Subgroups — C₁₃×#61898 #15748237

Order 3328.

1844 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3399	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3396	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3370	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3114	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3100	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	—	2	1	no	—
19	C₁₃×#559	—	2	1	no	—
20	C₁₃×#559	—	2	2	no	—
21	C₁₃×#559	C₂²	1	2	yes	—
22	C₁₃×#559	C₂²	1	4	yes	—
23	C₁₃×#559	C₂²	1	2	yes	—
24	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#559	C₂²	1	2	yes	complemented
26	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#554	C₂²	1	2	yes	complemented
29	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#548	—	2	1	no	—
31	C₁₃×#547	—	2	1	no	—
32	C₁₃×#547	—	2	2	no	—
33	C₁₃×#542	—	2	2	no	—
34	C₁₃×#542	—	2	1	no	—
35	C₁₃×#532	C₂²	1	2	yes	—
36	C₁₃×#532	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
38	C₁₃×#529	C₂²	1	1	yes	characteristic
39	C₁₃×#529	C₂²	1	2	yes	—
40	C₂×C₁₃×#124	—	2	1	no	—
41	C₂×C₁₃×#124	C₂²	1	2	yes	—
42	C₂×C₁₃×#123	—	2	2	no	—
43	C₁₃×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
48	C₁₃×#496	C₂²	1	2	yes	—
49	C₁₃×#496	C₂²	1	4	yes	complemented
50	C₁₃×#495	C₂²	1	4	yes	complemented
51	C₁₃×#493	C₂²	1	2	yes	—
52	C₁₃×#490	C₂²	1	2	yes	—
53	C₁₃×#489	C₂²	1	4	yes	complemented
54	C₁₃×#488	C₂²	1	4	yes	complemented
55	C₁₃×#486	C₂²	1	2	yes	—
56	C₁₃×#483	C₂²	1	1	yes	characteristic
57	C₁₃×#480	C₂²	1	1	yes	characteristic
58	C₁₃×#480	C₂²	1	2	yes	—
59	C₁₃×#479	C₂²	1	2	yes	complemented
60	C₁₃×#478	C₂²	1	4	yes	complemented
61	C₁₃×#477	C₂²	1	2	yes	complemented
62	C₁₃×#474	C₂²	1	4	yes	complemented
63	C₁₃×#464	C₂²	1	2	yes	complemented
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#463	C₂²	1	4	yes	complemented
66	C₁₃×#463	C₂²	1	4	yes	complemented
67	C₁₃×#463	C₂²	1	4	yes	complemented
68	C₁₃×#463	C₂²	1	4	yes	complemented
69	C₁₃×#460	C₂²	1	2	yes	—
70	C₁₃×#460	C₂²	1	2	yes	complemented
71	C₁₃×#459	C₂²	1	2	yes	—
72	C₁₃×#459	C₂²	1	4	yes	—
73	C₁₃×#459	C₂²	1	4	yes	complemented
74	C₁₃×#451	C₂²	1	1	yes	characteristic
75	C₁₃×#450	C₂²	1	2	yes	—
76	C₁₃×#448	C₂²	1	1	yes	characteristic
77	C₁₃×#448	C₂²	1	2	yes	—
78	C₁₃×#447	C₂²	1	2	yes	—
79	C₁₃×#447	C₂²	1	2	yes	—
80	C₁₃×#447	C₂²	1	2	yes	—
81	C₁₃×#446	C₂²	1	4	yes	complemented
82	C₁₃×#446	C₂²	1	2	yes	complemented
83	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
84	C₁₃×#442	C₂²	1	4	yes	complemented
85	C₁₃×#440	C₂²	1	4	yes	complemented
86	C₁₃×#440	C₂²	1	4	yes	complemented
87	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
88	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
89	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
90	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
91	C₁₃×#432	C₂²	1	1	yes	characteristic
92	C₁₃×#432	C₂²	1	2	yes	—
93	C₁₃×#431	C₂²	1	2	yes	—
94	C₁₃×#431	C₂²	1	1	yes	characteristic
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	—	2	1	no	—
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃	—	2	2	no	—
104	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×D₈	C₂³	1	4	yes	—
109	C₂×C₁₃×D₈	C₂³	1	4	yes	—
