Subgroups — C₂×C₁₃×#3564 #15749073

Order 3328.

6598 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3564	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#563	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#556	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#554	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#551	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#551	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#542	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#541	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#541	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#539	C₂	1	2	yes	maximal, complemented
17	C₂×C₁₃×#538	C₂	1	1	yes	maximal, characteristic
18	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₁₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#563	C₂²	1	32	yes	complemented
22	C₁₃×#563	C₂²	1	32	yes	complemented
23	C₁₃×#556	C₂²	1	32	yes	complemented
24	C₁₃×#554	C₂²	1	32	yes	complemented
25	C₁₃×#552	C₂²	1	32	yes	complemented
26	C₁₃×#552	C₂²	1	32	yes	complemented
27	C₁₃×#551	C₂²	1	32	yes	complemented
28	C₁₃×#551	C₂²	1	32	yes	complemented
29	C₁₃×#544	C₂²	1	16	yes	complemented
30	C₁₃×#543	C₂²	1	16	yes	complemented
31	C₁₃×#542	C₂²	1	32	yes	complemented
32	C₁₃×#541	C₂²	1	32	yes	complemented
33	C₁₃×#541	C₂²	1	32	yes	complemented
34	C₁₃×#539	C₂²	1	16	yes	complemented
35	C₁₃×#539	C₂²	1	32	yes	complemented
36	C₁₃×#538	C₂²	1	16	yes	—
37	C₁₃×#533	C₂²	1	16	yes	complemented
38	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
43	C₁₃×#529	C₂²	1	16	yes	complemented
44	C₂×C₁₃×#126	C₂²	1	2	yes	—
45	C₂×C₁₃×#126	C₂²	1	2	yes	—
46	C₂×C₁₃×#126	C₂²	1	2	yes	—
47	C₂×C₁₃×#126	C₂²	1	2	yes	—
48	C₂×C₁₃×#126	C₂²	1	2	yes	—
49	C₂×C₁₃×#126	C₂²	1	2	yes	—
50	C₂×C₁₃×#126	C₂²	1	2	yes	—
51	C₂×C₁₃×#126	C₂²	1	2	yes	—
52	C₂×C₁₃×#126	C₂²	1	2	yes	—
53	C₂×C₁₃×#126	C₂²	1	16	yes	complemented
54	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
55	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
56	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
57	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
58	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
59	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
60	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
61	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
62	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
64	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
65	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
66	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
67	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
68	C₂×C₁₃×#124	C₂²	1	2	yes	—
69	C₂×C₁₃×#124	C₂²	1	2	yes	—
70	C₂×C₁₃×#124	C₂²	1	2	yes	—
71	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₁₃×#123	C₂²	1	2	yes	—
73	C₂×C₁₃×#123	C₂²	1	2	yes	—
74	C₂×C₁₃×#123	C₂²	1	2	yes	—
75	C₂×C₁₃×#123	C₂²	1	2	yes	—
76	C₂×C₁₃×#123	C₂²	1	2	yes	—
77	C₂×C₁₃×#123	C₂²	1	2	yes	—
78	C₂×C₁₃×#123	C₂²	1	2	yes	—
79	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
80	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
81	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
82	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
83	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
84	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
87	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
88	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
89	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
90	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
91	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
92	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
93	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
94	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
95	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
96	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
97	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
98	C₂×C₁₃×#121	C₂²	1	2	yes	—
99	C₂×C₁₃×#120	C₂²	1	2	yes	—
100	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
102	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
105	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
107	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
108	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
109	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
110	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
111	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₁₃×#117	C₂²	1	2	yes	—
113	C₂×C₁₃×#117	C₂²	1	2	yes	—
114	C₂×C₁₃×#117	C₂²	1	2	yes	—
115	C₂×C₁₃×#117	C₂²	1	2	yes	—
116	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
117	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
118	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
121	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
122	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
123	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
124	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
126	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
127	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
130	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
132	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
133	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
135	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
145	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
149	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
150	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
151	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
152	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
153	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
154	C₁₃×#126	C₂³	1	16	yes	—
155	C₁₃×#126	C₂³	1	16	yes	—
156	C₁₃×#126	C₂³	1	16	yes	—
157	C₁₃×#126	C₂³	1	16	yes	—
158	C₁₃×#126	C₂³	1	16	yes	—
159	C₁₃×#126	C₂³	1	16	yes	—
160	C₁₃×#126	C₂³	1	16	yes	—
161	C₁₃×#126	C₂³	1	16	yes	—
162	C₁₃×#126	C₂³	1	16	yes	—
163	C₁₃×#126	C₂³	1	16	yes	complemented
164	C₁₃×#126	C₂³	1	16	yes	complemented
165	C₁₃×#126	C₂³	1	16	yes	complemented
166	C₁₃×#126	C₂³	1	16	yes	complemented
167	C₁₃×#125	C₂³	1	8	yes	complemented
168	C₁₃×#125	C₂³	1	16	yes	complemented
169	C₁₃×#125	C₂³	1	16	yes	complemented
170	C₁₃×#125	C₂³	1	16	yes	complemented
171	C₁₃×#125	C₂³	1	16	yes	complemented
172	C₁₃×#125	C₂³	1	16	yes	complemented
