Subgroups — C₁₃×#62110 #15748449

Order 3328.

2030 conjugacy classes of subgroups.

The subgroup lattice has 938 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	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3384	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3354	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3345	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3325	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3318	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3253	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3235	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3109	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	—	2	1	no	—
19	C₁₃×#556	—	2	1	no	—
20	C₁₃×#555	C₂²	1	2	yes	complemented
21	C₁₃×#554	C₂²	1	2	yes	complemented
22	C₁₃×#553	C₂²	1	4	yes	complemented
23	C₁₃×#550	C₂²	1	1	yes	characteristic
24	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#548	—	2	1	no	—
26	C₁₃×#548	—	2	2	no	—
27	C₁₃×#547	—	2	1	no	—
28	C₁₃×#547	C₂²	1	2	yes	—
29	C₁₃×#547	C₂²	1	1	yes	characteristic
30	C₁₃×#546	—	2	1	no	—
31	C₁₃×#546	—	2	2	no	—
32	D₄²×C₁₃	C₂²	1	2	yes	—
33	D₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#542	—	2	2	no	—
35	C₁₃×#537	—	2	1	no	—
36	C₁₃×#533	C₂²	1	2	yes	complemented
37	C₁₃×#532	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	2	yes	—
39	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#532	C₂²	1	2	yes	complemented
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#525	—	2	1	no	—
43	C₁₃×#525	—	2	2	no	—
44	C₁₃×#520	—	2	1	no	—
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
48	C₁₃×#501	C₂²	1	4	yes	complemented
49	C₁₃×#498	C₂²	1	2	yes	complemented
50	C₁₃×#490	C₂²	1	4	yes	complemented
51	C₁₃×#486	C₂²	1	2	yes	complemented
52	C₁₃×#482	C₂²	1	4	yes	complemented
53	C₁₃×#482	C₂²	1	4	yes	complemented
54	C₁₃×#481	C₂²	1	4	yes	complemented
55	C₁₃×#481	C₂²	1	4	yes	complemented
56	C₁₃×#480	C₂²	1	2	yes	complemented
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#478	C₂²	1	4	yes	complemented
59	C₁₃×#476	C₂²	1	2	yes	—
60	C₁₃×#476	C₂²	1	2	yes	—
61	C₁₃×#476	C₂²	1	2	yes	complemented
62	C₁₃×#476	C₂²	1	2	yes	complemented
63	C₁₃×#476	C₂²	1	2	yes	complemented
64	C₁₃×#476	C₂²	1	4	yes	complemented
65	C₁₃×#476	C₂²	1	2	yes	complemented
66	C₁₃×#474	C₂²	1	1	yes	characteristic
67	C₁₃×#474	C₂²	1	2	yes	complemented
68	C₁₃×#474	C₂²	1	2	yes	complemented
69	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#469	C₂²	1	4	yes	complemented
71	C₁₃×#469	C₂²	1	4	yes	complemented
72	C₁₃×#466	C₂²	1	4	yes	complemented
73	C₁₃×#459	C₂²	1	1	yes	characteristic
74	C₁₃×#459	C₂²	1	4	yes	complemented
75	C₁₃×#459	C₂²	1	2	yes	complemented
76	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#459	C₂²	1	2	yes	complemented
78	C₁₃×#447	C₂²	1	2	yes	—
79	C₁₃×#447	C₂²	1	4	yes	—
80	C₁₃×#446	C₂²	1	2	yes	complemented
81	C₁₃×#442	C₂²	1	4	yes	—
82	C₁₃×#442	C₂²	1	4	yes	complemented
83	C₄×C₁₃×D₈	C₂²	1	2	yes	—
84	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
85	C₁₃×#436	C₂²	1	2	yes	complemented
86	C₁₃×#435	C₂²	1	4	yes	complemented
87	C₁₃×#432	C₂²	1	2	yes	complemented
88	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#428	C₂²	1	4	yes	complemented
90	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#418	C₂²	1	4	yes	—
94	C₂×C₁₃×#102	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂×C₁₃×#41	—	2	1	no	—
99	C₂×C₁₃×#41	—	2	2	no	—
100	C₂×C₁₃×#41	—	2	1	no	—
101	C₂×C₁₃×#41	—	2	2	no	—
102	C₂×C₁₃×#41	—	4	8	no	—
103	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
104	C₂²×Q₈×C₁₃	—	2	1	no	—
