	2	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	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₁₃×#121	—	2	2	no	—
169	C₁₃×#121	—	2	2	no	—
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	2	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	—	2	2	no	—
177	C₁₃×#121	—	2	2	no	—
178	C₁₃×#121	C₂³	1	2	yes	—
179	C₁₃×#121	C₂³	1	2	yes	—
180	C₁₃×#121	C₂³	1	2	yes	—
181	C₁₃×#121	C₂³	1	2	yes	—
182	C₁₃×#121	C₂³	1	2	yes	—
183	C₁₃×#121	C₂³	1	2	yes	—
184	C₁₃×#120	—	2	2	no	—
185	C₁₃×#120	—	2	2	no	—
186	C₁₃×#120	—	2	2	no	—
187	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
188	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	2	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	—	2	2	no	—
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	C₂³	1	2	yes	—
200	C₄×D₄×C₁₃	C₂³	1	2	yes	—
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₄×D₄×C₁₃	C₂³	1	2	yes	—
203	C₄×D₄×C₁₃	C₂³	1	2	yes	—
204	C₄×D₄×C₁₃	C₂³	1	2	yes	—
205	C₁₃×#117	—	2	2	no	—
206	C₁₃×#117	—	2	2	no	—
207	C₁₃×#117	—	2	2	no	—
208	C₁₃×#117	D₄	1	2	yes	—
209	C₁₃×#117	D₄	1	2	yes	—
210	C₁₃×#117	C₂³	1	2	yes	—
211	C₁₃×#117	C₂³	1	2	yes	—
212	C₁₃×#117	C₂³	1	2	yes	—
213	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
215	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
217	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
218	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
219	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
220	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
222	C₁₃×#107	C₂³	1	2	yes	—
223	C₁₃×#107	C₂³	1	2	yes	—
224	C₁₃×#107	C₂³	1	2	yes	—
225	C₁₃×#106	C₂³	1	2	yes	—
226	C₁₃×#106	C₂³	1	2	yes	—
227	C₁₃×#106	C₂³	1	1	yes	characteristic
228	C₁₃×#106	C₂³	1	1	yes	characteristic
229	C₁₃×#106	C₂³	1	2	yes	—
230	C₁₃×#106	C₂³	1	1	yes	characteristic
231	C₁₃×#106	C₂³	1	1	yes	characteristic
232	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
233	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
234	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₁₃×#103	C₂³	1	2	yes	—
237	C₁₃×#103	C₂³	1	2	yes	—
238	C₁₃×#103	C₂³	1	2	yes	—
239	C₁₃×#103	C₂³	1	2	yes	—
240	C₁₃×#102	C₂³	1	2	yes	—
241	C₁₃×#102	C₂³	1	2	yes	—
242	C₁₃×#102	C₂³	1	2	yes	—
243	C₁₃×#102	C₂³	1	2	yes	—
244	C₁₃×#102	C₂³	1	2	yes	—
245	C₁₃×#102	C₂³	1	2	yes	—
246	C₁₃×#102	C₂³	1	2	yes	—
247	C₁₃×#102	C₂³	1	2	yes	—
248	C₁₃×#102	C₂³	1	2	yes	—
249	C₁₃×#102	C₂³	1	2	yes	—
250	C₁₃×#102	C₂³	1	2	yes	—
251	C₁₃×#102	C₂³	1	2	yes	—
252	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₁₃×#97	C₂³	1	1	yes	characteristic
257	C₁₃×#97	C₂³	1	1	yes	characteristic
258	C₁₃×#97	C₂³	1	2	yes	—
259	C₄×C₈×C₁₃	C₂³	1	2	yes	—
260	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
262	#61003	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂⁴×C₁₃	—	2	2	no	—
264	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₁₃×#41	—	4	2	no	—
266	C₁₃×#41	—	4	2	no	—
267	C₁₃×#41	—	8	4	no	—
268	C₁₃×#41	—	8	4	no	—
269	C₂×Q₈×C₁₃	—	2	2	no	—
270	C₂×Q₈×C₁₃	—	2	2	no	—
271	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	2	no	—
274	C₂×D₄×C₁₃	—	2	2	no	—
