Subgroups — C₂×C₁₃×#3547 #15749089

Order 3328.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3547	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#562	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#555	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#553	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#552	C₂	1	2	yes	maximal, complemented
8	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#548	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#544	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#542	C₂	1	4	yes	maximal, complemented
13	C₂×C₁₃×#540	C₂	1	2	yes	maximal, complemented
14	C₂×C₁₃×#537	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#536	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	2	yes	—
20	C₂²×C₁₃×#41	C₂²	1	2	yes	—
21	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#562	C₂²	1	64	yes	complemented
23	C₁₃×#555	C₂²	1	32	yes	complemented
24	C₁₃×#555	C₂²	1	16	yes	complemented
25	C₁₃×#554	C₂²	1	16	yes	complemented
26	C₁₃×#553	C₂²	1	32	yes	complemented
27	C₁₃×#552	C₂²	1	32	yes	complemented
28	D₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
29	C₁₃×#548	C₂²	1	32	yes	complemented
30	C₁₃×#547	C₂²	1	16	yes	complemented
31	C₁₃×#544	C₂²	1	32	yes	complemented
32	C₁₃×#542	C₂²	1	64	yes	complemented
33	C₁₃×#540	C₂²	1	32	yes	complemented
34	C₁₃×#537	C₂²	1	32	yes	complemented
35	C₁₃×#536	C₂²	1	32	yes	complemented
36	C₁₃×#533	C₂²	1	16	yes	complemented
37	C₁₃×#532	C₂²	1	16	yes	complemented
38	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
42	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
43	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
44	C₁₃×#529	C₂²	1	16	yes	complemented
45	C₂×C₁₃×#126	C₂²	1	2	yes	—
46	C₂×C₁₃×#126	C₂²	1	4	yes	—
47	C₂×C₁₃×#125	C₂²	1	4	yes	—
48	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#125	C₂²	1	2	yes	—
50	C₂×C₁₃×#125	C₂²	1	2	yes	—
51	C₂×C₁₃×#124	C₂²	1	4	yes	—
52	C₂×C₁₃×#124	C₂²	1	4	yes	—
53	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#124	C₂²	1	2	yes	—
55	C₂×C₁₃×#124	C₂²	1	4	yes	—
56	C₂×C₁₃×#123	C₂²	1	2	yes	—
57	C₂×C₁₃×#123	C₂²	1	4	yes	—
58	C₂×C₁₃×#123	C₂²	1	4	yes	—
59	C₂×C₁₃×#123	C₂²	1	4	yes	—
60	C₂×C₁₃×#123	C₂²	1	4	yes	—
61	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
62	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
63	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
64	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
65	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
67	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
68	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
69	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
70	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
71	C₂×C₁₃×#121	C₂²	1	2	yes	—
72	C₂×C₁₃×#121	C₂²	1	4	yes	—
73	C₂×C₁₃×#121	C₂²	1	4	yes	—
74	C₂×C₁₃×#121	C₂²	1	4	yes	—
75	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
76	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
77	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
78	C₂×C₁₃×#121	C₂²	1	4	yes	—
79	C₂×C₁₃×#121	C₂²	1	2	yes	—
80	C₂×C₁₃×#121	C₂²	1	2	yes	—
81	C₂×C₁₃×#121	C₂²	1	2	yes	—
82	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
83	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
84	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
85	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
86	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
87	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
88	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
89	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
90	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
91	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
92	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
93	C₂×C₁₃×#117	C₂²	1	2	yes	—
94	C₂×C₁₃×#117	C₂²	1	2	yes	—
95	C₂×C₁₃×#117	C₂²	1	2	yes	—
96	C₂×C₁₃×#117	C₂²	1	4	yes	—
97	C₂×C₁₃×#117	C₂²	1	2	yes	—
98	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
