Subgroups — C₁₃×#61998 #15748337

Order 3328.

1840 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3393	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3330	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3327	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3277	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3212	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3104	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	4	yes	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₁₃×#557	C₂²	1	1	yes	characteristic
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	C₂²	1	2	yes	—
23	C₁₃×#556	C₂²	1	1	yes	characteristic
24	C₁₃×#555	—	2	1	no	—
25	C₁₃×#554	—	2	1	no	—
26	C₁₃×#553	—	2	2	no	—
27	C₁₃×#552	—	2	2	no	—
28	C₁₃×#552	C₂²	1	2	yes	—
29	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#548	C₂²	1	2	yes	—
31	C₁₃×#548	C₂²	1	4	yes	—
32	C₁₃×#547	—	2	1	no	—
33	C₁₃×#547	C₂²	1	2	yes	—
34	C₁₃×#547	C₂²	1	1	yes	characteristic
35	C₁₃×#542	—	2	2	no	—
36	C₁₃×#537	—	2	1	no	—
37	C₁₃×#533	—	2	1	no	—
38	C₁₃×#533	C₂²	1	2	yes	—
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₁₃×#532	C₂²	1	2	yes	—
41	C₁₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₁₃×#529	—	2	2	no	—
44	C₁₃×#529	C₂²	1	2	yes	—
45	C₁₃×#520	—	2	1	no	—
46	C₄×C₁₃×#41	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
50	C₁₃×#495	C₂²	1	4	yes	—
51	C₁₃×#494	C₂²	1	2	yes	—
52	C₁₃×#488	C₂²	1	4	yes	—
53	C₁₃×#487	C₂²	1	2	yes	—
54	C₁₃×#484	C₂²	1	4	yes	—
55	C₁₃×#482	C₂²	1	2	yes	—
56	C₁₃×#479	C₂²	1	4	yes	—
57	C₁₃×#477	C₂²	1	1	yes	characteristic
58	C₁₃×#477	C₂²	1	2	yes	—
59	C₁₃×#476	C₂²	1	1	yes	characteristic
60	C₁₃×#474	C₂²	1	2	yes	—
61	C₁₃×#470	C₂²	1	4	yes	—
62	C₁₃×#468	C₂²	1	4	yes	—
63	C₁₃×#468	C₂²	1	4	yes	—
64	C₁₃×#464	C₂²	1	4	yes	—
65	C₁₃×#464	C₂²	1	4	yes	—
66	C₁₃×#464	C₂²	1	4	yes	—
67	C₁₃×#462	C₂²	1	2	yes	—
68	C₁₃×#462	C₂²	1	2	yes	—
69	C₁₃×#462	C₂²	1	2	yes	—
70	C₁₃×#462	C₂²	1	2	yes	—
71	C₁₃×#461	C₂²	1	2	yes	—
72	C₁₃×#461	C₂²	1	2	yes	—
73	C₁₃×#461	C₂²	1	2	yes	—
74	C₁₃×#460	C₂²	1	1	yes	characteristic
75	C₁₃×#460	C₂²	1	2	yes	—
76	C₁₃×#459	C₂²	1	1	yes	characteristic
77	C₁₃×#452	C₂²	1	4	yes	—
78	C₁₃×#451	C₂²	1	4	yes	—
79	C₁₃×#451	C₂²	1	4	yes	—
80	C₁₃×#449	C₂²	1	2	yes	—
81	C₁₃×#449	C₂²	1	4	yes	—
82	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
83	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
84	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
86	C₄×C₁₃×D₈	C₂²	1	2	yes	—
87	C₁₃×#436	C₂²	1	2	yes	—
88	C₁₃×#436	C₂²	1	4	yes	—
89	C₁₃×#431	C₂²	1	2	yes	—
90	C₁₃×#431	C₂²	1	1	yes	characteristic
91	C₁₃×#423	C₂²	1	2	yes	—
92	C₁₃×#423	C₂²	1	1	yes	characteristic
93	C₁₃×#419	C₂²	1	2	yes	—
94	C₁₃×#417	C₂²	1	4	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	4	yes	—
100	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
101	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
102	C₁₃×#137	—	4	8	no	—
103	C₁₃×#137	—	4	4	no	—
104	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×D₈	C₂³	1	2	yes	—
111	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	—	2	1	no	—
116	C₁₃×C₄⋊Q₈	—	2	1	no	—
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₁₃×#127	C₂³	1	1	yes	characteristic
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	4	no	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	—	2	2	no	—