275	C₂×D₄×C₁₃	—	2	2	no	—
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	—	2	2	no	—
280	C₂×D₄×C₁₃	—	2	2	no	—
281	C₂×D₄×C₁₃	—	2	2	no	—
282	C₂×D₄×C₁₃	—	2	2	no	—
283	C₂×D₄×C₁₃	—	2	2	no	—
284	C₂×D₄×C₁₃	—	4	2	no	—
285	C₂×D₄×C₁₃	—	4	2	no	—
286	C₂×D₄×C₁₃	—	8	4	no	—
287	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	—	2	2	no	—
291	C₂²×C₄×C₁₃	—	2	2	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	2	no	—
294	C₂²×C₄×C₁₃	—	2	2	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	—	4	1	no	—
299	C₂²×C₄×C₁₃	—	4	1	no	—
300	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
301	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
303	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₁₃×Q₁₆	—	4	1	no	—
307	C₁₃×SD₁₆	—	4	2	no	—
308	C₁₃×SD₁₆	—	4	2	no	—
309	C₁₃×SD₁₆	—	4	2	no	—
310	C₁₃×D₈	—	4	2	no	—
311	C₁₃×D₈	—	4	1	no	—
312	C₁₃×D₈	—	4	1	no	—
313	C₁₃×D₈	—	4	2	no	—
314	C₁₃×D₈	—	4	2	no	—
315	C₁₃×D₈	—	4	1	no	—
316	C₁₃×M₁₆	—	4	1	no	—
317	C₁₃×M₁₆	—	4	1	no	—
318	C₁₃×M₁₆	—	4	1	no	—
319	C₁₃×M₁₆	—	4	1	no	—
320	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
321	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
323	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
324	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
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	C₂⁴	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×C₂²⋊C₄	—	2	2	no	—
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	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	—	2	2	no	—
364	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
365	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
366	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
367	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
368	C₄²×C₁₃	—	2	2	no	—
369	C₄²×C₁₃	—	2	2	no	—
370	C₄²×C₁₃	—	2	2	no	—
371	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₁₃	C₂×D₄	1	2	yes	—
373	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₄²×C₁₃	C₂⁴	1	2	yes	—
377	#3494	C₂×C₁₃	1	2	yes	complemented
378	#3256	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#3253	C₂×C₁₃	1	1	yes	characteristic, complemented
380	#3251	C₂×C₁₃	1	2	yes	complemented
381	#3244	C₂×C₁₃	1	2	yes	complemented
382	#3241	C₂×C₁₃	1	2	yes	complemented
383	#3224	C₂×C₁₃	1	2	yes	complemented
384	#3220	C₂×C₁₃	1	2	yes	complemented
385	#3197	C₂×C₁₃	1	1	yes	characteristic, complemented
386	#3194	C₂×C₁₃	1	2	yes	complemented
387	#3192	C₂×C₁₃	1	1	yes	characteristic, complemented
388	#3184	C₂×C₁₃	1	1	yes	characteristic, complemented
389	#3183	C₂×C₁₃	1	1	yes	characteristic, complemented
390	#3171	C₂×C₁₃	1	2	yes	complemented
391	#3125	C₂×C₁₃	1	2	yes	complemented
392	#3122	C₂×C₁₃	1	2	yes	complemented
393	#3119	C₂×C₁₃	1	2	yes	complemented
394	#3118	C₂×C₁₃	1	2	yes	complemented
395	#2921	C₂×C₁₃	1	1	yes	characteristic, complemented
396	C₂³×C₁₃	—	2	2	no	—
397	C₂³×C₁₃	—	2	2	no	—
398	C₂³×C₁₃	—	2	2	no	—
399	C₂³×C₁₃	—	4	1	no	—
400	C₂³×C₁₃	—	4	2	no	—
401	C₂³×C₁₃	—	4	4	no	—
402	C₂³×C₁₃	—	8	2	no	—
403	C₂³×C₁₃	—	8	2	no	—
404	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	Q₈×C₁₃	—	2	2	no	—