110	C₂×C₁₃×D₈	C₂³	1	4	yes	—
111	C₁₃×C₄⋊Q₈	—	2	1	no	—
112	C₁₃×C₄⋊Q₈	—	2	2	no	—
113	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×#127	—	2	1	no	—
116	C₁₃×#127	—	2	1	no	—
117	C₁₃×#127	C₂³	1	2	yes	—
118	C₁₃×#127	C₂³	1	2	yes	—
119	C₁₃×#127	C₂³	1	2	yes	—
120	C₁₃×#127	C₂³	1	1	yes	characteristic
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#126	—	2	1	no	—
123	C₁₃×#125	C₂³	1	2	yes	—
124	C₁₃×#125	C₂³	1	1	yes	characteristic
125	C₁₃×#124	—	2	2	no	—
126	C₁₃×#124	—	2	2	no	—
127	C₁₃×#124	—	2	4	no	—
128	C₁₃×#124	—	2	1	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	1	no	—
134	C₁₃×#124	C₂³	1	4	yes	—
135	C₁₃×#124	C₂³	1	2	yes	—
136	C₁₃×#124	C₂³	1	4	yes	—
137	C₁₃×#124	C₂³	1	1	yes	characteristic
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	1	no	—
140	C₁₃×#123	—	2	4	no	—
141	C₁₃×#123	—	2	4	no	—
142	C₁₃×#123	—	2	4	no	—
143	C₁₃×#123	—	2	4	no	—
144	C₁₃×#123	—	2	2	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	1	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	C₂³	1	2	yes	—
158	C₁₃×#121	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₁₃	—	2	1	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	1	no	—
162	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	D₄	1	2	yes	—
164	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	4	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	2	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	4	yes	—
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	4	yes	—
189	C₄×D₄×C₁₃	C₂³	1	2	yes	—
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²×C₁₃	—	2	1	no	—
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₁₃×#107	C₂³	1	2	yes	—
205	C₁₃×#107	C₂³	1	4	yes	—
206	C₁₃×#106	C₂³	1	2	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	2	yes	—
213	C₁₃×#103	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#102	C₂³	1	2	yes	—
216	C₁₃×#102	C₂³	1	4	yes	—
217	C₁₃×#102	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
223	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₁₃×#97	C₂³	1	2	yes	—
225	C₁₃×#97	C₂³	1	4	yes	—
226	C₄×C₈×C₁₃	C₂³	1	4	yes	—
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#61898	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	2	no	—
230	C₁₃×#41	—	4	4	no	—
231	C₁₃×#41	—	8	4	no	—
232	C₁₃×#41	—	8	2	no	—
233	C₂×Q₈×C₁₃	—	2	1	no	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	4	2	no	—
237	C₂×Q₈×C₁₃	—	4	2	no	—
238	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
241	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	4	4	no	—
255	C₂×D₄×C₁₃	—	4	4	no	—
256	C₂×D₄×C₁₃	—	8	2	no	—
257	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	—	2	4	no	—
269	C₂²×C₄×C₁₃	—	8	4	no	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₁₃×Q₁₆	—	4	2	no	—
276	C₁₃×SD₁₆	—	4	2	no	—
277	C₁₃×SD₁₆	—	4	4	no	—
278	C₁₃×SD₁₆	—	4	4	no	—
279	C₁₃×D₈	—	4	4	no	—
280	C₁₃×D₈	—	4	4	no	—
281	C₁₃×D₈	—	4	4	no	—
282	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
283	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
284	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₂²⋊C₄	—	2	1	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	—	2	1	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	1	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	C₂×D₄	1	2	yes	—