129	C₁₃×#125	—	2	1	no	—
130	C₁₃×#125	—	2	2	no	—
131	C₁₃×#125	C₂³	1	2	yes	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	4	no	—
134	C₁₃×#124	—	2	1	no	—
135	C₁₃×#124	C₂³	1	4	yes	—
136	C₁₃×#124	C₂³	1	2	yes	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	4	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	1	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	4	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	4	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	2	no	—
162	C₄×Q₈×C₁₃	—	2	2	no	—
163	C₄×Q₈×C₁₃	—	2	1	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	4	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	1	no	—
182	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₁₃	D₄	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₁₃	C₂³	1	2	yes	—
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	1	no	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	—	2	2	no	—
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	D₄	1	1	yes	characteristic
197	C₁₃×#117	D₄	1	2	yes	—
198	C₁₃×#117	C₂³	1	1	yes	characteristic
199	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₄²×C₁₃	—	2	2	no	—
205	C₂×C₄²×C₁₃	—	2	1	no	—
206	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
207	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
208	C₁₃×#107	C₂³	1	2	yes	—
209	C₁₃×#107	C₂³	1	4	yes	—
210	C₁₃×#106	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	C₄×C₈×C₁₃	C₂³	1	4	yes	—
230	#61998	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₁₃×#41	—	2	2	no	—
232	C₁₃×#41	—	4	2	no	—
233	C₁₃×#41	—	4	1	no	—
234	C₁₃×#41	—	4	4	no	—
235	C₁₃×#41	—	4	4	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	2	1	no	—
240	C₂×Q₈×C₁₃	—	2	1	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	4	no	—
243	C₂×Q₈×C₁₃	—	4	2	no	—
244	C₂×Q₈×C₁₃	—	4	2	no	—
245	C₂×Q₈×C₁₃	—	4	2	no	—
246	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
249	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	1	no	—
255	C₂×D₄×C₁₃	—	2	1	no	—
256	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	4	no	—
268	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₁₃×Q₁₆	—	2	8	no	—
275	C₁₃×Q₁₆	—	4	4	no	—
276	C₁₃×Q₁₆	—	4	4	no	—
277	C₁₃×SD₁₆	—	2	4	no	—
278	C₁₃×SD₁₆	—	4	4	no	—
279	C₁₃×SD₁₆	—	4	4	no	—
280	C₁₃×D₈	—	4	2	no	—
281	C₁₃×M₁₆	—	4	4	no	—
282	C₁₃×M₁₆	—	4	2	no	—
283	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
284	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	4	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	1	no	—
301	C₁₃×C₄⋊C₄	—	2	1	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	1	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	4	no	—
306	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
307	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
308	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	1	no	—
318	C₁₃×C₂²⋊C₄	—	2	4	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	1	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
328	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₄²×C₁₃	—	2	1	no	—
331	C₄²×C₁₃	—	2	1	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	1	no	—
335	C₄²×C₁₃	—	2	2	no	—
336	C₄²×C₁₃	—	2	4	no	—