173	C₁₃×#125	C₂³	1	16	yes	complemented
174	C₁₃×#125	C₂³	1	16	yes	complemented
175	C₁₃×#125	C₂³	1	16	yes	complemented
176	C₁₃×#125	C₂³	1	16	yes	complemented
177	C₁₃×#124	C₂³	1	16	yes	—
178	C₁₃×#124	C₂³	1	16	yes	—
179	C₁₃×#124	C₂³	1	16	yes	—
180	C₁₃×#124	C₂³	1	8	yes	complemented
181	C₁₃×#123	C₂³	1	16	yes	—
182	C₁₃×#123	C₂³	1	16	yes	—
183	C₁₃×#123	C₂³	1	16	yes	—
184	C₁₃×#123	C₂³	1	16	yes	—
185	C₁₃×#123	C₂³	1	16	yes	—
186	C₁₃×#123	C₂³	1	16	yes	—
187	C₁₃×#123	C₂³	1	16	yes	—
188	C₁₃×#123	C₂³	1	16	yes	complemented
189	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
190	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
191	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
200	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
201	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
202	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
203	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
204	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
205	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
206	C₁₃×#121	C₂³	1	8	yes	—
207	C₁₃×#121	C₂³	1	16	yes	—
208	C₁₃×#120	C₂³	1	16	yes	—
209	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
210	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
211	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
212	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
213	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
214	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
215	C₄×D₄×C₁₃	C₂³	1	16	yes	—
216	C₄×D₄×C₁₃	C₂³	1	16	yes	—
217	C₄×D₄×C₁₃	C₂³	1	16	yes	—
218	C₄×D₄×C₁₃	C₂³	1	16	yes	—
219	C₄×D₄×C₁₃	C₂³	1	16	yes	—
220	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
221	C₁₃×#117	C₂³	1	16	yes	—
222	C₁₃×#117	C₂³	1	16	yes	—
223	C₁₃×#117	C₂³	1	16	yes	—
224	C₁₃×#117	C₂³	1	16	yes	—
225	C₁₃×#117	C₂³	1	16	yes	complemented
226	C₁₃×#117	C₂³	1	16	yes	complemented
227	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
228	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
229	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
230	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
231	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
232	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
233	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
234	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
235	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
236	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
238	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
239	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
240	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
241	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
242	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
243	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
244	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
245	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
246	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
248	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
249	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
250	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
251	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
252	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
253	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
255	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
264	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
265	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
266	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
267	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
268	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
269	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
270	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
271	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
272	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
273	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
274	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
275	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
276	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
277	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
278	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
279	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
280	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
281	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
282	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
283	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
284	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
285	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
286	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
287	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
288	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
289	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
294	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
295	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
296	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
297	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
298	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
299	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
300	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
301	C₂×#3564	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂⁴×C₁₃	—	2	4	no	—
303	C₂⁴×C₁₃	—	4	2	no	—
304	C₂⁴×C₁₃	—	4	2	no	—
305	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
306	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
307	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
309	C₂×Q₈×C₁₃	—	4	2	no	—
310	C₂×Q₈×C₁₃	—	4	4	no	—
311	C₂×Q₈×C₁₃	—	4	4	no	—
312	C₂×Q₈×C₁₃	—	4	2	no	—
313	C₂×Q₈×C₁₃	—	4	4	no	—
314	C₂×Q₈×C₁₃	—	4	2	no	—
315	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
316	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
317	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
318	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
319	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
320	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
321	C₂×D₄×C₁₃	—	2	8	no	—
322	C₂×D₄×C₁₃	—	4	4	no	—
323	C₂×D₄×C₁₃	—	4	2	no	—
324	C₂×D₄×C₁₃	—	4	4	no	—
325	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
326	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
