Subgroups — #15829752

Order 3328.

954 conjugacy classes of subgroups.

The subgroup lattice has 910 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	#13113305	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	#13113287	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113279	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	#13113261	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113253	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	#13113235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3460	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×#540	—	2	1	no	—
21	C₁₃×#540	C₄	1	1	yes	characteristic
22	C₁₃×#540	C₄	1	1	yes	characteristic
23	C₁₃×#538	—	2	1	no	—
24	C₁₃×#538	—	2	1	no	—
25	C₁₃×#537	C₄	1	1	yes	characteristic
26	C₁₃×#535	C₄	1	1	yes	characteristic
27	C₁₃×#535	C₄	1	1	yes	characteristic
28	C₁₃×#532	—	2	1	no	—
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₁₃×#532	C₂²	1	1	yes	characteristic
31	C₁₃×#529	—	2	1	no	—
32	C₁₃×#529	C₂²	1	1	yes	characteristic
33	C₁₃×#529	C₂²	1	1	yes	characteristic
34	C₁₃×#525	—	2	1	no	—
35	C₁₃×#525	—	2	1	no	—
36	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×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, complemented
49	#11718586	C₂²	1	1	yes	characteristic
50	#11718586	C₂²	1	1	yes	characteristic, complemented
51	#11718586	C₂²	1	1	yes	characteristic, complemented
52	#11718586	C₂²	1	1	yes	characteristic, complemented
53	#11718585	C₂²	1	1	yes	characteristic
54	#11718585	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
56	C₄×#6099	C₂²	1	1	yes	characteristic
57	C₄×#6099	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×#1055	C₂²	1	1	yes	characteristic, complemented
59	Q₈⋊#1055	C₂²	1	1	yes	characteristic, complemented
60	Q₈⋊#1055	C₂²	1	1	yes	characteristic, complemented
61	Q₈⋊#1055	C₂²	1	1	yes	characteristic, complemented
62	Q₈⋊#1055	C₂²	1	1	yes	characteristic, complemented
63	D₄⋊#1055	C₂²	1	1	yes	characteristic
64	D₄⋊#1055	C₂²	1	1	yes	characteristic
65	D₄⋊#1055	C₂²	1	1	yes	characteristic
66	D₄⋊#1055	C₂²	1	1	yes	characteristic
67	D₄⋊#1055	C₂²	1	1	yes	characteristic
68	D₄⋊#1055	C₂²	1	1	yes	characteristic
69	D₄⋊#1055	C₂²	1	1	yes	characteristic
70	D₄⋊#1055	C₂²	1	1	yes	characteristic
71	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
72	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
73	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
74	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	—	2	1	no	—
77	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#127	—	2	1	no	—
85	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
86	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
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×#125	—	2	1	no	—
92	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
94	C₁₃×#124	—	2	1	no	—
95	C₁₃×#124	—	2	1	no	—
96	C₁₃×#124	—	2	1	no	—
97	C₁₃×#124	—	2	1	no	—
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
100	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
101	C₁₃×#123	—	2	1	no	—
102	C₁₃×#123	—	2	1	no	—
103	C₁₃×#123	—	2	1	no	—
104	C₁₃×#123	—	2	1	no	—
105	C₁₃×#123	—	2	1	no	—
106	C₁₃×#123	—	2	1	no	—
107	C₁₃×#123	—	2	1	no	—
108	C₁₃×#123	—	2	1	no	—
109	C₁₃×C₂²⋊Q₈	—	2	1	no	—
110	C₁₃×C₂²⋊Q₈	—	2	1	no	—
111	C₁₃×C₂²⋊Q₈	—	2	1	no	—
112	C₁₃×C₂²⋊Q₈	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	1	no	—
114	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
115	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
116	C₁₃×#121	—	2	1	no	—
117	C₁₃×#121	—	2	1	no	—
118	C₁₃×#121	—	2	1	no	—
119	C₁₃×#121	—	2	1	no	—
120	C₁₃×#121	—	2	1	no	—
121	C₁₃×#121	—	2	1	no	—
122	C₁₃×#121	—	2	1	no	—
123	C₁₃×#121	—	2	1	no	—
124	C₁₃×#121	—	2	1	no	—
