Subgroups — #16728046

Order 3328.

1872 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	#13124004	C₂	1	2	yes	maximal, complemented
3	#13124001	C₂	1	2	yes	maximal, complemented
4	#13123998	C₂	1	1	yes	maximal, characteristic, complemented
5	#13123996	C₂	1	1	yes	maximal, characteristic, complemented
6	#13123992	C₂	1	1	yes	maximal, characteristic, complemented
7	#13123988	C₂	1	1	yes	maximal, characteristic, complemented
8	#13123986	C₂	1	1	yes	maximal, characteristic, complemented
9	#13123984	C₂	1	1	yes	maximal, characteristic, complemented
10	#13123980	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123976	C₂	1	2	yes	maximal, complemented
12	#13123969	C₂	1	2	yes	maximal, complemented
13	#13123788	C₂	1	1	yes	maximal, characteristic, complemented
14	Q₈×#6094	C₂	1	1	yes	maximal, characteristic, complemented
15	#13123572	C₂	1	1	yes	maximal, characteristic, complemented
16	#13123569	C₂	1	2	yes	maximal, complemented
17	D₄×#6094	C₂	1	2	yes	maximal, complemented
18	D₄×#6094	C₂	1	1	yes	maximal, characteristic, complemented
19	#13123470	C₂	1	2	yes	maximal, complemented
20	#13123464	C₂	1	1	yes	maximal, characteristic, complemented
21	#13123397	C₂	1	2	yes	maximal, complemented
22	C₂×#11718498	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#529	C₂²	1	1	yes	characteristic
25	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
26	C₂²×#6094	C₂²	1	2	yes	—
27	C₂²×#6094	C₂²	1	2	yes	—
28	#11719411	C₄	1	2	yes	—
29	D₁₃×#126	C₄	1	2	yes	—
30	#11719396	C₄	1	1	yes	characteristic
31	D₁₃×#125	C₄	1	1	yes	characteristic
32	#11719385	C₄	1	1	yes	characteristic
33	D₁₃×#124	C₄	1	1	yes	characteristic
34	D₁₃×#123	C₄	1	2	yes	—
35	#11719354	C₄	1	2	yes	—
36	D₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
37	#11719329	C₄	1	1	yes	characteristic
38	D₁₃×#121	C₄	1	1	yes	characteristic
39	#11719305	C₄	1	1	yes	characteristic
40	#11719285	C₂²	1	1	yes	characteristic
41	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
42	#11719262	C₂²	1	1	yes	characteristic
43	C₄×D₄×D₁₃	C₂²	1	2	yes	—
44	C₄×D₄×D₁₃	C₂²	1	1	yes	characteristic
45	#11719243	C₂²	1	2	yes	—
46	#11719233	C₂²	1	2	yes	—
47	D₁₃×#117	C₂²	1	2	yes	—
48	#11719184	C₂²	1	1	yes	characteristic
49	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
51	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#435	C₂²	1	2	yes	complemented
54	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
55	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#433	C₂²	1	2	yes	complemented
57	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#424	C₂²	1	2	yes	complemented
59	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	#11718789	C₂²	1	2	yes	complemented
61	#11718788	C₂²	1	2	yes	complemented
62	#11718780	C₂²	1	2	yes	complemented
63	#11718772	C₂²	1	2	yes	complemented
64	#11718772	C₂²	1	2	yes	complemented
65	#11718772	C₂²	1	2	yes	complemented
66	C₈×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
67	#11718763	C₂²	1	2	yes	complemented
68	C₂×#88054	C₂²	1	2	yes	complemented
69	#11718685	C₂²	1	1	yes	characteristic, complemented
70	Q₈×#1055	C₂²	1	1	yes	characteristic, complemented
71	#11718673	C₂²	1	1	yes	characteristic, complemented
72	#11718672	C₂²	1	2	yes	complemented
73	D₄×#1055	C₂²	1	2	yes	complemented
74	D₄×#1055	C₂²	1	1	yes	characteristic, complemented
75	#11718661	C₂²	1	2	yes	complemented
76	#11718660	C₂²	1	2	yes	complemented
77	#11718586	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
79	#11718501	C₂²	1	2	yes	complemented
80	#11718501	C₂²	1	2	yes	complemented
81	#11718500	C₂²	1	2	yes	complemented
82	#11718500	C₂²	1	2	yes	complemented
83	#11718500	C₂²	1	2	yes	complemented
84	#11718500	C₂²	1	2	yes	complemented
85	#11718499	C₂²	1	1	yes	characteristic, complemented
86	#11718499	C₂²	1	2	yes	complemented
87	#11718498	C₂²	1	2	yes	—
88	#11718498	C₂²	1	1	yes	characteristic
89	#11718498	C₂²	1	1	yes	characteristic
90	#11718498	C₂²	1	1	yes	characteristic
91	#11718498	C₂²	1	2	yes	—
92	#11718498	C₂²	1	2	yes	—
93	#11718498	C₂²	1	1	yes	characteristic
94	#11718498	C₂²	1	1	yes	characteristic, complemented
95	#11718498	C₂²	1	1	yes	characteristic, complemented
96	#11718498	C₂²	1	2	yes	complemented
97	#11718497	C₂²	1	2	yes	complemented
98	#11718496	C₂²	1	1	yes	characteristic, complemented
99	#11718496	C₂²	1	1	yes	characteristic, complemented
100	#11718495	C₂²	1	1	yes	characteristic, complemented
101	#11718492	C₂²	1	2	yes	complemented
102	#11718492	C₂²	1	1	yes	characteristic, complemented
103	#11718491	C₂²	1	1	yes	characteristic, complemented
104	#11718489	C₂²	1	2	yes	complemented
105	#11718391	C₂²	1	2	yes	complemented
106	#11718391	C₂²	1	2	yes	complemented
107	#11718391	C₂²	1	2	yes	complemented
108	#11718390	C₂²	1	2	yes	complemented
109	#11718389	C₂²	1	2	yes	complemented
110	#11718387	C₂²	1	1	yes	characteristic
111	#11718387	C₂²	1	1	yes	characteristic
112	#11718387	C₂²	1	2	yes	—
113	#11718387	C₂²	1	2	yes	—
114	#11718386	C₂²	1	2	yes	complemented
115	#11718381	C₂²	1	2	yes	complemented
116	#11718381	C₂²	1	2	yes	complemented
117	#11718380	C₂²	1	1	yes	characteristic, complemented