327	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
328	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
329	C₂²×C₄×C₁₃	—	2	4	no	—
330	C₂²×C₄×C₁₃	—	2	4	no	—
331	C₂²×C₄×C₁₃	—	4	4	no	—
332	C₂²×C₄×C₁₃	—	4	2	no	—
333	C₂²×C₄×C₁₃	—	4	2	no	—
334	C₂²×C₄×C₁₃	—	4	2	no	—
335	C₂²×C₄×C₁₃	—	4	4	no	—
336	C₂²×C₄×C₁₃	—	4	4	no	—
337	C₂²×C₄×C₁₃	—	4	4	no	—
338	C₂²×C₄×C₁₃	—	4	4	no	—
339	C₂²×C₄×C₁₃	—	4	2	no	—
340	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
341	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
361	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
362	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
363	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
364	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
365	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
366	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
369	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
370	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
371	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
372	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
373	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
374	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
375	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
376	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
377	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
378	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
379	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
380	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
381	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
382	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
383	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
384	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
385	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
386	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
387	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
388	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
389	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
390	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
391	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
392	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
393	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
394	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
395	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
396	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
397	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
398	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
399	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
400	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
401	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
402	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
403	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
404	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
405	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
406	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
407	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
408	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
409	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
410	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
411	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
412	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
413	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
414	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
415	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
416	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
417	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
418	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
419	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
420	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
421	C₄²×C₁₃	C₂⁴	1	4	yes	—
422	C₄²×C₁₃	C₂⁴	1	4	yes	—
423	C₄²×C₁₃	C₂⁴	1	4	yes	—
424	C₄²×C₁₃	C₂⁴	1	4	yes	—
425	C₄²×C₁₃	C₂⁴	1	8	yes	—
426	C₄²×C₁₃	C₂⁴	1	8	yes	—
427	C₄²×C₁₃	C₂⁴	1	8	yes	—
428	C₄²×C₁₃	C₂⁴	1	8	yes	—
429	C₄²×C₁₃	C₂⁴	1	8	yes	—
430	C₄²×C₁₃	C₂⁴	1	8	yes	—
431	C₄²×C₁₃	C₂⁴	1	8	yes	—
432	#3564	C₂×C₁₃	1	32	yes	direct product factor
433	C₂×#563	C₂×C₁₃	1	2	yes	complemented
434	C₂×#563	C₂×C₁₃	1	2	yes	complemented
435	C₂×#556	C₂×C₁₃	1	2	yes	complemented
436	C₂×#554	C₂×C₁₃	1	2	yes	complemented
437	C₂×#552	C₂×C₁₃	1	2	yes	complemented
438	C₂×#552	C₂×C₁₃	1	2	yes	complemented
439	C₂×#551	C₂×C₁₃	1	2	yes	complemented
440	C₂×#551	C₂×C₁₃	1	2	yes	complemented
441	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
442	C₂×#543	C₂×C₁₃	1	1	yes	characteristic, complemented
443	C₂×#542	C₂×C₁₃	1	2	yes	complemented
444	C₂×#541	C₂×C₁₃	1	2	yes	complemented
445	C₂×#541	C₂×C₁₃	1	2	yes	complemented
446	C₂×#539	C₂×C₁₃	1	1	yes	characteristic, complemented
447	C₂×#539	C₂×C₁₃	1	2	yes	complemented
448	C₂×#538	C₂×C₁₃	1	1	yes	characteristic
449	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
450	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
451	C₂²×#126	C₂×C₁₃	1	1	yes	characteristic, complemented
452	C₂³×C₁₃	—	2	2	no	—
453	C₂³×C₁₃	—	2	2	no	—
454	C₂³×C₁₃	—	2	4	no	—
455	C₂³×C₁₃	—	2	4	no	—
456	C₂³×C₁₃	—	2	4	no	—
457	C₂³×C₁₃	—	2	4	no	—
458	C₂³×C₁₃	—	2	4	no	—
459	C₂³×C₁₃	—	2	4	no	—
460	C₂³×C₁₃	—	2	8	no	—
461	C₂³×C₁₃	—	4	4	no	—
462	C₂³×C₁₃	—	4	4	no	—
463	C₂³×C₁₃	—	8	8	no	—
464	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
465	C₂³×C₁₃	C₂⁵	1	4	yes	—
466	C₂³×C₁₃	C₂⁵	1	4	yes	—
467	C₂³×C₁₃	C₂⁵	1	2	yes	—
468	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
469	Q₈×C₁₃	—	4	4	no	—
470	Q₈×C₁₃	—	4	8	no	—
471	Q₈×C₁₃	—	4	8	no	—
472	Q₈×C₁₃	—	4	4	no	—
473	Q₈×C₁₃	—	4	8	no	—
474	Q₈×C₁₃	—	4	4	no	—
475	D₄×C₁₃	—	2	16	no	—
476	D₄×C₁₃	—	4	8	no	—
477	D₄×C₁₃	—	4	4	no	—
478	D₄×C₁₃	—	4	8	no	—
479	C₂×C₄×C₁₃	—	2	8	no	—
480	C₂×C₄×C₁₃	—	2	8	no	—
481	C₂×C₄×C₁₃	—	2	2	no	—
482	C₂×C₄×C₁₃	—	2	2	no	—
483	C₂×C₄×C₁₃	—	2	4	no	—
484	C₂×C₄×C₁₃	—	2	4	no	—
485	C₂×C₄×C₁₃	—	2	2	no	—
486	C₂×C₄×C₁₃	—	2	4	no	—
487	C₂×C₄×C₁₃	—	2	4	no	—
488	C₂×C₄×C₁₃	—	2	4	no	—
489	C₂×C₄×C₁₃	—	2	4	no	—
490	C₂×C₄×C₁₃	—	2	4	no	—
491	C₂×C₄×C₁₃	—	2	2	no	—
492	C₂×C₄×C₁₃	—	2	2	no	—
493	C₂×C₄×C₁₃	—	2	4	no	—
494	C₂×C₄×C₁₃	—	2	4	no	—
495	C₂×C₄×C₁₃	—	2	2	no	—
496	C₂×C₄×C₁₃	—	2	4	no	—
497	C₂×C₄×C₁₃	—	4	8	no	—
498	C₂×C₄×C₁₃	—	4	4	no	—
499	C₂×C₄×C₁₃	—	4	4	no	—
