Subgroups — #15829767

Order 3328.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123953	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123803	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113309	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113301	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113296	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113291	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113283	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113275	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113270	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113265	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113257	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113249	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113244	C₂	1	1	yes	maximal, characteristic, complemented
14	#13113239	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3461	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#544	C₄	1	1	yes	characteristic
17	C₁₃×#542	—	2	1	no	—
18	C₁₃×#542	C₄	1	1	yes	characteristic
19	C₁₃×#542	C₄	1	1	yes	characteristic
20	C₁₃×#541	—	2	1	no	—
21	C₁₃×#541	C₄	1	1	yes	characteristic
22	C₁₃×#541	C₄	1	1	yes	characteristic
23	C₁₃×#539	—	2	1	no	—
24	C₁₃×#539	—	2	1	no	—
25	C₁₃×#537	C₄	1	1	yes	characteristic
26	C₁₃×#536	C₄	1	1	yes	characteristic
27	C₁₃×#536	C₄	1	1	yes	characteristic
28	C₁₃×#533	—	2	1	no	—
29	C₁₃×#533	C₂²	1	1	yes	characteristic
30	C₁₃×#533	C₂²	1	1	yes	characteristic
31	C₁₃×#529	—	2	1	no	—
32	C₁₃×#529	—	2	1	no	—
33	C₁₃×#529	—	2	1	no	—
34	C₁₃×#529	C₂²	1	1	yes	characteristic
35	C₁₃×#529	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
39	#11718685	—	2	1	no	—
40	#11718685	—	2	1	no	—
41	#11718673	—	2	1	no	—
42	#11718673	—	2	1	no	—
43	#11718672	—	2	1	no	—
44	#11718672	—	2	1	no	—
45	#11718672	—	2	1	no	—
46	#11718672	—	2	1	no	—
47	#11718587	C₂²	1	1	yes	characteristic
48	#11718587	C₂²	1	1	yes	characteristic
49	#11718586	C₂²	1	1	yes	characteristic
50	#11718586	C₂²	1	1	yes	characteristic
51	#11718586	C₂²	1	1	yes	characteristic
52	#11718586	C₂²	1	1	yes	characteristic
53	#11718585	C₂²	1	1	yes	characteristic
54	#11718585	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
56	C₄×#6099	C₂²	1	1	yes	characteristic
57	C₄×#6099	C₂²	1	1	yes	characteristic
58	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
59	Q₈⋊#1055	C₂²	1	1	yes	characteristic
60	Q₈⋊#1055	C₂²	1	1	yes	characteristic
61	Q₈⋊#1055	C₂²	1	1	yes	characteristic
62	Q₈⋊#1055	C₂²	1	1	yes	characteristic
63	Q₈⋊#1055	C₂²	1	1	yes	characteristic
64	Q₈⋊#1055	C₂²	1	1	yes	characteristic
65	Q₈⋊#1055	C₂²	1	1	yes	characteristic
66	Q₈⋊#1055	C₂²	1	1	yes	characteristic
67	Q₈⋊#1055	C₂²	1	1	yes	characteristic
68	Q₈⋊#1055	C₂²	1	1	yes	characteristic
69	Q₈⋊#1055	C₂²	1	1	yes	characteristic
70	Q₈⋊#1055	C₂²	1	1	yes	characteristic
71	D₄⋊#1055	C₂²	1	1	yes	characteristic
72	D₄⋊#1055	C₂²	1	1	yes	characteristic
73	D₄⋊#1055	C₂²	1	1	yes	characteristic
74	D₄⋊#1055	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
77	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#126	—	2	1	no	—
85	C₁₃×#126	—	2	1	no	—
86	C₁₃×#126	—	2	1	no	—
87	C₁₃×#126	—	2	1	no	—
88	C₁₃×#126	—	2	1	no	—
89	C₁₃×#126	—	2	1	no	—
90	C₁₃×#126	—	2	1	no	—
91	C₁₃×#126	—	2	1	no	—
92	C₁₃×#125	—	2	1	no	—
93	C₁₃×#125	—	2	1	no	—
94	C₁₃×#125	—	2	1	no	—
95	C₁₃×#125	—	2	1	no	—
96	C₁₃×#125	—	2	1	no	—
97	C₁₃×#125	—	2	1	no	—
98	C₁₃×#125	—	2	1	no	—