99	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
100	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
101	C₂×C₁₃×#41	—	4	8	no	—
102	C₂×C₁₃×#41	—	4	8	no	—
103	C₂×C₁₃×#41	C₂³	1	16	yes	—
104	C₂×C₁₃×#41	C₂³	1	16	yes	—
105	C₂²×Q₈×C₁₃	—	4	8	no	—
106	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
110	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
111	C₂²×Q₈×C₁₃	C₂³	1	16	yes	—
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
119	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
120	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
121	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
129	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
130	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
131	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
132	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
133	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	32	yes	—
135	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
136	C₁₃×#127	C₂³	1	8	yes	—
137	C₁₃×#126	C₂³	1	16	yes	—
138	C₁₃×#126	C₂³	1	32	yes	—
139	C₁₃×#125	C₂³	1	8	yes	—
140	C₁₃×#125	C₂³	1	16	yes	—
141	C₁₃×#125	C₂³	1	32	yes	—
142	C₁₃×#125	C₂³	1	16	yes	—
143	C₁₃×#124	C₂³	1	8	yes	—
144	C₁₃×#124	C₂³	1	16	yes	—
145	C₁₃×#124	C₂³	1	32	yes	—
146	C₁₃×#124	C₂³	1	32	yes	—
147	C₁₃×#124	C₂³	1	32	yes	—
148	C₁₃×#123	C₂³	1	16	yes	—
149	C₁₃×#123	C₂³	1	32	yes	—
150	C₁₃×#123	C₂³	1	32	yes	—
151	C₁₃×#123	C₂³	1	32	yes	—
152	C₁₃×#123	C₂³	1	32	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
157	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
158	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
159	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
160	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
161	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
162	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
163	C₁₃×#121	C₂³	1	8	yes	—
164	C₁₃×#121	C₂³	1	8	yes	—
165	C₁₃×#121	C₂³	1	8	yes	—
166	C₁₃×#121	C₂³	1	16	yes	—
167	C₁₃×#121	C₂³	1	32	yes	—
168	C₁₃×#121	C₂³	1	16	yes	—
169	C₁₃×#121	C₂³	1	32	yes	—
170	C₁₃×#121	C₂³	1	32	yes	—
171	C₁₃×#121	C₂³	1	16	yes	—
172	C₁₃×#121	C₂³	1	32	yes	—
173	C₁₃×#121	C₂³	1	16	yes	—
174	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
175	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
177	C₄×D₄×C₁₃	C₂³	1	8	yes	—
178	C₄×D₄×C₁₃	C₂³	1	16	yes	—
179	C₄×D₄×C₁₃	C₂³	1	8	yes	—
180	C₄×D₄×C₁₃	C₂³	1	16	yes	—
181	C₄×D₄×C₁₃	C₂³	1	8	yes	—
182	C₄×D₄×C₁₃	C₂³	1	16	yes	—
183	C₄×D₄×C₁₃	C₂³	1	16	yes	—
184	C₄×D₄×C₁₃	C₂³	1	32	yes	—
185	C₁₃×#117	C₂³	1	16	yes	—
186	C₁₃×#117	C₂³	1	16	yes	—
187	C₁₃×#117	C₂³	1	16	yes	—
188	C₁₃×#117	C₂³	1	32	yes	—
189	C₁₃×#117	C₂³	1	16	yes	—
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
207	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
209	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
211	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
214	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
216	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
218	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
223	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
231	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
232	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
233	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
234	C₂×#3547	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
236	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
238	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
239	C₁₃×#41	—	4	32	no	—
240	C₁₃×#41	—	4	32	no	—
241	C₂×Q₈×C₁₃	—	2	4	no	—
242	C₂×Q₈×C₁₃	—	2	8	no	—
243	C₂×Q₈×C₁₃	—	4	8	no	—
244	C₂×Q₈×C₁₃	—	4	4	no	—
245	C₂×Q₈×C₁₃	—	4	4	no	—
246	C₂×Q₈×C₁₃	—	4	32	no	—
247	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
249	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
250	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
251	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
252	C₂×D₄×C₁₃	—	2	4	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	4	4	no	—