125	C₁₃×#121	—	2	1	no	—
126	C₁₃×#121	—	2	1	no	—
127	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
128	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
129	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
130	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
131	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
132	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
133	C₁₃×#120	—	2	1	no	—
134	C₁₃×#120	—	2	1	no	—
135	C₁₃×#120	—	2	1	no	—
136	C₁₃×#120	—	2	1	no	—
137	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
138	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
139	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
140	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₄×D₄×C₁₃	—	2	1	no	—
142	C₄×D₄×C₁₃	—	2	1	no	—
143	C₄×D₄×C₁₃	—	2	1	no	—
144	C₄×D₄×C₁₃	—	2	1	no	—
145	C₄×D₄×C₁₃	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
150	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
151	C₄×D₄×C₁₃	C₂×C₄	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	D₄	1	1	yes	characteristic
158	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
159	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
161	C₁₃×#117	—	2	1	no	—
162	C₁₃×#117	—	2	1	no	—
163	C₁₃×#117	—	2	1	no	—
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	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
168	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
169	C₂×C₁₃×C₂²⋊C₄	—	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	#17505	—	13	1	no	maximal, Sylow
207	C₂⁴×C₁₃	—	2	1	no	—
208	C₁₃×#41	—	4	2	no	—
209	C₁₃×#41	—	4	2	no	—
210	C₁₃×#41	—	8	1	no	—
211	C₁₃×#41	—	8	1	no	—
212	C₁₃×#41	—	8	1	no	—
213	C₁₃×#41	—	8	1	no	—
214	C₂×Q₈×C₁₃	—	2	1	no	—
215	C₂×Q₈×C₁₃	—	2	1	no	—
216	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
217	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×D₄×C₁₃	—	2	1	no	—
219	C₂×D₄×C₁₃	—	2	1	no	—
220	C₂×D₄×C₁₃	—	2	1	no	—
221	C₂×D₄×C₁₃	—	2	1	no	—
222	C₂×D₄×C₁₃	—	2	1	no	—
223	C₂×D₄×C₁₃	—	2	1	no	—
224	C₂×D₄×C₁₃	—	2	1	no	—
225	C₂×D₄×C₁₃	—	2	1	no	—
226	C₂×D₄×C₁₃	—	2	1	no	—
227	C₂×D₄×C₁₃	—	2	1	no	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	4	2	no	—
231	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
232	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
233	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
234	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
235	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
236	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	1	no	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	8	1	no	—
246	C₂²×C₄×C₁₃	—	8	1	no	—
247	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
249	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
272	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
273	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
274	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
275	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
276	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	2	1	no	—
291	C₁₃×C₂²⋊C₄	—	2	1	no	—
292	C₁₃×C₂²⋊C₄	—	2	1	no	—
293	C₁₃×C₂²⋊C₄	—	2	1	no	—
294	C₁₃×C₂²⋊C₄	—	2	1	no	—
295	C₁₃×C₂²⋊C₄	—	2	1	no	—
296	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
297	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
298	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
299	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
300	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
301	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
302	C₄²×C₁₃	—	2	1	no	—
303	C₄²×C₁₃	—	2	1	no	—
304	C₄²×C₁₃	—	2	1	no	—
305	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
306	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