407	Q₈×C₁₃	—	2	2	no	—
408	Q₈×C₁₃	—	8	2	no	—
409	Q₈×C₁₃	—	8	2	no	—
410	D₄×C₁₃	—	2	2	no	—
411	D₄×C₁₃	—	2	2	no	—
412	D₄×C₁₃	—	2	2	no	—
413	D₄×C₁₃	—	2	2	no	—
414	D₄×C₁₃	—	2	2	no	—
415	D₄×C₁₃	—	2	2	no	—
416	D₄×C₁₃	—	4	4	no	—
417	D₄×C₁₃	—	4	4	no	—
418	D₄×C₁₃	—	4	4	no	—
419	D₄×C₁₃	—	4	4	no	—
420	D₄×C₁₃	—	4	4	no	—
421	D₄×C₁₃	—	8	2	no	—
422	D₄×C₁₃	—	8	2	no	—
423	D₄×C₁₃	—	8	2	no	—
424	D₄×C₁₃	—	8	2	no	—
425	D₄×C₁₃	—	8	2	no	—
426	D₄×C₁₃	—	8	2	no	—
427	D₄×C₁₃	—	8	2	no	—
428	C₂×C₄×C₁₃	—	2	1	no	—
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	4	1	no	—
438	C₂×C₄×C₁₃	—	4	2	no	—
439	C₂×C₄×C₁₃	—	4	2	no	—
440	C₂×C₄×C₁₃	—	4	2	no	—
441	C₂×C₄×C₁₃	—	4	4	no	—
442	C₂×C₄×C₁₃	—	8	2	no	—
443	C₂×C₄×C₁₃	—	8	2	no	—
444	C₂×C₄×C₁₃	—	8	2	no	—
445	C₂×C₄×C₁₃	—	8	2	no	—
446	C₂×C₄×C₁₃	—	8	2	no	—
447	C₂×C₄×C₁₃	—	8	2	no	—
448	C₂×C₄×C₁₃	—	8	2	no	—
449	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
456	C₈×C₁₃	—	2	1	no	—
457	C₈×C₁₃	—	2	1	no	—
458	C₈×C₁₃	—	2	2	no	—
459	C₈×C₁₃	—	2	2	no	—
460	C₈×C₁₃	—	2	1	no	—
461	C₈×C₁₃	—	2	1	no	—
462	#555	—	2	2	no	—
463	#553	—	2	2	no	—
464	#553	—	2	2	no	—
465	#551	—	2	2	no	—
466	#551	—	2	2	no	—
467	#547	—	2	2	no	—
468	#546	—	2	2	no	—
469	#546	—	2	2	no	—
470	#544	C₂²×C₁₃	1	2	yes	complemented
471	#542	C₂²×C₁₃	1	2	yes	—
472	#542	C₂²×C₁₃	1	2	yes	—
473	#540	C₂²×C₁₃	1	2	yes	—
474	#540	C₂²×C₁₃	1	2	yes	—
475	#535	C₂²×C₁₃	1	2	yes	complemented
476	#532	C₂²×C₁₃	1	2	yes	complemented
477	#532	C₂²×C₁₃	1	2	yes	complemented
478	#529	C₂²×C₁₃	1	2	yes	complemented
479	#529	C₂²×C₁₃	1	2	yes	complemented
480	#525	C₂²×C₁₃	1	2	yes	—
481	C₂×#121	C₂²×C₁₃	1	2	yes	—
482	#520	C₂²×C₁₃	1	2	yes	complemented
483	#518	C₂²×C₁₃	1	2	yes	complemented
484	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
485	#501	C₂²×C₁₃	1	2	yes	complemented
486	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	#496	C₂²×C₁₃	1	2	yes	complemented
489	#495	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	#490	C₂²×C₁₃	1	2	yes	complemented
492	#489	C₂²×C₁₃	1	2	yes	complemented
493	#488	C₂²×C₁₃	1	2	yes	complemented
494	#486	C₂²×C₁₃	1	2	yes	complemented
495	#485	C₂²×C₁₃	1	2	yes	complemented
496	#483	C₂²×C₁₃	1	2	yes	complemented
497	#482	C₂²×C₁₃	1	2	yes	—
498	#482	C₂²×C₁₃	1	2	yes	—
499	#482	C₂²×C₁₃	1	2	yes	complemented
500	#481	C₂²×C₁₃	1	2	yes	—
501	#481	C₂²×C₁₃	1	2	yes	—
502	#480	C₂²×C₁₃	1	2	yes	complemented
503	#479	C₂²×C₁₃	1	2	yes	complemented
504	#478	C₂²×C₁₃	1	2	yes	complemented
505	#478	C₂²×C₁₃	1	2	yes	complemented
506	#478	C₂²×C₁₃	1	2	yes	complemented
507	#476	C₂²×C₁₃	1	2	yes	complemented
508	#476	C₂²×C₁₃	1	2	yes	complemented
509	#475	C₂²×C₁₃	1	2	yes	complemented
510	#474	C₂²×C₁₃	1	2	yes	complemented
511	#470	C₂²×C₁₃	1	1	yes	characteristic, complemented
512	#469	C₂²×C₁₃	1	2	yes	—
513	#469	C₂²×C₁₃	1	1	yes	characteristic
514	#469	C₂²×C₁₃	1	1	yes	characteristic
515	#469	C₂²×C₁₃	1	2	yes	complemented
516	#469	C₂²×C₁₃	1	2	yes	complemented
517	#469	C₂²×C₁₃	1	1	yes	characteristic, complemented
518	#468	C₂²×C₁₃	1	2	yes	complemented
519	#468	C₂²×C₁₃	1	2	yes	complemented