99	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
100	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
101	C₁₃×#124	—	2	1	no	—
102	C₁₃×#124	—	2	1	no	—
103	C₁₃×#124	—	2	1	no	—
104	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
105	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
106	C₁₃×#123	—	2	1	no	—
107	C₁₃×#123	—	2	1	no	—
108	C₁₃×#123	—	2	1	no	—
109	C₁₃×#123	—	2	1	no	—
110	C₁₃×#123	—	2	1	no	—
111	C₁₃×#123	—	2	1	no	—
112	C₁₃×#123	—	2	1	no	—
113	C₁₃×#123	—	2	1	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×C₂²⋊Q₈	—	2	1	no	—
117	C₁₃×C₂²⋊Q₈	—	2	1	no	—
118	C₁₃×C₂²⋊Q₈	—	2	1	no	—
119	C₁₃×C₂²⋊Q₈	—	2	1	no	—
120	C₁₃×C₂²⋊Q₈	—	2	1	no	—
121	C₁₃×C₂²⋊Q₈	—	2	1	no	—
122	C₁₃×C₂²⋊Q₈	—	2	1	no	—
123	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
124	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
125	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
126	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
127	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
128	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
129	C₁₃×#121	—	2	1	no	—
130	C₁₃×#121	—	2	1	no	—
131	C₁₃×#121	—	2	1	no	—
132	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
133	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
134	C₄×Q₈×C₁₃	—	2	1	no	—
135	C₄×Q₈×C₁₃	—	2	1	no	—
136	C₄×Q₈×C₁₃	—	2	1	no	—
137	C₄×Q₈×C₁₃	—	2	1	no	—
138	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
139	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
140	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
141	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
142	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
143	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
145	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
146	C₄×D₄×C₁₃	—	2	1	no	—
147	C₄×D₄×C₁₃	—	2	1	no	—
148	C₄×D₄×C₁₃	—	2	1	no	—
149	C₄×D₄×C₁₃	—	2	1	no	—
150	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
151	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
152	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
153	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
154	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
155	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
156	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
157	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
158	C₁₃×#117	—	2	1	no	—
159	C₁₃×#117	—	2	1	no	—
160	C₁₃×#117	—	2	1	no	—
161	C₁₃×#117	—	2	1	no	—
162	C₁₃×#117	—	2	1	no	—
163	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
164	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
165	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
166	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
167	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
169	C₂×C₄²×C₁₃	—	2	1	no	—
170	C₂×C₄²×C₁₃	—	2	1	no	—
171	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₂×#6099	—	2	1	no	—
175	C₂×#6099	—	2	1	no	—
176	C₂×#6099	—	2	1	no	—
177	C₂×#6099	—	2	1	no	—
178	C₂²×#1055	—	2	1	no	—
179	C₂²×#1055	—	2	1	no	—
180	C₂²⋊#1055	—	2	1	no	—
181	C₂²⋊#1055	—	2	1	no	—
182	C₂²⋊#1055	—	2	1	no	—
183	C₂²⋊#1055	—	2	1	no	—
184	C₂²⋊#1055	—	2	1	no	—
185	C₂²⋊#1055	—	2	1	no	—
186	C₄⋊#1055	—	2	1	no	—
187	C₄⋊#1055	—	2	1	no	—
188	C₄⋊#1055	—	2	1	no	—
189	C₄⋊#1055	—	2	1	no	—
190	C₄⋊#1055	—	2	1	no	—
191	C₄⋊#1055	—	2	1	no	—
192	C₄⋊#1055	C₂³	1	1	yes	characteristic
193	C₄⋊#1055	C₂³	1	1	yes	characteristic
194	C₄⋊#1055	C₂³	1	1	yes	characteristic
