Subgroups — C₂×C₁₃×#3565 #15749080

Order 3328.

6554 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3565	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#556	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#542	C₂	1	2	yes	maximal, complemented
19	C₂×C₁₃×#542	C₂	1	2	yes	maximal, complemented
20	C₂×C₁₃×#541	C₂	1	2	yes	maximal, complemented
21	C₂×C₁₃×#539	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
25	C₁₃×#563	C₂²	1	32	yes	complemented
26	C₁₃×#562	C₂²	1	32	yes	complemented
27	C₁₃×#557	C₂²	1	16	yes	complemented
28	C₁₃×#556	C₂²	1	32	yes	complemented
29	C₁₃×#556	C₂²	1	16	yes	complemented
30	C₁₃×#555	C₂²	1	16	yes	complemented
31	C₁₃×#554	C₂²	1	16	yes	complemented
32	C₁₃×#553	C₂²	1	16	yes	complemented
33	C₁₃×#553	C₂²	1	16	yes	complemented
34	C₁₃×#552	C₂²	1	32	yes	complemented
35	C₁₃×#552	C₂²	1	16	yes	complemented
36	C₁₃×#552	C₂²	1	16	yes	complemented
37	C₁₃×#544	C₂²	1	16	yes	complemented
38	C₁₃×#544	C₂²	1	16	yes	complemented
39	C₁₃×#542	C₂²	1	16	yes	complemented
40	C₁₃×#542	C₂²	1	16	yes	complemented
41	C₁₃×#542	C₂²	1	32	yes	complemented
42	C₁₃×#542	C₂²	1	32	yes	complemented
43	C₁₃×#541	C₂²	1	32	yes	complemented
44	C₁₃×#539	C₂²	1	32	yes	complemented
45	C₁₃×#533	C₂²	1	16	yes	complemented
46	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
47	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
48	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
51	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
53	C₁₃×#529	C₂²	1	16	yes	complemented
54	C₁₃×#529	C₂²	1	16	yes	complemented
55	C₂×C₁₃×#126	C₂²	1	2	yes	—
56	C₂×C₁₃×#126	C₂²	1	2	yes	—
57	C₂×C₁₃×#126	C₂²	1	2	yes	—
58	C₂×C₁₃×#126	C₂²	1	2	yes	—
59	C₂×C₁₃×#126	C₂²	1	2	yes	—
60	C₂×C₁₃×#126	C₂²	1	1	yes	characteristic
61	C₂×C₁₃×#126	C₂²	1	1	yes	characteristic
62	C₂×C₁₃×#126	C₂²	1	2	yes	—
63	C₂×C₁₃×#126	C₂²	1	2	yes	—
64	C₂×C₁₃×#126	C₂²	1	2	yes	—
65	C₂×C₁₃×#126	C₂²	1	2	yes	—
66	C₂×C₁₃×#125	C₂²	1	2	yes	—
67	C₂×C₁₃×#125	C₂²	1	2	yes	—
68	C₂×C₁₃×#125	C₂²	1	2	yes	—
69	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
72	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
73	C₂×C₁₃×#125	C₂²	1	2	yes	—
74	C₂×C₁₃×#125	C₂²	1	2	yes	—
75	C₂×C₁₃×#125	C₂²	1	2	yes	—
76	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
77	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
78	C₂×C₁₃×#124	C₂²	1	2	yes	—
79	C₂×C₁₃×#124	C₂²	1	2	yes	—
80	C₂×C₁₃×#124	C₂²	1	2	yes	—
81	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
82	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
83	C₂×C₁₃×#124	C₂²	1	2	yes	—
84	C₂×C₁₃×#124	C₂²	1	2	yes	—
85	C₂×C₁₃×#123	C₂²	1	2	yes	—
86	C₂×C₁₃×#123	C₂²	1	2	yes	—
87	C₂×C₁₃×#123	C₂²	1	2	yes	—
88	C₂×C₁₃×#123	C₂²	1	2	yes	—
89	C₂×C₁₃×#123	C₂²	1	2	yes	—
90	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
91	C₂×C₁₃×#123	C₂²	1	1	yes	characteristic
92	C₂×C₁₃×#123	C₂²	1	2	yes	—
93	C₂×C₁₃×#123	C₂²	1	2	yes	—
94	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
95	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
96	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
97	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
98	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
99	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
100	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
101	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
102	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
103	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
104	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
105	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
106	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
107	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
108	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
109	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
110	C₂×C₁₃×#121	C₂²	1	2	yes	—
111	C₂×C₁₃×#121	C₂²	1	2	yes	—
112	C₂×C₁₃×#121	C₂²	1	2	yes	—
113	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
114	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
115	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
116	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
117	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
118	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
119	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
120	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
121	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
122	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
123	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
124	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
125	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
126	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
127	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
128	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
129	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
130	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
131	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
132	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
133	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
134	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#117	C₂²	1	2	yes	—
136	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
137	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
138	C₂×C₁₃×#117	C₂²	1	2	yes	—
139	C₂×C₁₃×#117	C₂²	1	2	yes	—
140	C₂×C₁₃×#117	C₂²	1	2	yes	—
141	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
142	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
143	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
144	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
145	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
146	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
147	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
150	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
151	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
153	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
155	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
156	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
158	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
159	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
160	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
161	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
162	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
163	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
164	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
165	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
166	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
167	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
168	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
169	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