307	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
308	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
315	#6099	—	4	2	no	—
316	#6099	—	4	2	no	—
317	#6099	—	8	1	no	—
318	#6099	—	8	1	no	—
319	C₂×#1055	—	2	1	no	—
320	C₂×#1055	—	2	1	no	—
321	C₂×#1055	—	2	1	no	—
322	C₂×#1055	—	2	1	no	—
323	C₂×#1055	—	2	1	no	—
324	C₂×#1055	—	2	1	no	—
325	C₂×#1055	—	2	1	no	—
326	C₂×#1055	—	2	1	no	—
327	C₂×#1055	—	4	2	no	—
328	C₂×#1055	—	8	1	no	—
329	#3460	D₁₃	1	1	yes	characteristic
330	#2989	—	13	1	no	—
331	#2965	—	13	1	no	—
332	#1496	—	13	1	no	—
333	#1495	—	13	1	no	—
334	#1494	—	13	1	no	—
335	#1492	—	13	1	no	—
336	#1490	—	13	1	no	—
337	#1489	—	13	1	no	—
338	#1488	—	13	1	no	—
339	#1486	—	13	1	no	—
340	#1484	—	13	1	no	—
341	#1483	—	13	1	no	—
342	#1482	—	13	1	no	—
343	#1480	—	13	1	no	—
344	C₂³×C₁₃	—	2	1	no	—
345	C₂³×C₁₃	—	2	1	no	—
346	C₂³×C₁₃	—	2	1	no	—
347	C₂³×C₁₃	—	4	2	no	—
348	C₂³×C₁₃	—	8	1	no	—
349	C₂³×C₁₃	—	8	1	no	—
350	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
351	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
352	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
353	Q₈×C₁₃	—	2	2	no	—
354	Q₈×C₁₃	—	4	1	no	—
355	Q₈×C₁₃	—	8	1	no	—
356	Q₈×C₁₃	—	8	1	no	—
357	D₄×C₁₃	—	2	2	no	—
358	D₄×C₁₃	—	2	2	no	—
359	D₄×C₁₃	—	2	2	no	—
360	D₄×C₁₃	—	4	1	no	—
361	D₄×C₁₃	—	4	1	no	—
362	D₄×C₁₃	—	4	1	no	—
363	D₄×C₁₃	—	4	2	no	—
364	D₄×C₁₃	—	4	2	no	—
365	D₄×C₁₃	—	8	1	no	—
366	D₄×C₁₃	—	8	1	no	—
367	D₄×C₁₃	—	8	1	no	—
368	D₄×C₁₃	—	8	1	no	—
369	D₄×C₁₃	—	8	1	no	—
370	D₄×C₁₃	—	8	1	no	—
371	D₄×C₁₃	—	8	1	no	—
372	D₄×C₁₃	—	8	1	no	—
373	D₄×C₁₃	—	8	1	no	—
374	D₄×C₁₃	—	8	1	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	1	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	4	1	no	—
390	C₂×C₄×C₁₃	—	4	1	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	4	1	no	—
394	C₂×C₄×C₁₃	—	4	1	no	—
395	C₂×C₄×C₁₃	—	4	1	no	—
396	C₂×C₄×C₁₃	—	4	1	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	1	no	—
399	C₂×C₄×C₁₃	—	8	1	no	—
400	C₂×C₄×C₁₃	—	8	1	no	—
401	C₂×C₄×C₁₃	—	8	1	no	—
402	C₂×C₄×C₁₃	—	8	1	no	—
403	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	#1055	—	2	2	no	—
416	#1055	—	4	1	no	—
417	#1055	—	4	1	no	—
418	#1055	—	4	1	no	—
419	#1055	—	4	1	no	—
420	#1055	—	4	1	no	—
421	#1055	—	4	1	no	—
422	#1055	—	4	1	no	—
423	#544	Dic₁₃	1	1	yes	characteristic
424	#542	—	2	1	no	—
425	#542	Dic₁₃	1	1	yes	characteristic
426	#542	Dic₁₃	1	1	yes	characteristic
427	#540	—	2	1	no	—
428	#540	Dic₁₃	1	1	yes	characteristic
429	#540	Dic₁₃	1	1	yes	characteristic
430	#538	—	2	1	no	—
431	#538	—	2	1	no	—
432	#537	Dic₁₃	1	1	yes	characteristic
433	#535	Dic₁₃	1	1	yes	characteristic
434	#535	Dic₁₃	1	1	yes	characteristic
435	#532	—	2	1	no	—
436	#532	C₂×D₁₃	1	1	yes	characteristic
437	#532	C₂×D₁₃	1	1	yes	characteristic
438	#529	—	2	1	no	—
439	#529	C₂×D₁₃	1	1	yes	characteristic
440	#529	C₂×D₁₃	1	1	yes	characteristic
441	#525	—	2	1	no	—
442	#525	—	2	1	no	—
443	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
444	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
446	#446	—	26	1	no	—
447	#446	—	26	1	no	—
448	#436	—	26	1	no	—
449	#436	—	26	1	no	—
450	#435	—	26	1	no	—
451	#435	—	26	1	no	—
452	#435	—	26	1	no	—
453	#435	—	26	1	no	—
454	#432	—	13	1	no	—
455	#432	—	13	1	no	—
456	#431	—	13	1	no	—
457	#431	—	13	1	no	—
458	#431	—	13	1	no	—
459	#431	—	13	1	no	—
460	#423	—	13	1	no	—
461	#423	—	13	1	no	—
462	C₂×C₄⋊C₈	—	13	1	no	—
463	C₄×M₁₆	—	13	1	no	—
464	C₄×M₁₆	—	13	1	no	—
465	C₂×C₄×C₈	—	13	1	no	—
466	Q₈⋊C₈	—	13	1	no	—
467	Q₈⋊C₈	—	13	1	no	—
468	Q₈⋊C₈	—	13	1	no	—
469	Q₈⋊C₈	—	13	1	no	—
470	D₄⋊C₈	—	13	1	no	—
471	D₄⋊C₈	—	13	1	no	—
472	D₄⋊C₈	—	13	1	no	—
473	D₄⋊C₈	—	13	1	no	—
474	D₄⋊C₈	—	13	1	no	—