195	C₄⋊#1055	C₂³	1	1	yes	characteristic
196	#88043	—	2	1	no	—
197	#88043	—	2	1	no	—
198	#88043	—	2	1	no	—
199	#88043	—	2	1	no	—
200	C₄×#1055	—	2	1	no	—
201	C₄×#1055	—	2	1	no	—
202	C₄×#1055	C₂³	1	1	yes	characteristic
203	C₄×#1055	C₂³	1	1	yes	characteristic
204	C₄×#1055	C₂³	1	1	yes	characteristic
205	C₄×#1055	C₂³	1	1	yes	characteristic
206	#17506	—	13	1	no	maximal, Sylow
207	C₁₃×#41	—	4	2	no	—
208	C₁₃×#41	—	4	2	no	—
209	C₂×Q₈×C₁₃	—	2	1	no	—
210	C₂×Q₈×C₁₃	—	2	1	no	—
211	C₂×Q₈×C₁₃	—	2	1	no	—
212	C₂×Q₈×C₁₃	—	4	2	no	—
213	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
214	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
215	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
216	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
217	C₂×D₄×C₁₃	—	2	1	no	—
218	C₂×D₄×C₁₃	—	2	1	no	—
219	C₂×D₄×C₁₃	—	2	1	no	—
220	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
221	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
222	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
223	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	no	—
228	C₂²×C₄×C₁₃	—	2	1	no	—
229	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
262	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
263	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
264	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
265	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
266	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
267	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
268	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
269	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
270	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
271	C₁₃×C₂²⋊C₄	—	2	1	no	—
272	C₁₃×C₂²⋊C₄	—	2	1	no	—
273	C₁₃×C₂²⋊C₄	—	2	1	no	—
274	C₁₃×C₂²⋊C₄	—	2	1	no	—
275	C₁₃×C₂²⋊C₄	—	2	1	no	—
276	C₁₃×C₂²⋊C₄	—	2	1	no	—
277	C₁₃×C₂²⋊C₄	—	2	1	no	—
278	C₁₃×C₂²⋊C₄	—	2	1	no	—
279	C₁₃×C₂²⋊C₄	—	2	1	no	—
280	C₁₃×C₂²⋊C₄	—	2	1	no	—
281	C₁₃×C₂²⋊C₄	—	2	1	no	—
282	C₁₃×C₂²⋊C₄	—	2	1	no	—
283	C₁₃×C₂²⋊C₄	—	2	1	no	—
284	C₁₃×C₂²⋊C₄	—	2	1	no	—
285	C₁₃×C₂²⋊C₄	—	2	1	no	—
286	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
287	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
288	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
289	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
290	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
291	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
292	C₄²×C₁₃	—	2	1	no	—
293	C₄²×C₁₃	—	2	1	no	—
294	C₄²×C₁₃	—	2	1	no	—
295	C₄²×C₁₃	—	2	1	no	—
296	C₄²×C₁₃	—	2	1	no	—
297	C₄²×C₁₃	—	2	1	no	—
298	C₄²×C₁₃	—	2	1	no	—
299	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
300	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
301	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
302	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
309	#6099	—	4	2	no	—
310	#6099	—	4	2	no	—
311	#6099	—	8	1	no	—
312	#6099	—	8	1	no	—
313	C₂×#1055	—	2	1	no	—
314	C₂×#1055	—	2	1	no	—
315	C₂×#1055	—	2	1	no	—
316	C₂×#1055	—	2	1	no	—
317	C₂×#1055	—	2	1	no	—
318	C₂×#1055	—	2	1	no	—
319	C₂×#1055	—	2	1	no	—
320	C₂×#1055	—	2	1	no	—
321	C₂×#1055	—	4	2	no	—
322	C₂×#1055	—	8	1	no	—
323	#3461	D₁₃	1	1	yes	characteristic
324	#2989	—	13	1	no	—
325	#2965	—	13	1	no	—
326	#1497	—	13	1	no	—
327	#1495	—	13	1	no	—
328	#1494	—	13	1	no	—
329	#1493	—	13	1	no	—
330	#1491	—	13	1	no	—
331	#1489	—	13	1	no	—
332	#1488	—	13	1	no	—
333	#1487	—	13	1	no	—
334	#1485	—	13	1	no	—