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂×D₄	1	2	yes	—
333	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₁₃	C₂⁴	1	2	yes	—
335	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₄²×C₁₃	C₂⁴	1	2	yes	—
337	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
338	#3522	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#3403	C₂×C₁₃	1	4	yes	complemented
341	#3399	C₂×C₁₃	1	2	yes	complemented
342	#3396	C₂×C₁₃	1	2	yes	complemented
343	#3375	C₂×C₁₃	1	2	yes	complemented
344	#3370	C₂×C₁₃	1	4	yes	complemented
345	#3361	C₂×C₁₃	1	2	yes	complemented
346	#3217	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3213	C₂×C₁₃	1	2	yes	complemented
348	#3211	C₂×C₁₃	1	2	yes	complemented
349	#3205	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3114	C₂×C₁₃	1	2	yes	complemented
351	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3100	C₂×C₁₃	1	2	yes	complemented
354	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	2	1	no	—
357	C₂³×C₁₃	—	2	4	no	—
358	C₂³×C₁₃	—	4	4	no	—
359	C₂³×C₁₃	—	4	4	no	—
360	C₂³×C₁₃	—	4	4	no	—
361	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	2	no	—
365	Q₈×C₁₃	—	2	2	no	—
366	Q₈×C₁₃	—	2	2	no	—
367	Q₈×C₁₃	—	4	2	no	—
368	Q₈×C₁₃	—	4	2	no	—
369	Q₈×C₁₃	—	8	2	no	—
370	Q₈×C₁₃	—	8	1	no	—
371	D₄×C₁₃	—	2	4	no	—
372	D₄×C₁₃	—	2	2	no	—
373	D₄×C₁₃	—	2	4	no	—
374	D₄×C₁₃	—	2	4	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	4	4	no	—
377	D₄×C₁₃	—	4	4	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	4	4	no	—
380	D₄×C₁₃	—	4	4	no	—
381	D₄×C₁₃	—	4	2	no	—
382	D₄×C₁₃	—	8	2	no	—
383	D₄×C₁₃	—	8	2	no	—
384	D₄×C₁₃	—	8	2	no	—
385	D₄×C₁₃	—	8	1	no	—
386	C₂×C₄×C₁₃	—	2	4	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	4	2	no	—
397	C₂×C₄×C₁₃	—	4	4	no	—
398	C₂×C₄×C₁₃	—	4	2	no	—
399	C₂×C₄×C₁₃	—	4	2	no	—
400	C₂×C₄×C₁₃	—	4	2	no	—
401	C₂×C₄×C₁₃	—	8	4	no	—
402	C₂×C₄×C₁₃	—	8	4	no	—
403	C₂×C₄×C₁₃	—	8	2	no	—
404	C₂×C₄×C₁₃	—	8	2	no	—
405	C₂×C₄×C₁₃	—	8	2	no	—
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
416	C₈×C₁₃	—	2	2	no	—
417	C₈×C₁₃	—	2	2	no	—
418	C₈×C₁₃	—	2	4	no	—
419	#559	—	2	1	no	—
420	#559	—	2	1	no	—
421	#559	—	2	2	no	—
422	#559	C₂²×C₁₃	1	2	yes	—
423	#559	C₂²×C₁₃	1	4	yes	—
424	#559	C₂²×C₁₃	1	2	yes	—
425	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	#559	C₂²×C₁₃	1	2	yes	complemented
427	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	#554	C₂²×C₁₃	1	2	yes	complemented
430	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
431	#548	—	2	1	no	—
432	#547	—	2	1	no	—
433	#547	—	2	2	no	—
434	#542	—	2	2	no	—
435	#542	—	2	1	no	—
436	#532	C₂²×C₁₃	1	2	yes	—
437	#532	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
439	#529	C₂²×C₁₃	1	1	yes	characteristic
440	#529	C₂²×C₁₃	1	2	yes	—
441	C₂×#124	—	2	1	no	—
442	C₂×#124	C₂²×C₁₃	1	2	yes	—
443	C₂×#123	—	2	2	no	—
444	#520	—	2	1	no	—
445	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×C₄×D₄	—	2	1	no	—
448	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
449	#496	C₂²×C₁₃	1	2	yes	—
450	#496	C₂²×C₁₃	1	4	yes	complemented
451	#495	C₂²×C₁₃	1	4	yes	complemented