520	#468	C₂²×C₁₃	1	2	yes	complemented
521	#464	C₂²×C₁₃	1	2	yes	complemented
522	#463	C₂²×C₁₃	1	2	yes	complemented
523	#463	C₂²×C₁₃	1	2	yes	complemented
524	#463	C₂²×C₁₃	1	2	yes	complemented
525	#460	C₂²×C₁₃	1	2	yes	complemented
526	#459	C₂²×C₁₃	1	2	yes	complemented
527	#459	C₂²×C₁₃	1	2	yes	complemented
528	#459	C₂²×C₁₃	1	2	yes	complemented
529	#452	C₂²×C₁₃	1	2	yes	complemented
530	#450	C₂²×C₁₃	1	2	yes	complemented
531	#449	C₂²×C₁₃	1	2	yes	—
532	#449	C₂²×C₁₃	1	2	yes	—
533	#449	C₂²×C₁₃	1	2	yes	complemented
534	#447	C₂²×C₁₃	1	2	yes	—
535	#447	C₂²×C₁₃	1	2	yes	—
536	#447	C₂²×C₁₃	1	2	yes	complemented
537	#442	C₂²×C₁₃	1	1	yes	characteristic, complemented
538	#442	C₂²×C₁₃	1	1	yes	characteristic, complemented
539	#442	C₂²×C₁₃	1	1	yes	characteristic, complemented
540	#442	C₂²×C₁₃	1	2	yes	complemented
541	#441	C₂²×C₁₃	1	1	yes	characteristic, complemented
542	#440	C₂²×C₁₃	1	2	yes	complemented
543	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
544	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
545	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
546	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
547	#433	C₂²×C₁₃	1	2	yes	complemented
548	#433	C₂²×C₁₃	1	2	yes	complemented
549	#433	C₂²×C₁₃	1	2	yes	complemented
550	#433	C₂²×C₁₃	1	2	yes	complemented
551	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
552	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
553	#407	C₂²×C₁₃	1	1	yes	characteristic
554	#407	C₂²×C₁₃	1	1	yes	characteristic
555	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
556	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
557	C₂²×C₁₃	—	2	2	no	—
558	C₂²×C₁₃	—	2	2	no	—
559	C₂²×C₁₃	—	2	2	no	—
560	C₂²×C₁₃	—	2	2	no	—
561	C₂²×C₁₃	—	2	1	no	—
562	C₂²×C₁₃	—	4	2	no	—
563	C₂²×C₁₃	—	4	2	no	—
564	C₂²×C₁₃	—	4	2	no	—
565	C₂²×C₁₃	—	4	2	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	—	4	2	no	—
568	C₂²×C₁₃	—	4	2	no	—
569	C₂²×C₁₃	—	4	2	no	—
570	C₂²×C₁₃	—	4	2	no	—
571	C₂²×C₁₃	—	8	2	no	—
572	C₂²×C₁₃	—	16	4	no	—
573	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
574	C₄×C₁₃	—	2	2	no	—
575	C₄×C₁₃	—	2	2	no	—
576	C₄×C₁₃	—	2	2	no	—
577	C₄×C₁₃	—	2	2	no	—
578	C₄×C₁₃	—	2	2	no	—
579	C₄×C₁₃	—	2	1	no	—
580	C₄×C₁₃	—	4	2	no	—
581	C₄×C₁₃	—	4	2	no	—
582	C₄×C₁₃	—	4	2	no	—
583	C₄×C₁₃	—	4	2	no	—
584	C₄×C₁₃	—	4	2	no	—
585	C₄×C₁₃	#585	1	1	yes	characteristic
586	C₄×C₁₃	#585	1	1	yes	characteristic
587	C₂×#41	—	2	2	no	—
588	C₂×#41	—	2	2	no	—
589	C₂×#41	C₂³×C₁₃	1	2	yes	—
590	C₂²×D₄	—	2	2	no	—
591	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
592	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
594	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
596	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
597	C₂×D₈	C₂³×C₁₃	1	2	yes	—
598	C₂×D₈	C₂³×C₁₃	1	2	yes	—
599	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₂×D₈	C₂³×C₁₃	1	2	yes	—
602	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
603	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
604	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
606	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