335	#1483	—	13	1	no	—
336	#1482	—	13	1	no	—
337	#1481	—	13	1	no	—
338	C₂³×C₁₃	—	2	1	no	—
339	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
340	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
341	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	Q₈×C₁₃	—	2	2	no	—
343	Q₈×C₁₃	—	2	2	no	—
344	Q₈×C₁₃	—	2	2	no	—
345	Q₈×C₁₃	—	4	1	no	—
346	Q₈×C₁₃	—	4	2	no	—
347	Q₈×C₁₃	—	8	1	no	—
348	Q₈×C₁₃	—	8	1	no	—
349	D₄×C₁₃	—	2	2	no	—
350	D₄×C₁₃	—	4	1	no	—
351	D₄×C₁₃	—	4	1	no	—
352	D₄×C₁₃	—	4	1	no	—
353	D₄×C₁₃	—	4	2	no	—
354	D₄×C₁₃	—	8	1	no	—
355	D₄×C₁₃	—	8	1	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	1	no	—
360	C₂×C₄×C₁₃	—	2	1	no	—
361	C₂×C₄×C₁₃	—	2	1	no	—
362	C₂×C₄×C₁₃	—	2	1	no	—
363	C₂×C₄×C₁₃	—	2	1	no	—
364	C₂×C₄×C₁₃	—	2	1	no	—
365	C₂×C₄×C₁₃	—	2	1	no	—
366	C₂×C₄×C₁₃	—	2	1	no	—
367	C₂×C₄×C₁₃	—	2	1	no	—
368	C₂×C₄×C₁₃	—	2	1	no	—
369	C₂×C₄×C₁₃	—	2	1	no	—
370	C₂×C₄×C₁₃	—	2	1	no	—
371	C₂×C₄×C₁₃	—	2	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	1	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	—	4	2	no	—
376	C₂×C₄×C₁₃	—	4	2	no	—
377	C₂×C₄×C₁₃	—	4	1	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	8	1	no	—
380	C₂×C₄×C₁₃	—	8	1	no	—
381	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
387	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
388	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
391	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
393	#1055	—	2	2	no	—
394	#1055	—	4	1	no	—
395	#1055	—	4	1	no	—
396	#1055	—	4	1	no	—
397	#1055	—	4	1	no	—
398	#1055	—	4	1	no	—
399	#1055	—	4	1	no	—
400	#1055	—	4	1	no	—
401	#544	Dic₁₃	1	1	yes	characteristic
402	#542	—	2	1	no	—
403	#542	Dic₁₃	1	1	yes	characteristic
404	#542	Dic₁₃	1	1	yes	characteristic
405	#541	—	2	1	no	—
406	#541	Dic₁₃	1	1	yes	characteristic
407	#541	Dic₁₃	1	1	yes	characteristic
408	#539	—	2	1	no	—
409	#539	—	2	1	no	—
410	#537	Dic₁₃	1	1	yes	characteristic
411	#536	Dic₁₃	1	1	yes	characteristic
412	#536	Dic₁₃	1	1	yes	characteristic
413	#533	—	2	1	no	—
414	#533	C₂×D₁₃	1	1	yes	characteristic
415	#533	C₂×D₁₃	1	1	yes	characteristic
416	#529	—	2	1	no	—
417	#529	—	2	1	no	—
418	#529	—	2	1	no	—
419	#529	C₂×D₁₃	1	1	yes	characteristic
420	#529	C₂×D₁₃	1	1	yes	characteristic
421	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
422	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
423	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
424	#446	—	26	1	no	—
425	#446	—	26	1	no	—
426	#436	—	26	1	no	—
427	#436	—	26	1	no	—
428	#435	—	26	1	no	—
429	#435	—	26	1	no	—
430	#435	—	26	1	no	—
431	#435	—	26	1	no	—
432	#432	—	13	1	no	—
433	#432	—	13	1	no	—
434	#431	—	13	1	no	—
435	#431	—	13	1	no	—
436	#431	—	13	1	no	—
437	#431	—	13	1	no	—
438	#423	—	13	1	no	—
439	#423	—	13	1	no	—
440	C₂×C₄⋊C₈	—	13	1	no	—
441	C₄×M₁₆	—	13	1	no	—
442	C₄×M₁₆	—	13	1	no	—
443	C₂×C₄×C₈	—	13	1	no	—
444	Q₈⋊C₈	—	13	1	no	—
445	Q₈⋊C₈	—	13	1	no	—
446	Q₈⋊C₈	—	13	1	no	—
447	Q₈⋊C₈	—	13	1	no	—
448	Q₈⋊C₈	—	13	1	no	—
449	Q₈⋊C₈	—	13	1	no	—
450	Q₈⋊C₈	—	13	1	no	—
451	Q₈⋊C₈	—	13	1	no	—
452	Q₈⋊C₈	—	13	1	no	—
453	Q₈⋊C₈	—	13	1	no	—
454	Q₈⋊C₈	—	13	1	no	—
455	Q₈⋊C₈	—	13	1	no	—
456	D₄⋊C₈	—	13	1	no	—
457	D₄⋊C₈	—	13	1	no	—
458	D₄⋊C₈	—	13	1	no	—
459	D₄⋊C₈	—	13	1	no	—
460	C₂²×C₁₃	—	2	1	no	—
461	C₂²×C₁₃	—	2	1	no	—
462	C₂²×C₁₃	—	2	1	no	—
463	C₂²×C₁₃	—	2	1	no	—
464	C₂²×C₁₃	—	2	1	no	—
465	C₂²×C₁₃	—	2	1	no	—
466	C₂²×C₁₃	—	2	1	no	—
467	C₂²×C₁₃	—	2	1	no	—
468	C₂²×C₁₃	—	2	1	no	—
469	C₂²×C₁₃	—	4	1	no	—