170	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
171	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
172	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
173	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
174	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
175	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
176	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
177	C₁₃×#126	C₂³	1	16	yes	—
178	C₁₃×#126	C₂³	1	8	yes	—
179	C₁₃×#126	C₂³	1	8	yes	—
180	C₁₃×#126	C₂³	1	16	yes	—
181	C₁₃×#126	C₂³	1	16	yes	—
182	C₁₃×#126	C₂³	1	16	yes	—
183	C₁₃×#126	C₂³	1	16	yes	—
184	C₁₃×#126	C₂³	1	16	yes	—
185	C₁₃×#126	C₂³	1	16	yes	—
186	C₁₃×#126	C₂³	1	16	yes	—
187	C₁₃×#126	C₂³	1	16	yes	—
188	C₁₃×#125	C₂³	1	8	yes	—
189	C₁₃×#125	C₂³	1	8	yes	—
190	C₁₃×#125	C₂³	1	8	yes	—
191	C₁₃×#125	C₂³	1	8	yes	—
192	C₁₃×#125	C₂³	1	16	yes	—
193	C₁₃×#125	C₂³	1	16	yes	—
194	C₁₃×#125	C₂³	1	16	yes	—
195	C₁₃×#125	C₂³	1	16	yes	—
196	C₁₃×#125	C₂³	1	16	yes	—
197	C₁₃×#125	C₂³	1	8	yes	—
198	C₁₃×#125	C₂³	1	16	yes	—
199	C₁₃×#125	C₂³	1	8	yes	—
200	C₁₃×#124	C₂³	1	8	yes	—
201	C₁₃×#124	C₂³	1	8	yes	—
202	C₁₃×#124	C₂³	1	16	yes	—
203	C₁₃×#124	C₂³	1	16	yes	—
204	C₁₃×#124	C₂³	1	16	yes	—
205	C₁₃×#124	C₂³	1	16	yes	—
206	C₁₃×#124	C₂³	1	16	yes	—
207	C₁₃×#123	C₂³	1	8	yes	—
208	C₁₃×#123	C₂³	1	8	yes	—
209	C₁₃×#123	C₂³	1	16	yes	—
210	C₁₃×#123	C₂³	1	16	yes	—
211	C₁₃×#123	C₂³	1	16	yes	—
212	C₁₃×#123	C₂³	1	16	yes	—
213	C₁₃×#123	C₂³	1	16	yes	—
214	C₁₃×#123	C₂³	1	16	yes	—
215	C₁₃×#123	C₂³	1	16	yes	—
216	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
217	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
218	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
219	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
220	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
221	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
222	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
223	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
224	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
225	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
226	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
227	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
228	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
229	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
230	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
231	C₁₃×#121	C₂³	1	8	yes	—
232	C₁₃×#121	C₂³	1	8	yes	—
233	C₁₃×#121	C₂³	1	16	yes	—
234	C₁₃×#121	C₂³	1	8	yes	—
235	C₁₃×#121	C₂³	1	8	yes	—
236	C₁₃×#121	C₂³	1	16	yes	—
237	C₁₃×#121	C₂³	1	16	yes	—
238	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
239	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
240	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
241	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
242	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
243	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
244	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
245	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
246	C₄×D₄×C₁₃	C₂³	1	16	yes	—
247	C₄×D₄×C₁₃	C₂³	1	8	yes	—
248	C₄×D₄×C₁₃	C₂³	1	8	yes	—
249	C₄×D₄×C₁₃	C₂³	1	8	yes	—
250	C₄×D₄×C₁₃	C₂³	1	8	yes	—
251	C₄×D₄×C₁₃	C₂³	1	16	yes	—
252	C₄×D₄×C₁₃	C₂³	1	16	yes	—
253	C₄×D₄×C₁₃	C₂³	1	8	yes	—
254	C₄×D₄×C₁₃	C₂³	1	8	yes	—
255	C₁₃×#117	C₂³	1	8	yes	—
256	C₁₃×#117	C₂³	1	8	yes	—
257	C₁₃×#117	C₂³	1	16	yes	—
258	C₁₃×#117	C₂³	1	8	yes	—
259	C₁₃×#117	C₂³	1	8	yes	—
260	C₁₃×#117	C₂³	1	16	yes	—
261	C₁₃×#117	C₂³	1	16	yes	—
262	C₁₃×#117	C₂³	1	16	yes	—
263	C₁₃×#117	C₂³	1	8	yes	—
264	C₁₃×#117	C₂³	1	8	yes	—
265	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
274	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
276	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
277	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
278	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
282	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
283	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
285	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
286	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
287	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
288	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
289	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
291	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
293	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
294	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
296	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
297	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
298	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
299	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
300	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
301	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
302	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
303	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
304	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
305	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
306	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
307	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
308	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
310	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
311	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
312	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
313	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
314	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
315	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
316	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
317	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
318	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
319	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
320	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
321	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
322	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
323	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
324	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
325	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
326	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
327	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
328	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
329	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
330	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
331	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
332	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
333	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
334	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
335	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
336	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