500	C₂×C₄×C₁₃	—	4	4	no	—
501	C₂×C₄×C₁₃	—	4	8	no	—
502	C₂×C₄×C₁₃	—	4	8	no	—
503	C₂×C₄×C₁₃	—	4	8	no	—
504	C₂×C₄×C₁₃	—	4	8	no	—
505	C₂×C₄×C₁₃	—	4	4	no	—
506	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
507	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
508	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
509	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
510	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
511	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
512	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
513	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
514	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
515	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
516	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
517	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
518	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
519	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
520	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
521	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
522	#563	C₂²×C₁₃	1	32	yes	complemented
523	#563	C₂²×C₁₃	1	32	yes	complemented
524	#556	C₂²×C₁₃	1	32	yes	complemented
525	#554	C₂²×C₁₃	1	32	yes	complemented
526	#552	C₂²×C₁₃	1	32	yes	complemented
527	#552	C₂²×C₁₃	1	32	yes	complemented
528	#551	C₂²×C₁₃	1	32	yes	complemented
529	#551	C₂²×C₁₃	1	32	yes	complemented
530	#544	C₂²×C₁₃	1	16	yes	complemented
531	#543	C₂²×C₁₃	1	16	yes	complemented
532	#542	C₂²×C₁₃	1	32	yes	complemented
533	#541	C₂²×C₁₃	1	32	yes	complemented
534	#541	C₂²×C₁₃	1	32	yes	complemented
535	#539	C₂²×C₁₃	1	16	yes	complemented
536	#539	C₂²×C₁₃	1	32	yes	complemented
537	#538	C₂²×C₁₃	1	16	yes	—
538	#533	C₂²×C₁₃	1	16	yes	complemented
539	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
540	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
541	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
542	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
543	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
544	#529	C₂²×C₁₃	1	16	yes	complemented
545	C₂×#126	C₂²×C₁₃	1	2	yes	—
546	C₂×#126	C₂²×C₁₃	1	2	yes	—
547	C₂×#126	C₂²×C₁₃	1	2	yes	—
548	C₂×#126	C₂²×C₁₃	1	2	yes	—
549	C₂×#126	C₂²×C₁₃	1	2	yes	—
550	C₂×#126	C₂²×C₁₃	1	2	yes	—
551	C₂×#126	C₂²×C₁₃	1	2	yes	—
552	C₂×#126	C₂²×C₁₃	1	2	yes	—
553	C₂×#126	C₂²×C₁₃	1	2	yes	—
554	C₂×#126	C₂²×C₁₃	1	16	yes	complemented
555	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
556	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
557	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
558	C₂×#126	C₂²×C₁₃	1	2	yes	complemented
559	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
560	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
561	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
562	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
563	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
564	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
565	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
566	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
567	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
568	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
569	C₂×#124	C₂²×C₁₃	1	2	yes	—
570	C₂×#124	C₂²×C₁₃	1	2	yes	—
571	C₂×#124	C₂²×C₁₃	1	2	yes	—
572	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
573	C₂×#123	C₂²×C₁₃	1	2	yes	—
574	C₂×#123	C₂²×C₁₃	1	2	yes	—
575	C₂×#123	C₂²×C₁₃	1	2	yes	—
576	C₂×#123	C₂²×C₁₃	1	2	yes	—
577	C₂×#123	C₂²×C₁₃	1	2	yes	—
578	C₂×#123	C₂²×C₁₃	1	2	yes	—
579	C₂×#123	C₂²×C₁₃	1	2	yes	—
580	C₂×#123	C₂²×C₁₃	1	2	yes	complemented
581	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
582	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
583	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
584	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
585	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
586	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
587	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
588	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
589	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
590	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
591	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
592	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
593	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
594	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
595	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
596	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
597	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
598	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
599	C₂×#121	C₂²×C₁₃	1	2	yes	—
600	C₂×#120	C₂²×C₁₃	1	2	yes	—
601	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
602	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
603	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
604	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
606	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
607	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
608	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
609	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
610	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
611	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
612	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	C₂×#117	C₂²×C₁₃	1	2	yes	—
614	C₂×#117	C₂²×C₁₃	1	2	yes	—
615	C₂×#117	C₂²×C₁₃	1	2	yes	—
616	C₂×#117	C₂²×C₁₃	1	2	yes	—
617	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
618	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
619	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
620	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
621	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
622	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
623	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
624	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
625	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
626	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
627	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
628	C₂²×C₁₃	—	2	2	no	—
629	C₂²×C₁₃	—	2	2	no	—
630	C₂²×C₁₃	—	2	8	no	—
631	C₂²×C₁₃	—	2	4	no	—
632	C₂²×C₁₃	—	2	4	no	—
633	C₂²×C₁₃	—	2	4	no	—
634	C₂²×C₁₃	—	2	4	no	—
635	C₂²×C₁₃	—	2	4	no	—
636	C₂²×C₁₃	—	2	4	no	—
637	C₂²×C₁₃	—	4	8	no	—
638	C₂²×C₁₃	—	4	8	no	—