118	#11718380	C₂²	1	1	yes	characteristic, complemented
119	#11718370	C₂²	1	2	yes	complemented
120	#11718368	C₂²	1	2	yes	—
121	#11718367	C₂²	1	2	yes	complemented
122	#11718362	C₂²	1	2	yes	complemented
123	#11718351	C₂²	1	2	yes	complemented
124	#11718349	C₂²	1	2	yes	complemented
125	#11718349	C₂²	1	1	yes	characteristic, complemented
126	C₄×#6094	C₂²	1	1	yes	characteristic
127	C₄×#6094	C₂²	1	1	yes	characteristic
128	C₄×#6094	C₂²	1	2	yes	—
129	C₈×D₅₂	C₂²	1	1	yes	characteristic, complemented
130	#11718346	C₂²	1	1	yes	characteristic, complemented
131	#11718346	C₂²	1	1	yes	characteristic, complemented
132	#11718340	C₂²	1	2	yes	complemented
133	#11718340	C₂²	1	1	yes	characteristic, complemented
134	C₈×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
135	C₂×Q₈×D₁₃	C₂×C₄	1	1	yes	characteristic
136	C₂×D₄×D₁₃	C₂×C₄	1	2	yes	—
137	C₂×D₄×D₁₃	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
139	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
140	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
142	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
143	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
144	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
145	C₁₃×#126	C₂×C₄	1	2	yes	—
146	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
147	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
148	C₁₃×#123	C₂×C₄	1	2	yes	—
149	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
150	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
151	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
152	C₄×D₄×C₁₃	C₂³	1	2	yes	—
153	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
154	C₁₃×#117	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
156	#88201	C₂×C₄	1	1	yes	characteristic
157	#88200	C₂×C₄	1	1	yes	characteristic
158	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
159	#88193	C₂×C₄	1	2	yes	—
160	#88192	C₂×C₄	1	1	yes	characteristic
161	#88190	C₂×C₄	1	1	yes	characteristic
162	#88189	C₂×C₄	1	2	yes	—
163	D₄×Dic₁₃	C₂×C₄	1	2	yes	—
164	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
165	#88184	C₂×C₄	1	1	yes	characteristic
166	#88183	C₂×C₄	1	2	yes	—
167	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
168	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
169	C₄×C₂²⋊D₁₃	C₂³	1	2	yes	—
170	#88180	C₂³	1	2	yes	—
171	#88178	C₂×C₄	1	1	yes	characteristic
172	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
173	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
174	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
175	C₂×#6099	C₂³	1	2	yes	—
176	C₂²×#1055	C₂³	1	2	yes	—
177	C₂²×#1055	C₂³	1	2	yes	—
178	M₁₆×D₁₃	—	4	4	no	—
179	C₂×#6094	—	4	4	no	—
180	C₂×#6094	—	4	4	no	—
181	C₂×#6094	C₂³	1	2	yes	—
182	C₂×#6094	C₂³	1	1	yes	characteristic
183	C₂×#6094	C₂³	1	2	yes	—
184	C₂×#6094	C₂³	1	1	yes	characteristic
185	C₂×#6094	C₂³	1	1	yes	characteristic
186	C₂×#6094	C₂³	1	1	yes	characteristic
187	C₂×#6094	C₂³	1	2	yes	—
188	C₂×#6094	C₂³	1	2	yes	—
189	C₂×#6094	C₂³	1	2	yes	—
190	C₂×#6094	C₂³	1	2	yes	—
191	C₂×C₈×D₁₃	C₂³	1	2	yes	—
192	C₂×C₈×D₁₃	C₂³	1	2	yes	—
193	#88152	C₂×C₄	1	2	yes	—
194	#88152	C₂×C₄	1	2	yes	—
195	#88152	C₂×C₄	1	2	yes	—
196	#88151	C₂×C₄	1	1	yes	characteristic
197	#88150	C₂×C₄	1	2	yes	—
198	#88149	C₂×C₄	1	1	yes	characteristic
199	#88148	C₂×C₄	1	2	yes	—
200	#88148	C₂×C₄	1	2	yes	—
201	#88147	C₂×C₄	1	1	yes	characteristic
202	#88147	C₂×C₄	1	2	yes	—
203	#88146	C₂×C₄	1	2	yes	—
204	#88146	C₂×C₄	1	2	yes	—
205	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
206	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
207	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
208	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
209	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
210	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
211	#88144	C₂×C₄	1	1	yes	characteristic
212	#88144	C₂×C₄	1	1	yes	characteristic
213	#88143	C₂×C₄	1	2	yes	—
214	#88143	C₂×C₄	1	2	yes	—
215	#88141	C₂×C₄	1	1	yes	characteristic
216	#88141	C₂×C₄	1	2	yes	—
217	#88140	C₂×C₄	1	2	yes	—
218	#88139	C₂×C₄	1	2	yes	—
219	#88139	C₂×C₄	1	2	yes	—
220	#88138	C₂×C₄	1	2	yes	—
221	#88137	C₂×C₄	1	2	yes	—
222	#88137	C₂×C₄	1	2	yes	—
223	#88135	C₂×C₄	1	2	yes	—
224	#88135	C₂×C₄	1	2	yes	—
225	#88135	C₂×C₄	1	2	yes	—
226	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
227	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
228	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
229	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
230	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
231	#88133	C₂×C₄	1	2	yes	—
232	#88133	C₂×C₄	1	2	yes	—
233	#88133	C₂×C₄	1	2	yes	—
234	#88132	C₂×C₄	1	2	yes	—
235	#88131	C₂×C₄	1	2	yes	—
236	#88131	C₂×C₄	1	2	yes	—
237	#88130	C₂×C₄	1	2	yes	—
238	#88129	C₂×C₄	1	1	yes	characteristic
239	C₄×D₅₂	C₂³	1	1	yes	characteristic
240	C₄×D₅₂	C₂³	1	2	yes	—
241	#88126	C₂³	1	2	yes	—
242	#88126	C₂³	1	2	yes	—
243	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
244	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
245	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