337	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
338	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
339	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
340	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
343	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
344	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
345	C₂×#3565	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
350	C₂×Q₈×C₁₃	—	2	4	no	—
351	C₂×Q₈×C₁₃	—	4	2	no	—
352	C₂×Q₈×C₁₃	—	4	4	no	—
353	C₂×Q₈×C₁₃	—	4	4	no	—
354	C₂×Q₈×C₁₃	—	4	4	no	—
355	C₂×Q₈×C₁₃	—	4	4	no	—
356	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
357	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
358	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
359	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
360	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
361	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
362	C₂×D₄×C₁₃	—	2	4	no	—
363	C₂×D₄×C₁₃	—	4	2	no	—
364	C₂×D₄×C₁₃	—	4	2	no	—
365	C₂×D₄×C₁₃	—	4	4	no	—
366	C₂×D₄×C₁₃	—	4	4	no	—
367	C₂×D₄×C₁₃	—	4	2	no	—
368	C₂×D₄×C₁₃	—	4	4	no	—
369	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
370	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
371	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
372	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
373	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
374	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
375	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
376	C₂²×C₄×C₁₃	—	2	4	no	—
377	C₂²×C₄×C₁₃	—	2	4	no	—
378	C₂²×C₄×C₁₃	—	2	4	no	—
379	C₂²×C₄×C₁₃	—	4	4	no	—
380	C₂²×C₄×C₁₃	—	4	2	no	—
381	C₂²×C₄×C₁₃	—	4	4	no	—
382	C₂²×C₄×C₁₃	—	4	4	no	—
383	C₂²×C₄×C₁₃	—	4	4	no	—
384	C₂²×C₄×C₁₃	—	4	4	no	—
385	C₂²×C₄×C₁₃	—	4	2	no	—
386	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
387	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
388	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
389	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
392	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
394	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
400	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
402	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
403	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
404	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
408	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
409	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
410	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
411	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
412	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
413	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
414	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
415	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
416	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
417	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
418	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
419	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
420	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
421	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
422	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
423	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
424	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
425	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
426	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
427	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
428	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
429	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
430	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
431	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
432	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
433	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
434	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
435	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
436	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
437	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
438	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
439	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
440	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
441	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
442	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
443	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
444	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
445	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
446	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
447	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
448	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
449	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
450	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
451	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
452	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
453	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
454	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
455	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
456	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
457	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
458	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
459	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
460	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
461	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
462	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
463	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
464	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
465	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
466	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
467	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
468	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
469	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
470	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
471	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
472	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
473	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
474	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
475	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
476	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
477	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
478	C₄²×C₁₃	C₂⁴	1	4	yes	—
479	C₄²×C₁₃	C₂⁴	1	4	yes	—
480	C₄²×C₁₃	C₂⁴	1	4	yes	—
481	C₄²×C₁₃	C₂⁴	1	4	yes	—
482	C₄²×C₁₃	C₂⁴	1	8	yes	—
483	C₄²×C₁₃	C₂⁴	1	8	yes	—
484	C₄²×C₁₃	C₂⁴	1	8	yes	—
485	C₄²×C₁₃	C₂⁴	1	8	yes	—
486	C₄²×C₁₃	C₂⁴	1	4	yes	—
487	C₄²×C₁₃	C₂⁴	1	4	yes	—
488	C₄²×C₁₃	C₂⁴	1	8	yes	—
489	C₄²×C₁₃	C₂⁴	1	8	yes	—