475	D₄⋊C₈	—	13	1	no	—
476	D₄⋊C₈	—	13	1	no	—
477	D₄⋊C₈	—	13	1	no	—
478	D₄⋊C₈	—	13	1	no	—
479	D₄⋊C₈	—	13	1	no	—
480	D₄⋊C₈	—	13	1	no	—
481	D₄⋊C₈	—	13	1	no	—
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	1	no	—
489	C₂²×C₁₃	—	2	1	no	—
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	4	1	no	—
492	C₂²×C₁₃	—	4	1	no	—
493	C₂²×C₁₃	—	4	1	no	—
494	C₂²×C₁₃	—	4	1	no	—
495	C₂²×C₁₃	—	4	1	no	—
496	C₂²×C₁₃	—	4	1	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	—	4	1	no	—
499	C₂²×C₁₃	—	4	1	no	—
500	C₂²×C₁₃	—	8	4	no	—
501	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
502	C₄×C₁₃	—	2	1	no	—
503	C₄×C₁₃	—	2	1	no	—
504	C₄×C₁₃	—	2	1	no	—
505	C₄×C₁₃	—	2	1	no	—
506	C₄×C₁₃	—	2	1	no	—
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	1	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	1	no	—
511	C₄×C₁₃	—	2	1	no	—
512	C₄×C₁₃	—	4	1	no	—
513	C₄×C₁₃	—	4	1	no	—
514	C₄×C₁₃	—	4	1	no	—
515	C₄×C₁₃	—	4	1	no	—
516	C₄×C₁₃	—	4	1	no	—
517	C₄×C₁₃	#568	1	2	yes	—
518	C₄×C₁₃	#576	1	1	yes	characteristic
519	C₄×C₁₃	#577	1	1	yes	characteristic
520	C₂×#41	—	2	1	no	—
521	C₂×#41	—	2	1	no	—
522	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
523	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
524	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
525	C₂³×C₄	—	2	1	no	—
526	C₂×M₁₆	—	26	1	no	—
527	C₂×M₁₆	—	26	1	no	—
528	C₂×M₁₆	—	26	1	no	—
529	C₂×M₁₆	—	26	1	no	—
530	C₂²×C₈	—	26	1	no	—
531	C₂²×C₈	—	26	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
534	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
535	#127	—	2	1	no	—
536	#127	C₂×Dic₁₃	1	1	yes	characteristic
537	#127	C₂×Dic₁₃	1	1	yes	characteristic
538	#126	—	2	1	no	—
539	#126	—	2	1	no	—
540	#126	—	2	1	no	—
541	#126	—	2	1	no	—
542	#125	—	2	1	no	—
543	#125	C₂×Dic₁₃	1	1	yes	characteristic
544	#125	C₂×Dic₁₃	1	1	yes	characteristic
545	#124	—	2	1	no	—
546	#124	—	2	1	no	—
547	#124	—	2	1	no	—
548	#124	—	2	1	no	—
549	#124	—	2	1	no	—
550	#124	C₂×Dic₁₃	1	1	yes	characteristic
551	#124	C₂×Dic₁₃	1	1	yes	characteristic
552	#123	—	2	1	no	—
553	#123	—	2	1	no	—
554	#123	—	2	1	no	—
555	#123	—	2	1	no	—
556	#123	—	2	1	no	—
557	#123	—	2	1	no	—
558	#123	—	2	1	no	—
559	#123	—	2	1	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
566	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
567	#121	—	2	1	no	—
568	#121	—	2	1	no	—
569	#121	—	2	1	no	—
570	#121	—	2	1	no	—
571	#121	—	2	1	no	—
572	#121	—	2	1	no	—
573	#121	—	2	1	no	—
574	#121	—	2	1	no	—
575	#121	—	2	1	no	—
576	#121	—	2	1	no	—
577	#121	—	2	1	no	—
578	#121	C₂×Dic₁₃	1	1	yes	characteristic
579	#121	C₂×Dic₁₃	1	1	yes	characteristic
580	#121	C₂×Dic₁₃	1	1	yes	characteristic
581	#121	C₂×Dic₁₃	1	1	yes	characteristic
582	#121	C₂×Dic₁₃	1	1	yes	characteristic
583	#121	C₂×Dic₁₃	1	1	yes	characteristic
584	#120	—	2	1	no	—
585	#120	—	2	1	no	—
586	#120	—	2	1	no	—
587	#120	—	2	1	no	—
588	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
589	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
590	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
591	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
601	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
602	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
603	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
604	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
605	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
606	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
607	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
608	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
609	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
610	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