246	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
247	C₄²×D₁₃	C₂³	1	1	yes	characteristic
248	C₄²×D₁₃	C₂³	1	1	yes	characteristic
249	C₄²×D₁₃	C₂³	1	1	yes	characteristic
250	C₄²×D₁₃	C₂³	1	1	yes	characteristic
251	C₄²×D₁₃	C₂³	1	2	yes	—
252	#88124	C₂×C₄	1	1	yes	characteristic
253	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
254	C₄×Dic₂₆	C₂³	1	2	yes	—
255	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
260	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
261	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
263	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
264	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₁₃×#97	C₂³	1	2	yes	—
267	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
268	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
269	C₄×C₈×C₁₃	C₂³	1	2	yes	—
270	C₂²⋊#1055	C₂³	1	2	yes	—
271	C₂²⋊#1055	C₂³	1	2	yes	—
272	C₂²⋊#1055	C₂³	1	1	yes	characteristic
273	C₂²⋊#1055	C₂³	1	1	yes	characteristic
274	#88060	C₂³	1	2	yes	—
275	#88060	C₂³	1	1	yes	characteristic
276	#88060	C₂³	1	1	yes	characteristic
277	#88060	C₂³	1	1	yes	characteristic
278	#88060	C₂³	1	1	yes	characteristic
279	#88060	C₂³	1	2	yes	—
280	#88060	C₂³	1	2	yes	—
281	#88060	C₂³	1	2	yes	—
282	#88055	C₂³	1	1	yes	characteristic
283	#88055	C₂³	1	1	yes	characteristic
284	#88055	C₂³	1	2	yes	—
285	#88055	C₂³	1	1	yes	characteristic
286	#88055	C₂³	1	1	yes	characteristic
287	#88055	C₂³	1	2	yes	—
288	#88054	C₂³	1	2	yes	—
289	#88054	C₂³	1	2	yes	—
290	#88054	C₂³	1	2	yes	—
291	#88054	C₂³	1	2	yes	—
292	#88054	C₂³	1	2	yes	—
293	#88054	C₂³	1	2	yes	—
294	#88054	C₂³	1	2	yes	—
295	#88054	C₂³	1	2	yes	—
296	#88054	C₂³	1	1	yes	characteristic
297	#88054	C₂³	1	1	yes	characteristic
298	#88054	C₂³	1	1	yes	characteristic
299	#88054	C₂³	1	1	yes	characteristic
300	C₈×Dic₁₃	C₂³	1	2	yes	—
301	C₈×Dic₁₃	C₂³	1	2	yes	—
302	C₄⋊#1055	C₂³	1	1	yes	characteristic
303	C₄⋊#1055	C₂³	1	2	yes	—
304	C₄⋊#1055	C₂³	1	2	yes	—
305	C₄⋊#1055	C₂³	1	2	yes	—
306	C₄⋊#1055	C₂³	1	1	yes	characteristic
307	C₄⋊#1055	C₂³	1	1	yes	characteristic
308	C₄⋊#1055	C₂³	1	1	yes	characteristic
309	#88043	C₂³	1	2	yes	—
310	C₄×#1055	C₂³	1	2	yes	—
311	C₄×#1055	C₂³	1	1	yes	characteristic
312	C₄×#1055	C₂³	1	1	yes	characteristic
313	#60264	—	13	1	no	maximal, Sylow
314	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
315	C₂³×D₁₃	C₂²×C₄	1	2	yes	—
316	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
317	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
318	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
319	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
321	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
323	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
324	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
325	C₂×C₂²⋊D₁₃	C₂²×C₄	1	2	yes	—
326	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
327	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
328	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
329	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
330	Q₈×D₁₃	—	4	2	no	—
331	D₄×D₁₃	—	4	2	no	—
332	D₄×D₁₃	—	4	4	no	—
333	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
334	C₂×D₅₂	C₂²×C₄	1	2	yes	—
335	C₂×C₄×D₁₃	—	2	2	no	—
336	C₂×C₄×D₁₃	—	2	4	no	—
337	C₂×C₄×D₁₃	—	2	2	no	—
338	C₂×C₄×D₁₃	—	2	4	no	—
339	C₂×C₄×D₁₃	—	4	2	no	—
340	C₂×C₄×D₁₃	—	4	2	no	—
341	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
343	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
346	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
347	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
348	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
349	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
351	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
352	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
353	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
354	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
355	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
357	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
358	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
359	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
360	C₁₃×M₁₆	—	4	2	no	—
361	C₂×C₈×C₁₃	—	4	2	no	—
362	C₂×C₈×C₁₃	—	4	2	no	—
363	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
368	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
369	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
370	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
371	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
372	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
373	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
374	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
375	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
376	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
377	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
378	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
379	C₁₃×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
380	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