639	C₂²×C₁₃	—	8	8	no	—
640	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
641	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
642	C₂²×C₁₃	#585	1	2	yes	—
643	C₂²×C₁₃	#585	1	2	yes	—
644	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
645	C₄×C₁₃	—	2	2	no	—
646	C₄×C₁₃	—	2	2	no	—
647	C₄×C₁₃	—	2	4	no	—
648	C₄×C₁₃	—	2	4	no	—
649	C₄×C₁₃	—	2	2	no	—
650	C₄×C₁₃	—	2	4	no	—
651	C₄×C₁₃	—	2	4	no	—
652	C₄×C₁₃	—	2	4	no	—
653	C₄×C₁₃	—	2	4	no	—
654	C₄×C₁₃	—	2	4	no	—
655	C₄×C₁₃	—	2	2	no	—
656	C₄×C₁₃	—	2	2	no	—
657	C₄×C₁₃	—	2	4	no	—
658	C₄×C₁₃	—	2	4	no	—
659	C₄×C₁₃	—	2	2	no	—
660	C₄×C₁₃	—	2	4	no	—
661	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
662	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
663	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
664	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
665	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
666	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
667	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
668	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
669	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
670	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
671	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
672	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
673	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
674	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
675	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
676	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
677	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
678	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
679	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
680	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
681	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
682	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
683	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
684	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
685	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
686	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
687	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
688	#126	C₂³×C₁₃	1	16	yes	—
689	#126	C₂³×C₁₃	1	16	yes	—
690	#126	C₂³×C₁₃	1	16	yes	—
691	#126	C₂³×C₁₃	1	16	yes	—
692	#126	C₂³×C₁₃	1	16	yes	—
693	#126	C₂³×C₁₃	1	16	yes	—
694	#126	C₂³×C₁₃	1	16	yes	—
695	#126	C₂³×C₁₃	1	16	yes	—
696	#126	C₂³×C₁₃	1	16	yes	—
697	#126	C₂³×C₁₃	1	16	yes	complemented
698	#126	C₂³×C₁₃	1	16	yes	complemented
699	#126	C₂³×C₁₃	1	16	yes	complemented
700	#126	C₂³×C₁₃	1	16	yes	complemented
701	#125	C₂³×C₁₃	1	8	yes	complemented
702	#125	C₂³×C₁₃	1	16	yes	complemented
703	#125	C₂³×C₁₃	1	16	yes	complemented
704	#125	C₂³×C₁₃	1	16	yes	complemented
705	#125	C₂³×C₁₃	1	16	yes	complemented
706	#125	C₂³×C₁₃	1	16	yes	complemented
707	#125	C₂³×C₁₃	1	16	yes	complemented
708	#125	C₂³×C₁₃	1	16	yes	complemented
709	#125	C₂³×C₁₃	1	16	yes	complemented
710	#125	C₂³×C₁₃	1	16	yes	complemented
711	#124	C₂³×C₁₃	1	16	yes	—
712	#124	C₂³×C₁₃	1	16	yes	—
713	#124	C₂³×C₁₃	1	16	yes	—
714	#124	C₂³×C₁₃	1	8	yes	complemented
715	#123	C₂³×C₁₃	1	16	yes	—
716	#123	C₂³×C₁₃	1	16	yes	—
717	#123	C₂³×C₁₃	1	16	yes	—
718	#123	C₂³×C₁₃	1	16	yes	—
719	#123	C₂³×C₁₃	1	16	yes	—
720	#123	C₂³×C₁₃	1	16	yes	—
721	#123	C₂³×C₁₃	1	16	yes	—
722	#123	C₂³×C₁₃	1	16	yes	complemented
723	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
724	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
725	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
726	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
727	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
728	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
729	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
730	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
731	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
732	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
733	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
734	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
735	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
736	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
737	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
738	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
739	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
740	#121	C₂³×C₁₃	1	8	yes	—
741	#121	C₂³×C₁₃	1	16	yes	—
742	#120	C₂³×C₁₃	1	16	yes	—
743	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
744	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
745	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
746	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
747	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
748	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
749	C₄×D₄	C₂³×C₁₃	1	16	yes	—
750	C₄×D₄	C₂³×C₁₃	1	16	yes	—
751	C₄×D₄	C₂³×C₁₃	1	16	yes	—
752	C₄×D₄	C₂³×C₁₃	1	16	yes	—
753	C₄×D₄	C₂³×C₁₃	1	16	yes	—
754	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
755	#117	C₂³×C₁₃	1	16	yes	—
756	#117	C₂³×C₁₃	1	16	yes	—
757	#117	C₂³×C₁₃	1	16	yes	—
758	#117	C₂³×C₁₃	1	16	yes	—
759	#117	C₂³×C₁₃	1	16	yes	complemented
760	#117	C₂³×C₁₃	1	16	yes	complemented
761	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
762	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
763	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
764	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
765	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
766	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
767	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
768	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
769	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
770	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
771	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
772	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
773	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
774	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
775	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
776	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
777	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
778	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
779	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
780	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