337	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₁₃	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	C₂×D₄	1	2	yes	—
341	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₄²×C₁₃	C₂⁴	1	2	yes	—
343	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
344	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3482	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3393	C₂×C₁₃	1	2	yes	complemented
347	#3364	C₂×C₁₃	1	2	yes	complemented
348	#3330	C₂×C₁₃	1	2	yes	complemented
349	#3327	C₂×C₁₃	1	4	yes	complemented
350	#3277	C₂×C₁₃	1	4	yes	complemented
351	#3276	C₂×C₁₃	1	2	yes	complemented
352	#3254	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3252	C₂×C₁₃	1	2	yes	complemented
354	#3212	C₂×C₁₃	1	2	yes	complemented
355	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#3106	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#3104	C₂×C₁₃	1	2	yes	complemented
358	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#3037	C₂×C₁₃	1	2	yes	complemented
360	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
364	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	Q₈×C₁₃	—	2	2	no	—
366	Q₈×C₁₃	—	2	1	no	—
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	4	no	—
369	Q₈×C₁₃	—	2	2	no	—
370	Q₈×C₁₃	—	2	4	no	—
371	Q₈×C₁₃	—	4	4	no	—
372	Q₈×C₁₃	—	4	2	no	—
373	Q₈×C₁₃	—	4	2	no	—
374	Q₈×C₁₃	—	8	2	no	—
375	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
376	D₄×C₁₃	—	2	2	no	—
377	D₄×C₁₃	—	2	2	no	—
378	D₄×C₁₃	—	2	1	no	—
379	D₄×C₁₃	—	2	1	no	—
380	D₄×C₁₃	—	2	2	no	—
381	D₄×C₁₃	—	4	2	no	—
382	D₄×C₁₃	—	4	2	no	—
383	D₄×C₁₃	—	4	2	no	—
384	D₄×C₁₃	—	4	4	no	—
385	D₄×C₁₃	—	4	4	no	—
386	D₄×C₁₃	—	4	2	no	—
387	D₄×C₁₃	—	8	4	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	4	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	4	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	4	no	—
405	C₂×C₄×C₁₃	—	4	4	no	—
406	C₂×C₄×C₁₃	—	4	2	no	—
407	C₂×C₄×C₁₃	—	4	4	no	—
408	C₂×C₄×C₁₃	—	4	2	no	—
409	C₂×C₄×C₁₃	—	8	4	no	—
410	C₂×C₄×C₁₃	—	8	2	no	—
411	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
420	C₈×C₁₃	—	2	2	no	—
421	C₈×C₁₃	—	2	4	no	—
422	C₈×C₁₃	—	2	2	no	—
423	C₂×#137	C₂²×C₁₃	1	4	yes	—
424	C₂×#137	C₂²×C₁₃	1	2	yes	—
425	#557	C₂²×C₁₃	1	1	yes	characteristic
426	#556	—	2	1	no	—
427	#556	C₂²×C₁₃	1	2	yes	—
428	#556	C₂²×C₁₃	1	1	yes	characteristic
429	#555	—	2	1	no	—
430	#554	—	2	1	no	—
431	#553	—	2	2	no	—
432	#552	—	2	2	no	—
433	#552	C₂²×C₁₃	1	2	yes	—
434	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
435	#548	C₂²×C₁₃	1	2	yes	—
436	#548	C₂²×C₁₃	1	4	yes	—
437	#547	—	2	1	no	—
438	#547	C₂²×C₁₃	1	2	yes	—
439	#547	C₂²×C₁₃	1	1	yes	characteristic
440	#542	—	2	2	no	—
441	#537	—	2	1	no	—
442	#533	—	2	1	no	—
443	#533	C₂²×C₁₃	1	2	yes	—
444	#533	C₂²×C₁₃	1	1	yes	characteristic
445	#532	C₂²×C₁₃	1	2	yes	—
446	#532	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
448	#529	—	2	2	no	—
449	#529	C₂²×C₁₃	1	2	yes	—
450	#520	—	2	1	no	—
451	C₄×#41	—	2	1	no	—
452	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
453	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
455	#495	C₂²×C₁₃	1	4	yes	—
456	#494	C₂²×C₁₃	1	2	yes	—
457	#488	C₂²×C₁₃	1	4	yes	—
458	#487	C₂²×C₁₃	1	2	yes	—
459	#484	C₂²×C₁₃	1	4	yes	—
460	#482	C₂²×C₁₃	1	2	yes	—
461	#479	C₂²×C₁₃	1	4	yes	—
462	#477	C₂²×C₁₃	1	1	yes	characteristic