381	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
382	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₄²×C₁₃	C₂⁴	1	2	yes	—
384	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
386	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
387	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
388	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
389	C₂²⋊Dic₁₃	C₂²×C₄	1	2	yes	—
390	#6103	C₂²×C₄	1	2	yes	—
391	#6103	C₂²×C₄	1	2	yes	—
392	#6103	C₂²×C₄	1	2	yes	—
393	#6103	C₂²×C₄	1	2	yes	—
394	#6103	C₂²×C₄	1	2	yes	—
395	#6103	C₂²×C₄	1	2	yes	—
396	#6103	C₂²×C₄	1	2	yes	—
397	#6103	C₂²×C₄	1	2	yes	—
398	#6103	C₂²×C₄	1	2	yes	—
399	#6103	C₂²×C₄	1	2	yes	—
400	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
402	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
403	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
404	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
405	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
406	#6101	C₂²×C₄	1	2	yes	—
407	#6101	C₂²×C₄	1	2	yes	—
408	#6101	C₂²×C₄	1	2	yes	—
409	#6101	C₂²×C₄	1	2	yes	—
410	#6101	C₂²×C₄	1	2	yes	—
411	#6101	C₂²×C₄	1	2	yes	—
412	#6101	C₂²×C₄	1	2	yes	—
413	#6101	C₂²×C₄	1	2	yes	—
414	#6101	C₂²×C₄	1	2	yes	—
415	#6101	C₂²×C₄	1	2	yes	—
416	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
417	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
418	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
419	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
420	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
421	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
422	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
423	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
424	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
425	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
426	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
427	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
428	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
429	C₄×Dic₁₃	C₂⁴	1	2	yes	—
430	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
431	#6099	—	4	2	no	—
432	C₂×#1055	—	4	2	no	—
433	C₂×#1055	—	4	2	no	—
434	C₂×#1055	C₂⁴	1	1	yes	characteristic
435	C₂×#1055	C₂⁴	1	1	yes	characteristic
436	C₂×#1055	C₂⁴	1	1	yes	characteristic
437	C₂×#1055	C₂⁴	1	2	yes	—
438	C₂×#1055	C₂⁴	1	2	yes	—
439	C₂×#1055	C₂⁴	1	1	yes	characteristic
440	#6094	—	2	2	no	—
441	#6094	—	2	4	no	—
442	#6094	—	2	4	no	—
443	#6094	—	2	2	no	—
444	#6094	—	2	2	no	—
445	#6094	—	2	2	no	—
446	#6094	—	4	2	no	—
447	#6094	—	4	2	no	—
448	#6094	—	4	2	no	—
449	#6094	—	4	2	no	—
450	C₈×D₁₃	—	4	2	no	—
451	C₈×D₁₃	—	4	2	no	—
452	C₂×#529	—	13	1	no	—
453	#2995	—	13	2	no	—
454	#2995	—	13	2	no	—
455	#2994	—	13	1	no	—
456	#2994	—	13	1	no	—
457	#2994	—	13	1	no	—
458	#2994	D₁₃	1	1	yes	characteristic, complemented
459	#2993	—	13	1	no	—
460	#2993	—	13	1	no	—
461	#2993	—	13	1	no	—
462	#2993	—	13	1	no	—
463	#2992	—	13	2	no	—
464	#2992	—	13	2	no	—
465	Q₈×M₁₆	—	13	1	no	—
466	Q₈×M₁₆	—	13	1	no	—
467	D₄×M₁₆	—	13	1	no	—
468	D₄×M₁₆	—	13	2	no	—
469	D₄×M₁₆	—	13	2	no	—
470	D₄×M₁₆	—	13	1	no	—
471	#2921	—	13	2	no	—
472	#2920	—	13	1	no	—
473	#2905	—	13	2	no	—
474	C₂×#423	—	13	1	no	—
475	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
476	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
477	C₂²×D₁₃	—	2	2	no	—
478	C₂²×D₁₃	—	2	2	no	—
479	C₂²×D₁₃	—	2	4	no	—
480	C₂²×D₁₃	—	4	1	no	—
481	C₂²×D₁₃	—	4	2	no	—
482	C₂²×D₁₃	—	4	2	no	—
483	C₂²×D₁₃	C₂³×C₄	1	2	yes	—
484	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
485	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
486	Q₈×C₁₃	—	2	2	no	—
487	D₄×C₁₃	—	2	4	no	—
488	D₄×C₁₃	—	2	2	no	—
489	C₂×C₄×C₁₃	—	2	2	no	—
490	C₂×C₄×C₁₃	—	2	2	no	—
491	C₂×C₄×C₁₃	—	2	1	no	—
492	C₂×C₄×C₁₃	—	2	2	no	—
493	C₂×C₄×C₁₃	—	2	1	no	—
494	C₂×C₄×C₁₃	—	2	2	no	—
495	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
497	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
498	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
499	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
500	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
501	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
502	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
503	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
504	C₂²⋊D₁₃	—	2	4	no	—
505	C₂²⋊D₁₃	—	4	2	no	—
506	C₂²⋊D₁₃	—	4	2	no	—
507	C₂×Dic₁₃	—	2	2	no	—
508	C₂×Dic₁₃	—	2	2	no	—
509	C₂×Dic₁₃	—	2	4	no	—
510	C₂×Dic₁₃	—	4	1	no	—
511	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
512	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
513	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
514	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
515	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
516	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
517	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
518	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
519	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
520	D₅₂	—	2	2	no	—
521	D₅₂	—	4	2	no	—