490	C₄²×C₁₃	C₂⁴	1	8	yes	—
491	#3565	C₂×C₁₃	1	32	yes	direct product factor
492	C₂×#563	C₂×C₁₃	1	2	yes	complemented
493	C₂×#562	C₂×C₁₃	1	2	yes	complemented
494	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
495	C₂×#556	C₂×C₁₃	1	2	yes	complemented
496	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
497	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
498	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
499	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
500	C₂×#553	C₂×C₁₃	1	1	yes	characteristic, complemented
501	C₂×#552	C₂×C₁₃	1	2	yes	complemented
502	C₂×#552	C₂×C₁₃	1	1	yes	characteristic, complemented
503	C₂×#552	C₂×C₁₃	1	1	yes	characteristic, complemented
504	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
505	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
506	C₂×#542	C₂×C₁₃	1	1	yes	characteristic, complemented
507	C₂×#542	C₂×C₁₃	1	1	yes	characteristic, complemented
508	C₂×#542	C₂×C₁₃	1	2	yes	complemented
509	C₂×#542	C₂×C₁₃	1	2	yes	complemented
510	C₂×#541	C₂×C₁₃	1	2	yes	complemented
511	C₂×#539	C₂×C₁₃	1	2	yes	complemented
512	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
513	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
514	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
515	C₂³×C₁₃	—	2	2	no	—
516	C₂³×C₁₃	—	2	2	no	—
517	C₂³×C₁₃	—	2	2	no	—
518	C₂³×C₁₃	—	2	4	no	—
519	C₂³×C₁₃	—	2	2	no	—
520	C₂³×C₁₃	—	2	2	no	—
521	C₂³×C₁₃	—	2	4	no	—
522	C₂³×C₁₃	—	2	2	no	—
523	C₂³×C₁₃	—	2	2	no	—
524	C₂³×C₁₃	—	2	4	no	—
525	C₂³×C₁₃	—	2	2	no	—
526	C₂³×C₁₃	—	2	2	no	—
527	C₂³×C₁₃	C₂⁵	1	2	yes	—
528	C₂³×C₁₃	C₂⁵	1	2	yes	—
529	C₂³×C₁₃	C₂⁵	1	2	yes	—
530	C₂³×C₁₃	C₂⁵	1	4	yes	—
531	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
532	Q₈×C₁₃	—	2	8	no	—
533	Q₈×C₁₃	—	4	4	no	—
534	Q₈×C₁₃	—	4	8	no	—
535	Q₈×C₁₃	—	4	8	no	—
536	Q₈×C₁₃	—	4	8	no	—
537	Q₈×C₁₃	—	4	8	no	—
538	D₄×C₁₃	—	2	8	no	—
539	D₄×C₁₃	—	4	4	no	—
540	D₄×C₁₃	—	4	4	no	—
541	D₄×C₁₃	—	4	8	no	—
542	D₄×C₁₃	—	4	8	no	—
543	D₄×C₁₃	—	4	4	no	—
544	D₄×C₁₃	—	4	8	no	—
545	C₂×C₄×C₁₃	—	2	2	no	—
546	C₂×C₄×C₁₃	—	2	2	no	—
547	C₂×C₄×C₁₃	—	2	2	no	—
548	C₂×C₄×C₁₃	—	2	4	no	—
549	C₂×C₄×C₁₃	—	2	2	no	—
550	C₂×C₄×C₁₃	—	2	2	no	—
551	C₂×C₄×C₁₃	—	2	4	no	—
552	C₂×C₄×C₁₃	—	2	2	no	—
553	C₂×C₄×C₁₃	—	2	4	no	—
554	C₂×C₄×C₁₃	—	2	4	no	—
555	C₂×C₄×C₁₃	—	2	4	no	—
556	C₂×C₄×C₁₃	—	2	2	no	—
557	C₂×C₄×C₁₃	—	2	2	no	—
558	C₂×C₄×C₁₃	—	2	4	no	—
559	C₂×C₄×C₁₃	—	2	2	no	—
560	C₂×C₄×C₁₃	—	2	2	no	—
561	C₂×C₄×C₁₃	—	2	4	no	—
562	C₂×C₄×C₁₃	—	2	2	no	—
563	C₂×C₄×C₁₃	—	2	8	no	—
564	C₂×C₄×C₁₃	—	2	8	no	—
565	C₂×C₄×C₁₃	—	2	8	no	—
566	C₂×C₄×C₁₃	—	4	8	no	—
567	C₂×C₄×C₁₃	—	4	4	no	—
568	C₂×C₄×C₁₃	—	4	8	no	—
569	C₂×C₄×C₁₃	—	4	8	no	—
570	C₂×C₄×C₁₃	—	4	8	no	—
571	C₂×C₄×C₁₃	—	4	8	no	—
572	C₂×C₄×C₁₃	—	4	4	no	—
573	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
574	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
575	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
576	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
577	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
578	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
579	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
580	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
581	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
582	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
583	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
584	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
585	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
586	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
587	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
588	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
589	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
590	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
591	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
592	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
593	#563	C₂²×C₁₃	1	32	yes	complemented
594	#562	C₂²×C₁₃	1	32	yes	complemented
595	#557	C₂²×C₁₃	1	16	yes	complemented
596	#556	C₂²×C₁₃	1	32	yes	complemented
597	#556	C₂²×C₁₃	1	16	yes	complemented
598	#555	C₂²×C₁₃	1	16	yes	complemented
599	#554	C₂²×C₁₃	1	16	yes	complemented
600	#553	C₂²×C₁₃	1	16	yes	complemented
601	#553	C₂²×C₁₃	1	16	yes	complemented
602	#552	C₂²×C₁₃	1	32	yes	complemented
603	#552	C₂²×C₁₃	1	16	yes	complemented
604	#552	C₂²×C₁₃	1	16	yes	complemented
605	#544	C₂²×C₁₃	1	16	yes	complemented
606	#544	C₂²×C₁₃	1	16	yes	complemented
607	#542	C₂²×C₁₃	1	16	yes	complemented
608	#542	C₂²×C₁₃	1	16	yes	complemented
609	#542	C₂²×C₁₃	1	32	yes	complemented
610	#542	C₂²×C₁₃	1	32	yes	complemented
611	#541	C₂²×C₁₃	1	32	yes	complemented
612	#539	C₂²×C₁₃	1	32	yes	complemented
613	#533	C₂²×C₁₃	1	16	yes	complemented
614	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
615	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
616	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
617	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
618	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
619	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
620	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
621	#529	C₂²×C₁₃	1	16	yes	complemented
622	#529	C₂²×C₁₃	1	16	yes	complemented
623	C₂×#126	C₂²×C₁₃	1	2	yes	—
624	C₂×#126	C₂²×C₁₃	1	1	yes	characteristic
625	C₂×#126	C₂²×C₁₃	1	1	yes	characteristic
626	C₂×#126	C₂²×C₁₃	1	2	yes	—
627	C₂×#126	C₂²×C₁₃	1	2	yes	—
628	C₂×#126	C₂²×C₁₃	1	2	yes	—
629	C₂×#126	C₂²×C₁₃	1	2	yes	—
630	C₂×#126	C₂²×C₁₃	1	2	yes	—
631	C₂×#126	C₂²×C₁₃	1	2	yes	—
632	C₂×#126	C₂²×C₁₃	1	2	yes	—
633	C₂×#126	C₂²×C₁₃	1	2	yes	—
634	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
635	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
636	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
637	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
638	C₂×#125	C₂²×C₁₃	1	2	yes	—
639	C₂×#125	C₂²×C₁₃	1	2	yes	—
640	C₂×#125	C₂²×C₁₃	1	2	yes	—
641	C₂×#125	C₂²×C₁₃	1	2	yes	—
642	C₂×#125	C₂²×C₁₃	1	2	yes	—
643	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
644	C₂×#125	C₂²×C₁₃	1	2	yes	—
645	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
646	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
647	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
648	C₂×#124	C₂²×C₁₃	1	2	yes	—
649	C₂×#124	C₂²×C₁₃	1	2	yes	—
650	C₂×#124	C₂²×C₁₃	1	2	yes	—
651	C₂×#124	C₂²×C₁₃	1	2	yes	—
652	C₂×#124	C₂²×C₁₃	1	2	yes	—
653	C₂×#123	C₂²×C₁₃	1	1	yes	characteristic
654	C₂×#123	C₂²×C₁₃	1	1	yes	characteristic
655	C₂×#123	C₂²×C₁₃	1	2	yes	—
656	C₂×#123	C₂²×C₁₃	1	2	yes	—
657	C₂×#123	C₂²×C₁₃	1	2	yes	—
658	C₂×#123	C₂²×C₁₃	1	2	yes	—
659	C₂×#123	C₂²×C₁₃	1	2	yes	—
660	C₂×#123	C₂²×C₁₃	1	2	yes	—
661	C₂×#123	C₂²×C₁₃	1	2	yes	—
662	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
663	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
