Subgroups — C₁₃×#61706 #15748045

Order 3328.

2022 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3345	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3343	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3308	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3306	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3238	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3194	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3114	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3092	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	—	2	1	no	—
17	C₁₃×#553	—	2	2	no	—
18	C₁₃×#553	C₂²	1	2	yes	complemented
19	C₁₃×#552	C₂²	1	2	yes	complemented
20	C₁₃×#551	—	2	2	no	—
21	C₁₃×#548	C₂²	1	2	yes	complemented
22	C₁₃×#547	—	2	2	no	—
23	C₁₃×#547	—	2	2	no	—
24	C₁₃×#547	C₂²	1	4	yes	—
25	C₁₃×#547	C₂²	1	4	yes	complemented
26	C₁₃×#546	C₂²	1	2	yes	complemented
27	C₁₃×#539	—	2	1	no	—
28	C₁₃×#538	—	2	1	no	—
29	C₁₃×#534	—	2	1	no	—
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#529	C₂²	1	2	yes	—
32	C₁₃×#525	C₂²	1	2	yes	—
33	C₂×C₁₃×#123	—	2	1	no	—
34	C₂×C₁₃×#123	—	2	1	no	—
35	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#518	—	2	1	no	—
41	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#501	C₂²	1	4	yes	complemented
46	C₁₃×#489	C₂²	1	4	yes	complemented
47	C₁₃×#484	C₂²	1	4	yes	complemented
48	C₁₃×#483	C₂²	1	4	yes	complemented
49	C₁₃×#483	C₂²	1	2	yes	complemented
50	C₁₃×#483	C₂²	1	2	yes	complemented
51	C₁₃×#483	C₂²	1	2	yes	complemented
52	C₁₃×#482	C₂²	1	4	yes	complemented
53	C₁₃×#481	C₂²	1	4	yes	complemented
54	C₁₃×#481	C₂²	1	2	yes	complemented
55	C₁₃×#480	C₂²	1	2	yes	—
56	C₁₃×#480	C₂²	1	2	yes	—
57	C₁₃×#480	C₂²	1	2	yes	—
58	C₁₃×#480	C₂²	1	4	yes	complemented
59	C₁₃×#480	C₂²	1	2	yes	complemented
60	C₁₃×#478	C₂²	1	4	yes	complemented
61	C₁₃×#477	C₂²	1	4	yes	complemented
62	C₁₃×#476	C₂²	1	4	yes	complemented
63	C₁₃×#469	C₂²	1	4	yes	complemented
64	C₁₃×#468	C₂²	1	4	yes	complemented
65	C₁₃×#466	C₂²	1	4	yes	complemented
66	C₁₃×#465	C₂²	1	4	yes	complemented
67	C₁₃×#463	C₂²	1	4	yes	complemented
68	C₁₃×#450	C₂²	1	2	yes	complemented
69	C₁₃×#449	C₂²	1	4	yes	complemented
70	C₁₃×#448	C₂²	1	2	yes	complemented
71	C₁₃×#447	C₂²	1	2	yes	—
72	C₁₃×#447	C₂²	1	2	yes	complemented
73	C₁₃×#442	C₂²	1	4	yes	complemented
74	C₁₃×#440	C₂²	1	4	yes	complemented
75	C₁₃×#435	C₂²	1	4	yes	complemented
76	C₁₃×#435	C₂²	1	4	yes	complemented
77	C₁₃×#432	C₂²	1	2	yes	complemented
78	C₁₃×#428	C₂²	1	4	yes	complemented
79	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
80	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
81	C₁₃×#417	C₂²	1	4	yes	complemented
82	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
83	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
84	C₁₃×#407	C₂²	1	2	yes	complemented
85	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
87	C₂×C₁₃×#41	—	2	4	no	—
88	C₂×C₁₃×#41	—	2	4	no	—
89	C₂×C₁₃×#41	—	4	8	no	—
90	C₂×C₁₃×#41	C₂³	1	2	yes	—
91	C₂²×Q₈×C₁₃	—	2	1	no	—
92	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	—	2	1	no	—