781	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
782	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
783	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
784	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
785	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
786	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
787	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
788	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
789	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
791	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
792	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
793	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
794	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
796	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
797	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
798	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
816	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
818	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
823	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
824	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
825	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
826	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
827	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
828	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
829	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
830	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
831	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
832	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
833	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
834	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
835	C₂×C₁₃	—	2	4	no	—
836	C₂×C₁₃	—	4	4	no	—
837	C₂×C₁₃	—	4	4	no	—
838	C₂×C₁₃	#3564	1	4	yes	direct product factor
839	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
840	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
841	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
842	C₂⁴	—	2	4	no	—
843	C₂⁴	—	4	2	no	—
844	C₂⁴	—	4	2	no	—
845	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
846	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
847	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
848	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
849	C₂×Q₈	—	4	2	no	—
850	C₂×Q₈	—	4	4	no	—
851	C₂×Q₈	—	4	4	no	—
852	C₂×Q₈	—	4	2	no	—
853	C₂×Q₈	—	4	4	no	—
854	C₂×Q₈	—	4	2	no	—
855	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
856	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
857	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
858	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
859	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
860	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
861	C₂×D₄	—	2	8	no	—
862	C₂×D₄	—	4	4	no	—
863	C₂×D₄	—	4	2	no	—
864	C₂×D₄	—	4	4	no	—
865	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
866	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
867	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
868	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
869	C₂²×C₄	—	2	4	no	—
870	C₂²×C₄	—	2	4	no	—
871	C₂²×C₄	—	4	4	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	4	no	—
876	C₂²×C₄	—	4	4	no	—
877	C₂²×C₄	—	4	4	no	—
878	C₂²×C₄	—	4	4	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
883	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
885	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
887	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
891	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
893	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
894	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
897	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
898	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
899	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
900	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
901	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
902	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
903	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
904	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
905	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
906	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
907	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
908	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
909	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
910	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
911	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
912	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
913	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
914	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
915	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
916	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
917	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
918	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
919	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
920	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
921	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
922	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
923	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
924	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
925	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
926	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
927	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
928	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
929	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
930	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
931	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
932	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
933	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
934	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
935	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
936	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
937	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
938	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
939	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
940	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
941	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