664	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
665	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
666	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
667	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
668	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
669	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
670	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
671	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
672	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
673	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
674	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
675	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
676	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
677	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
678	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
679	C₂×#121	C₂²×C₁₃	1	2	yes	—
680	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
681	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
682	C₂×#121	C₂²×C₁₃	1	2	yes	—
683	C₂×#121	C₂²×C₁₃	1	2	yes	—
684	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
685	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
686	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
687	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
688	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
689	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
690	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
691	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
692	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
693	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
694	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
695	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
696	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
697	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
698	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
699	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
700	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
701	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
702	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
703	C₂×#117	C₂²×C₁₃	1	2	yes	—
704	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
705	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
706	C₂×#117	C₂²×C₁₃	1	2	yes	—
707	C₂×#117	C₂²×C₁₃	1	2	yes	—
708	C₂×#117	C₂²×C₁₃	1	2	yes	—
709	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
710	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
711	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
712	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
713	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
714	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
715	C₂²×C₁₃	—	2	2	no	—
716	C₂²×C₁₃	—	2	2	no	—
717	C₂²×C₁₃	—	2	2	no	—
718	C₂²×C₁₃	—	2	4	no	—
719	C₂²×C₁₃	—	2	2	no	—
720	C₂²×C₁₃	—	2	2	no	—
721	C₂²×C₁₃	—	2	4	no	—
722	C₂²×C₁₃	—	2	2	no	—
723	C₂²×C₁₃	—	2	2	no	—
724	C₂²×C₁₃	—	2	4	no	—
725	C₂²×C₁₃	—	2	2	no	—
726	C₂²×C₁₃	—	2	2	no	—
727	C₂²×C₁₃	—	4	4	no	—
728	C₂²×C₁₃	—	4	4	no	—
729	C₂²×C₁₃	—	4	4	no	—
730	C₂²×C₁₃	—	4	8	no	—
731	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
732	C₂²×C₁₃	#585	1	2	yes	—
733	C₂²×C₁₃	#585	1	2	yes	—
734	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
735	C₄×C₁₃	—	2	2	no	—
736	C₄×C₁₃	—	2	2	no	—
737	C₄×C₁₃	—	2	2	no	—
738	C₄×C₁₃	—	2	4	no	—
739	C₄×C₁₃	—	2	2	no	—
740	C₄×C₁₃	—	2	2	no	—
741	C₄×C₁₃	—	2	4	no	—
742	C₄×C₁₃	—	2	2	no	—
743	C₄×C₁₃	—	2	4	no	—
744	C₄×C₁₃	—	2	4	no	—
745	C₄×C₁₃	—	2	4	no	—
746	C₄×C₁₃	—	2	2	no	—
747	C₄×C₁₃	—	2	2	no	—
748	C₄×C₁₃	—	2	4	no	—
749	C₄×C₁₃	—	2	2	no	—
750	C₄×C₁₃	—	2	2	no	—
751	C₄×C₁₃	—	2	4	no	—
752	C₄×C₁₃	—	2	2	no	—
753	C₄×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
754	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
755	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
756	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
757	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
758	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
759	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
760	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
761	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
762	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
763	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
764	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
765	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
766	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
767	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
768	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
769	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
770	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
771	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
772	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
773	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
774	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
775	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
776	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
777	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
778	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
779	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
780	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
781	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
782	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
783	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
784	#126	C₂³×C₁₃	1	16	yes	—
785	#126	C₂³×C₁₃	1	8	yes	—
786	#126	C₂³×C₁₃	1	8	yes	—
787	#126	C₂³×C₁₃	1	16	yes	—
788	#126	C₂³×C₁₃	1	16	yes	—
789	#126	C₂³×C₁₃	1	16	yes	—
790	#126	C₂³×C₁₃	1	16	yes	—
791	#126	C₂³×C₁₃	1	16	yes	—
792	#126	C₂³×C₁₃	1	16	yes	—
793	#126	C₂³×C₁₃	1	16	yes	—
794	#126	C₂³×C₁₃	1	16	yes	—
795	#125	C₂³×C₁₃	1	8	yes	—
796	#125	C₂³×C₁₃	1	8	yes	—
797	#125	C₂³×C₁₃	1	8	yes	—
798	#125	C₂³×C₁₃	1	8	yes	—
799	#125	C₂³×C₁₃	1	16	yes	—
800	#125	C₂³×C₁₃	1	16	yes	—
801	#125	C₂³×C₁₃	1	16	yes	—
802	#125	C₂³×C₁₃	1	16	yes	—
803	#125	C₂³×C₁₃	1	16	yes	—
804	#125	C₂³×C₁₃	1	8	yes	—
805	#125	C₂³×C₁₃	1	16	yes	—
806	#125	C₂³×C₁₃	1	8	yes	—
807	#124	C₂³×C₁₃	1	8	yes	—
808	#124	C₂³×C₁₃	1	8	yes	—
809	#124	C₂³×C₁₃	1	16	yes	—
810	#124	C₂³×C₁₃	1	16	yes	—
811	#124	C₂³×C₁₃	1	16	yes	—
812	#124	C₂³×C₁₃	1	16	yes	—
813	#124	C₂³×C₁₃	1	16	yes	—
814	#123	C₂³×C₁₃	1	8	yes	—
815	#123	C₂³×C₁₃	1	8	yes	—
816	#123	C₂³×C₁₃	1	16	yes	—
817	#123	C₂³×C₁₃	1	16	yes	—
818	#123	C₂³×C₁₃	1	16	yes	—
819	#123	C₂³×C₁₃	1	16	yes	—
820	#123	C₂³×C₁₃	1	16	yes	—
821	#123	C₂³×C₁₃	1	16	yes	—
822	#123	C₂³×C₁₃	1	16	yes	—
823	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
824	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
825	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