256	C₂×D₄×C₁₃	—	4	4	no	—
257	C₂×D₄×C₁₃	—	4	8	no	—
258	C₂×D₄×C₁₃	—	4	4	no	—
259	C₂×D₄×C₁₃	—	4	4	no	—
260	C₂×D₄×C₁₃	—	4	4	no	—
261	C₂×D₄×C₁₃	—	4	8	no	—
262	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
263	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
264	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
265	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
266	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
267	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
268	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
269	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
270	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
271	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
272	C₂²×C₄×C₁₃	—	2	8	no	—
273	C₂²×C₄×C₁₃	—	2	8	no	—
274	C₂²×C₄×C₁₃	—	2	4	no	—
275	C₂²×C₄×C₁₃	—	2	4	no	—
276	C₂²×C₄×C₁₃	—	2	8	no	—
277	C₂²×C₄×C₁₃	—	4	8	no	—
278	C₂²×C₄×C₁₃	—	4	2	no	—
279	C₂²×C₄×C₁₃	—	4	8	no	—
280	C₂²×C₄×C₁₃	—	4	8	no	—
281	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
284	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
285	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
286	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
298	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
301	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
322	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
323	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
324	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
325	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
326	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
327	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
328	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
329	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
330	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
331	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
332	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
334	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
335	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
336	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
337	C₄²×C₁₃	C₂⁴	1	4	yes	—
338	C₄²×C₁₃	C₂⁴	1	4	yes	—
339	C₄²×C₁₃	C₂⁴	1	4	yes	—
340	C₄²×C₁₃	C₂⁴	1	4	yes	—
341	C₄²×C₁₃	C₂⁴	1	16	yes	—
342	C₄²×C₁₃	C₂⁴	1	16	yes	—
343	C₄²×C₁₃	C₂⁴	1	8	yes	—
344	#3547	C₂×C₁₃	1	32	yes	direct product factor
345	C₂×#562	C₂×C₁₃	1	4	yes	complemented
346	C₂×#555	C₂×C₁₃	1	2	yes	complemented
347	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
348	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
349	C₂×#553	C₂×C₁₃	1	2	yes	complemented
350	C₂×#552	C₂×C₁₃	1	2	yes	complemented
351	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂×#548	C₂×C₁₃	1	2	yes	complemented
353	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
354	C₂×#544	C₂×C₁₃	1	2	yes	complemented
355	C₂×#542	C₂×C₁₃	1	4	yes	complemented
356	C₂×#540	C₂×C₁₃	1	2	yes	complemented
357	C₂×#537	C₂×C₁₃	1	2	yes	complemented
358	C₂×#536	C₂×C₁₃	1	2	yes	complemented
359	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
360	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
361	C₂×#529	C₂×C₁₃	1	1	yes	characteristic, complemented
362	C₂³×C₁₃	—	2	4	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	4	no	—
365	C₂³×C₁₃	—	2	4	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	4	no	—
368	C₂³×C₁₃	—	2	4	no	—
369	C₂³×C₁₃	—	2	4	no	—
370	C₂³×C₁₃	—	2	4	no	—
371	C₂³×C₁₃	—	2	2	no	—
372	C₂³×C₁₃	—	2	4	no	—
373	C₂³×C₁₃	—	2	4	no	—
374	C₂³×C₁₃	C₂⁵	1	4	yes	—
375	C₂³×C₁₃	C₂⁵	1	2	yes	—
376	C₂³×C₁₃	C₂⁵	1	4	yes	—
377	C₂³×C₁₃	C₂⁵	1	4	yes	—
378	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
379	Q₈×C₁₃	—	2	8	no	—
380	Q₈×C₁₃	—	2	16	no	—
381	Q₈×C₁₃	—	4	16	no	—
382	Q₈×C₁₃	—	4	8	no	—
383	Q₈×C₁₃	—	4	8	no	—
384	D₄×C₁₃	—	2	8	no	—
385	D₄×C₁₃	—	2	8	no	—
386	D₄×C₁₃	—	2	8	no	—
387	D₄×C₁₃	—	4	8	no	—
388	D₄×C₁₃	—	4	8	no	—
389	D₄×C₁₃	—	4	16	no	—
390	D₄×C₁₃	—	4	8	no	—
391	D₄×C₁₃	—	4	8	no	—
392	D₄×C₁₃	—	4	8	no	—
393	D₄×C₁₃	—	4	16	no	—