463	#477	C₂²×C₁₃	1	2	yes	—
464	#476	C₂²×C₁₃	1	1	yes	characteristic
465	#474	C₂²×C₁₃	1	2	yes	—
466	#470	C₂²×C₁₃	1	4	yes	—
467	#468	C₂²×C₁₃	1	4	yes	—
468	#468	C₂²×C₁₃	1	4	yes	—
469	#464	C₂²×C₁₃	1	4	yes	—
470	#464	C₂²×C₁₃	1	4	yes	—
471	#464	C₂²×C₁₃	1	4	yes	—
472	#462	C₂²×C₁₃	1	2	yes	—
473	#462	C₂²×C₁₃	1	2	yes	—
474	#462	C₂²×C₁₃	1	2	yes	—
475	#462	C₂²×C₁₃	1	2	yes	—
476	#461	C₂²×C₁₃	1	2	yes	—
477	#461	C₂²×C₁₃	1	2	yes	—
478	#461	C₂²×C₁₃	1	2	yes	—
479	#460	C₂²×C₁₃	1	1	yes	characteristic
480	#460	C₂²×C₁₃	1	2	yes	—
481	#459	C₂²×C₁₃	1	1	yes	characteristic
482	#452	C₂²×C₁₃	1	4	yes	—
483	#451	C₂²×C₁₃	1	4	yes	—
484	#451	C₂²×C₁₃	1	4	yes	—
485	#449	C₂²×C₁₃	1	4	yes	—
486	#449	C₂²×C₁₃	1	2	yes	—
487	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
488	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
489	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
490	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
491	C₄×D₈	C₂²×C₁₃	1	2	yes	—
492	#436	C₂²×C₁₃	1	2	yes	—
493	#436	C₂²×C₁₃	1	4	yes	—
494	#431	C₂²×C₁₃	1	2	yes	—
495	#431	C₂²×C₁₃	1	1	yes	characteristic
496	#423	C₂²×C₁₃	1	2	yes	—
497	#423	C₂²×C₁₃	1	1	yes	characteristic
498	#419	C₂²×C₁₃	1	2	yes	—
499	#417	C₂²×C₁₃	1	4	yes	—
500	C₂²×C₁₃	—	2	2	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	4	1	no	—
507	C₂²×C₁₃	—	4	2	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	1	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
513	C₄×C₁₃	—	2	1	no	—
514	C₄×C₁₃	—	2	2	no	—
515	C₄×C₁₃	—	2	2	no	—
516	C₄×C₁₃	—	2	1	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	2	no	—
519	C₄×C₁₃	—	2	1	no	—
520	C₄×C₁₃	—	4	2	no	—
521	C₄×C₁₃	—	4	4	no	—
522	C₄×C₁₃	—	4	1	no	—
523	C₄×C₁₃	—	4	2	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	—	4	1	no	—
526	C₄×C₁₃	#575	1	2	yes	—
527	C₄×C₁₃	#578	1	2	yes	—
528	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
529	C₄×C₁₃	#585	1	1	yes	characteristic
530	C₂×#41	—	2	1	no	—
531	C₂×#41	—	2	1	no	—
532	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
533	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
534	C₂×#41	C₂³×C₁₃	1	4	yes	—
535	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
536	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
537	#137	—	4	8	no	—
538	#137	—	4	4	no	—
539	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
540	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
541	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
542	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
543	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
544	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
545	C₂×D₈	C₂³×C₁₃	1	2	yes	—
546	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
547	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
548	C₄⋊Q₈	—	2	1	no	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
554	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
556	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
557	#127	C₂³×C₁₃	1	1	yes	characteristic
558	#126	—	2	2	no	—
559	#126	—	2	4	no	—
560	#126	—	2	2	no	—
561	#126	—	2	2	no	—
562	#125	—	2	2	no	—
563	#125	—	2	2	no	—
564	#125	—	2	1	no	—
565	#125	—	2	2	no	—
566	#125	C₂³×C₁₃	1	2	yes	—
567	#124	—	2	2	no	—
568	#124	—	2	4	no	—
569	#124	—	2	1	no	—
570	#124	C₂³×C₁₃	1	2	yes	—