94	C₂²×D₄×C₁₃	—	2	1	no	—
95	C₂²×D₄×C₁₃	—	2	1	no	—
96	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃	—	2	1	no	—
100	C₂³×C₄×C₁₃	—	2	1	no	—
101	C₂³×C₄×C₁₃	—	2	1	no	—
102	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×D₈	C₂³	1	4	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
107	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
111	C₁₃×#126	—	2	2	no	—
112	C₁₃×#126	—	2	2	no	—
113	C₁₃×#126	—	2	2	no	—
114	C₁₃×#125	—	2	2	no	—
115	C₁₃×#125	C₂³	1	2	yes	—
116	C₁₃×#124	—	2	2	no	—
117	C₁₃×#124	C₂³	1	2	yes	—
118	C₁₃×#123	—	2	2	no	—
119	C₁₃×#123	—	2	2	no	—
120	C₁₃×#123	—	2	2	no	—
121	C₁₃×#123	—	2	2	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×#123	—	2	4	no	—
124	C₁₃×#123	—	2	4	no	—
125	C₁₃×#123	—	2	4	no	—
126	C₁₃×#123	—	2	2	no	—
127	C₁₃×C₂²⋊Q₈	—	2	1	no	—
128	C₁₃×C₂²⋊Q₈	—	2	1	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	2	no	—
132	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×#121	—	2	2	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	1	no	—
138	C₁₃×#121	—	2	1	no	—
139	C₁₃×#121	—	2	1	no	—
140	C₁₃×#121	—	2	1	no	—
141	C₁₃×#121	—	2	2	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	C₂³	1	2	yes	—
144	C₁₃×#121	C₂³	1	2	yes	—
145	C₁₃×#121	C₂³	1	2	yes	—
146	C₁₃×#121	C₂³	1	4	yes	—
147	C₁₃×#121	C₂³	1	2	yes	—
148	C₁₃×#121	C₂³	1	2	yes	—
149	C₁₃×#120	—	2	2	no	—
150	C₁₃×#120	—	2	2	no	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×D₄×C₁₃	—	2	2	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	—	2	2	no	—
155	C₄×D₄×C₁₃	—	2	2	no	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	2	no	—
158	C₄×D₄×C₁₃	D₄	1	2	yes	—
159	C₄×D₄×C₁₃	D₄	1	2	yes	—
160	C₄×D₄×C₁₃	C₂³	1	4	yes	—
161	C₄×D₄×C₁₃	C₂³	1	2	yes	—
162	C₄×D₄×C₁₃	C₂³	1	2	yes	—
163	C₄×D₄×C₁₃	C₂³	1	2	yes	—
164	C₁₃×#117	—	2	2	no	—
165	C₁₃×#117	—	2	2	no	—
166	C₁₃×#117	C₂³	1	2	yes	—
167	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
188	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
189	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
190	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
192	C₁₃×#107	C₂³	1	4	yes	—
193	C₁₃×#107	C₂³	1	4	yes	—
194	C₁₃×#107	C₂³	1	4	yes	—
195	C₁₃×#106	C₂³	1	4	yes	—
196	C₁₃×#106	C₂³	1	4	yes	—
197	C₁₃×#106	C₂³	1	4	yes	—
198	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
199	C₁₃×#103	C₂³	1	4	yes	—
200	C₁₃×#103	C₂³	1	4	yes	—
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#102	C₂³	1	4	yes	—
203	C₁₃×#102	C₂³	1	4	yes	—
204	C₁₃×#102	C₂³	1	4	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
209	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
210	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
212	C₁₃×#97	C₂³	1	4	yes	—
213	#61706	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂⁴×C₁₃	—	2	1	no	—
215	C₂⁴×C₁₃	—	2	1	no	—
216	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₁₃×#41	—	4	4	no	—
219	C₁₃×#41	—	4	16	no	—
220	C₁₃×#41	—	4	16	no	—
221	C₂×Q₈×C₁₃	—	2	4	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	4	4	no	—
224	C₂×Q₈×C₁₃	—	4	2	no	—