394	C₂×C₄×C₁₃	—	2	4	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	4	no	—
397	C₂×C₄×C₁₃	—	2	8	no	—
398	C₂×C₄×C₁₃	—	2	4	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	4	no	—
401	C₂×C₄×C₁₃	—	2	4	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	8	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	16	no	—
406	C₂×C₄×C₁₃	—	2	16	no	—
407	C₂×C₄×C₁₃	—	2	8	no	—
408	C₂×C₄×C₁₃	—	2	8	no	—
409	C₂×C₄×C₁₃	—	2	16	no	—
410	C₂×C₄×C₁₃	—	4	16	no	—
411	C₂×C₄×C₁₃	—	4	4	no	—
412	C₂×C₄×C₁₃	—	4	16	no	—
413	C₂×C₄×C₁₃	—	4	16	no	—
414	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
415	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
416	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
417	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
418	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
419	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
420	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
421	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
422	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
423	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
424	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
425	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
426	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
427	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
428	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
429	C₂²×#41	C₂²×C₁₃	1	2	yes	—
430	C₂²×#41	C₂²×C₁₃	1	2	yes	—
431	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
432	#562	C₂²×C₁₃	1	64	yes	complemented
433	#555	C₂²×C₁₃	1	32	yes	complemented
434	#555	C₂²×C₁₃	1	16	yes	complemented
435	#554	C₂²×C₁₃	1	16	yes	complemented
436	#553	C₂²×C₁₃	1	32	yes	complemented
437	#552	C₂²×C₁₃	1	32	yes	complemented
438	D₄×Q₈	C₂²×C₁₃	1	16	yes	complemented
439	#548	C₂²×C₁₃	1	32	yes	complemented
440	#547	C₂²×C₁₃	1	16	yes	complemented
441	#544	C₂²×C₁₃	1	32	yes	complemented
442	#542	C₂²×C₁₃	1	64	yes	complemented
443	#540	C₂²×C₁₃	1	32	yes	complemented
444	#537	C₂²×C₁₃	1	32	yes	complemented
445	#536	C₂²×C₁₃	1	32	yes	complemented
446	#533	C₂²×C₁₃	1	16	yes	complemented
447	#532	C₂²×C₁₃	1	16	yes	complemented
448	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
449	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
452	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
453	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
454	#529	C₂²×C₁₃	1	16	yes	complemented
455	C₂×#126	C₂²×C₁₃	1	2	yes	—
456	C₂×#126	C₂²×C₁₃	1	4	yes	—
457	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×#125	C₂²×C₁₃	1	2	yes	—
459	C₂×#125	C₂²×C₁₃	1	4	yes	—
460	C₂×#125	C₂²×C₁₃	1	2	yes	—
461	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
462	C₂×#124	C₂²×C₁₃	1	2	yes	—
463	C₂×#124	C₂²×C₁₃	1	4	yes	—
464	C₂×#124	C₂²×C₁₃	1	4	yes	—
465	C₂×#124	C₂²×C₁₃	1	4	yes	—
466	C₂×#123	C₂²×C₁₃	1	2	yes	—
467	C₂×#123	C₂²×C₁₃	1	4	yes	—
468	C₂×#123	C₂²×C₁₃	1	4	yes	—
469	C₂×#123	C₂²×C₁₃	1	4	yes	—
470	C₂×#123	C₂²×C₁₃	1	4	yes	—
471	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
473	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
474	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
475	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
476	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
477	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
478	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
479	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
480	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
481	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
482	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×#121	C₂²×C₁₃	1	2	yes	—
485	C₂×#121	C₂²×C₁₃	1	4	yes	—
486	C₂×#121	C₂²×C₁₃	1	2	yes	—
487	C₂×#121	C₂²×C₁₃	1	4	yes	—
488	C₂×#121	C₂²×C₁₃	1	4	yes	—
489	C₂×#121	C₂²×C₁₃	1	2	yes	—
490	C₂×#121	C₂²×C₁₃	1	4	yes	—
491	C₂×#121	C₂²×C₁₃	1	2	yes	—
492	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
493	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