522	C₄×D₁₃	—	2	2	no	—
523	C₄×D₁₃	—	2	4	no	—
524	C₄×D₁₃	—	2	2	no	—
525	C₄×D₁₃	—	2	2	no	—
526	C₄×D₁₃	—	2	2	no	—
527	C₄×D₁₃	—	2	1	no	—
528	C₄×D₁₃	—	2	1	no	—
529	C₄×D₁₃	—	2	2	no	—
530	C₄×D₁₃	—	2	2	no	—
531	C₄×D₁₃	—	2	4	no	—
532	C₄×D₁₃	—	4	1	no	—
533	C₄×D₁₃	—	4	1	no	—
534	C₄×D₁₃	—	4	1	no	—
535	C₄×D₁₃	—	4	1	no	—
536	C₄×D₁₃	—	4	1	no	—
537	C₄×D₁₃	—	4	1	no	—
538	C₄×D₁₃	—	4	2	no	—
539	C₄×D₁₃	—	4	2	no	—
540	C₄×D₁₃	H(5,𝔽₂)	1	2	yes	—
541	C₄×D₁₃	2₋¹⁺⁴	1	2	yes	—
542	Dic₂₆	—	2	2	no	—
543	Dic₂₆	—	4	2	no	—
544	C₈×C₁₃	—	2	1	no	—
545	C₈×C₁₃	—	2	2	no	—
546	C₈×C₁₃	—	2	2	no	—
547	C₈×C₁₃	—	2	1	no	—
548	C₈×C₁₃	—	2	1	no	—
549	C₈×C₁₃	—	2	1	no	—
550	#1055	—	2	1	no	—
551	#1055	—	2	2	no	—
552	#1055	—	2	2	no	—
553	#1055	—	2	1	no	—
554	#1055	—	2	1	no	—
555	#1055	—	2	1	no	—
556	C₂²×M₁₆	—	13	2	no	—
557	C₂²×M₁₆	—	13	2	no	—
558	C₂²×M₁₆	—	13	2	no	—
559	#529	—	13	2	no	—
560	#529	—	13	1	no	—
561	#529	—	13	1	no	—
562	#529	—	13	2	no	—
563	#529	—	13	1	no	—
564	#529	—	13	1	no	—
565	#529	—	13	1	no	—
566	#529	—	13	2	no	—
567	#529	—	13	1	no	—
568	#529	—	13	2	no	—
569	#529	—	13	1	no	—
570	#529	C₂×D₁₃	1	1	yes	characteristic
571	C₂×#126	—	13	2	no	—
572	C₂×#125	—	13	1	no	—
573	C₂×#124	—	13	1	no	—
574	C₂×#123	—	13	2	no	—
575	C₂×C₂²⋊Q₈	—	13	1	no	—
576	C₂×#121	—	13	1	no	—
577	C₂×C₄×Q₈	—	13	1	no	—
578	C₂×C₄×D₄	—	13	2	no	—
579	C₂×C₄×D₄	—	13	1	no	—
580	C₂×#117	—	13	2	no	—
581	C₂²×C₄²	—	13	1	no	—
582	#446	—	13	1	no	—
583	#446	—	13	2	no	—
584	#446	—	13	2	no	—
585	#446	—	13	1	no	—
586	#446	—	13	2	no	—
587	#446	—	13	2	no	—
588	#446	—	13	1	no	—
589	#446	C₂×D₁₃	1	1	yes	characteristic, complemented
590	C₈×Q₈	—	13	1	no	—
591	C₈×Q₈	—	13	1	no	—
592	C₈×Q₈	—	13	1	no	—
593	C₈×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
594	#436	—	13	2	no	—
595	#436	—	13	1	no	—
596	#436	—	13	1	no	—
597	#436	—	13	2	no	—
598	#436	—	13	2	no	—
599	#436	—	13	1	no	—
600	#436	—	13	2	no	—
601	#436	C₂×D₁₃	1	1	yes	characteristic, complemented
602	#435	—	13	2	no	—
603	#435	—	13	2	no	—
604	#435	—	13	2	no	—
605	#435	—	13	2	no	—
606	#435	—	13	2	no	—
607	#435	—	13	2	no	—
608	#435	—	13	2	no	—
609	#435	—	13	2	no	—
610	#435	—	13	2	no	—
611	#435	—	13	2	no	—
612	#435	—	13	2	no	—
613	#435	C₂×D₁₃	1	2	yes	complemented
614	C₈×D₄	—	13	2	no	—
615	C₈×D₄	—	13	2	no	—
616	C₈×D₄	—	13	1	no	—
617	C₈×D₄	—	13	1	no	—
618	C₈×D₄	—	13	2	no	—
619	C₈×D₄	—	13	1	no	—
620	C₈×D₄	C₂×D₁₃	1	2	yes	complemented
621	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
622	#433	—	13	2	no	—
623	#433	—	13	2	no	—
624	#433	—	13	2	no	—
625	#433	—	13	2	no	—
626	#433	—	13	2	no	—
627	#433	—	13	2	no	—
628	#433	—	13	2	no	—
629	#433	C₂×D₁₃	1	2	yes	complemented
630	#432	—	13	1	no	—
631	#432	—	13	1	no	—
632	#432	—	13	1	no	—
633	#432	—	13	1	no	—
634	#431	—	13	1	no	—
635	#431	—	13	1	no	—
636	#431	—	13	1	no	—
637	#431	C₂×D₁₃	1	1	yes	characteristic, complemented
638	#424	—	13	2	no	—
639	#424	—	13	2	no	—
640	#424	—	13	2	no	—
641	#424	—	13	2	no	—
642	#424	—	13	2	no	—
643	#424	—	13	2	no	—
644	#424	—	13	2	no	—
645	#424	C₂×D₁₃	1	2	yes	complemented
646	#423	—	13	2	no	—
647	#423	—	13	1	no	—
648	#423	—	13	1	no	—
649	#423	—	13	1	no	—
650	#423	—	13	1	no	—
651	#423	—	13	2	no	—
652	#423	—	13	1	no	—
653	#423	—	13	2	no	—
654	#423	—	13	2	no	—
655	#423	—	13	1	no	—
656	C₂×C₄⋊C₈	—	13	2	no	—
657	C₂×C₄⋊C₈	—	13	1	no	—
658	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
659	#407	—	13	1	no	—
660	#407	—	13	1	no	—
661	#407	—	13	2	no	—
662	#407	—	13	2	no	—
663	C₄×M₁₆	—	13	2	no	—
664	C₄×M₁₆	—	13	1	no	—
665	C₄×M₁₆	—	13	1	no	—
666	C₄×M₁₆	—	13	2	no	—
667	C₂²×C₁₃	—	2	1	no	—
668	C₂²×C₁₃	—	2	1	no	—
669	C₂²×C₁₃	—	2	2	no	—
670	C₂²×C₁₃	—	2	2	no	—
671	C₂²×C₁₃	—	2	2	no	—
672	C₂²×C₁₃	#568	1	2	yes	—
673	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
674	C₂×D₁₃	—	2	1	no	—
675	C₂×D₁₃	—	2	1	no	—
676	C₂×D₁₃	—	2	1	no	—
677	C₂×D₁₃	—	2	2	no	—
678	C₂×D₁₃	—	2	1	no	—
679	C₂×D₁₃	—	2	1	no	—
680	C₂×D₁₃	—	2	2	no	—
681	C₂×D₁₃	—	2	2	no	—
682	C₂×D₁₃	—	4	4	no	—
683	C₂×D₁₃	—	8	4	no	—
684	C₂×D₁₃	#520	1	2	yes	—
685	C₄×C₁₃	—	2	1	no	—
686	C₄×C₁₃	—	2	2	no	—
687	C₄×C₁₃	—	2	2	no	—
688	C₄×C₁₃	—	2	1	no	—
689	C₄×C₁₃	—	2	1	no	—
690	C₄×C₁₃	—	2	1	no	—
691	C₄×C₁₃	—	2	2	no	—
692	C₄×C₁₃	#568	1	2	yes	—
693	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
694	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
695	Dic₁₃	—	2	2	no	—
696	Dic₁₃	—	2	1	no	—
697	Dic₁₃	—	2	2	no	—
698	Dic₁₃	—	2	1	no	—
699	Dic₁₃	—	2	1	no	—
700	Dic₁₃	—	2	1	no	—
701	Dic₁₃	—	2	1	no	—
702	Dic₁₃	—	2	2	no	—
703	Dic₁₃	#520	1	2	yes	—
704	C₂²×Q₈	—	13	1	no	—
705	C₂²×D₄	—	13	2	no	—
706	C₂²×D₄	—	13	1	no	—
707	C₂³×C₄	—	13	2	no	—
708	C₂³×C₄	—	13	1	no	—
709	C₂³×C₄	—	13	1	no	—
710	C₂³×C₄	—	13	1	no	—
711	C₂×M₁₆	—	13	2	no	—
712	C₂×M₁₆	—	13	2	no	—
713	C₂×M₁₆	—	13	1	no	—
714	C₂×M₁₆	—	13	2	no	—
715	C₂×M₁₆	—	13	1	no	—
716	C₂×M₁₆	—	13	1	no	—
717	C₂×M₁₆	—	13	1	no	—
718	C₂×M₁₆	—	13	2	no	—
719	C₂×M₁₆	—	13	2	no	—
720	C₂×M₁₆	—	13	2	no	—
721	C₂×M₁₆	—	13	2	no	—
722	C₂×M₁₆	—	52	4	no	—
723	C₂×M₁₆	—	52	4	no	—
724	C₂×M₁₆	—	52	4	no	—
725	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
726	C₂²×C₈	—	13	2	no	—
727	C₂²×C₈	—	13	2	no	—