452	#493	C₂²×C₁₃	1	2	yes	—
453	#490	C₂²×C₁₃	1	2	yes	—
454	#489	C₂²×C₁₃	1	4	yes	complemented
455	#488	C₂²×C₁₃	1	4	yes	complemented
456	#486	C₂²×C₁₃	1	2	yes	—
457	#483	C₂²×C₁₃	1	1	yes	characteristic
458	#480	C₂²×C₁₃	1	1	yes	characteristic
459	#480	C₂²×C₁₃	1	2	yes	—
460	#479	C₂²×C₁₃	1	2	yes	complemented
461	#478	C₂²×C₁₃	1	4	yes	complemented
462	#477	C₂²×C₁₃	1	2	yes	complemented
463	#474	C₂²×C₁₃	1	4	yes	complemented
464	#464	C₂²×C₁₃	1	2	yes	complemented
465	#464	C₂²×C₁₃	1	4	yes	complemented
466	#463	C₂²×C₁₃	1	4	yes	complemented
467	#463	C₂²×C₁₃	1	4	yes	complemented
468	#463	C₂²×C₁₃	1	4	yes	complemented
469	#463	C₂²×C₁₃	1	4	yes	complemented
470	#460	C₂²×C₁₃	1	2	yes	—
471	#460	C₂²×C₁₃	1	2	yes	complemented
472	#459	C₂²×C₁₃	1	2	yes	—
473	#459	C₂²×C₁₃	1	4	yes	—
474	#459	C₂²×C₁₃	1	4	yes	complemented
475	#451	C₂²×C₁₃	1	1	yes	characteristic
476	#450	C₂²×C₁₃	1	2	yes	—
477	#448	C₂²×C₁₃	1	1	yes	characteristic
478	#448	C₂²×C₁₃	1	2	yes	—
479	#447	C₂²×C₁₃	1	2	yes	—
480	#447	C₂²×C₁₃	1	2	yes	—
481	#447	C₂²×C₁₃	1	2	yes	—
482	#446	C₂²×C₁₃	1	4	yes	complemented
483	#446	C₂²×C₁₃	1	2	yes	complemented
484	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
485	#442	C₂²×C₁₃	1	4	yes	complemented
486	#440	C₂²×C₁₃	1	4	yes	complemented
487	#440	C₂²×C₁₃	1	4	yes	complemented
488	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
489	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
490	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
491	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
492	#432	C₂²×C₁₃	1	1	yes	characteristic
493	#432	C₂²×C₁₃	1	2	yes	—
494	#431	C₂²×C₁₃	1	2	yes	—
495	#431	C₂²×C₁₃	1	1	yes	characteristic
496	C₂²×C₁₃	—	2	1	no	—
497	C₂²×C₁₃	—	2	1	no	—
498	C₂²×C₁₃	—	4	4	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	1	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	—	4	1	no	—
503	C₂²×C₁₃	—	4	4	no	—
504	C₂²×C₁₃	—	4	1	no	—
505	C₂²×C₁₃	—	4	2	no	—
506	C₂²×C₁₃	—	4	4	no	—
507	C₂²×C₁₃	—	8	8	no	—
508	C₂²×C₁₃	#576	1	2	yes	—
509	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
510	C₄×C₁₃	—	2	1	no	—
511	C₄×C₁₃	—	2	1	no	—
512	C₄×C₁₃	—	2	2	no	—
513	C₄×C₁₃	—	2	2	no	—
514	C₄×C₁₃	—	2	2	no	—
515	C₄×C₁₃	—	2	1	no	—
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	—	2	1	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	1	no	—
520	C₄×C₁₃	—	4	1	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₄×C₁₃	#575	1	2	yes	—
525	C₄×C₁₃	#585	1	2	yes	—
526	C₂×#41	—	2	1	no	—
527	C₂×#41	—	2	2	no	—
528	C₂×#41	—	2	1	no	—
529	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
530	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
534	C₂³×C₄	—	2	2	no	—
535	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
537	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
538	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
539	C₂×D₈	C₂³×C₁₃	1	4	yes	—
540	C₂×D₈	C₂³×C₁₃	1	4	yes	—
541	C₂×D₈	C₂³×C₁₃	1	4	yes	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	2	no	—
544	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
545	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
546	#127	—	2	1	no	—
547	#127	—	2	1	no	—
548	#127	C₂³×C₁₃	1	2	yes	—