494	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
495	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
496	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
497	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
498	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
499	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
501	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
502	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
503	C₂×#117	C₂²×C₁₃	1	2	yes	—
504	C₂×#117	C₂²×C₁₃	1	2	yes	—
505	C₂×#117	C₂²×C₁₃	1	2	yes	—
506	C₂×#117	C₂²×C₁₃	1	4	yes	—
507	C₂×#117	C₂²×C₁₃	1	2	yes	—
508	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
509	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
510	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
511	C₂²×C₁₃	—	2	4	no	—
512	C₂²×C₁₃	—	2	2	no	—
513	C₂²×C₁₃	—	2	4	no	—
514	C₂²×C₁₃	—	2	4	no	—
515	C₂²×C₁₃	—	2	2	no	—
516	C₂²×C₁₃	—	2	4	no	—
517	C₂²×C₁₃	—	2	4	no	—
518	C₂²×C₁₃	—	2	4	no	—
519	C₂²×C₁₃	—	2	4	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	4	no	—
522	C₂²×C₁₃	—	2	4	no	—
523	C₂²×C₁₃	—	4	8	no	—
524	C₂²×C₁₃	—	4	4	no	—
525	C₂²×C₁₃	—	4	8	no	—
526	C₂²×C₁₃	—	4	8	no	—
527	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
528	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
529	C₂²×C₁₃	#585	1	2	yes	—
530	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
531	C₄×C₁₃	—	2	4	no	—
532	C₄×C₁₃	—	2	2	no	—
533	C₄×C₁₃	—	2	4	no	—
534	C₄×C₁₃	—	2	8	no	—
535	C₄×C₁₃	—	2	4	no	—
536	C₄×C₁₃	—	2	2	no	—
537	C₄×C₁₃	—	2	4	no	—
538	C₄×C₁₃	—	2	4	no	—
539	C₄×C₁₃	—	2	2	no	—
540	C₄×C₁₃	—	2	8	no	—
541	C₄×C₁₃	—	2	2	no	—
542	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
543	C₄×C₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
544	C₂×#41	—	4	8	no	—
545	C₂×#41	—	4	8	no	—
546	C₂×#41	C₂³×C₁₃	1	16	yes	—
547	C₂×#41	C₂³×C₁₃	1	16	yes	—
548	C₂²×Q₈	—	4	8	no	—
549	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
550	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
551	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
552	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
553	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
554	C₂²×Q₈	C₂³×C₁₃	1	16	yes	—
555	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
559	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
560	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
561	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
562	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
563	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
564	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
565	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
566	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
567	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
569	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
571	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
572	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
573	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
574	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
575	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
576	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
577	C₄⋊Q₈	C₂³×C₁₃	1	32	yes	—
578	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
579	#127	C₂³×C₁₃	1	8	yes	—
580	#126	C₂³×C₁₃	1	16	yes	—
581	#126	C₂³×C₁₃	1	32	yes	—
582	#125	C₂³×C₁₃	1	8	yes	—
583	#125	C₂³×C₁₃	1	16	yes	—
584	#125	C₂³×C₁₃	1	32	yes	—
585	#125	C₂³×C₁₃	1	16	yes	—
586	#124	C₂³×C₁₃	1	8	yes	—
587	#124	C₂³×C₁₃	1	16	yes	—
588	#124	C₂³×C₁₃	1	32	yes	—
589	#124	C₂³×C₁₃	1	32	yes	—
590	#124	C₂³×C₁₃	1	32	yes	—
591	#123	C₂³×C₁₃	1	16	yes	—
592	#123	C₂³×C₁₃	1	32	yes	—
593	#123	C₂³×C₁₃	1	32	yes	—
594	#123	C₂³×C₁₃	1	32	yes	—
595	#123	C₂³×C₁₃	1	32	yes	—
596	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
597	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
598	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
599	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