826	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
827	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
828	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
829	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
830	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
831	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
832	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
833	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
834	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
835	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
836	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
837	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
838	#121	C₂³×C₁₃	1	8	yes	—
839	#121	C₂³×C₁₃	1	8	yes	—
840	#121	C₂³×C₁₃	1	16	yes	—
841	#121	C₂³×C₁₃	1	8	yes	—
842	#121	C₂³×C₁₃	1	8	yes	—
843	#121	C₂³×C₁₃	1	16	yes	—
844	#121	C₂³×C₁₃	1	16	yes	—
845	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
846	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
847	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
848	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
849	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
850	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
851	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
852	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
853	C₄×D₄	C₂³×C₁₃	1	16	yes	—
854	C₄×D₄	C₂³×C₁₃	1	8	yes	—
855	C₄×D₄	C₂³×C₁₃	1	8	yes	—
856	C₄×D₄	C₂³×C₁₃	1	8	yes	—
857	C₄×D₄	C₂³×C₁₃	1	8	yes	—
858	C₄×D₄	C₂³×C₁₃	1	16	yes	—
859	C₄×D₄	C₂³×C₁₃	1	16	yes	—
860	C₄×D₄	C₂³×C₁₃	1	8	yes	—
861	C₄×D₄	C₂³×C₁₃	1	8	yes	—
862	#117	C₂³×C₁₃	1	8	yes	—
863	#117	C₂³×C₁₃	1	8	yes	—
864	#117	C₂³×C₁₃	1	16	yes	—
865	#117	C₂³×C₁₃	1	8	yes	—
866	#117	C₂³×C₁₃	1	8	yes	—
867	#117	C₂³×C₁₃	1	16	yes	—
868	#117	C₂³×C₁₃	1	16	yes	—
869	#117	C₂³×C₁₃	1	16	yes	—
870	#117	C₂³×C₁₃	1	8	yes	—
871	#117	C₂³×C₁₃	1	8	yes	—
872	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
873	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
875	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
876	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
877	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
878	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
879	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
880	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
881	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
882	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
883	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
884	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
885	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
889	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
890	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
891	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
892	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
893	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
894	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
895	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
898	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
899	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
900	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
901	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
904	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
905	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
906	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
907	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
908	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
909	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
910	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
911	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
912	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
913	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
914	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
915	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
916	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
917	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
918	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
919	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
920	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
921	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
922	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
923	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
924	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
926	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
927	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
928	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
929	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
930	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
931	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
932	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
933	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
934	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
935	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
936	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
937	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
938	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
939	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
940	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
941	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
942	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
943	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
944	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
945	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
946	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
947	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
948	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
949	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
950	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
951	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
952	C₂×C₁₃	—	4	2	no	—
953	C₂×C₁₃	—	4	2	no	—
954	C₂×C₁₃	—	4	2	no	—
955	C₂×C₁₃	—	4	4	no	—
956	C₂×C₁₃	#3565	1	4	yes	direct product factor
957	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
958	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
959	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
960	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
961	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
962	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
963	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
964	C₂×Q₈	—	2	4	no	—
965	C₂×Q₈	—	4	2	no	—
966	C₂×Q₈	—	4	4	no	—
967	C₂×Q₈	—	4	4	no	—
968	C₂×Q₈	—	4	4	no	—
969	C₂×Q₈	—	4	4	no	—
970	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