105	C₂²×Q₈×C₁₃	—	2	1	no	—
106	C₂²×D₄×C₁₃	—	2	2	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	—	2	2	no	—
111	C₂³×C₄×C₁₃	—	2	1	no	—
112	C₂×C₁₃×D₈	C₂³	1	2	yes	—
113	C₂×C₁₃×D₈	C₂³	1	2	yes	—
114	C₂×C₁₃×D₈	C₂³	1	4	yes	—
115	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
116	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	—	2	1	no	—
118	C₁₃×C₄⋊Q₈	—	2	1	no	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₁₃×#127	C₂³	1	1	yes	characteristic
125	C₁₃×#127	C₂³	1	1	yes	characteristic
126	C₁₃×#127	C₂³	1	2	yes	—
127	C₁₃×#126	—	2	4	no	—
128	C₁₃×#125	C₂³	1	4	yes	—
129	C₁₃×#124	—	2	4	no	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	—	2	1	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	4	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	4	no	—
146	C₁₃×#121	—	2	2	no	—
147	C₁₃×#121	—	2	4	no	—
148	C₁₃×#121	—	2	1	no	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	2	no	—
156	C₁₃×#121	C₂³	1	2	yes	—
157	C₁₃×#121	C₂³	1	4	yes	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#121	C₂³	1	2	yes	—
161	C₁₃×#120	—	2	2	no	—
162	C₁₃×#120	—	2	2	no	—
163	C₁₃×#120	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	—	2	2	no	—
166	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₁₃	—	2	4	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	1	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	2	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	D₄	1	1	yes	characteristic
178	C₄×D₄×C₁₃	D₄	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₁₃	C₂³	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	4	yes	—
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₄×D₄×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	D₄	1	1	yes	characteristic
192	C₁₃×#117	D₄	1	2	yes	—
193	C₁₃×#117	C₂³	1	4	yes	—
194	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₁₃×#107	C₂³	1	2	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#107	C₂³	1	2	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×#106	C₂³	1	4	yes	—
208	C₁₃×#106	C₂³	1	4	yes	—
209	C₁₃×#106	C₂³	1	4	yes	—
210	C₁₃×C₄⋊C₈	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	4	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×#102	C₂³	1	4	yes	—
216	C₁₃×#102	C₂³	1	4	yes	—
217	C₁₃×#102	C₂³	1	2	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₁₃×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₁₃	C₂³	1	2	yes	—
229	#62110	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂⁴×C₁₃	—	2	2	no	—
231	C₂⁴×C₁₃	—	2	1	no	—
232	C₁₃×#41	—	2	4	no	—
233	C₁₃×#41	—	4	8	no	—
234	C₁₃×#41	—	4	8	no	—
235	C₁₃×#41	—	4	4	no	—
236	C₁₃×#41	—	4	4	no	—
237	C₁₃×#41	—	4	4	no	—
238	C₁₃×#41	—	4	4	no	—
239	C₁₃×#41	—	8	4	no	—
240	C₂×Q₈×C₁₃	—	2	1	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	2	no	—
243	C₂×Q₈×C₁₃	—	2	1	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	—	4	4	no	—
246	C₂×Q₈×C₁₃	—	8	2	no	—
247	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	4	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	2	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	1	no	—
257	C₂×D₄×C₁₃	—	2	1	no	—
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	1	no	—
261	C₂×D₄×C₁₃	—	2	1	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	4	1	no	—
264	C₂×D₄×C₁₃	—	4	2	no	—
265	C₂×D₄×C₁₃	—	4	8	no	—
266	C₂×D₄×C₁₃	—	4	4	no	—
267	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
268	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
271	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	2	1	no	—
275	C₂²×C₄×C₁₃	—	2	2	no	—
276	C₂²×C₄×C₁₃	—	2	2	no	—