549	#127	C₂³×C₁₃	1	2	yes	—
550	#127	C₂³×C₁₃	1	2	yes	—
551	#127	C₂³×C₁₃	1	1	yes	characteristic
552	#126	—	2	2	no	—
553	#126	—	2	1	no	—
554	#125	C₂³×C₁₃	1	2	yes	—
555	#125	C₂³×C₁₃	1	1	yes	characteristic
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	—	2	4	no	—
559	#124	—	2	1	no	—
560	#124	—	2	2	no	—
561	#124	—	2	2	no	—
562	#124	—	2	2	no	—
563	#124	—	2	2	no	—
564	#124	—	2	1	no	—
565	#124	C₂³×C₁₃	1	4	yes	—
566	#124	C₂³×C₁₃	1	4	yes	—
567	#124	C₂³×C₁₃	1	2	yes	—
568	#124	C₂³×C₁₃	1	1	yes	characteristic
569	#123	—	2	2	no	—
570	#123	—	2	1	no	—
571	#123	—	2	4	no	—
572	#123	—	2	4	no	—
573	#123	—	2	4	no	—
574	#123	—	2	4	no	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	—	2	1	no	—
587	#121	—	2	2	no	—
588	#121	C₂³×C₁₃	1	1	yes	characteristic
589	#121	C₂³×C₁₃	1	2	yes	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	—	2	1	no	—
592	C₄×Q₈	—	2	1	no	—
593	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
594	C₄×Q₈	D₄×C₁₃	1	2	yes	—
595	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
596	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
597	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
600	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	4	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	C₂³×C₁₃	1	4	yes	—
615	C₄×D₄	C₂³×C₁₃	1	4	yes	—
616	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₁₃	1	2	yes	—
618	C₄×D₄	C₂³×C₁₃	1	2	yes	—
619	C₄×D₄	C₂³×C₁₃	1	2	yes	—
620	C₄×D₄	C₂³×C₁₃	1	2	yes	—
621	#117	—	2	2	no	—
622	#117	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	2	no	—
626	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
627	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₂²⋊C₄	—	2	2	no	—
631	C₂×C₂²⋊C₄	—	2	2	no	—
632	C₂×C₄²	—	2	1	no	—
633	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
634	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
635	#107	C₂³×C₁₃	1	2	yes	—
636	#107	C₂³×C₁₃	1	4	yes	—
637	#106	C₂³×C₁₃	1	2	yes	—
638	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
639	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
640	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
641	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
642	#103	C₂³×C₁₃	1	2	yes	—
643	#103	C₂³×C₁₃	1	2	yes	—
644	#103	C₂³×C₁₃	1	2	yes	—
645	#103	C₂³×C₁₃	1	4	yes	—
646	#102	C₂³×C₁₃	1	2	yes	—
647	#102	C₂³×C₁₃	1	4	yes	—
648	#102	C₂³×C₁₃	1	4	yes	—
649	#102	C₂³×C₁₃	1	4	yes	—
650	#102	C₂³×C₁₃	1	4	yes	—
651	#102	C₂³×C₁₃	1	4	yes	—
652	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
653	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
654	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
655	#97	C₂³×C₁₃	1	2	yes	—
656	#97	C₂³×C₁₃	1	4	yes	—
657	C₄×C₈	C₂³×C₁₃	1	4	yes	—
658	C₄×C₈	C₂³×C₁₃	1	2	yes	—
659	C₂×C₁₃	—	2	2	no	—
660	C₂×C₁₃	—	8	2	no	—
661	C₂×C₁₃	—	8	1	no	—
662	C₂×C₁₃	—	8	4	no	—
663	C₂×C₁₃	#3487	1	1	yes	characteristic
664	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
665	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
666	C₂⁴	—	2	2	no	—
667	#41	—	4	4	no	—
668	#41	—	8	4	no	—
669	#41	—	8	2	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
676	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