728	C₂²×C₈	—	13	2	no	—
729	C₂²×C₈	—	13	2	no	—
730	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
731	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
732	#126	—	13	2	no	—
733	#126	—	13	2	no	—
734	#126	—	13	2	no	—
735	#126	—	13	2	no	—
736	#126	—	13	2	no	—
737	#126	—	13	2	no	—
738	#126	—	13	2	no	—
739	#126	C₄×D₁₃	1	2	yes	—
740	#125	—	13	2	no	—
741	#125	—	13	2	no	—
742	#125	—	13	1	no	—
743	#125	—	13	1	no	—
744	#125	—	13	1	no	—
745	#125	C₄×D₁₃	1	1	yes	characteristic
746	#124	—	13	1	no	—
747	#124	—	13	1	no	—
748	#124	—	13	2	no	—
749	#124	—	13	2	no	—
750	#124	—	13	1	no	—
751	#124	C₄×D₁₃	1	1	yes	characteristic
752	#123	—	13	2	no	—
753	#123	—	13	2	no	—
754	#123	—	13	2	no	—
755	#123	—	13	2	no	—
756	#123	—	13	2	no	—
757	#123	—	13	2	no	—
758	#123	—	13	2	no	—
759	#123	C₄×D₁₃	1	2	yes	—
760	C₂²⋊Q₈	—	13	1	no	—
761	C₂²⋊Q₈	—	13	1	no	—
762	C₂²⋊Q₈	—	13	2	no	—
763	C₂²⋊Q₈	—	13	1	no	—
764	C₂²⋊Q₈	—	13	2	no	—
765	C₂²⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
766	#121	—	13	1	no	—
767	#121	—	13	2	no	—
768	#121	—	13	1	no	—
769	#121	—	13	1	no	—
770	#121	—	13	2	no	—
771	#121	C₄×D₁₃	1	1	yes	characteristic
772	C₄×Q₈	—	13	1	no	—
773	C₄×Q₈	—	13	2	no	—
774	C₄×Q₈	—	13	1	no	—
775	C₄×Q₈	—	13	1	no	—
776	C₄×Q₈	—	13	2	no	—
777	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
778	C₄×D₄	—	13	1	no	—
779	C₄×D₄	—	13	2	no	—
780	C₄×D₄	—	13	2	no	—
781	C₄×D₄	—	13	2	no	—
782	C₄×D₄	—	13	2	no	—
783	C₄×D₄	—	13	1	no	—
784	C₄×D₄	—	13	2	no	—
785	C₄×D₄	—	13	2	no	—
786	C₄×D₄	—	13	2	no	—
787	C₄×D₄	—	13	2	no	—
788	C₄×D₄	—	13	1	no	—
789	C₄×D₄	—	13	2	no	—
790	C₄×D₄	C₂²×D₁₃	1	2	yes	—
791	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
792	#117	—	13	2	no	—
793	#117	—	13	2	no	—
794	#117	—	13	2	no	—
795	#117	—	13	2	no	—
796	#117	—	13	2	no	—
797	#117	—	13	2	no	—
798	#117	—	13	2	no	—
799	#117	C₂²×D₁₃	1	2	yes	—
800	C₂×C₄⋊C₄	—	13	2	no	—
801	C₂×C₄⋊C₄	—	13	2	no	—
802	C₂×C₄⋊C₄	—	13	1	no	—
803	C₂×C₄⋊C₄	—	13	2	no	—
804	C₂×C₄⋊C₄	—	13	1	no	—
805	C₂×C₄⋊C₄	—	13	2	no	—
806	C₂×C₂²⋊C₄	—	13	2	no	—
807	C₂×C₂²⋊C₄	—	13	2	no	—
808	C₂×C₂²⋊C₄	—	13	2	no	—
809	C₂×C₂²⋊C₄	—	13	2	no	—
810	C₂×C₂²⋊C₄	—	13	2	no	—
811	C₂×C₄²	—	13	1	no	—
812	C₂×C₄²	—	13	1	no	—
813	C₂×C₄²	—	13	1	no	—
814	C₂×C₄²	—	13	1	no	—
815	C₂×C₄²	—	13	1	no	—
816	C₂×C₄²	—	13	1	no	—
817	C₂×C₄²	—	13	1	no	—
818	C₂×C₄²	—	13	1	no	—
819	C₂×C₄²	—	13	2	no	—
820	C₂×C₄²	—	13	1	no	—
821	C₂×C₄²	—	13	1	no	—
822	C₂×C₄²	—	13	1	no	—
823	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
824	C₄⋊C₈	—	13	2	no	—
825	C₄⋊C₈	—	13	2	no	—
826	C₄⋊C₈	—	13	2	no	—
827	C₄⋊C₈	—	13	2	no	—
828	C₄⋊C₈	—	13	1	no	—
829	C₄⋊C₈	—	13	1	no	—
830	C₄⋊C₈	—	13	2	no	—
831	C₄⋊C₈	—	13	2	no	—
832	C₄⋊C₈	—	13	2	no	—
833	C₄⋊C₈	—	13	2	no	—
834	C₄⋊C₈	—	13	1	no	—
835	C₄⋊C₈	—	13	1	no	—
836	C₄⋊C₈	—	13	2	no	—
837	C₄⋊C₈	—	13	1	no	—
838	C₄⋊C₈	—	13	1	no	—
839	C₄⋊C₈	—	13	1	no	—
840	C₄⋊C₈	—	13	2	no	—
841	C₄⋊C₈	—	13	2	no	—
842	C₄⋊C₈	—	13	1	no	—
843	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
844	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
845	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
846	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
847	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
848	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
849	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
850	C₂²⋊C₈	—	13	1	no	—
851	C₂²⋊C₈	—	13	1	no	—
852	C₂²⋊C₈	—	13	2	no	—
853	C₂²⋊C₈	—	13	2	no	—
854	C₂²⋊C₈	—	13	1	no	—
855	C₂²⋊C₈	—	13	1	no	—
856	C₂²⋊C₈	—	13	1	no	—
857	C₂²⋊C₈	—	13	1	no	—
858	C₂²⋊C₈	—	13	2	no	—
859	C₂²⋊C₈	—	13	2	no	—
860	C₂²⋊C₈	—	13	2	no	—
861	C₂²⋊C₈	—	13	2	no	—
862	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
863	C₂²⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
864	C₂²⋊C₈	C₂²×D₁₃	1	2	yes	—
865	C₂²⋊C₈	C₂²×D₁₃	1	2	yes	—
866	#97	—	13	1	no	—
867	#97	—	13	1	no	—
868	#97	—	13	1	no	—
869	#97	—	13	1	no	—
870	#97	—	13	2	no	—
871	#97	—	13	2	no	—
872	#97	—	13	2	no	—
873	#97	C₂²×D₁₃	1	2	yes	—
874	C₄×C₈	—	13	2	no	—
875	C₄×C₈	—	13	2	no	—
876	C₄×C₈	—	13	1	no	—
877	C₄×C₈	—	13	1	no	—
878	C₄×C₈	—	13	2	no	—
879	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
880	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
881	C₄×C₈	C₂²×D₁₃	1	2	yes	—
882	C₂×C₁₃	—	2	2	no	—
883	C₂×C₁₃	—	4	2	no	—
884	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
885	C₂×C₁₃	C₂×#568	1	1	yes	characteristic
886	C₂×C₁₃	C₂×#568	1	1	yes	characteristic
887	D₁₃	—	2	2	no	—
888	D₁₃	—	4	1	no	—
889	D₁₃	—	4	2	no	—
890	C₂⁴	—	13	1	no	—
891	C₂⁴	—	13	2	no	—
892	C₂×Q₈	—	13	1	no	—
893	C₂×Q₈	—	13	2	no	—
894	C₂×Q₈	—	52	2	no	—
895	C₂×Q₈	C₂×C₄×D₁₃	1	1	yes	characteristic
896	C₂×D₄	—	13	2	no	—
897	C₂×D₄	—	13	2	no	—
898	C₂×D₄	—	13	2	no	—
899	C₂×D₄	—	13	1	no	—
900	C₂×D₄	—	13	2	no	—
901	C₂×D₄	—	52	2	no	—
902	C₂×D₄	—	52	4	no	—
903	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
904	C₂×D₄	C₂×C₄×D₁₃	1	1	yes	characteristic
905	C₂²×C₄	—	13	1	no	—
906	C₂²×C₄	—	13	1	no	—
907	C₂²×C₄	—	13	1	no	—
908	C₂²×C₄	—	13	2	no	—
909	C₂²×C₄	—	13	1	no	—
910	C₂²×C₄	—	13	1	no	—
911	C₂²×C₄	—	13	1	no	—
912	C₂²×C₄	—	13	1	no	—
913	C₂²×C₄	—	13	1	no	—
914	C₂²×C₄	—	13	2	no	—