470	C₂²×C₁₃	—	4	1	no	—
471	C₂²×C₁₃	—	4	1	no	—
472	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
473	C₄×C₁₃	—	2	1	no	—
474	C₄×C₁₃	—	2	1	no	—
475	C₄×C₁₃	—	2	1	no	—
476	C₄×C₁₃	—	2	1	no	—
477	C₄×C₁₃	—	2	1	no	—
478	C₄×C₁₃	—	2	1	no	—
479	C₄×C₁₃	—	2	1	no	—
480	C₄×C₁₃	—	2	1	no	—
481	C₄×C₁₃	—	2	1	no	—
482	C₄×C₁₃	—	2	1	no	—
483	C₄×C₁₃	—	4	1	no	—
484	C₄×C₁₃	—	4	1	no	—
485	C₄×C₁₃	—	4	1	no	—
486	C₄×C₁₃	—	4	1	no	—
487	C₄×C₁₃	—	4	1	no	—
488	C₄×C₁₃	—	4	1	no	—
489	C₄×C₁₃	—	4	1	no	—
490	C₄×C₁₃	#568	1	2	yes	—
491	C₄×C₁₃	#577	1	1	yes	characteristic
492	C₄×C₁₃	#578	1	1	yes	characteristic
493	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
494	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
495	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
496	C₂×M₁₆	—	26	1	no	—
497	C₂×M₁₆	—	26	1	no	—
498	C₂×M₁₆	—	26	1	no	—
499	C₂×M₁₆	—	26	1	no	—
500	C₂²×C₈	—	26	1	no	—
501	C₂²×C₈	—	26	1	no	—
502	C₄⋊Q₈	—	2	1	no	—
503	C₄⋊Q₈	—	2	1	no	—
504	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
505	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
506	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
507	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
508	#126	—	2	1	no	—
509	#126	—	2	1	no	—
510	#126	—	2	1	no	—
511	#126	—	2	1	no	—
512	#126	—	2	1	no	—
513	#126	—	2	1	no	—
514	#126	—	2	1	no	—
515	#126	—	2	1	no	—
516	#125	—	2	1	no	—
517	#125	—	2	1	no	—
518	#125	—	2	1	no	—
519	#125	—	2	1	no	—
520	#125	—	2	1	no	—
521	#125	—	2	1	no	—
522	#125	—	2	1	no	—
523	#125	C₂×Dic₁₃	1	1	yes	characteristic
524	#125	C₂×Dic₁₃	1	1	yes	characteristic
525	#124	—	2	1	no	—
526	#124	—	2	1	no	—
527	#124	—	2	1	no	—
528	#124	C₂×Dic₁₃	1	1	yes	characteristic
529	#124	C₂×Dic₁₃	1	1	yes	characteristic
530	#123	—	2	1	no	—
531	#123	—	2	1	no	—
532	#123	—	2	1	no	—
533	#123	—	2	1	no	—
534	#123	—	2	1	no	—
535	#123	—	2	1	no	—
536	#123	—	2	1	no	—
537	#123	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	—	2	1	no	—
544	C₂²⋊Q₈	—	2	1	no	—
545	C₂²⋊Q₈	—	2	1	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
548	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
549	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
550	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
551	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
552	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
553	#121	—	2	1	no	—
554	#121	—	2	1	no	—
555	#121	—	2	1	no	—
556	#121	C₂×Dic₁₃	1	1	yes	characteristic
557	#121	C₂×Dic₁₃	1	1	yes	characteristic
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
563	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
564	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
565	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
566	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
567	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
568	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
569	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
575	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
576	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
577	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
578	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
579	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
580	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
581	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
582	#117	—	2	1	no	—
583	#117	—	2	1	no	—
584	#117	—	2	1	no	—
585	#117	—	2	1	no	—
586	#117	—	2	1	no	—