225	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₁₃	—	2	4	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	2	no	—
229	C₂×D₄×C₁₃	—	2	4	no	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	2	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	1	no	—
236	C₂×D₄×C₁₃	—	4	2	no	—
237	C₂×D₄×C₁₃	—	4	2	no	—
238	C₂×D₄×C₁₃	—	4	4	no	—
239	C₂×D₄×C₁₃	—	4	4	no	—
240	C₂×D₄×C₁₃	—	4	4	no	—
241	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
242	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
243	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	4	no	—
250	C₂²×C₄×C₁₃	—	2	2	no	—
251	C₂²×C₄×C₁₃	—	2	2	no	—
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	4	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	4	2	no	—
258	C₂²×C₄×C₁₃	—	4	2	no	—
259	C₂²×C₄×C₁₃	—	4	4	no	—
260	C₂²×C₄×C₁₃	—	4	4	no	—
261	C₂²×C₄×C₁₃	—	4	4	no	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₁₃×SD₁₆	—	4	4	no	—
274	C₁₃×D₈	—	4	4	no	—
275	C₁₃×M₁₆	—	4	4	no	—
276	C₂×C₈×C₁₃	—	4	2	no	—
277	C₂×C₈×C₁₃	—	4	2	no	—
278	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
279	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
280	C₁₃×C₄⋊C₄	—	2	1	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	—	2	4	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	2	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	4	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
296	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
297	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
298	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₁₃×C₂²⋊C₄	—	2	2	no	—
303	C₁₃×C₂²⋊C₄	—	2	2	no	—
304	C₁₃×C₂²⋊C₄	—	2	2	no	—
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
317	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
318	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
319	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
320	C₄²×C₁₃	—	2	2	no	—
321	C₄²×C₁₃	—	2	2	no	—
322	C₄²×C₁₃	C₂×D₄	1	2	yes	—
323	C₄²×C₁₃	C₂⁴	1	2	yes	—
324	#3505	C₂×C₁₃	1	1	yes	characteristic, complemented
325	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
326	#3345	C₂×C₁₃	1	4	yes	complemented
327	#3343	C₂×C₁₃	1	4	yes	complemented
328	#3308	C₂×C₁₃	1	4	yes	complemented
329	#3306	C₂×C₁₃	1	4	yes	complemented
330	#3238	C₂×C₁₃	1	2	yes	complemented
331	#3194	C₂×C₁₃	1	2	yes	complemented
332	#3187	C₂×C₁₃	1	1	yes	characteristic, complemented
333	#3186	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#3114	C₂×C₁₃	1	2	yes	complemented
335	#3092	C₂×C₁₃	1	2	yes	complemented
336	C₂×#483	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#480	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#2973	C₂×C₁₃	1	1	yes	characteristic, complemented
339	C₂³×C₁₃	—	2	2	no	—
340	C₂³×C₁₃	—	2	2	no	—
341	C₂³×C₁₃	—	2	2	no	—
342	C₂³×C₁₃	—	4	1	no	—
343	C₂³×C₁₃	—	4	1	no	—
344	C₂³×C₁₃	—	4	1	no	—
345	C₂³×C₁₃	—	4	1	no	—
346	C₂³×C₁₃	—	4	2	no	—
347	C₂³×C₁₃	—	4	2	no	—
348	C₂³×C₁₃	—	4	2	no	—
349	C₂³×C₁₃	—	4	2	no	—
350	C₂³×C₁₃	—	8	1	no	—
351	C₂³×C₁₃	—	8	1	no	—