915	C₂²×C₄	—	13	2	no	—
916	C₂²×C₄	—	13	1	no	—
917	C₂²×C₄	—	13	2	no	—
918	C₂²×C₄	—	13	1	no	—
919	C₂²×C₄	—	13	1	no	—
920	C₂²×C₄	—	13	1	no	—
921	C₂²×C₄	—	13	1	no	—
922	C₂²×C₄	—	13	1	no	—
923	C₂²×C₄	—	13	1	no	—
924	C₂²×C₄	—	13	2	no	—
925	C₂²×C₄	—	13	2	no	—
926	C₂²×C₄	—	26	2	no	—
927	C₂²×C₄	—	26	4	no	—
928	C₂²×C₄	—	26	2	no	—
929	C₂²×C₄	—	26	4	no	—
930	C₂²×C₄	—	52	2	no	—
931	C₂²×C₄	—	52	2	no	—
932	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
933	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
934	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
935	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
936	M₁₆	—	4	2	no	—
937	M₁₆	—	26	4	no	—
938	M₁₆	—	26	2	no	—
939	M₁₆	—	26	4	no	—
940	M₁₆	—	26	2	no	—
941	M₁₆	—	26	2	no	—
942	M₁₆	—	26	2	no	—
943	M₁₆	—	52	2	no	—
944	M₁₆	—	52	2	no	—
945	M₁₆	—	52	2	no	—
946	M₁₆	—	52	2	no	—
947	M₁₆	—	52	2	no	—
948	C₂×C₈	—	4	2	no	—
949	C₂×C₈	—	4	2	no	—
950	C₂×C₈	—	13	1	no	—
951	C₂×C₈	—	13	1	no	—
952	C₂×C₈	—	13	2	no	—
953	C₂×C₈	—	13	1	no	—
954	C₂×C₈	—	13	1	no	—
955	C₂×C₈	—	13	2	no	—
956	C₂×C₈	—	52	2	no	—
957	C₂×C₈	—	52	2	no	—
958	C₂×C₈	—	52	2	no	—
959	C₂×C₈	—	52	2	no	—
960	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
961	C₂×C₈	C₂³×D₁₃	1	2	yes	—
962	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
963	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
964	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
965	C₂×C₈	C₂³×D₁₃	1	2	yes	—
966	C₄⋊C₄	—	13	2	no	—
967	C₄⋊C₄	—	13	2	no	—
968	C₄⋊C₄	—	13	2	no	—
969	C₄⋊C₄	—	13	2	no	—
970	C₄⋊C₄	—	13	2	no	—
971	C₄⋊C₄	—	13	2	no	—
972	C₄⋊C₄	—	13	2	no	—
973	C₄⋊C₄	—	13	1	no	—
974	C₄⋊C₄	—	13	2	no	—
975	C₄⋊C₄	—	13	2	no	—
976	C₄⋊C₄	—	13	2	no	—
977	C₄⋊C₄	—	13	2	no	—
978	C₄⋊C₄	—	13	1	no	—
979	C₄⋊C₄	—	13	2	no	—
980	C₄⋊C₄	—	13	2	no	—
981	C₄⋊C₄	—	13	2	no	—
982	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
983	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
984	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
986	C₄⋊C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
988	C₂²⋊C₄	—	13	2	no	—
989	C₂²⋊C₄	—	13	2	no	—
990	C₂²⋊C₄	—	13	2	no	—
991	C₂²⋊C₄	—	13	2	no	—
992	C₂²⋊C₄	—	13	2	no	—
993	C₂²⋊C₄	—	13	2	no	—
994	C₂²⋊C₄	—	13	2	no	—
995	C₂²⋊C₄	—	13	2	no	—
996	C₂²⋊C₄	—	13	2	no	—
997	C₂²⋊C₄	—	13	2	no	—
998	C₂²⋊C₄	—	13	2	no	—
999	C₂²⋊C₄	—	13	2	no	—
1000	C₂²⋊C₄	—	13	2	no	—
1001	C₂²⋊C₄	—	13	2	no	—
1002	C₂²⋊C₄	—	13	2	no	—
1003	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1004	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1005	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1006	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1007	C₂²⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
1008	C₄²	—	13	1	no	—
1009	C₄²	—	13	1	no	—
1010	C₄²	—	13	1	no	—
1011	C₄²	—	13	1	no	—
1012	C₄²	—	13	1	no	—
1013	C₄²	—	13	1	no	—
1014	C₄²	—	13	1	no	—
1015	C₄²	—	13	1	no	—
1016	C₄²	—	13	1	no	—
1017	C₄²	—	13	1	no	—
1018	C₄²	—	13	2	no	—
1019	C₄²	—	13	2	no	—
1020	C₄²	—	13	2	no	—
1021	C₄²	—	13	1	no	—
1022	C₄²	—	13	1	no	—
1023	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
1024	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
1025	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1026	C₄²	C₂³×D₁₃	1	2	yes	—
1027	C₄²	C₂³×D₁₃	1	1	yes	characteristic
1028	C₁₃	#60264	1	1	yes	characteristic, complemented, Sylow
1029	C₂³	—	13	1	no	—
1030	C₂³	—	13	2	no	—
1031	C₂³	—	13	1	no	—
1032	C₂³	—	26	2	no	—
1033	C₂³	—	26	4	no	—
1034	C₂³	—	26	2	no	—
1035	C₂³	—	52	1	no	—
1036	C₂³	—	52	2	no	—
1037	C₂³	—	52	2	no	—
1038	C₂³	C₂²×C₄×D₁₃	1	2	yes	—
1039	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
1040	Q₈	—	2	2	no	—
1041	Q₈	—	26	2	no	—
1042	Q₈	—	52	2	no	—
1043	D₄	—	2	4	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	26	4	no	—
1046	D₄	—	26	2	no	—
1047	D₄	—	52	2	no	—
1048	D₄	—	52	2	no	—
1049	D₄	—	52	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	13	1	no	—
1057	C₂×C₄	—	13	2	no	—
1058	C₂×C₄	—	13	2	no	—
1059	C₂×C₄	—	13	1	no	—
1060	C₂×C₄	—	13	1	no	—
1061	C₂×C₄	—	13	1	no	—
1062	C₂×C₄	—	13	1	no	—
1063	C₂×C₄	—	13	1	no	—
1064	C₂×C₄	—	13	2	no	—
1065	C₂×C₄	—	13	2	no	—
1066	C₂×C₄	—	13	2	no	—
1067	C₂×C₄	—	26	2	no	—
1068	C₂×C₄	—	26	4	no	—
1069	C₂×C₄	—	26	2	no	—
1070	C₂×C₄	—	26	4	no	—
1071	C₂×C₄	—	26	2	no	—
1072	C₂×C₄	—	26	4	no	—
1073	C₂×C₄	—	26	2	no	—
1074	C₂×C₄	—	26	2	no	—
1075	C₂×C₄	—	26	2	no	—
1076	C₂×C₄	—	26	2	no	—
1077	C₂×C₄	—	26	1	no	—
1078	C₂×C₄	—	26	1	no	—
1079	C₂×C₄	—	26	2	no	—
1080	C₂×C₄	—	52	1	no	—
1081	C₂×C₄	—	52	1	no	—
1082	C₂×C₄	—	52	1	no	—
1083	C₂×C₄	—	52	1	no	—
1084	C₂×C₄	—	52	1	no	—
1085	C₂×C₄	—	52	1	no	—
1086	C₂×C₄	—	52	2	no	—
1087	C₂×C₄	—	52	2	no	—
1088	C₂×C₄	—	52	1	no	—
1089	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1090	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1091	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1092	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1093	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1094	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1095	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