277	C₂²×C₄×C₁₃	—	2	1	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	2	1	no	—
280	C₂²×C₄×C₁₃	—	2	2	no	—
281	C₂²×C₄×C₁₃	—	2	1	no	—
282	C₂²×C₄×C₁₃	—	2	2	no	—
283	C₂²×C₄×C₁₃	—	2	1	no	—
284	C₂²×C₄×C₁₃	—	2	4	no	—
285	C₂²×C₄×C₁₃	—	4	8	no	—
286	C₂²×C₄×C₁₃	—	4	4	no	—
287	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₁₃×D₈	—	2	4	no	—
294	C₁₃×D₈	—	4	4	no	—
295	C₁₃×D₈	—	4	2	no	—
296	C₁₃×M₁₆	—	4	4	no	—
297	C₂×C₈×C₁₃	—	4	2	no	—
298	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
300	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	4	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	4	no	—
311	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
312	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
313	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
318	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
319	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
320	C₁₃×C₂²⋊C₄	—	2	4	no	—
321	C₁₃×C₂²⋊C₄	—	2	1	no	—
322	C₁₃×C₂²⋊C₄	—	2	1	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	1	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	1	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	4	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	2	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	—	2	4	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
336	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
337	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
338	C₄²×C₁₃	—	2	4	no	—
339	C₄²×C₁₃	C₂×D₄	1	2	yes	—
340	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₁₃	C₂×D₄	1	2	yes	—
343	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₄²×C₁₃	C₂⁴	1	2	yes	—
345	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
346	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
347	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3384	C₂×C₁₃	1	2	yes	complemented
349	#3366	C₂×C₁₃	1	2	yes	complemented
350	#3354	C₂×C₁₃	1	2	yes	complemented
351	#3345	C₂×C₁₃	1	4	yes	complemented
352	#3325	C₂×C₁₃	1	2	yes	complemented
353	#3318	C₂×C₁₃	1	4	yes	complemented
354	#3253	C₂×C₁₃	1	2	yes	complemented
355	#3245	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#3235	C₂×C₁₃	1	2	yes	complemented
357	#3227	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3109	C₂×C₁₃	1	2	yes	complemented
359	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3077	C₂×C₁₃	1	2	yes	complemented
361	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
363	C₂³×C₁₃	—	2	1	no	—
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	2	2	no	—
366	C₂³×C₁₃	—	2	1	no	—
367	C₂³×C₁₃	—	4	2	no	—
368	C₂³×C₁₃	—	4	4	no	—
369	C₂³×C₁₃	—	4	4	no	—
370	C₂³×C₁₃	—	4	2	no	—
371	C₂³×C₁₃	—	8	1	no	—
372	C₂³×C₁₃	—	8	2	no	—
373	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
374	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
375	Q₈×C₁₃	—	2	2	no	—
376	Q₈×C₁₃	—	4	4	no	—
377	Q₈×C₁₃	—	4	4	no	—
378	Q₈×C₁₃	—	4	2	no	—
379	Q₈×C₁₃	—	4	2	no	—
380	Q₈×C₁₃	—	8	2	no	—
381	D₄×C₁₃	—	2	4	no	—
382	D₄×C₁₃	—	2	2	no	—
383	D₄×C₁₃	—	2	2	no	—
384	D₄×C₁₃	—	2	1	no	—
385	D₄×C₁₃	—	2	2	no	—
386	D₄×C₁₃	—	2	1	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	2	2	no	—
389	D₄×C₁₃	—	2	1	no	—
390	D₄×C₁₃	—	4	2	no	—
391	D₄×C₁₃	—	4	4	no	—
392	D₄×C₁₃	—	4	4	no	—
393	D₄×C₁₃	—	4	2	no	—
394	D₄×C₁₃	—	4	4	no	—
395	D₄×C₁₃	—	4	4	no	—
396	D₄×C₁₃	—	4	4	no	—
397	D₄×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	4	2	no	—
399	D₄×C₁₃	—	4	2	no	—
400	D₄×C₁₃	—	8	2	no	—
401	D₄×C₁₃	—	8	1	no	—
402	D₄×C₁₃	—	8	4	no	—
403	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