942	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
943	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
944	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
945	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
946	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
947	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
948	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
949	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
950	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
951	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
952	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
953	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
954	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
955	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
956	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
957	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
958	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
959	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
960	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
961	C₄²	C₂⁴×C₁₃	1	4	yes	—
962	C₄²	C₂⁴×C₁₃	1	4	yes	—
963	C₄²	C₂⁴×C₁₃	1	4	yes	—
964	C₄²	C₂⁴×C₁₃	1	4	yes	—
965	C₄²	C₂⁴×C₁₃	1	8	yes	—
966	C₄²	C₂⁴×C₁₃	1	8	yes	—
967	C₄²	C₂⁴×C₁₃	1	8	yes	—
968	C₄²	C₂⁴×C₁₃	1	8	yes	—
969	C₄²	C₂⁴×C₁₃	1	8	yes	—
970	C₄²	C₂⁴×C₁₃	1	8	yes	—
971	C₄²	C₂⁴×C₁₃	1	8	yes	—
972	C₁₃	C₂×#3564	1	1	yes	characteristic, direct product factor, Sylow
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	4	no	—
976	C₂³	—	2	4	no	—
977	C₂³	—	2	4	no	—
978	C₂³	—	2	4	no	—
979	C₂³	—	2	4	no	—
980	C₂³	—	2	4	no	—
981	C₂³	—	2	8	no	—
982	C₂³	—	4	4	no	—
983	C₂³	—	4	4	no	—
984	C₂³	—	8	8	no	—
985	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
986	C₂³	C₂⁵×C₁₃	1	4	yes	—
987	C₂³	C₂⁵×C₁₃	1	4	yes	—
988	C₂³	C₂⁵×C₁₃	1	2	yes	—
989	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
990	Q₈	—	4	4	no	—
991	Q₈	—	4	8	no	—
992	Q₈	—	4	8	no	—
993	Q₈	—	4	4	no	—
994	Q₈	—	4	8	no	—
995	Q₈	—	4	4	no	—
996	D₄	—	2	16	no	—
997	D₄	—	4	8	no	—
998	D₄	—	4	4	no	—
999	D₄	—	4	8	no	—
1000	C₂×C₄	—	2	8	no	—
1001	C₂×C₄	—	2	8	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	4	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	4	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	4	no	—
1008	C₂×C₄	—	2	4	no	—
1009	C₂×C₄	—	2	4	no	—
1010	C₂×C₄	—	2	4	no	—
1011	C₂×C₄	—	2	4	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	4	no	—
1015	C₂×C₄	—	2	4	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	4	no	—
1018	C₂×C₄	—	4	8	no	—
1019	C₂×C₄	—	4	4	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	4	no	—
1022	C₂×C₄	—	4	8	no	—
1023	C₂×C₄	—	4	8	no	—
1024	C₂×C₄	—	4	8	no	—
1025	C₂×C₄	—	4	8	no	—
1026	C₂×C₄	—	4	4	no	—
1027	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1028	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1029	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1030	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1031	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1032	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1033	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1034	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1035	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1036	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1037	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1038	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1039	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1040	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1041	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1042	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1043	C₂²	—	2	8	no	—
1044	C₂²	—	2	2	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	4	no	—
1047	C₂²	—	2	4	no	—
1048	C₂²	—	2	4	no	—
1049	C₂²	—	2	4	no	—
1050	C₂²	—	2	4	no	—
1051	C₂²	—	2	4	no	—
1052	C₂²	—	4	8	no	—
1053	C₂²	—	4	8	no	—
1054	C₂²	—	8	8	no	—
1055	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
1056	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
1057	C₂²	C₁₃×#585	1	2	yes	—
1058	C₂²	C₁₃×#585	1	2	yes	—
1059	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
1060	C₄	—	2	2	no	—
1061	C₄	—	2	2	no	—
1062	C₄	—	2	4	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	4	no	—
1066	C₄	—	2	4	no	—
1067	C₄	—	2	4	no	—
1068	C₄	—	2	4	no	—
1069	C₄	—	2	4	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	4	no	—
1073	C₄	—	2	4	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	4	no	—
1076	C₂	—	2	4	no	—
1077	C₂	—	4	4	no	—
1078	C₂	—	4	4	no	—
1079	C₂	C₁₃×#3564	1	4	yes	direct product factor
1080	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1081	C₂	C₂×C₁₃×#585	1	1	yes	characteristic
1082	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂×C₁₃×#538	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3564	C₂	direct (N × H)
2. C₂×C₁₃×#563	C₂	semidirect
3. C₂×C₁₃×#563	C₂	semidirect
4. C₂×C₁₃×#556	C₂	semidirect
5. C₂×C₁₃×#554	C₂	semidirect
6. C₂×C₁₃×#552	C₂	semidirect
7. C₂×C₁₃×#552	C₂	semidirect
8. C₂×C₁₃×#551	C₂	semidirect
9. C₂×C₁₃×#551	C₂	semidirect
10. C₂×C₁₃×#544	C₂	semidirect
11. C₂×C₁₃×#543	C₂	semidirect
12. C₂×C₁₃×#542	C₂	semidirect
13. C₂×C₁₃×#541	C₂	semidirect
14. C₂×C₁₃×#541	C₂	semidirect
15. C₂×C₁₃×#539	C₂	semidirect
16. C₂×C₁₃×#539	C₂	semidirect
18. C₂×C₁₃×#533	C₂	semidirect
19. C₂×C₁₃×#529	C₂	semidirect
20. C₂²×C₁₃×#126	C₂	semidirect
21. C₁₃×#563	C₂²	semidirect
22. C₁₃×#563	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
25. C₁₃×#552	C₂²	semidirect
26. C₁₃×#552	C₂²	semidirect
27. C₁₃×#551	C₂²	semidirect
28. C₁₃×#551	C₂²	semidirect
29. C₁₃×#544	C₂²	semidirect
30. C₁₃×#543	C₂²	semidirect
31. C₁₃×#542	C₂²	semidirect
32. C₁₃×#541	C₂²	semidirect
33. C₁₃×#541	C₂²	semidirect
34. C₁₃×#539	C₂²	semidirect
35. C₁₃×#539	C₂²	semidirect
37. C₁₃×#533	C₂²	semidirect
38. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
40. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
43. C₁₃×#529	C₂²	semidirect
53. C₂×C₁₃×#126	C₂²	semidirect
54. C₂×C₁₃×#126	C₂²	semidirect
55. C₂×C₁₃×#126	C₂²	semidirect
56. C₂×C₁₃×#126	C₂²	semidirect
57. C₂×C₁₃×#126	C₂²	semidirect
58. C₂×C₁₃×#125	C₂²	semidirect
59. C₂×C₁₃×#125	C₂²	semidirect
60. C₂×C₁₃×#125	C₂²	semidirect
61. C₂×C₁₃×#125	C₂²	semidirect
62. C₂×C₁₃×#125	C₂²	semidirect
63. C₂×C₁₃×#125	C₂²	semidirect
64. C₂×C₁₃×#125	C₂²	semidirect