352	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
353	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
354	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
355	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
357	Q₈×C₁₃	—	2	4	no	—
358	Q₈×C₁₃	—	4	8	no	—
359	Q₈×C₁₃	—	8	1	no	—
360	D₄×C₁₃	—	2	4	no	—
361	D₄×C₁₃	—	2	4	no	—
362	D₄×C₁₃	—	2	4	no	—
363	D₄×C₁₃	—	2	4	no	—
364	D₄×C₁₃	—	4	2	no	—
365	D₄×C₁₃	—	4	8	no	—
366	D₄×C₁₃	—	4	4	no	—
367	D₄×C₁₃	—	4	4	no	—
368	D₄×C₁₃	—	4	4	no	—
369	D₄×C₁₃	—	4	4	no	—
370	D₄×C₁₃	—	8	1	no	—
371	D₄×C₁₃	—	8	2	no	—
372	D₄×C₁₃	—	8	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	4	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	4	2	no	—
385	C₂×C₄×C₁₃	—	4	1	no	—
386	C₂×C₄×C₁₃	—	4	1	no	—
387	C₂×C₄×C₁₃	—	4	1	no	—
388	C₂×C₄×C₁₃	—	4	1	no	—
389	C₂×C₄×C₁₃	—	4	1	no	—
390	C₂×C₄×C₁₃	—	4	8	no	—
391	C₂×C₄×C₁₃	—	4	8	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	4	2	no	—
395	C₂×C₄×C₁₃	—	4	4	no	—
396	C₂×C₄×C₁₃	—	4	4	no	—
397	C₂×C₄×C₁₃	—	4	2	no	—
398	C₂×C₄×C₁₃	—	8	2	no	—
399	C₂×C₄×C₁₃	—	8	2	no	—
400	C₂×C₄×C₁₃	—	8	1	no	—
401	C₂×C₄×C₁₃	—	8	1	no	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
409	C₈×C₁₃	—	2	4	no	—
410	C₈×C₁₃	—	2	4	no	—
411	C₂²×#41	—	2	1	no	—
412	#553	—	2	2	no	—
413	#553	C₂²×C₁₃	1	2	yes	complemented
414	#552	C₂²×C₁₃	1	2	yes	complemented
415	#551	—	2	2	no	—
416	#548	C₂²×C₁₃	1	2	yes	complemented
417	#547	—	2	2	no	—
418	#547	—	2	2	no	—
419	#547	C₂²×C₁₃	1	4	yes	—
420	#547	C₂²×C₁₃	1	4	yes	complemented
421	#546	C₂²×C₁₃	1	2	yes	complemented
422	#539	—	2	1	no	—
423	#538	—	2	1	no	—
424	#534	—	2	1	no	—
425	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	#529	C₂²×C₁₃	1	2	yes	—
427	#525	C₂²×C₁₃	1	2	yes	—
428	C₂×#123	—	2	1	no	—
429	C₂×#123	—	2	1	no	—
430	C₂×C₂²⋊Q₈	—	2	1	no	—
431	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
434	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	#518	—	2	1	no	—
436	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
439	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
440	#501	C₂²×C₁₃	1	4	yes	complemented
441	#489	C₂²×C₁₃	1	4	yes	complemented
442	#484	C₂²×C₁₃	1	4	yes	complemented
443	#483	C₂²×C₁₃	1	4	yes	complemented
444	#483	C₂²×C₁₃	1	2	yes	complemented
445	#483	C₂²×C₁₃	1	2	yes	complemented
446	#483	C₂²×C₁₃	1	2	yes	complemented
447	#482	C₂²×C₁₃	1	4	yes	complemented
448	#481	C₂²×C₁₃	1	2	yes	complemented
449	#481	C₂²×C₁₃	1	4	yes	complemented
450	#480	C₂²×C₁₃	1	2	yes	—
451	#480	C₂²×C₁₃	1	2	yes	—
452	#480	C₂²×C₁₃	1	2	yes	—
453	#480	C₂²×C₁₃	1	4	yes	complemented
454	#480	C₂²×C₁₃	1	2	yes	complemented
455	#478	C₂²×C₁₃	1	4	yes	complemented
456	#477	C₂²×C₁₃	1	4	yes	complemented
457	#476	C₂²×C₁₃	1	4	yes	complemented
458	#469	C₂²×C₁₃	1	4	yes	complemented
459	#468	C₂²×C₁₃	1	4	yes	complemented
460	#466	C₂²×C₁₃	1	4	yes	complemented
461	#465	C₂²×C₁₃	1	4	yes	complemented
462	#463	C₂²×C₁₃	1	4	yes	complemented
463	#450	C₂²×C₁₃	1	2	yes	complemented
464	#449	C₂²×C₁₃	1	4	yes	complemented
465	#448	C₂²×C₁₃	1	2	yes	complemented
466	#447	C₂²×C₁₃	1	2	yes	—