1096	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
1097	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	—	2	2	no	—
1101	C₈	—	2	1	no	—
1102	C₈	—	2	1	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	26	1	no	—
1105	C₈	—	26	2	no	—
1106	C₈	—	26	1	no	—
1107	C₈	—	26	2	no	—
1108	C₈	—	26	1	no	—
1109	C₈	—	26	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	13	2	no	—
1116	C₂²	—	26	1	no	—
1117	C₂²	—	26	1	no	—
1118	C₂²	—	26	1	no	—
1119	C₂²	—	26	1	no	—
1120	C₂²	—	26	2	no	—
1121	C₂²	—	26	2	no	—
1122	C₂²	—	26	1	no	—
1123	C₂²	—	26	2	no	—
1124	C₂²	—	52	4	no	—
1125	C₂²	—	104	4	no	—
1126	C₂²	#11719455	1	2	yes	—
1127	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
1128	C₄	—	2	1	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	13	2	no	—
1136	C₄	—	26	1	no	—
1137	C₄	—	26	1	no	—
1138	C₄	—	26	1	no	—
1139	C₄	—	26	1	no	—
1140	C₄	—	26	2	no	—
1141	C₄	—	26	2	no	—
1142	C₄	—	26	1	no	—
1143	C₄	—	26	2	no	—
1144	C₄	#11719455	1	2	yes	—
1145	C₄	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1146	C₄	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1147	C₂	—	2	2	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	26	2	no	—
1150	C₂	—	52	1	no	—
1151	C₂	—	52	2	no	—
1152	C₂	D₁₃×#520	1	1	yes	characteristic
1153	C₂	C₂×#11719455	1	1	yes	characteristic
1154	C₂	C₂×#11719455	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₁₃
commutator, socle	C₂²×C₁₃	C₂⁴×C₄
Fitting	C₁₃×#2994	C₂
prime radical	D₁₃×#121	C₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	#2994	D₁₃
hypocenter	C₁₃	#60264
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #2994

Complements

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

N	H ≅ G/N	type
2. #13124004	C₂	semidirect
3. #13124001	C₂	semidirect
4. #13123998	C₂	semidirect
5. #13123996	C₂	semidirect
6. #13123992	C₂	semidirect
7. #13123988	C₂	semidirect
8. #13123986	C₂	semidirect
9. #13123984	C₂	semidirect
10. #13123980	C₂	semidirect
11. #13123976	C₂	semidirect
12. #13123969	C₂	semidirect
13. #13123788	C₂	semidirect
14. Q₈×#6094	C₂	semidirect
15. #13123572	C₂	semidirect
16. #13123569	C₂	semidirect
17. D₄×#6094	C₂	semidirect
18. D₄×#6094	C₂	semidirect
19. #13123470	C₂	semidirect
20. #13123464	C₂	semidirect
21. #13123397	C₂	semidirect
22. C₂×#11718498	C₂	semidirect
23. C₁₃×#2994	C₂	semidirect
50. C₁₃×#446	C₂²	semidirect
51. C₈×Q₈×C₁₃	C₂²	semidirect
52. C₁₃×#436	C₂²	semidirect
53. C₁₃×#435	C₂²	semidirect
54. C₈×D₄×C₁₃	C₂²	semidirect
55. C₈×D₄×C₁₃	C₂²	semidirect
56. C₁₃×#433	C₂²	semidirect
57. C₁₃×#431	C₂²	semidirect
58. C₁₃×#424	C₂²	semidirect
59. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
60. #11718789	C₂²	semidirect
61. #11718788	C₂²	semidirect
62. #11718780	C₂²	semidirect
63. #11718772	C₂²	semidirect
64. #11718772	C₂²	semidirect
65. #11718772	C₂²	semidirect
66. C₈×C₂²⋊D₁₃	C₂²	semidirect
67. #11718763	C₂²	semidirect
68. C₂×#88054	C₂²	semidirect
69. #11718685	C₂²	semidirect
70. Q₈×#1055	C₂²	semidirect
71. #11718673	C₂²	semidirect
72. #11718672	C₂²	semidirect
73. D₄×#1055	C₂²	semidirect
74. D₄×#1055	C₂²	semidirect
75. #11718661	C₂²	semidirect
76. #11718660	C₂²	semidirect
77. #11718586	C₂²	semidirect
78. C₂×C₄⋊#1055	C₂²	semidirect
79. #11718501	C₂²	semidirect
80. #11718501	C₂²	semidirect
81. #11718500	C₂²	semidirect
82. #11718500	C₂²	semidirect
83. #11718500	C₂²	semidirect
84. #11718500	C₂²	semidirect
85. #11718499	C₂²	semidirect
86. #11718499	C₂²	semidirect
94. #11718498	C₂²	semidirect
95. #11718498	C₂²	semidirect
96. #11718498	C₂²	semidirect
97. #11718497	C₂²	semidirect
98. #11718496	C₂²	semidirect
99. #11718496	C₂²	semidirect
100. #11718495	C₂²	semidirect
101. #11718492	C₂²	semidirect
102. #11718492	C₂²	semidirect
103. #11718491	C₂²	semidirect
104. #11718489	C₂²	semidirect
105. #11718391	C₂²	semidirect
106. #11718391	C₂²	semidirect
107. #11718391	C₂²	semidirect
108. #11718390	C₂²	semidirect
109. #11718389	C₂²	semidirect
114. #11718386	C₂²	semidirect
115. #11718381	C₂²	semidirect
116. #11718381	C₂²	semidirect
117. #11718380	C₂²	semidirect
118. #11718380	C₂²	semidirect
119. #11718370	C₂²	semidirect
121. #11718367	C₂²	semidirect
122. #11718362	C₂²	semidirect
123. #11718351	C₂²	semidirect
124. #11718349	C₂²	semidirect
125. #11718349	C₂²	semidirect
129. C₈×D₅₂	C₂²	semidirect
130. #11718346	C₂²	semidirect
131. #11718346	C₂²	semidirect
132. #11718340	C₂²	semidirect
133. #11718340	C₂²	semidirect
134. C₈×Dic₂₆	C₂²	semidirect
458. #2994	D₁₃	semidirect
589. #446	C₂×D₁₃	semidirect
593. C₈×Q₈	C₂×D₁₃	semidirect
601. #436	C₂×D₁₃	semidirect
613. #435	C₂×D₁₃	semidirect
620. C₈×D₄	C₂×D₁₃	semidirect
621. C₈×D₄	C₂×D₁₃	semidirect
629. #433	C₂×D₁₃	semidirect
637. #431	C₂×D₁₃	semidirect
645. #424	C₂×D₁₃	semidirect
658. C₂×C₄⋊C₈	C₂×D₁₃	semidirect
1028. C₁₃	#60264	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₃×#529	2
#13124004	2
#13124001	2
#13123998	2
#13123996	2
#13123992	2
#13123988	2
#13123986	2
#13123984	2
#13123980	2
#13123976	2
#13123969	2
#13123788	2
Q₈×#6094	2
#13123572	2
#13123569	2
D₄×#6094	2
#13123470	2
#13123464	2
#13123397	2
C₂×#11718498	2
C₁₃×#2994	2
#60264	13