404	C₂×C₄×C₁₃	—	2	4	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	4	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	4	1	no	—
415	C₂×C₄×C₁₃	—	4	2	no	—
416	C₂×C₄×C₁₃	—	4	4	no	—
417	C₂×C₄×C₁₃	—	4	4	no	—
418	C₂×C₄×C₁₃	—	4	4	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	—	4	2	no	—
421	C₂×C₄×C₁₃	—	4	2	no	—
422	C₂×C₄×C₁₃	—	4	2	no	—
423	C₂×C₄×C₁₃	—	4	4	no	—
424	C₂×C₄×C₁₃	—	4	2	no	—
425	C₂×C₄×C₁₃	—	4	4	no	—
426	C₂×C₄×C₁₃	—	8	4	no	—
427	C₂×C₄×C₁₃	—	8	2	no	—
428	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
429	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
438	C₈×C₁₃	—	2	2	no	—
439	C₈×C₁₃	—	2	4	no	—
440	C₈×C₁₃	—	2	2	no	—
441	C₂²×#41	—	2	1	no	—
442	#556	—	2	1	no	—
443	#555	C₂²×C₁₃	1	2	yes	complemented
444	#554	C₂²×C₁₃	1	2	yes	complemented
445	#553	C₂²×C₁₃	1	4	yes	complemented
446	#550	C₂²×C₁₃	1	1	yes	characteristic
447	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
448	#548	—	2	1	no	—
449	#548	—	2	2	no	—
450	#547	—	2	1	no	—
451	#547	C₂²×C₁₃	1	2	yes	—
452	#547	C₂²×C₁₃	1	1	yes	characteristic
453	#546	—	2	1	no	—
454	#546	—	2	2	no	—
455	D₄²	C₂²×C₁₃	1	2	yes	—
456	D₄²	C₂²×C₁₃	1	1	yes	characteristic
457	#542	—	2	2	no	—
458	#537	—	2	1	no	—
459	#533	C₂²×C₁₃	1	2	yes	complemented
460	#532	C₂²×C₁₃	1	1	yes	characteristic
461	#532	C₂²×C₁₃	1	2	yes	—
462	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	#532	C₂²×C₁₃	1	2	yes	complemented
464	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	#525	—	2	1	no	—
466	#525	—	2	2	no	—
467	#520	—	2	1	no	—
468	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
470	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
471	#501	C₂²×C₁₃	1	4	yes	complemented
472	#498	C₂²×C₁₃	1	2	yes	complemented
473	#490	C₂²×C₁₃	1	4	yes	complemented
474	#486	C₂²×C₁₃	1	2	yes	complemented
475	#482	C₂²×C₁₃	1	4	yes	complemented
476	#482	C₂²×C₁₃	1	4	yes	complemented
477	#481	C₂²×C₁₃	1	4	yes	complemented
478	#481	C₂²×C₁₃	1	4	yes	complemented
479	#480	C₂²×C₁₃	1	2	yes	complemented
480	#478	C₂²×C₁₃	1	4	yes	—
481	#478	C₂²×C₁₃	1	4	yes	complemented
482	#476	C₂²×C₁₃	1	2	yes	—
483	#476	C₂²×C₁₃	1	2	yes	—
484	#476	C₂²×C₁₃	1	2	yes	complemented
485	#476	C₂²×C₁₃	1	4	yes	complemented
486	#476	C₂²×C₁₃	1	2	yes	complemented
487	#476	C₂²×C₁₃	1	2	yes	complemented
488	#476	C₂²×C₁₃	1	2	yes	complemented
489	#474	C₂²×C₁₃	1	1	yes	characteristic
490	#474	C₂²×C₁₃	1	2	yes	complemented
491	#474	C₂²×C₁₃	1	2	yes	complemented
492	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	#469	C₂²×C₁₃	1	4	yes	complemented
494	#469	C₂²×C₁₃	1	4	yes	complemented
495	#466	C₂²×C₁₃	1	4	yes	complemented
496	#459	C₂²×C₁₃	1	1	yes	characteristic
497	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	#459	C₂²×C₁₃	1	2	yes	complemented
499	#459	C₂²×C₁₃	1	2	yes	complemented
500	#459	C₂²×C₁₃	1	4	yes	complemented
501	#447	C₂²×C₁₃	1	2	yes	—
502	#447	C₂²×C₁₃	1	4	yes	—
503	#446	C₂²×C₁₃	1	2	yes	complemented
504	#442	C₂²×C₁₃	1	4	yes	—
505	#442	C₂²×C₁₃	1	4	yes	complemented
506	C₄×D₈	C₂²×C₁₃	1	2	yes	—
507	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
508	#436	C₂²×C₁₃	1	2	yes	complemented
509	#435	C₂²×C₁₃	1	4	yes	complemented
510	#432	C₂²×C₁₃	1	2	yes	complemented
511	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
512	#428	C₂²×C₁₃	1	4	yes	complemented
513	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
514	#423	C₂²×C₁₃	1	2	yes	complemented
515	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
516	#418	C₂²×C₁₃	1	4	yes	—
517	C₂×#102	C₂²×C₁₃	1	2	yes	—
518	C₂²×C₁₃	—	2	1	no	—
519	C₂²×C₁₃	—	2	1	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	2	no	—