467	#447	C₂²×C₁₃	1	2	yes	complemented
468	#442	C₂²×C₁₃	1	4	yes	complemented
469	#440	C₂²×C₁₃	1	4	yes	complemented
470	#435	C₂²×C₁₃	1	4	yes	complemented
471	#435	C₂²×C₁₃	1	4	yes	complemented
472	#432	C₂²×C₁₃	1	2	yes	complemented
473	#428	C₂²×C₁₃	1	4	yes	complemented
474	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
475	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
476	#417	C₂²×C₁₃	1	4	yes	complemented
477	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
478	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
479	#407	C₂²×C₁₃	1	2	yes	complemented
480	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
481	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
482	C₂²×C₁₃	—	2	1	no	—
483	C₂²×C₁₃	—	2	1	no	—
484	C₂²×C₁₃	—	2	1	no	—
485	C₂²×C₁₃	—	2	1	no	—
486	C₂²×C₁₃	—	2	1	no	—
487	C₂²×C₁₃	—	2	1	no	—
488	C₂²×C₁₃	—	2	2	no	—
489	C₂²×C₁₃	—	2	2	no	—
490	C₂²×C₁₃	—	2	2	no	—
491	C₂²×C₁₃	—	4	4	no	—
492	C₂²×C₁₃	—	4	4	no	—
493	C₂²×C₁₃	—	4	2	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	4	2	no	—
496	C₂²×C₁₃	—	4	2	no	—
497	C₂²×C₁₃	—	4	2	no	—
498	C₂²×C₁₃	—	4	2	no	—
499	C₂²×C₁₃	—	8	4	no	—
500	C₂²×C₁₃	—	16	2	no	—
501	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
502	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
503	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
504	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
505	C₄×C₁₃	—	2	2	no	—
506	C₄×C₁₃	—	2	1	no	—
507	C₄×C₁₃	—	2	2	no	—
508	C₄×C₁₃	—	2	1	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	4	2	no	—
512	C₄×C₁₃	—	4	2	no	—
513	C₄×C₁₃	—	4	2	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₄×C₁₃	—	4	2	no	—
516	C₄×C₁₃	—	4	2	no	—
517	C₄×C₁₃	#585	1	2	yes	—
518	C₂×#41	—	2	4	no	—
519	C₂×#41	—	2	4	no	—
520	C₂×#41	—	4	8	no	—
521	C₂×#41	C₂³×C₁₃	1	2	yes	—
522	C₂²×Q₈	—	2	1	no	—
523	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	—	2	1	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
530	C₂³×C₄	—	2	1	no	—
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	—	2	1	no	—
533	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
536	C₂×D₈	C₂³×C₁₃	1	4	yes	—
537	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
538	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
539	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
542	#126	—	2	2	no	—
543	#126	—	2	2	no	—
544	#126	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	C₂³×C₁₃	1	2	yes	—
547	#124	—	2	2	no	—
548	#124	C₂³×C₁₃	1	2	yes	—
549	#123	—	2	2	no	—
550	#123	—	2	2	no	—
551	#123	—	2	2	no	—
552	#123	—	2	2	no	—
553	#123	—	2	4	no	—
554	#123	—	2	4	no	—
555	#123	—	2	4	no	—
556	#123	—	2	4	no	—
557	#123	—	2	2	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	4	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
564	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
565	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
566	#121	—	2	2	no	—
567	#121	—	2	2	no	—
568	#121	—	2	1	no	—
569	#121	—	2	1	no	—
570	#121	—	2	1	no	—
571	#121	—	2	1	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	C₂³×C₁₃	1	2	yes	—