65. C₂×C₁₃×#125	C₂²	semidirect
66. C₂×C₁₃×#125	C₂²	semidirect
67. C₂×C₁₃×#125	C₂²	semidirect
71. C₂×C₁₃×#124	C₂²	semidirect
79. C₂×C₁₃×#123	C₂²	semidirect
92. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
94. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
95. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
96. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
100. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
101. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
102. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
103. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
104. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
105. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
111. C₂×C₄×D₄×C₁₃	C₂²	semidirect
116. C₂×C₁₃×#117	C₂²	semidirect
117. C₂×C₁₃×#117	C₂²	semidirect
121. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
149. C₁₃×C₄⋊Q₈	C₂³	semidirect
150. C₁₃×C₄⋊Q₈	C₂³	semidirect
151. C₁₃×C₄⋊Q₈	C₂³	semidirect
152. C₁₃×C₄⋊Q₈	C₂³	semidirect
153. C₁₃×C₄⋊Q₈	C₂³	semidirect
163. C₁₃×#126	C₂³	semidirect
164. C₁₃×#126	C₂³	semidirect
165. C₁₃×#126	C₂³	semidirect
166. C₁₃×#126	C₂³	semidirect
167. C₁₃×#125	C₂³	semidirect
168. C₁₃×#125	C₂³	semidirect
169. C₁₃×#125	C₂³	semidirect
170. C₁₃×#125	C₂³	semidirect
171. C₁₃×#125	C₂³	semidirect
172. C₁₃×#125	C₂³	semidirect
173. C₁₃×#125	C₂³	semidirect
174. C₁₃×#125	C₂³	semidirect
175. C₁₃×#125	C₂³	semidirect
176. C₁₃×#125	C₂³	semidirect
180. C₁₃×#124	C₂³	semidirect
188. C₁₃×#123	C₂³	semidirect
201. C₁₃×C₂²⋊Q₈	C₂³	semidirect
202. C₁₃×C₂²⋊Q₈	C₂³	semidirect
203. C₁₃×C₂²⋊Q₈	C₂³	semidirect
204. C₁₃×C₂²⋊Q₈	C₂³	semidirect
205. C₁₃×C₂²⋊Q₈	C₂³	semidirect
209. C₄×Q₈×C₁₃	C₂³	semidirect
210. C₄×Q₈×C₁₃	C₂³	semidirect
211. C₄×Q₈×C₁₃	C₂³	semidirect
212. C₄×Q₈×C₁₃	C₂³	semidirect
213. C₄×Q₈×C₁₃	C₂³	semidirect
214. C₄×Q₈×C₁₃	C₂³	semidirect
220. C₄×D₄×C₁₃	C₂³	semidirect
225. C₁₃×#117	C₂³	semidirect
226. C₁₃×#117	C₂³	semidirect
263. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
301. C₂×#3564	C₁₃	direct (N × H)
432. #3564	C₂×C₁₃	direct (N × H)
433. C₂×#563	C₂×C₁₃	semidirect
434. C₂×#563	C₂×C₁₃	semidirect
435. C₂×#556	C₂×C₁₃	semidirect
436. C₂×#554	C₂×C₁₃	semidirect
437. C₂×#552	C₂×C₁₃	semidirect
438. C₂×#552	C₂×C₁₃	semidirect
439. C₂×#551	C₂×C₁₃	semidirect
440. C₂×#551	C₂×C₁₃	semidirect
441. C₂×#544	C₂×C₁₃	semidirect
442. C₂×#543	C₂×C₁₃	semidirect
443. C₂×#542	C₂×C₁₃	semidirect
444. C₂×#541	C₂×C₁₃	semidirect
445. C₂×#541	C₂×C₁₃	semidirect
446. C₂×#539	C₂×C₁₃	semidirect
447. C₂×#539	C₂×C₁₃	semidirect
449. C₂×#533	C₂×C₁₃	semidirect
450. C₂×#529	C₂×C₁₃	semidirect
451. C₂²×#126	C₂×C₁₃	semidirect
522. #563	C₂²×C₁₃	semidirect
523. #563	C₂²×C₁₃	semidirect
524. #556	C₂²×C₁₃	semidirect
525. #554	C₂²×C₁₃	semidirect
526. #552	C₂²×C₁₃	semidirect
527. #552	C₂²×C₁₃	semidirect
528. #551	C₂²×C₁₃	semidirect
529. #551	C₂²×C₁₃	semidirect
530. #544	C₂²×C₁₃	semidirect
531. #543	C₂²×C₁₃	semidirect
532. #542	C₂²×C₁₃	semidirect
533. #541	C₂²×C₁₃	semidirect
534. #541	C₂²×C₁₃	semidirect
535. #539	C₂²×C₁₃	semidirect
536. #539	C₂²×C₁₃	semidirect
538. #533	C₂²×C₁₃	semidirect
539. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
540. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
541. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
542. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
543. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
544. #529	C₂²×C₁₃	semidirect
554. C₂×#126	C₂²×C₁₃	semidirect
555. C₂×#126	C₂²×C₁₃	semidirect
556. C₂×#126	C₂²×C₁₃	semidirect
557. C₂×#126	C₂²×C₁₃	semidirect
558. C₂×#126	C₂²×C₁₃	semidirect
559. C₂×#125	C₂²×C₁₃	semidirect
560. C₂×#125	C₂²×C₁₃	semidirect
561. C₂×#125	C₂²×C₁₃	semidirect
562. C₂×#125	C₂²×C₁₃	semidirect
563. C₂×#125	C₂²×C₁₃	semidirect
564. C₂×#125	C₂²×C₁₃	semidirect
565. C₂×#125	C₂²×C₁₃	semidirect
566. C₂×#125	C₂²×C₁₃	semidirect
567. C₂×#125	C₂²×C₁₃	semidirect
568. C₂×#125	C₂²×C₁₃	semidirect
572. C₂×#124	C₂²×C₁₃	semidirect
580. C₂×#123	C₂²×C₁₃	semidirect
593. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
594. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
595. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
596. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
597. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
601. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
602. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
603. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
604. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
605. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
606. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
612. C₂×C₄×D₄	C₂²×C₁₃	semidirect
617. C₂×#117	C₂²×C₁₃	semidirect
618. C₂×#117	C₂²×C₁₃	semidirect
622. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
683. C₄⋊Q₈	C₂³×C₁₃	semidirect
684. C₄⋊Q₈	C₂³×C₁₃	semidirect
685. C₄⋊Q₈	C₂³×C₁₃	semidirect
686. C₄⋊Q₈	C₂³×C₁₃	semidirect
687. C₄⋊Q₈	C₂³×C₁₃	semidirect
697. #126	C₂³×C₁₃	semidirect
698. #126	C₂³×C₁₃	semidirect
699. #126	C₂³×C₁₃	semidirect
700. #126	C₂³×C₁₃	semidirect
701. #125	C₂³×C₁₃	semidirect
702. #125	C₂³×C₁₃	semidirect
703. #125	C₂³×C₁₃	semidirect
704. #125	C₂³×C₁₃	semidirect
705. #125	C₂³×C₁₃	semidirect
706. #125	C₂³×C₁₃	semidirect
707. #125	C₂³×C₁₃	semidirect
708. #125	C₂³×C₁₃	semidirect
709. #125	C₂³×C₁₃	semidirect
710. #125	C₂³×C₁₃	semidirect
714. #124	C₂³×C₁₃	semidirect
722. #123	C₂³×C₁₃	semidirect
735. C₂²⋊Q₈	C₂³×C₁₃	semidirect
736. C₂²⋊Q₈	C₂³×C₁₃	semidirect
737. C₂²⋊Q₈	C₂³×C₁₃	semidirect
738. C₂²⋊Q₈	C₂³×C₁₃	semidirect
739. C₂²⋊Q₈	C₂³×C₁₃	semidirect
743. C₄×Q₈	C₂³×C₁₃	semidirect
744. C₄×Q₈	C₂³×C₁₃	semidirect
745. C₄×Q₈	C₂³×C₁₃	semidirect
746. C₄×Q₈	C₂³×C₁₃	semidirect
747. C₄×Q₈	C₂³×C₁₃	semidirect
748. C₄×Q₈	C₂³×C₁₃	semidirect
754. C₄×D₄	C₂³×C₁₃	semidirect
759. #117	C₂³×C₁₃	semidirect
760. #117	C₂³×C₁₃	semidirect
797. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
838. C₂×C₁₃	#3564	direct (N × H)
972. C₁₃	C₂×#3564	direct (N × H)
1079. C₂	C₁₃×#3564	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×#3564	2
C₂×C₁₃×#563	2
C₂×C₁₃×#556	2
C₂×C₁₃×#554	2
C₂×C₁₃×#552	2
C₂×C₁₃×#551	2
C₂×C₁₃×#544	2
C₂×C₁₃×#543	2
C₂×C₁₃×#542	2
C₂×C₁₃×#541	2
C₂×C₁₃×#539	2
C₂×C₁₃×#538	2
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₂²×C₁₃×#126	2
C₂×#3564	13

Subgroups — C2×C13×#3564 #15749073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3564 #15749073