971	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
972	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
973	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
974	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
975	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
976	C₂×D₄	—	2	4	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	2	no	—
979	C₂×D₄	—	4	4	no	—
980	C₂×D₄	—	4	4	no	—
981	C₂×D₄	—	4	2	no	—
982	C₂×D₄	—	4	4	no	—
983	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
984	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
985	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
986	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
987	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
988	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
989	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
990	C₂²×C₄	—	2	4	no	—
991	C₂²×C₄	—	2	4	no	—
992	C₂²×C₄	—	2	4	no	—
993	C₂²×C₄	—	4	4	no	—
994	C₂²×C₄	—	4	2	no	—
995	C₂²×C₄	—	4	4	no	—
996	C₂²×C₄	—	4	4	no	—
997	C₂²×C₄	—	4	4	no	—
998	C₂²×C₄	—	4	4	no	—
999	C₂²×C₄	—	4	2	no	—
1000	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1001	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1002	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1003	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1004	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1005	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1006	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1007	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1009	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1010	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1012	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1013	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
1015	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1016	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
1018	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
1020	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
1021	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
1022	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
1023	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
1024	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
1025	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
1026	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
1027	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
1028	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1029	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1030	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1031	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1032	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1033	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1034	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1035	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1036	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1037	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1038	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1039	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1040	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1041	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1042	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1043	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1044	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1045	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1046	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1047	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1048	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1049	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1050	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1051	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1052	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1053	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1054	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1055	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1056	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1057	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1058	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1059	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1060	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1061	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1062	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1063	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1064	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1065	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1066	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1067	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1068	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1069	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1070	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1071	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1072	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1073	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1074	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1075	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1076	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1077	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1078	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1079	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1080	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1081	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1082	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1083	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1084	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1085	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1086	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1087	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1088	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1089	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1090	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
1091	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
1092	C₄²	C₂⁴×C₁₃	1	4	yes	—
1093	C₄²	C₂⁴×C₁₃	1	4	yes	—
1094	C₄²	C₂⁴×C₁₃	1	4	yes	—
1095	C₄²	C₂⁴×C₁₃	1	4	yes	—
1096	C₄²	C₂⁴×C₁₃	1	8	yes	—
1097	C₄²	C₂⁴×C₁₃	1	8	yes	—
1098	C₄²	C₂⁴×C₁₃	1	8	yes	—
1099	C₄²	C₂⁴×C₁₃	1	8	yes	—
1100	C₄²	C₂⁴×C₁₃	1	4	yes	—
1101	C₄²	C₂⁴×C₁₃	1	4	yes	—
1102	C₄²	C₂⁴×C₁₃	1	8	yes	—
1103	C₄²	C₂⁴×C₁₃	1	8	yes	—
1104	C₄²	C₂⁴×C₁₃	1	8	yes	—
1105	C₁₃	C₂×#3565	1	1	yes	characteristic, direct product factor, Sylow
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	2	no	—
1108	C₂³	—	2	2	no	—
1109	C₂³	—	2	4	no	—
1110	C₂³	—	2	2	no	—
1111	C₂³	—	2	2	no	—
1112	C₂³	—	2	4	no	—
1113	C₂³	—	2	2	no	—