607	C₄⋊Q₈	—	2	2	no	—
608	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
609	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
610	#127	C₂³×C₁₃	1	2	yes	—
611	#127	C₂³×C₁₃	1	2	yes	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#125	—	2	2	no	—
617	#125	C₂³×C₁₃	1	2	yes	—
618	#125	C₂³×C₁₃	1	2	yes	—
619	#124	—	2	2	no	—
620	#124	—	2	2	no	—
621	#124	—	2	2	no	—
622	#124	—	2	2	no	—
623	#124	C₂³×C₁₃	1	2	yes	—
624	#124	C₂³×C₁₃	1	2	yes	—
625	#123	—	2	2	no	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
639	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
640	#121	—	2	2	no	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	2	no	—
644	#121	—	2	2	no	—
645	#121	—	2	2	no	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	C₂³×C₁₃	1	2	yes	—
651	#121	C₂³×C₁₃	1	2	yes	—
652	#121	C₂³×C₁₃	1	2	yes	—
653	#121	C₂³×C₁₃	1	2	yes	—
654	#121	C₂³×C₁₃	1	2	yes	—
655	#121	C₂³×C₁₃	1	2	yes	—
656	#120	—	2	2	no	—
657	#120	—	2	2	no	—
658	#120	—	2	2	no	—
659	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
660	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	C₂³×C₁₃	1	2	yes	—
672	C₄×D₄	C₂³×C₁₃	1	2	yes	—
673	C₄×D₄	C₂³×C₁₃	1	2	yes	—
674	C₄×D₄	C₂³×C₁₃	1	2	yes	—
675	C₄×D₄	C₂³×C₁₃	1	2	yes	—
676	C₄×D₄	C₂³×C₁₃	1	2	yes	—
677	#117	—	2	2	no	—
678	#117	—	2	2	no	—
679	#117	—	2	2	no	—
680	#117	D₄×C₁₃	1	2	yes	—
681	#117	D₄×C₁₃	1	2	yes	—
682	#117	C₂³×C₁₃	1	2	yes	—
683	#117	C₂³×C₁₃	1	2	yes	—
684	#117	C₂³×C₁₃	1	2	yes	—
685	C₂×C₄⋊C₄	—	2	2	no	—
686	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
688	C₂×C₂²⋊C₄	—	2	2	no	—
689	C₂×C₂²⋊C₄	—	2	2	no	—
690	C₂×C₂²⋊C₄	—	2	2	no	—
691	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
692	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
694	#107	C₂³×C₁₃	1	2	yes	—
695	#107	C₂³×C₁₃	1	2	yes	—
696	#107	C₂³×C₁₃	1	2	yes	—
697	#106	C₂³×C₁₃	1	2	yes	—
698	#106	C₂³×C₁₃	1	2	yes	—
699	#106	C₂³×C₁₃	1	1	yes	characteristic
700	#106	C₂³×C₁₃	1	1	yes	characteristic
701	#106	C₂³×C₁₃	1	2	yes	—
702	#106	C₂³×C₁₃	1	1	yes	characteristic
703	#106	C₂³×C₁₃	1	1	yes	characteristic
704	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
705	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
706	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
707	C₄⋊C₈	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	#102	C₂³×C₁₃	1	2	yes	—
717	#102	C₂³×C₁₃	1	2	yes	—
718	#102	C₂³×C₁₃	1	2	yes	—
719	#102	C₂³×C₁₃	1	2	yes	—
720	#102	C₂³×C₁₃	1	2	yes	—
721	#102	C₂³×C₁₃	1	2	yes	—
722	#102	C₂³×C₁₃	1	2	yes	—
723	#102	C₂³×C₁₃	1	2	yes	—
724	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
726	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
727	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
728	#97	C₂³×C₁₃	1	1	yes	characteristic
729	#97	C₂³×C₁₃	1	1	yes	characteristic
730	#97	C₂³×C₁₃	1	2	yes	—
731	C₄×C₈	C₂³×C₁₃	1	2	yes	—
732	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
733	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
734	C₂×C₁₃	—	4	1	no	—
735	C₂×C₁₃	—	4	2	no	—
736	C₂×C₁₃	—	8	2	no	—
737	C₂×C₁₃	—	8	2	no	—
738	C₂×C₁₃	—	8	2	no	—