587	#117	C₂×Dic₁₃	1	1	yes	characteristic
588	#117	C₂×Dic₁₃	1	1	yes	characteristic
589	#117	C₂×Dic₁₃	1	1	yes	characteristic
590	#117	C₂×Dic₁₃	1	1	yes	characteristic
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
593	C₂×C₄²	—	2	1	no	—
594	C₂×C₄²	—	2	1	no	—
595	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
596	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
597	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
598	C₄⋊C₈	—	13	1	no	—
599	C₄⋊C₈	—	13	1	no	—
600	C₄⋊C₈	—	13	1	no	—
601	C₄⋊C₈	—	13	1	no	—
602	C₄⋊C₈	—	26	1	no	—
603	C₄⋊C₈	—	26	1	no	—
604	C₄⋊C₈	—	26	1	no	—
605	C₄⋊C₈	—	26	1	no	—
606	C₄⋊C₈	—	26	1	no	—
607	C₄⋊C₈	—	26	1	no	—
608	C₂²⋊C₈	—	26	1	no	—
609	C₂²⋊C₈	—	26	1	no	—
610	C₂²⋊C₈	—	26	1	no	—
611	C₂²⋊C₈	—	26	1	no	—
612	C₂²⋊C₈	—	26	1	no	—
613	C₂²⋊C₈	—	26	1	no	—
614	#97	—	26	1	no	—
615	#97	—	26	1	no	—
616	#97	—	26	1	no	—
617	#97	—	26	1	no	—
618	C₄×C₈	—	13	1	no	—
619	C₄×C₈	—	13	1	no	—
620	C₄×C₈	—	13	1	no	—
621	C₄×C₈	—	13	1	no	—
622	C₄×C₈	—	26	1	no	—
623	C₄×C₈	—	26	1	no	—
624	C₂×C₁₃	—	4	1	no	—
625	C₂×C₁₃	—	4	1	no	—
626	C₂×C₁₃	—	4	1	no	—
627	C₂×C₁₃	—	8	1	no	—
628	C₂×C₁₃	#2879	1	1	yes	characteristic
629	C₂×C₁₃	#2898	1	1	yes	characteristic
630	C₂×C₁₃	#2901	1	1	yes	characteristic
631	#41	—	4	2	no	—
632	#41	—	4	2	no	—
633	C₂×Q₈	—	2	1	no	—
634	C₂×Q₈	—	2	1	no	—
635	C₂×Q₈	—	2	1	no	—
636	C₂×Q₈	—	4	2	no	—
637	C₂×Q₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
638	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
639	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
640	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
645	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
646	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
647	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
654	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
657	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
659	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
660	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
661	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
662	M₁₆	—	52	2	no	—
663	M₁₆	—	52	2	no	—
664	M₁₆	—	104	1	no	—
665	M₁₆	—	104	1	no	—
666	C₂×C₈	—	26	1	no	—
667	C₂×C₈	—	26	1	no	—
668	C₂×C₈	—	26	1	no	—
669	C₂×C₈	—	26	1	no	—
670	C₂×C₈	—	26	1	no	—
671	C₂×C₈	—	26	1	no	—
672	C₂×C₈	—	26	1	no	—
673	C₂×C₈	—	26	1	no	—
674	C₂×C₈	—	52	2	no	—
675	C₂×C₈	—	104	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
700	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
701	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
702	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
703	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
704	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
705	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
706	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
707	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
708	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	1	no	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
725	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
726	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
727	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
728	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
729	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
730	C₄²	—	2	1	no	—
731	C₄²	—	2	1	no	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	1	no	—