575	#121	C₂³×C₁₃	1	2	yes	—
576	#121	C₂³×C₁₃	1	2	yes	—
577	#121	C₂³×C₁₃	1	2	yes	—
578	#121	C₂³×C₁₃	1	4	yes	—
579	#121	C₂³×C₁₃	1	2	yes	—
580	#120	—	2	2	no	—
581	#120	—	2	2	no	—
582	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	D₄×C₁₃	1	2	yes	—
590	C₄×D₄	D₄×C₁₃	1	2	yes	—
591	C₄×D₄	C₂³×C₁₃	1	4	yes	—
592	C₄×D₄	C₂³×C₁₃	1	2	yes	—
593	C₄×D₄	C₂³×C₁₃	1	2	yes	—
594	C₄×D₄	C₂³×C₁₃	1	2	yes	—
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	C₂³×C₁₃	1	2	yes	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	2	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
612	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	2	no	—
620	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
623	#107	C₂³×C₁₃	1	4	yes	—
624	#107	C₂³×C₁₃	1	4	yes	—
625	#107	C₂³×C₁₃	1	4	yes	—
626	#106	C₂³×C₁₃	1	4	yes	—
627	#106	C₂³×C₁₃	1	4	yes	—
628	#106	C₂³×C₁₃	1	4	yes	—
629	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
630	#103	C₂³×C₁₃	1	4	yes	—
631	#103	C₂³×C₁₃	1	4	yes	—
632	#103	C₂³×C₁₃	1	4	yes	—
633	#102	C₂³×C₁₃	1	4	yes	—
634	#102	C₂³×C₁₃	1	4	yes	—
635	#102	C₂³×C₁₃	1	4	yes	—
636	#102	C₂³×C₁₃	1	4	yes	—
637	#102	C₂³×C₁₃	1	4	yes	—
638	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
639	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
640	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
641	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
642	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
643	#97	C₂³×C₁₃	1	4	yes	—
644	C₂×C₁₃	—	2	2	no	—
645	C₂×C₁₃	—	2	2	no	—
646	C₂×C₁₃	—	2	2	no	—
647	C₂×C₁₃	—	4	2	no	—
648	C₂×C₁₃	—	8	2	no	—
649	C₂×C₁₃	—	8	2	no	—
650	C₂×C₁₃	#3485	1	1	yes	characteristic
651	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
652	C₂×C₁₃	#3586	1	1	yes	characteristic
653	C₂⁴	—	2	1	no	—
654	C₂⁴	—	2	1	no	—
655	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
657	#41	—	4	4	no	—
658	#41	—	4	16	no	—
659	#41	—	4	16	no	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	—	4	2	no	—
664	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	4	no	—
678	C₂×D₄	—	4	4	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
681	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
682	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
683	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	4	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	4	no	—
699	C₂²×C₄	—	4	4	no	—
700	C₂²×C₄	—	4	4	no	—
701	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
703	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
705	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
712	SD₁₆	—	4	4	no	—
713	D₈	—	4	4	no	—
714	M₁₆	—	4	4	no	—
715	C₂×C₈	—	4	2	no	—
716	C₂×C₈	—	4	2	no	—
717	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
718	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
756	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
757	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
758	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	C₂×D₄×C₁₃	1	2	yes	—