739	C₂×C₁₃	#3449	1	1	yes	characteristic
740	C₂×C₁₃	#3585	1	2	yes	—
741	C₂⁴	—	2	2	no	—
742	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
743	#41	—	4	2	no	—
744	#41	—	4	2	no	—
745	#41	—	8	4	no	—
746	#41	—	8	4	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	2	2	no	—
749	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	4	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	—	8	4	no	—
765	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
766	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
767	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	4	1	no	—
777	C₂²×C₄	—	4	1	no	—
778	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
779	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
780	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
781	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
784	Q₁₆	—	4	1	no	—
785	SD₁₆	—	4	2	no	—
786	SD₁₆	—	4	2	no	—
787	SD₁₆	—	4	2	no	—
788	D₈	—	4	2	no	—
789	D₈	—	4	1	no	—
790	D₈	—	4	1	no	—
791	D₈	—	4	2	no	—
792	D₈	—	4	2	no	—
793	D₈	—	4	1	no	—
794	M₁₆	—	4	1	no	—
795	M₁₆	—	4	1	no	—
796	M₁₆	—	4	1	no	—
797	M₁₆	—	4	1	no	—
798	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
799	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
800	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
801	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
802	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
803	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
816	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
817	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
818	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
821	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
822	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
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	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
843	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
845	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
850	C₄²	C₂×D₄×C₁₃	1	2	yes	—
851	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
852	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
853	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
854	C₄²	C₂⁴×C₁₃	1	2	yes	—
855	C₁₃	#61003	1	1	yes	characteristic, direct product factor, Sylow
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	4	2	no	—
861	C₂³	—	4	4	no	—
862	C₂³	—	8	2	no	—
863	C₂³	—	8	2	no	—
864	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
865	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
866	Q₈	—	2	2	no	—
867	Q₈	—	2	2	no	—
868	Q₈	—	8	2	no	—
869	Q₈	—	8	2	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	4	no	—
881	D₄	—	8	2	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	2	no	—
886	D₄	—	8	2	no	—
887	D₄	—	8	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	8	2	no	—
903	C₂×C₄	—	8	2	no	—
904	C₂×C₄	—	8	2	no	—
905	C₂×C₄	—	8	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
910	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
913	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