677	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
678	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
679	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	4	4	no	—
692	C₂×D₄	—	4	4	no	—
693	C₂×D₄	—	8	2	no	—
694	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
695	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
696	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	8	4	no	—
707	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
709	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
712	Q₁₆	—	4	2	no	—
713	SD₁₆	—	4	2	no	—
714	SD₁₆	—	4	4	no	—
715	SD₁₆	—	4	4	no	—
716	D₈	—	4	4	no	—
717	D₈	—	4	4	no	—
718	D₈	—	4	4	no	—
719	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
720	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
721	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
738	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
739	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
743	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
744	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	1	no	—
767	C₄²	C₂×D₄×C₁₃	1	2	yes	—
768	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₁₃	1	2	yes	—
770	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
771	C₄²	C₂⁴×C₁₃	1	2	yes	—
772	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
773	C₄²	C₂⁴×C₁₃	1	2	yes	—
774	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
775	C₁₃	#61898	1	1	yes	characteristic, direct product factor, Sylow
776	C₂³	—	2	2	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	4	4	no	—
781	C₂³	—	4	4	no	—
782	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
783	Q₈	—	2	2	no	—
784	Q₈	—	2	2	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	4	2	no	—
789	Q₈	—	4	2	no	—
790	Q₈	—	8	2	no	—
791	Q₈	—	8	1	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	4	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	2	no	—
803	D₄	—	8	2	no	—
804	D₄	—	8	2	no	—
805	D₄	—	8	2	no	—
806	D₄	—	8	1	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
832	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
836	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
837	C₈	—	2	2	no	—
838	C₈	—	2	2	no	—
839	C₈	—	2	4	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	4	no	—
848	C₂²	—	4	4	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	8	8	no	—
852	C₂²	C₁₃×#576	1	2	yes	—
853	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
854	C₄	—	2	1	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	2	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	1	no	—
868	C₄	C₁₃×#575	1	2	yes	—
869	C₄	C₁₃×#585	1	2	yes	—
870	C₂	—	2	2	no	—
871	C₂	—	8	4	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	1	no	—
874	C₂	C₁₃×#3487	1	1	yes	characteristic
875	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
876	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	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×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3522	C₂	semidirect
2. C₂×C₁₃×#559	C₂	semidirect
3. C₁₃×#3403	C₂	semidirect
4. C₁₃×#3399	C₂	semidirect
5. C₁₃×#3396	C₂	semidirect
6. C₁₃×#3375	C₂	semidirect