600	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
601	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
602	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
603	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
604	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
605	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
606	#121	C₂³×C₁₃	1	8	yes	—
607	#121	C₂³×C₁₃	1	8	yes	—
608	#121	C₂³×C₁₃	1	8	yes	—
609	#121	C₂³×C₁₃	1	16	yes	—
610	#121	C₂³×C₁₃	1	32	yes	—
611	#121	C₂³×C₁₃	1	16	yes	—
612	#121	C₂³×C₁₃	1	32	yes	—
613	#121	C₂³×C₁₃	1	32	yes	—
614	#121	C₂³×C₁₃	1	16	yes	—
615	#121	C₂³×C₁₃	1	32	yes	—
616	#121	C₂³×C₁₃	1	16	yes	—
617	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
618	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
619	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
620	C₄×D₄	C₂³×C₁₃	1	8	yes	—
621	C₄×D₄	C₂³×C₁₃	1	16	yes	—
622	C₄×D₄	C₂³×C₁₃	1	8	yes	—
623	C₄×D₄	C₂³×C₁₃	1	16	yes	—
624	C₄×D₄	C₂³×C₁₃	1	8	yes	—
625	C₄×D₄	C₂³×C₁₃	1	16	yes	—
626	C₄×D₄	C₂³×C₁₃	1	16	yes	—
627	C₄×D₄	C₂³×C₁₃	1	32	yes	—
628	#117	C₂³×C₁₃	1	16	yes	—
629	#117	C₂³×C₁₃	1	16	yes	—
630	#117	C₂³×C₁₃	1	16	yes	—
631	#117	C₂³×C₁₃	1	32	yes	—
632	#117	C₂³×C₁₃	1	16	yes	—
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
639	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
640	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
641	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
650	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
651	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
669	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
670	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
671	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
673	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
677	C₂×C₁₃	—	4	4	no	—
678	C₂×C₁₃	—	4	2	no	—
679	C₂×C₁₃	—	4	4	no	—
680	C₂×C₁₃	—	4	4	no	—
681	C₂×C₁₃	#3547	1	4	yes	direct product factor
682	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
683	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
684	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
685	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
686	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
687	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
688	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
689	#41	—	4	32	no	—
690	#41	—	4	32	no	—
691	C₂×Q₈	—	2	4	no	—
692	C₂×Q₈	—	2	8	no	—
693	C₂×Q₈	—	4	8	no	—
694	C₂×Q₈	—	4	4	no	—
695	C₂×Q₈	—	4	4	no	—
696	C₂×Q₈	—	4	32	no	—
697	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
698	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
699	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
700	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
701	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	4	8	no	—
709	C₂×D₄	—	4	4	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	8	no	—
712	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
713	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
714	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
715	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
716	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
717	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
718	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
719	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
720	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
721	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
722	C₂²×C₄	—	2	8	no	—
723	C₂²×C₄	—	2	8	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	8	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	4	8	no	—
728	C₂²×C₄	—	4	8	no	—
729	C₂²×C₄	—	4	8	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
735	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
739	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
743	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
745	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
746	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