762	C₄²	C₂⁴×C₁₃	1	2	yes	—
763	C₁₃	#61706	1	1	yes	characteristic, direct product factor, Sylow
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	4	1	no	—
768	C₂³	—	4	1	no	—
769	C₂³	—	4	1	no	—
770	C₂³	—	4	1	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	2	no	—
774	C₂³	—	4	2	no	—
775	C₂³	—	8	1	no	—
776	C₂³	—	8	1	no	—
777	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
778	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
779	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
780	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
781	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
782	Q₈	—	2	4	no	—
783	Q₈	—	4	8	no	—
784	Q₈	—	8	1	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	4	no	—
788	D₄	—	2	4	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	8	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	4	no	—
795	D₄	—	8	1	no	—
796	D₄	—	8	2	no	—
797	D₄	—	8	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	4	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	8	2	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	1	no	—
826	C₂×C₄	—	8	1	no	—
827	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
833	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
834	C₈	—	2	4	no	—
835	C₈	—	2	4	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	4	4	no	—
846	C₂²	—	4	4	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	8	4	no	—
854	C₂²	—	16	2	no	—
855	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
856	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
857	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
858	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	1	no	—
864	C₄	—	2	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	C₁₃×#585	1	2	yes	—
872	C₂	—	2	2	no	—
873	C₂	—	2	2	no	—
874	C₂	—	2	2	no	—
875	C₂	—	4	2	no	—
876	C₂	—	8	2	no	—
877	C₂	—	8	2	no	—
878	C₂	C₁₃×#3485	1	1	yes	characteristic
879	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
880	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3505	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3345	C₂	semidirect
4. C₁₃×#3343	C₂	semidirect
5. C₁₃×#3308	C₂	semidirect
6. C₁₃×#3306	C₂	semidirect
7. C₁₃×#3238	C₂	semidirect
8. C₁₃×#3194	C₂	semidirect
9. C₁₃×#3187	C₂	semidirect
10. C₁₃×#3186	C₂	semidirect
11. C₁₃×#3114	C₂	semidirect
12. C₁₃×#3092	C₂	semidirect
13. C₂×C₁₃×#483	C₂	semidirect
14. C₂×C₁₃×#480	C₂	semidirect
15. C₁₃×#2973	C₂	semidirect
18. C₁₃×#553	C₂²	semidirect
19. C₁₃×#552	C₂²	semidirect
21. C₁₃×#548	C₂²	semidirect
25. C₁₃×#547	C₂²	semidirect
26. C₁₃×#546	C₂²	semidirect
30. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₁₃×#121	C₂²	semidirect
42. C₂×C₄×D₄×C₁₃	C₂²	semidirect
44. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
45. C₁₃×#501	C₂²	semidirect
46. C₁₃×#489	C₂²	semidirect
47. C₁₃×#484	C₂²	semidirect
48. C₁₃×#483	C₂²	semidirect
49. C₁₃×#483	C₂²	semidirect
50. C₁₃×#483	C₂²	semidirect
51. C₁₃×#483	C₂²	semidirect
52. C₁₃×#482	C₂²	semidirect
53. C₁₃×#481	C₂²	semidirect
54. C₁₃×#481	C₂²	semidirect