7. C₁₃×#3370	C₂	semidirect
8. C₁₃×#3361	C₂	semidirect
9. C₁₃×#3217	C₂	semidirect
10. C₁₃×#3213	C₂	semidirect
11. C₁₃×#3211	C₂	semidirect
12. C₁₃×#3205	C₂	semidirect
13. C₁₃×#3114	C₂	semidirect
14. C₁₃×#3112	C₂	semidirect
15. C₁₃×#3108	C₂	semidirect
16. C₁₃×#3100	C₂	semidirect
17. C₁₃×#2984	C₂	semidirect
24. C₁₃×#559	C₂²	semidirect
25. C₁₃×#559	C₂²	semidirect
26. Q₈²×C₁₃	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
28. C₁₃×#554	C₂²	semidirect
29. C₁₃×#550	C₂²	semidirect
49. C₁₃×#496	C₂²	semidirect
50. C₁₃×#495	C₂²	semidirect
53. C₁₃×#489	C₂²	semidirect
54. C₁₃×#488	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
60. C₁₃×#478	C₂²	semidirect
61. C₁₃×#477	C₂²	semidirect
62. C₁₃×#474	C₂²	semidirect
63. C₁₃×#464	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
65. C₁₃×#463	C₂²	semidirect
66. C₁₃×#463	C₂²	semidirect
67. C₁₃×#463	C₂²	semidirect
68. C₁₃×#463	C₂²	semidirect
70. C₁₃×#460	C₂²	semidirect
73. C₁₃×#459	C₂²	semidirect
81. C₁₃×#446	C₂²	semidirect
82. C₁₃×#446	C₂²	semidirect
83. C₈×Q₈×C₁₃	C₂²	semidirect
84. C₁₃×#442	C₂²	semidirect
85. C₁₃×#440	C₂²	semidirect
86. C₁₃×#440	C₂²	semidirect
87. C₄×C₁₃×Q₁₆	C₂²	semidirect
88. C₄×C₁₃×SD₁₆	C₂²	semidirect
89. C₄×C₁₃×D₈	C₂²	semidirect
90. C₄×C₁₃×D₈	C₂²	semidirect
228. #61898	C₁₃	direct (N × H)
338. #3522	C₂×C₁₃	semidirect
339. C₂×#559	C₂×C₁₃	semidirect
340. #3403	C₂×C₁₃	semidirect
341. #3399	C₂×C₁₃	semidirect
342. #3396	C₂×C₁₃	semidirect
343. #3375	C₂×C₁₃	semidirect
344. #3370	C₂×C₁₃	semidirect
345. #3361	C₂×C₁₃	semidirect
346. #3217	C₂×C₁₃	semidirect
347. #3213	C₂×C₁₃	semidirect
348. #3211	C₂×C₁₃	semidirect
349. #3205	C₂×C₁₃	semidirect
350. #3114	C₂×C₁₃	semidirect
351. #3112	C₂×C₁₃	semidirect
352. #3108	C₂×C₁₃	semidirect
353. #3100	C₂×C₁₃	semidirect
354. #2984	C₂×C₁₃	semidirect
425. #559	C₂²×C₁₃	semidirect
426. #559	C₂²×C₁₃	semidirect
427. Q₈²	C₂²×C₁₃	semidirect
428. #554	C₂²×C₁₃	semidirect
429. #554	C₂²×C₁₃	semidirect
430. #550	C₂²×C₁₃	semidirect
450. #496	C₂²×C₁₃	semidirect
451. #495	C₂²×C₁₃	semidirect
454. #489	C₂²×C₁₃	semidirect
455. #488	C₂²×C₁₃	semidirect
460. #479	C₂²×C₁₃	semidirect
461. #478	C₂²×C₁₃	semidirect
462. #477	C₂²×C₁₃	semidirect
463. #474	C₂²×C₁₃	semidirect
464. #464	C₂²×C₁₃	semidirect
465. #464	C₂²×C₁₃	semidirect
466. #463	C₂²×C₁₃	semidirect
467. #463	C₂²×C₁₃	semidirect
468. #463	C₂²×C₁₃	semidirect
469. #463	C₂²×C₁₃	semidirect
471. #460	C₂²×C₁₃	semidirect
474. #459	C₂²×C₁₃	semidirect
482. #446	C₂²×C₁₃	semidirect
483. #446	C₂²×C₁₃	semidirect
484. C₈×Q₈	C₂²×C₁₃	semidirect
485. #442	C₂²×C₁₃	semidirect
486. #440	C₂²×C₁₃	semidirect
487. #440	C₂²×C₁₃	semidirect
488. C₄×Q₁₆	C₂²×C₁₃	semidirect
489. C₄×SD₁₆	C₂²×C₁₃	semidirect
490. C₄×D₈	C₂²×C₁₃	semidirect
491. C₄×D₈	C₂²×C₁₃	semidirect
775. C₁₃	#61898	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×#3522	2
C₂×C₁₃×#559	2
C₁₃×#3403	2
C₁₃×#3399	2
C₁₃×#3396	2
C₁₃×#3375	2
C₁₃×#3370	2
C₁₃×#3361	2
C₁₃×#3217	2
C₁₃×#3213	2
C₁₃×#3211	2
C₁₃×#3205	2
C₁₃×#3114	2
C₁₃×#3112	2
C₁₃×#3108	2
C₁₃×#3100	2
C₁₃×#2984	2
#61898	13

Subgroups — C13×#61898 #15748237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61898 #15748237