747	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
749	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
750	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
751	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
754	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
755	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
756	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
757	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
758	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
759	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
760	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
761	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
762	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
763	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
764	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
765	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
766	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
767	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
768	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
769	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
770	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
771	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
772	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
773	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
774	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
775	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
776	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
777	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
778	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
779	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
780	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
781	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
782	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
783	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
784	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
785	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
786	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
787	C₄²	C₂⁴×C₁₃	1	4	yes	—
788	C₄²	C₂⁴×C₁₃	1	4	yes	—
789	C₄²	C₂⁴×C₁₃	1	4	yes	—
790	C₄²	C₂⁴×C₁₃	1	4	yes	—
791	C₄²	C₂⁴×C₁₃	1	16	yes	—
792	C₄²	C₂⁴×C₁₃	1	16	yes	—
793	C₄²	C₂⁴×C₁₃	1	8	yes	—
794	C₁₃	C₂×#3547	1	1	yes	characteristic, direct product factor, Sylow
795	C₂³	—	2	4	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	4	no	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	4	no	—
802	C₂³	—	2	4	no	—
803	C₂³	—	2	4	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	4	no	—
806	C₂³	—	2	4	no	—
807	C₂³	C₂⁵×C₁₃	1	4	yes	—
808	C₂³	C₂⁵×C₁₃	1	2	yes	—
809	C₂³	C₂⁵×C₁₃	1	4	yes	—
810	C₂³	C₂⁵×C₁₃	1	4	yes	—
811	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
812	Q₈	—	2	8	no	—
813	Q₈	—	2	16	no	—
814	Q₈	—	4	16	no	—
815	Q₈	—	4	8	no	—
816	Q₈	—	4	8	no	—
817	D₄	—	2	8	no	—
818	D₄	—	2	8	no	—
819	D₄	—	2	8	no	—
820	D₄	—	4	8	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	16	no	—
823	D₄	—	4	8	no	—
824	D₄	—	4	8	no	—
825	D₄	—	4	8	no	—
826	D₄	—	4	16	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	8	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	8	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	16	no	—
839	C₂×C₄	—	2	16	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	8	no	—
842	C₂×C₄	—	2	16	no	—
843	C₂×C₄	—	4	16	no	—
844	C₂×C₄	—	4	4	no	—
845	C₂×C₄	—	4	16	no	—
846	C₂×C₄	—	4	16	no	—
847	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
848	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
849	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
850	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
851	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
852	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
853	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
854	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