914	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
915	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
916	C₈	—	2	1	no	—
917	C₈	—	2	1	no	—
918	C₈	—	2	2	no	—
919	C₈	—	2	2	no	—
920	C₈	—	2	1	no	—
921	C₈	—	2	1	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	8	2	no	—
937	C₂²	—	16	4	no	—
938	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	C₁₃×#585	1	1	yes	characteristic
951	C₄	C₁₃×#585	1	1	yes	characteristic
952	C₂	—	4	2	no	—
953	C₂	—	4	1	no	—
954	C₂	—	8	2	no	—
955	C₂	—	8	2	no	—
956	C₂	—	8	2	no	—
957	C₂	C₁₃×#3449	1	1	yes	characteristic
958	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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×#3494	C₂	semidirect
2. C₁₃×#3256	C₂	semidirect
3. C₁₃×#3253	C₂	semidirect
4. C₁₃×#3251	C₂	semidirect
5. C₁₃×#3244	C₂	semidirect
6. C₁₃×#3241	C₂	semidirect
7. C₁₃×#3224	C₂	semidirect
8. C₁₃×#3220	C₂	semidirect
9. C₁₃×#3197	C₂	semidirect
10. C₁₃×#3194	C₂	semidirect
11. C₁₃×#3192	C₂	semidirect
12. C₁₃×#3184	C₂	semidirect
13. C₁₃×#3183	C₂	semidirect
14. C₁₃×#3171	C₂	semidirect
15. C₁₃×#3125	C₂	semidirect
16. C₁₃×#3122	C₂	semidirect
17. C₁₃×#3119	C₂	semidirect
18. C₁₃×#3118	C₂	semidirect
19. C₁₃×#2921	C₂	semidirect
28. C₁₃×#544	C₂²	semidirect
33. C₁₃×#535	C₂²	semidirect
34. C₁₃×#532	C₂²	semidirect
35. C₁₃×#532	C₂²	semidirect
36. C₁₃×#529	C₂²	semidirect
37. C₁₃×#529	C₂²	semidirect
40. C₁₃×#520	C₂²	semidirect
41. C₁₃×#518	C₂²	semidirect
43. C₁₃×#501	C₂²	semidirect
44. C₁₃×#499	C₂²	semidirect
45. C₁₃×#498	C₂²	semidirect
46. C₁₃×#496	C₂²	semidirect
47. C₁₃×#495	C₂²	semidirect
48. C₁₃×#493	C₂²	semidirect
49. C₁₃×#490	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#488	C₂²	semidirect
52. C₁₃×#486	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
54. C₁₃×#483	C₂²	semidirect
57. C₁₃×#482	C₂²	semidirect
60. C₁₃×#480	C₂²	semidirect
61. C₁₃×#479	C₂²	semidirect
62. C₁₃×#478	C₂²	semidirect
63. C₁₃×#478	C₂²	semidirect
64. C₁₃×#478	C₂²	semidirect
65. C₁₃×#476	C₂²	semidirect
66. C₁₃×#476	C₂²	semidirect
67. C₁₃×#475	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
69. C₁₃×#470	C₂²	semidirect
73. C₁₃×#469	C₂²	semidirect
74. C₁₃×#469	C₂²	semidirect
75. C₁₃×#469	C₂²	semidirect
76. C₁₃×#468	C₂²	semidirect
77. C₁₃×#468	C₂²	semidirect
78. C₁₃×#468	C₂²	semidirect
79. C₁₃×#464	C₂²	semidirect
80. C₁₃×#463	C₂²	semidirect
81. C₁₃×#463	C₂²	semidirect
82. C₁₃×#463	C₂²	semidirect
83. C₁₃×#460	C₂²	semidirect
84. C₁₃×#459	C₂²	semidirect
85. C₁₃×#459	C₂²	semidirect
86. C₁₃×#459	C₂²	semidirect
87. C₁₃×#452	C₂²	semidirect
88. C₁₃×#450	C₂²	semidirect
91. C₁₃×#449	C₂²	semidirect
94. C₁₃×#447	C₂²	semidirect
95. C₁₃×#442	C₂²	semidirect
96. C₁₃×#442	C₂²	semidirect
97. C₁₃×#442	C₂²	semidirect
98. C₁₃×#442	C₂²	semidirect
99. C₁₃×#441	C₂²	semidirect
100. C₁₃×#440	C₂²	semidirect
101. C₄×C₁₃×SD₁₆	C₂²	semidirect
102. C₄×C₁₃×SD₁₆	C₂²	semidirect
103. C₄×C₁₃×D₈	C₂²	semidirect
104. C₄×C₁₃×D₈	C₂²	semidirect
105. C₁₃×#433	C₂²	semidirect
106. C₁₃×#433	C₂²	semidirect
107. C₁₃×#433	C₂²	semidirect
108. C₁₃×#433	C₂²	semidirect
109. C₁₃×#423	C₂²	semidirect