737	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
738	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
739	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
740	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
741	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
742	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
743	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
744	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
745	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
746	C₄²	C₂³×D₁₃	1	1	yes	characteristic
747	C₁₃	#17506	1	1	yes	characteristic, complemented, Sylow
748	C₂³	—	2	1	no	—
749	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
750	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
751	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	4	1	no	—
756	Q₈	—	4	2	no	—
757	Q₈	—	8	1	no	—
758	Q₈	—	8	1	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	D₄	—	4	1	no	—
763	D₄	—	4	2	no	—
764	D₄	—	8	1	no	—
765	D₄	—	8	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	8	1	no	—
790	C₂×C₄	—	8	1	no	—
791	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
792	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
793	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
794	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
795	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
796	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
797	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
798	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
799	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
800	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
803	C₈	—	26	2	no	—
804	C₈	—	52	1	no	—
805	C₈	—	52	1	no	—
806	C₈	—	52	1	no	—
807	C₈	—	52	1	no	—
808	C₈	—	52	1	no	—
809	C₈	—	52	1	no	—
810	C₈	—	52	1	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	2	1	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	1	no	—
822	C₂²	—	4	1	no	—
823	C₂²	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	2	1	no	—
827	C₄	—	2	1	no	—
828	C₄	—	2	1	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	1	no	—
841	C₄	#11719524	1	2	yes	—
842	C₄	#11719542	1	1	yes	characteristic
843	C₄	#11719543	1	1	yes	characteristic
844	C₂	—	4	1	no	—
845	C₂	—	4	1	no	—
846	C₂	—	4	1	no	—
847	C₂	—	8	1	no	—
848	C₂	#13123281	1	1	yes	characteristic
849	C₂	#13123369	1	1	yes	characteristic
850	C₂	#13123383	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#3461	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	C₁₃×#537	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3461	D₁₃
hypocenter	C₁₃	#17506
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3461

Complements

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

N	H ≅ G/N	type
1. #13123953	C₂	semidirect
2. #13123803	C₂	semidirect
3. #13113309	C₂	semidirect
4. #13113301	C₂	semidirect
5. #13113296	C₂	semidirect
6. #13113291	C₂	semidirect
7. #13113283	C₂	semidirect
8. #13113275	C₂	semidirect
9. #13113270	C₂	semidirect
10. #13113265	C₂	semidirect
11. #13113257	C₂	semidirect
12. #13113249	C₂	semidirect
13. #13113244	C₂	semidirect
14. #13113239	C₂	semidirect
747. C₁₃	#17506	semidirect

Maximal subgroups

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

subgroup	index
#13123953	2
#13123803	2
#13113309	2
#13113301	2
#13113296	2
#13113291	2
#13113283	2
#13113275	2
#13113270	2
#13113265	2
#13113257	2
#13113249	2
#13113244	2
#13113239	2
C₁₃×#3461	2
#17506	13