855	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
856	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
857	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
858	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
859	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
860	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
861	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
862	C₂²	—	2	4	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	4	8	no	—
875	C₂²	—	4	4	no	—
876	C₂²	—	4	8	no	—
877	C₂²	—	4	8	no	—
878	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
879	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
880	C₂²	C₁₃×#585	1	2	yes	—
881	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
882	C₄	—	2	4	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	8	no	—
886	C₄	—	2	4	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	8	no	—
892	C₄	—	2	2	no	—
893	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
894	C₄	C₂×C₁₃×2₋¹⁺⁴	1	4	yes	—
895	C₂	—	4	4	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	4	no	—
898	C₂	—	4	4	no	—
899	C₂	C₁₃×#3547	1	4	yes	direct product factor
900	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
901	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
902	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×#3547	C₂	direct (N × H)
2. C₂×C₁₃×#562	C₂	semidirect
3. C₂×C₁₃×#555	C₂	semidirect
4. C₂×C₁₃×#555	C₂	semidirect
5. C₂×C₁₃×#554	C₂	semidirect
6. C₂×C₁₃×#553	C₂	semidirect
7. C₂×C₁₃×#552	C₂	semidirect
8. C₂×D₄×Q₈×C₁₃	C₂	semidirect
9. C₂×C₁₃×#548	C₂	semidirect
10. C₂×C₁₃×#547	C₂	semidirect
11. C₂×C₁₃×#544	C₂	semidirect
12. C₂×C₁₃×#542	C₂	semidirect
13. C₂×C₁₃×#540	C₂	semidirect
14. C₂×C₁₃×#537	C₂	semidirect
15. C₂×C₁₃×#536	C₂	semidirect
16. C₂×C₁₃×#533	C₂	semidirect
17. C₂×C₁₃×#532	C₂	semidirect
18. C₂×C₁₃×#529	C₂	semidirect
22. C₁₃×#562	C₂²	semidirect
23. C₁₃×#555	C₂²	semidirect
24. C₁₃×#555	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
26. C₁₃×#553	C₂²	semidirect
27. C₁₃×#552	C₂²	semidirect
28. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₁₃×#548	C₂²	semidirect
30. C₁₃×#547	C₂²	semidirect
31. C₁₃×#544	C₂²	semidirect
32. C₁₃×#542	C₂²	semidirect
33. C₁₃×#540	C₂²	semidirect
34. C₁₃×#537	C₂²	semidirect
35. C₁₃×#536	C₂²	semidirect
36. C₁₃×#533	C₂²	semidirect
37. C₁₃×#532	C₂²	semidirect
44. C₁₃×#529	C₂²	semidirect
234. C₂×#3547	C₁₃	direct (N × H)
344. #3547	C₂×C₁₃	direct (N × H)
345. C₂×#562	C₂×C₁₃	semidirect
346. C₂×#555	C₂×C₁₃	semidirect
347. C₂×#555	C₂×C₁₃	semidirect
348. C₂×#554	C₂×C₁₃	semidirect
349. C₂×#553	C₂×C₁₃	semidirect
350. C₂×#552	C₂×C₁₃	semidirect
351. C₂×D₄×Q₈	C₂×C₁₃	semidirect
352. C₂×#548	C₂×C₁₃	semidirect
353. C₂×#547	C₂×C₁₃	semidirect
354. C₂×#544	C₂×C₁₃	semidirect
355. C₂×#542	C₂×C₁₃	semidirect
356. C₂×#540	C₂×C₁₃	semidirect
357. C₂×#537	C₂×C₁₃	semidirect
358. C₂×#536	C₂×C₁₃	semidirect
359. C₂×#533	C₂×C₁₃	semidirect
360. C₂×#532	C₂×C₁₃	semidirect
361. C₂×#529	C₂×C₁₃	semidirect
432. #562	C₂²×C₁₃	semidirect
433. #555	C₂²×C₁₃	semidirect
434. #555	C₂²×C₁₃	semidirect
435. #554	C₂²×C₁₃	semidirect
436. #553	C₂²×C₁₃	semidirect
437. #552	C₂²×C₁₃	semidirect
438. D₄×Q₈	C₂²×C₁₃	semidirect
439. #548	C₂²×C₁₃	semidirect
440. #547	C₂²×C₁₃	semidirect
441. #544	C₂²×C₁₃	semidirect
442. #542	C₂²×C₁₃	semidirect
443. #540	C₂²×C₁₃	semidirect
444. #537	C₂²×C₁₃	semidirect
445. #536	C₂²×C₁₃	semidirect
446. #533	C₂²×C₁₃	semidirect
447. #532	C₂²×C₁₃	semidirect
454. #529	C₂²×C₁₃	semidirect
681. C₂×C₁₃	#3547	direct (N × H)
794. C₁₃	C₂×#3547	direct (N × H)
899. C₂	C₁₃×#3547	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×#3547	2
C₂×C₁₃×#562	2
C₂×C₁₃×#555	2
C₂×C₁₃×#554	2
C₂×C₁₃×#553	2
C₂×C₁₃×#552	2
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#548	2
C₂×C₁₃×#547	2
C₂×C₁₃×#544	2
C₂×C₁₃×#542	2
C₂×C₁₃×#540	2
C₂×C₁₃×#537	2
C₂×C₁₃×#536	2
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×#3547	13

Subgroups — C2×C13×#3547 #15749089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3547 #15749089