1114	C₂³	—	2	2	no	—
1115	C₂³	—	2	4	no	—
1116	C₂³	—	2	2	no	—
1117	C₂³	—	2	2	no	—
1118	C₂³	C₂⁵×C₁₃	1	2	yes	—
1119	C₂³	C₂⁵×C₁₃	1	2	yes	—
1120	C₂³	C₂⁵×C₁₃	1	2	yes	—
1121	C₂³	C₂⁵×C₁₃	1	4	yes	—
1122	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
1123	Q₈	—	2	8	no	—
1124	Q₈	—	4	4	no	—
1125	Q₈	—	4	8	no	—
1126	Q₈	—	4	8	no	—
1127	Q₈	—	4	8	no	—
1128	Q₈	—	4	8	no	—
1129	D₄	—	2	8	no	—
1130	D₄	—	4	4	no	—
1131	D₄	—	4	4	no	—
1132	D₄	—	4	8	no	—
1133	D₄	—	4	8	no	—
1134	D₄	—	4	4	no	—
1135	D₄	—	4	8	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	4	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	4	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	4	no	—
1145	C₂×C₄	—	2	4	no	—
1146	C₂×C₄	—	2	4	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	2	2	no	—
1149	C₂×C₄	—	2	4	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	4	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	8	no	—
1155	C₂×C₄	—	2	8	no	—
1156	C₂×C₄	—	2	8	no	—
1157	C₂×C₄	—	4	8	no	—
1158	C₂×C₄	—	4	4	no	—
1159	C₂×C₄	—	4	8	no	—
1160	C₂×C₄	—	4	8	no	—
1161	C₂×C₄	—	4	8	no	—
1162	C₂×C₄	—	4	8	no	—
1163	C₂×C₄	—	4	4	no	—
1164	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
1165	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1166	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1167	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1168	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1169	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1170	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1171	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1172	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1173	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1174	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1175	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1176	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1177	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1178	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1179	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1180	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1181	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1182	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1183	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	4	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	2	4	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	4	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	4	4	no	—
1197	C₂²	—	4	4	no	—
1198	C₂²	—	4	4	no	—
1199	C₂²	—	4	8	no	—
1200	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
1201	C₂²	C₁₃×#585	1	2	yes	—
1202	C₂²	C₁₃×#585	1	2	yes	—
1203	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
1204	C₄	—	2	2	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	2	no	—
1207	C₄	—	2	4	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	2	4	no	—
1211	C₄	—	2	2	no	—
1212	C₄	—	2	4	no	—
1213	C₄	—	2	4	no	—
1214	C₄	—	2	4	no	—
1215	C₄	—	2	2	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	4	no	—
1218	C₄	—	2	2	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	2	4	no	—
1221	C₄	—	2	2	no	—
1222	C₄	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
1223	C₂	—	4	2	no	—
1224	C₂	—	4	2	no	—
1225	C₂	—	4	2	no	—
1226	C₂	—	4	4	no	—
1227	C₂	C₁₃×#3565	1	4	yes	direct product factor
1228	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1229	C₂	C₂×C₁₃×#585	1	1	yes	characteristic
1230	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
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×#3565	C₂	direct (N × H)
2. C₂×C₁₃×#563	C₂	semidirect
3. C₂×C₁₃×#562	C₂	semidirect
4. C₂×C₁₃×#557	C₂	semidirect
5. C₂×C₁₃×#556	C₂	semidirect
6. C₂×C₁₃×#556	C₂	semidirect
7. C₂×C₁₃×#555	C₂	semidirect
8. C₂×C₁₃×#554	C₂	semidirect
9. C₂×C₁₃×#553	C₂	semidirect
10. C₂×C₁₃×#553	C₂	semidirect
11. C₂×C₁₃×#552	C₂	semidirect
12. C₂×C₁₃×#552	C₂	semidirect
13. C₂×C₁₃×#552	C₂	semidirect
14. C₂×C₁₃×#544	C₂	semidirect
15. C₂×C₁₃×#544	C₂	semidirect
16. C₂×C₁₃×#542	C₂	semidirect
17. C₂×C₁₃×#542	C₂	semidirect
18. C₂×C₁₃×#542	C₂	semidirect
19. C₂×C₁₃×#542	C₂	semidirect
20. C₂×C₁₃×#541	C₂	semidirect
21. C₂×C₁₃×#539	C₂	semidirect
22. C₂×C₁₃×#533	C₂	semidirect
23. C₂×C₁₃×#529	C₂	semidirect
24. C₂×C₁₃×#529	C₂	semidirect
25. C₁₃×#563	C₂²	semidirect
26. C₁₃×#562	C₂²	semidirect
27. C₁₃×#557	C₂²	semidirect
28. C₁₃×#556	C₂²	semidirect
29. C₁₃×#556	C₂²	semidirect
30. C₁₃×#555	C₂²	semidirect
31. C₁₃×#554	C₂²	semidirect
32. C₁₃×#553	C₂²	semidirect
33. C₁₃×#553	C₂²	semidirect
34. C₁₃×#552	C₂²	semidirect
35. C₁₃×#552	C₂²	semidirect
36. C₁₃×#552	C₂²	semidirect
37. C₁₃×#544	C₂²	semidirect
38. C₁₃×#544	C₂²	semidirect
39. C₁₃×#542	C₂²	semidirect
40. C₁₃×#542	C₂²	semidirect
41. C₁₃×#542	C₂²	semidirect
42. C₁₃×#542	C₂²	semidirect
43. C₁₃×#541	C₂²	semidirect
44. C₁₃×#539	C₂²	semidirect
45. C₁₃×#533	C₂²	semidirect
53. C₁₃×#529	C₂²	semidirect
54. C₁₃×#529	C₂²	semidirect
345. C₂×#3565	C₁₃	direct (N × H)
491. #3565	C₂×C₁₃	direct (N × H)
492. C₂×#563	C₂×C₁₃	semidirect
493. C₂×#562	C₂×C₁₃	semidirect
494. C₂×#557	C₂×C₁₃	semidirect
495. C₂×#556	C₂×C₁₃	semidirect
496. C₂×#556	C₂×C₁₃	semidirect
497. C₂×#555	C₂×C₁₃	semidirect
498. C₂×#554	C₂×C₁₃	semidirect
499. C₂×#553	C₂×C₁₃	semidirect
500. C₂×#553	C₂×C₁₃	semidirect
501. C₂×#552	C₂×C₁₃	semidirect
502. C₂×#552	C₂×C₁₃	semidirect
503. C₂×#552	C₂×C₁₃	semidirect
504. C₂×#544	C₂×C₁₃	semidirect
505. C₂×#544	C₂×C₁₃	semidirect
506. C₂×#542	C₂×C₁₃	semidirect
507. C₂×#542	C₂×C₁₃	semidirect
508. C₂×#542	C₂×C₁₃	semidirect
509. C₂×#542	C₂×C₁₃	semidirect
510. C₂×#541	C₂×C₁₃	semidirect
511. C₂×#539	C₂×C₁₃	semidirect
512. C₂×#533	C₂×C₁₃	semidirect
513. C₂×#529	C₂×C₁₃	semidirect
514. C₂×#529	C₂×C₁₃	semidirect
593. #563	C₂²×C₁₃	semidirect
594. #562	C₂²×C₁₃	semidirect
595. #557	C₂²×C₁₃	semidirect
596. #556	C₂²×C₁₃	semidirect
597. #556	C₂²×C₁₃	semidirect
598. #555	C₂²×C₁₃	semidirect
599. #554	C₂²×C₁₃	semidirect
600. #553	C₂²×C₁₃	semidirect
601. #553	C₂²×C₁₃	semidirect
602. #552	C₂²×C₁₃	semidirect
603. #552	C₂²×C₁₃	semidirect
604. #552	C₂²×C₁₃	semidirect
605. #544	C₂²×C₁₃	semidirect
606. #544	C₂²×C₁₃	semidirect
607. #542	C₂²×C₁₃	semidirect
608. #542	C₂²×C₁₃	semidirect
609. #542	C₂²×C₁₃	semidirect
610. #542	C₂²×C₁₃	semidirect
611. #541	C₂²×C₁₃	semidirect
612. #539	C₂²×C₁₃	semidirect
613. #533	C₂²×C₁₃	semidirect
621. #529	C₂²×C₁₃	semidirect
622. #529	C₂²×C₁₃	semidirect
956. C₂×C₁₃	#3565	direct (N × H)
1105. C₁₃	C₂×#3565	direct (N × H)
1227. C₂	C₁₃×#3565	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×#3565	2
C₂×C₁₃×#563	2
C₂×C₁₃×#562	2
C₂×C₁₃×#557	2
C₂×C₁₃×#556	2
C₂×C₁₃×#555	2
C₂×C₁₃×#554	2
C₂×C₁₃×#553	2
C₂×C₁₃×#552	2
C₂×C₁₃×#544	2
C₂×C₁₃×#542	2
C₂×C₁₃×#541	2
C₂×C₁₃×#539	2
C₂×C₁₃×#533	2
C₂×C₁₃×#529	2
C₂×#3565	13

Subgroups — C2×C13×#3565 #15749080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3565 #15749080