571	#124	C₂³×C₁₃	1	4	yes	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	#123	—	2	4	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	4	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
585	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
586	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	4	no	—
590	#121	—	2	2	no	—
591	#121	—	2	1	no	—
592	#121	—	2	2	no	—
593	#121	C₂³×C₁₃	1	2	yes	—
594	#121	C₂³×C₁₃	1	2	yes	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
603	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
604	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
607	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	4	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
618	C₄×D₄	D₄×C₁₃	1	2	yes	—
619	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
621	C₄×D₄	C₂³×C₁₃	1	2	yes	—
622	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
623	C₄×D₄	C₂³×C₁₃	1	2	yes	—
624	#117	—	2	1	no	—
625	#117	—	2	2	no	—
626	#117	—	2	1	no	—
627	#117	—	2	2	no	—
628	#117	—	2	2	no	—
629	#117	—	2	1	no	—
630	#117	—	2	2	no	—
631	#117	D₄×C₁₃	1	1	yes	characteristic
632	#117	D₄×C₁₃	1	2	yes	—
633	#117	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	2	no	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
639	C₂×C₄²	—	2	2	no	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
642	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
643	#107	C₂³×C₁₃	1	2	yes	—
644	#107	C₂³×C₁₃	1	4	yes	—
645	#106	C₂³×C₁₃	1	2	yes	—
646	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
647	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
648	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
650	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
651	#103	C₂³×C₁₃	1	4	yes	—
652	#103	C₂³×C₁₃	1	4	yes	—
653	#103	C₂³×C₁₃	1	4	yes	—
654	#103	C₂³×C₁₃	1	2	yes	—
655	#103	C₂³×C₁₃	1	4	yes	—
656	#103	C₂³×C₁₃	1	4	yes	—
657	#102	C₂³×C₁₃	1	2	yes	—
658	#102	C₂³×C₁₃	1	4	yes	—
659	#102	C₂³×C₁₃	1	2	yes	—
660	#102	C₂³×C₁₃	1	2	yes	—
661	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
662	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
663	C₄×C₈	C₂³×C₁₃	1	2	yes	—
664	C₄×C₈	C₂³×C₁₃	1	4	yes	—
665	C₂×C₁₃	—	4	2	no	—
666	C₂×C₁₃	—	4	1	no	—
667	C₂×C₁₃	—	8	1	no	—
668	C₂×C₁₃	—	8	2	no	—
669	C₂×C₁₃	#3488	1	1	yes	characteristic
670	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
671	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
672	#41	—	2	2	no	—
673	#41	—	4	2	no	—
674	#41	—	4	1	no	—
675	#41	—	4	4	no	—
676	#41	—	4	4	no	—
677	#41	—	4	4	no	—
678	#41	—	4	4	no	—
679	C₂×Q₈	—	2	2	no	—
680	C₂×Q₈	—	2	1	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	4	no	—
684	C₂×Q₈	—	4	2	no	—
685	C₂×Q₈	—	4	2	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
689	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
690	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
699	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
700	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
715	Q₁₆	—	2	8	no	—
716	Q₁₆	—	4	4	no	—
717	Q₁₆	—	4	4	no	—
718	SD₁₆	—	2	4	no	—
719	SD₁₆	—	4	4	no	—
720	SD₁₆	—	4	4	no	—
721	D₈	—	4	2	no	—
722	M₁₆	—	4	4	no	—
723	M₁₆	—	4	2	no	—
724	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
725	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