58. C₁₃×#480	C₂²	semidirect
59. C₁₃×#480	C₂²	semidirect
60. C₁₃×#478	C₂²	semidirect
61. C₁₃×#477	C₂²	semidirect
62. C₁₃×#476	C₂²	semidirect
63. C₁₃×#469	C₂²	semidirect
64. C₁₃×#468	C₂²	semidirect
65. C₁₃×#466	C₂²	semidirect
66. C₁₃×#465	C₂²	semidirect
67. C₁₃×#463	C₂²	semidirect
68. C₁₃×#450	C₂²	semidirect
69. C₁₃×#449	C₂²	semidirect
70. C₁₃×#448	C₂²	semidirect
72. C₁₃×#447	C₂²	semidirect
73. C₁₃×#442	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₁₃×#435	C₂²	semidirect
76. C₁₃×#435	C₂²	semidirect
77. C₁₃×#432	C₂²	semidirect
78. C₁₃×#428	C₂²	semidirect
79. C₂×C₁₃×#107	C₂²	semidirect
80. C₂×C₁₃×#106	C₂²	semidirect
81. C₁₃×#417	C₂²	semidirect
82. C₂×C₁₃×#103	C₂²	semidirect
83. C₂×C₁₃×#102	C₂²	semidirect
84. C₁₃×#407	C₂²	semidirect
213. #61706	C₁₃	direct (N × H)
324. #3505	C₂×C₁₃	semidirect
325. C₂×#547	C₂×C₁₃	semidirect
326. #3345	C₂×C₁₃	semidirect
327. #3343	C₂×C₁₃	semidirect
328. #3308	C₂×C₁₃	semidirect
329. #3306	C₂×C₁₃	semidirect
330. #3238	C₂×C₁₃	semidirect
331. #3194	C₂×C₁₃	semidirect
332. #3187	C₂×C₁₃	semidirect
333. #3186	C₂×C₁₃	semidirect
334. #3114	C₂×C₁₃	semidirect
335. #3092	C₂×C₁₃	semidirect
336. C₂×#483	C₂×C₁₃	semidirect
337. C₂×#480	C₂×C₁₃	semidirect
338. #2973	C₂×C₁₃	semidirect
413. #553	C₂²×C₁₃	semidirect
414. #552	C₂²×C₁₃	semidirect
416. #548	C₂²×C₁₃	semidirect
420. #547	C₂²×C₁₃	semidirect
421. #546	C₂²×C₁₃	semidirect
425. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
434. C₂×#121	C₂²×C₁₃	semidirect
437. C₂×C₄×D₄	C₂²×C₁₃	semidirect
439. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
440. #501	C₂²×C₁₃	semidirect
441. #489	C₂²×C₁₃	semidirect
442. #484	C₂²×C₁₃	semidirect
443. #483	C₂²×C₁₃	semidirect
444. #483	C₂²×C₁₃	semidirect
445. #483	C₂²×C₁₃	semidirect
446. #483	C₂²×C₁₃	semidirect
447. #482	C₂²×C₁₃	semidirect
448. #481	C₂²×C₁₃	semidirect
449. #481	C₂²×C₁₃	semidirect
453. #480	C₂²×C₁₃	semidirect
454. #480	C₂²×C₁₃	semidirect
455. #478	C₂²×C₁₃	semidirect
456. #477	C₂²×C₁₃	semidirect
457. #476	C₂²×C₁₃	semidirect
458. #469	C₂²×C₁₃	semidirect
459. #468	C₂²×C₁₃	semidirect
460. #466	C₂²×C₁₃	semidirect
461. #465	C₂²×C₁₃	semidirect
462. #463	C₂²×C₁₃	semidirect
463. #450	C₂²×C₁₃	semidirect
464. #449	C₂²×C₁₃	semidirect
465. #448	C₂²×C₁₃	semidirect
467. #447	C₂²×C₁₃	semidirect
468. #442	C₂²×C₁₃	semidirect
469. #440	C₂²×C₁₃	semidirect
470. #435	C₂²×C₁₃	semidirect
471. #435	C₂²×C₁₃	semidirect
472. #432	C₂²×C₁₃	semidirect
473. #428	C₂²×C₁₃	semidirect
474. C₂×#107	C₂²×C₁₃	semidirect
475. C₂×#106	C₂²×C₁₃	semidirect
476. #417	C₂²×C₁₃	semidirect
477. C₂×#103	C₂²×C₁₃	semidirect
478. C₂×#102	C₂²×C₁₃	semidirect
479. #407	C₂²×C₁₃	semidirect
763. C₁₃	#61706	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×#3505	2
C₂×C₁₃×#547	2
C₁₃×#3345	2
C₁₃×#3343	2
C₁₃×#3308	2
C₁₃×#3306	2
C₁₃×#3238	2
C₁₃×#3194	2
C₁₃×#3187	2
C₁₃×#3186	2
C₁₃×#3114	2
C₁₃×#3092	2
C₂×C₁₃×#483	2
C₂×C₁₃×#480	2
C₁₃×#2973	2
#61706	13

Subgroups — C13×#61706 #15748045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61706 #15748045