110. C₁₃×#423	C₂²	semidirect
113. C₄×C₁₃×M₁₆	C₂²	semidirect
114. C₄×C₁₃×M₁₆	C₂²	semidirect
262. #61003	C₁₃	direct (N × H)
377. #3494	C₂×C₁₃	semidirect
378. #3256	C₂×C₁₃	semidirect
379. #3253	C₂×C₁₃	semidirect
380. #3251	C₂×C₁₃	semidirect
381. #3244	C₂×C₁₃	semidirect
382. #3241	C₂×C₁₃	semidirect
383. #3224	C₂×C₁₃	semidirect
384. #3220	C₂×C₁₃	semidirect
385. #3197	C₂×C₁₃	semidirect
386. #3194	C₂×C₁₃	semidirect
387. #3192	C₂×C₁₃	semidirect
388. #3184	C₂×C₁₃	semidirect
389. #3183	C₂×C₁₃	semidirect
390. #3171	C₂×C₁₃	semidirect
391. #3125	C₂×C₁₃	semidirect
392. #3122	C₂×C₁₃	semidirect
393. #3119	C₂×C₁₃	semidirect
394. #3118	C₂×C₁₃	semidirect
395. #2921	C₂×C₁₃	semidirect
470. #544	C₂²×C₁₃	semidirect
475. #535	C₂²×C₁₃	semidirect
476. #532	C₂²×C₁₃	semidirect
477. #532	C₂²×C₁₃	semidirect
478. #529	C₂²×C₁₃	semidirect
479. #529	C₂²×C₁₃	semidirect
482. #520	C₂²×C₁₃	semidirect
483. #518	C₂²×C₁₃	semidirect
485. #501	C₂²×C₁₃	semidirect
486. #499	C₂²×C₁₃	semidirect
487. #498	C₂²×C₁₃	semidirect
488. #496	C₂²×C₁₃	semidirect
489. #495	C₂²×C₁₃	semidirect
490. #493	C₂²×C₁₃	semidirect
491. #490	C₂²×C₁₃	semidirect
492. #489	C₂²×C₁₃	semidirect
493. #488	C₂²×C₁₃	semidirect
494. #486	C₂²×C₁₃	semidirect
495. #485	C₂²×C₁₃	semidirect
496. #483	C₂²×C₁₃	semidirect
499. #482	C₂²×C₁₃	semidirect
502. #480	C₂²×C₁₃	semidirect
503. #479	C₂²×C₁₃	semidirect
504. #478	C₂²×C₁₃	semidirect
505. #478	C₂²×C₁₃	semidirect
506. #478	C₂²×C₁₃	semidirect
507. #476	C₂²×C₁₃	semidirect
508. #476	C₂²×C₁₃	semidirect
509. #475	C₂²×C₁₃	semidirect
510. #474	C₂²×C₁₃	semidirect
511. #470	C₂²×C₁₃	semidirect
515. #469	C₂²×C₁₃	semidirect
516. #469	C₂²×C₁₃	semidirect
517. #469	C₂²×C₁₃	semidirect
518. #468	C₂²×C₁₃	semidirect
519. #468	C₂²×C₁₃	semidirect
520. #468	C₂²×C₁₃	semidirect
521. #464	C₂²×C₁₃	semidirect
522. #463	C₂²×C₁₃	semidirect
523. #463	C₂²×C₁₃	semidirect
524. #463	C₂²×C₁₃	semidirect
525. #460	C₂²×C₁₃	semidirect
526. #459	C₂²×C₁₃	semidirect
527. #459	C₂²×C₁₃	semidirect
528. #459	C₂²×C₁₃	semidirect
529. #452	C₂²×C₁₃	semidirect
530. #450	C₂²×C₁₃	semidirect
533. #449	C₂²×C₁₃	semidirect
536. #447	C₂²×C₁₃	semidirect
537. #442	C₂²×C₁₃	semidirect
538. #442	C₂²×C₁₃	semidirect
539. #442	C₂²×C₁₃	semidirect
540. #442	C₂²×C₁₃	semidirect
541. #441	C₂²×C₁₃	semidirect
542. #440	C₂²×C₁₃	semidirect
543. C₄×SD₁₆	C₂²×C₁₃	semidirect
544. C₄×SD₁₆	C₂²×C₁₃	semidirect
545. C₄×D₈	C₂²×C₁₃	semidirect
546. C₄×D₈	C₂²×C₁₃	semidirect
547. #433	C₂²×C₁₃	semidirect
548. #433	C₂²×C₁₃	semidirect
549. #433	C₂²×C₁₃	semidirect
550. #433	C₂²×C₁₃	semidirect
551. #423	C₂²×C₁₃	semidirect
552. #423	C₂²×C₁₃	semidirect
555. C₄×M₁₆	C₂²×C₁₃	semidirect
556. C₄×M₁₆	C₂²×C₁₃	semidirect
855. C₁₃	#61003	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×#3494	2
C₁₃×#3256	2
C₁₃×#3253	2
C₁₃×#3251	2
C₁₃×#3244	2
C₁₃×#3241	2
C₁₃×#3224	2
C₁₃×#3220	2
C₁₃×#3197	2
C₁₃×#3194	2
C₁₃×#3192	2
C₁₃×#3184	2
C₁₃×#3183	2
C₁₃×#3171	2
C₁₃×#3125	2
C₁₃×#3122	2
C₁₃×#3119	2
C₁₃×#3118	2
C₁₃×#2921	2
#61003	13

Subgroups — C13×#61003 #15747342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61003 #15747342