726	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
750	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
752	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
769	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
770	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
771	C₄²	—	2	1	no	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	4	no	—
778	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₁₃	1	2	yes	—
781	C₄²	C₂×D₄×C₁₃	1	2	yes	—
782	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₄²	C₂⁴×C₁₃	1	2	yes	—
784	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₁₃	#61998	1	1	yes	characteristic, direct product factor, Sylow
786	C₂³	—	2	1	no	—
787	C₂³	—	2	2	no	—
788	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
789	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	1	no	—
792	Q₈	—	2	2	no	—
793	Q₈	—	2	4	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	4	4	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	2	no	—
799	Q₈	—	8	2	no	—
800	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	1	no	—
805	D₄	—	2	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	2	no	—
812	D₄	—	8	4	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
837	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
845	C₈	—	2	2	no	—
846	C₈	—	2	4	no	—
847	C₈	—	2	2	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
861	C₄	—	2	1	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	2	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	4	no	—
874	C₄	C₁₃×#575	1	2	yes	—
875	C₄	C₁₃×#578	1	2	yes	—
876	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
877	C₄	C₁₃×#585	1	1	yes	characteristic
878	C₂	—	4	1	no	—
879	C₂	—	4	2	no	—
880	C₂	—	8	1	no	—
881	C₂	—	8	2	no	—
882	C₂	C₁₃×#3488	1	1	yes	characteristic
883	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
884	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3482	C₂	semidirect
3. C₁₃×#3393	C₂	semidirect
4. C₁₃×#3364	C₂	semidirect
5. C₁₃×#3330	C₂	semidirect
6. C₁₃×#3327	C₂	semidirect
7. C₁₃×#3277	C₂	semidirect
8. C₁₃×#3276	C₂	semidirect
9. C₁₃×#3254	C₂	semidirect
10. C₁₃×#3252	C₂	semidirect
11. C₁₃×#3212	C₂	semidirect
12. C₁₃×#3209	C₂	semidirect
13. C₁₃×#3106	C₂	semidirect
14. C₁₃×#3104	C₂	semidirect
15. C₁₃×#3039	C₂	semidirect
16. C₁₃×#3037	C₂	semidirect
17. C₁₃×#2991	C₂	semidirect
230. #61998	C₁₃	direct (N × H)
344. #3511	C₂×C₁₃	semidirect
345. #3482	C₂×C₁₃	semidirect
346. #3393	C₂×C₁₃	semidirect
347. #3364	C₂×C₁₃	semidirect
348. #3330	C₂×C₁₃	semidirect
349. #3327	C₂×C₁₃	semidirect
350. #3277	C₂×C₁₃	semidirect
351. #3276	C₂×C₁₃	semidirect
352. #3254	C₂×C₁₃	semidirect
353. #3252	C₂×C₁₃	semidirect
354. #3212	C₂×C₁₃	semidirect
355. #3209	C₂×C₁₃	semidirect
356. #3106	C₂×C₁₃	semidirect
357. #3104	C₂×C₁₃	semidirect
358. #3039	C₂×C₁₃	semidirect
359. #3037	C₂×C₁₃	semidirect
360. #2991	C₂×C₁₃	semidirect
785. C₁₃	#61998	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3511	2
C₁₃×#3482	2
C₁₃×#3393	2
C₁₃×#3364	2
C₁₃×#3330	2
C₁₃×#3327	2
C₁₃×#3277	2
C₁₃×#3276	2
C₁₃×#3254	2
C₁₃×#3252	2
C₁₃×#3212	2
C₁₃×#3209	2
C₁₃×#3106	2
C₁₃×#3104	2
C₁₃×#3039	2
C₁₃×#3037	2
C₁₃×#2991	2
#61998	13

Subgroups — C13×#61998 #15748337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61998 #15748337