611	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
612	#117	—	2	1	no	—
613	#117	—	2	1	no	—
614	#117	—	2	1	no	—
615	#117	C₂×Dic₁₃	1	1	yes	characteristic
616	#117	C₂×Dic₁₃	1	1	yes	characteristic
617	#117	C₂×Dic₁₃	1	1	yes	characteristic
618	#117	C₂×Dic₁₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₄²	—	2	1	no	—
622	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
623	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
624	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
625	C₄⋊C₈	—	13	1	no	—
626	C₄⋊C₈	—	13	1	no	—
627	C₄⋊C₈	—	13	1	no	—
628	C₄⋊C₈	—	13	1	no	—
629	C₄⋊C₈	—	26	1	no	—
630	C₄⋊C₈	—	26	1	no	—
631	C₄⋊C₈	—	26	1	no	—
632	C₄⋊C₈	—	26	1	no	—
633	C₄⋊C₈	—	26	1	no	—
634	C₄⋊C₈	—	26	1	no	—
635	C₂²⋊C₈	—	26	1	no	—
636	C₂²⋊C₈	—	26	1	no	—
637	C₂²⋊C₈	—	26	1	no	—
638	C₂²⋊C₈	—	26	1	no	—
639	C₂²⋊C₈	—	26	1	no	—
640	C₂²⋊C₈	—	26	1	no	—
641	#97	—	26	1	no	—
642	#97	—	26	1	no	—
643	#97	—	26	1	no	—
644	#97	—	26	1	no	—
645	C₄×C₈	—	13	1	no	—
646	C₄×C₈	—	13	1	no	—
647	C₄×C₈	—	13	1	no	—
648	C₄×C₈	—	13	1	no	—
649	C₄×C₈	—	26	1	no	—
650	C₄×C₈	—	26	1	no	—
651	C₂×C₁₃	—	4	1	no	—
652	C₂×C₁₃	—	4	1	no	—
653	C₂×C₁₃	—	4	1	no	—
654	C₂×C₁₃	—	8	1	no	—
655	C₂×C₁₃	—	8	1	no	—
656	C₂×C₁₃	—	8	1	no	—
657	C₂×C₁₃	#2879	1	1	yes	characteristic
658	C₂×C₁₃	#2897	1	1	yes	characteristic
659	C₂×C₁₃	#2901	1	1	yes	characteristic
660	C₂⁴	—	2	1	no	—
661	#41	—	4	2	no	—
662	#41	—	4	2	no	—
663	#41	—	8	1	no	—
664	#41	—	8	1	no	—
665	#41	—	8	1	no	—
666	#41	—	8	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
670	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
685	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
686	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
687	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
688	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
689	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	8	1	no	—
699	C₂²×C₄	—	8	1	no	—
700	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
701	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
702	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
703	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
704	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
705	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
706	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
707	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
708	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
709	M₁₆	—	52	2	no	—
710	M₁₆	—	52	2	no	—
711	M₁₆	—	104	1	no	—
712	M₁₆	—	104	1	no	—
713	C₂×C₈	—	26	1	no	—
714	C₂×C₈	—	26	1	no	—
715	C₂×C₈	—	26	1	no	—
716	C₂×C₈	—	26	1	no	—
717	C₂×C₈	—	26	1	no	—
718	C₂×C₈	—	26	1	no	—
719	C₂×C₈	—	26	1	no	—
720	C₂×C₈	—	26	1	no	—
721	C₂×C₈	—	52	2	no	—
722	C₂×C₈	—	104	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	1	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
764	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
765	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
766	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
767	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
768	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
769	C₄²	—	2	1	no	—
770	C₄²	—	2	1	no	—
771	C₄²	—	2	1	no	—
772	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
773	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
774	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
775	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
776	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
777	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
778	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
779	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
780	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
781	C₄²	C₂³×D₁₃	1	1	yes	characteristic
782	C₁₃	#17505	1	1	yes	characteristic, complemented, Sylow
783	C₂³	—	2	1	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	4	2	no	—
787	C₂³	—	8	1	no	—
788	C₂³	—	8	1	no	—
789	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
790	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
791	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
792	Q₈	—	2	2	no	—
793	Q₈	—	4	1	no	—
794	Q₈	—	8	1	no	—
795	Q₈	—	8	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	2	2	no	—
798	D₄	—	2	2	no	—
799	D₄	—	4	1	no	—
800	D₄	—	4	1	no	—
801	D₄	—	4	1	no	—
802	D₄	—	4	2	no	—
803	D₄	—	4	2	no	—
804	D₄	—	8	1	no	—
805	D₄	—	8	1	no	—
806	D₄	—	8	1	no	—
807	D₄	—	8	1	no	—
808	D₄	—	8	1	no	—
809	D₄	—	8	1	no	—
810	D₄	—	8	1	no	—
811	D₄	—	8	1	no	—
812	D₄	—	8	1	no	—
813	D₄	—	8	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	1	no	—
836	C₂×C₄	—	4	1	no	—
837	C₂×C₄	—	4	1	no	—
838	C₂×C₄	—	8	1	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	1	no	—
841	C₂×C₄	—	8	1	no	—
842	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
843	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
844	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
845	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
846	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
847	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
848	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
849	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
850	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
851	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
852	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
853	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
854	C₈	—	26	2	no	—
855	C₈	—	52	1	no	—
856	C₈	—	52	1	no	—
857	C₈	—	52	1	no	—
858	C₈	—	52	1	no	—
859	C₈	—	52	1	no	—
860	C₈	—	52	1	no	—
861	C₈	—	52	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	1	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	8	4	no	—
881	C₂²	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	1	no	—
897	C₄	#11719524	1	2	yes	—
898	C₄	#11719540	1	1	yes	characteristic
899	C₄	#11719541	1	1	yes	characteristic
900	C₂	—	4	1	no	—
901	C₂	—	4	1	no	—
902	C₂	—	4	1	no	—
903	C₂	—	8	1	no	—
904	C₂	—	8	1	no	—
905	C₂	—	8	1	no	—
906	C₂	#13123281	1	1	yes	characteristic
907	C₂	#13123362	1	1	yes	characteristic
908	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, prime radical	C₁₃×#3460	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3460	D₁₃
hypocenter	C₁₃	#17505
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3460

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. #13113305	C₂	semidirect
4. #13113301	C₂	semidirect
5. #13113296	C₂	semidirect
6. #13113287	C₂	semidirect
7. #13113279	C₂	semidirect
8. #13113275	C₂	semidirect
9. #13113270	C₂	semidirect
10. #13113261	C₂	semidirect
11. #13113253	C₂	semidirect
12. #13113249	C₂	semidirect
13. #13113244	C₂	semidirect
14. #13113235	C₂	semidirect
48. #11718587	C₂²	semidirect
50. #11718586	C₂²	semidirect
51. #11718586	C₂²	semidirect
52. #11718586	C₂²	semidirect
54. #11718585	C₂²	semidirect
55. C₂×C₄⋊#1055	C₂²	semidirect
57. C₄×#6099	C₂²	semidirect
58. C₂×C₄×#1055	C₂²	semidirect
59. Q₈⋊#1055	C₂²	semidirect
60. Q₈⋊#1055	C₂²	semidirect
61. Q₈⋊#1055	C₂²	semidirect
62. Q₈⋊#1055	C₂²	semidirect
71. D₄⋊#1055	C₂²	semidirect
72. D₄⋊#1055	C₂²	semidirect
73. D₄⋊#1055	C₂²	semidirect
74. D₄⋊#1055	C₂²	semidirect
782. C₁₃	#17505	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
#13113305	2
#13113301	2
#13113296	2
#13113287	2
#13113279	2
#13113275	2
#13113270	2
#13113261	2
#13113253	2
#13113249	2
#13113244	2
#13113235	2
C₁₃×#3460	2
#17505	13