522	C₂²×C₁₃	—	2	2	no	—
523	C₂²×C₁₃	—	2	2	no	—
524	C₂²×C₁₃	—	4	1	no	—
525	C₂²×C₁₃	—	4	1	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	1	no	—
528	C₂²×C₁₃	—	4	2	no	—
529	C₂²×C₁₃	—	4	1	no	—
530	C₂²×C₁₃	—	4	2	no	—
531	C₂²×C₁₃	—	4	2	no	—
532	C₂²×C₁₃	—	4	2	no	—
533	C₂²×C₁₃	—	4	1	no	—
534	C₂²×C₁₃	—	4	2	no	—
535	C₂²×C₁₃	—	8	4	no	—
536	C₂²×C₁₃	—	8	8	no	—
537	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
538	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₁₃	—	2	1	no	—
540	C₄×C₁₃	—	2	2	no	—
541	C₄×C₁₃	—	2	1	no	—
542	C₄×C₁₃	—	2	1	no	—
543	C₄×C₁₃	—	2	2	no	—
544	C₄×C₁₃	—	2	2	no	—
545	C₄×C₁₃	—	4	4	no	—
546	C₄×C₁₃	—	4	1	no	—
547	C₄×C₁₃	—	4	2	no	—
548	C₄×C₁₃	—	4	1	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
551	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
552	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₄×C₁₃	#585	1	1	yes	characteristic
554	C₂×#41	—	2	1	no	—
555	C₂×#41	—	2	2	no	—
556	C₂×#41	—	2	1	no	—
557	C₂×#41	—	2	1	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	—	2	1	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	—	4	8	no	—
562	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
563	C₂²×Q₈	—	2	1	no	—
564	C₂²×Q₈	—	2	1	no	—
565	C₂²×D₄	—	2	2	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
569	C₂³×C₄	—	2	2	no	—
570	C₂³×C₄	—	2	1	no	—
571	C₂×D₈	C₂³×C₁₃	1	2	yes	—
572	C₂×D₈	C₂³×C₁₃	1	2	yes	—
573	C₂×D₈	C₂³×C₁₃	1	4	yes	—
574	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
575	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
576	C₄⋊Q₈	—	2	1	no	—
577	C₄⋊Q₈	—	2	1	no	—
578	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
579	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
580	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
581	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
582	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
583	#127	C₂³×C₁₃	1	1	yes	characteristic
584	#127	C₂³×C₁₃	1	2	yes	—
585	#127	C₂³×C₁₃	1	1	yes	characteristic
586	#126	—	2	4	no	—
587	#125	C₂³×C₁₃	1	4	yes	—
588	#124	—	2	4	no	—
589	#124	—	2	1	no	—
590	#124	—	2	2	no	—
591	#124	—	2	1	no	—
592	#124	—	2	2	no	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	#123	—	2	2	no	—
596	#123	—	2	4	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	—	2	1	no	—
603	C₂²⋊Q₈	—	2	2	no	—
604	C₂²⋊Q₈	—	2	4	no	—
605	#121	—	2	2	no	—
606	#121	—	2	4	no	—
607	#121	—	2	1	no	—
608	#121	—	2	2	no	—
609	#121	—	2	2	no	—
610	#121	—	2	1	no	—
611	#121	—	2	1	no	—
612	#121	—	2	2	no	—
613	#121	—	2	1	no	—
614	#121	—	2	2	no	—
615	#121	C₂³×C₁₃	1	2	yes	—
616	#121	C₂³×C₁₃	1	2	yes	—
617	#121	C₂³×C₁₃	1	2	yes	—
618	#121	C₂³×C₁₃	1	2	yes	—
619	#121	C₂³×C₁₃	1	4	yes	—
620	#120	—	2	2	no	—
621	#120	—	2	2	no	—
622	#120	—	2	2	no	—
623	C₄×Q₈	—	2	2	no	—
624	C₄×Q₈	—	2	2	no	—
625	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
626	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
627	C₄×D₄	—	2	4	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
637	C₄×D₄	D₄×C₁₃	1	2	yes	—
638	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
639	C₄×D₄	C₂³×C₁₃	1	2	yes	—
640	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₄×D₄	C₂³×C₁₃	1	2	yes	—
643	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
644	C₄×D₄	C₂³×C₁₃	1	2	yes	—
645	C₄×D₄	C₂³×C₁₃	1	4	yes	—
646	C₄×D₄	C₂³×C₁₃	1	2	yes	—
647	C₄×D₄	C₂³×C₁₃	1	2	yes	—
648	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
649	#117	—	2	2	no	—
650	#117	D₄×C₁₃	1	1	yes	characteristic
651	#117	D₄×C₁₃	1	2	yes	—
652	#117	C₂³×C₁₃	1	4	yes	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	—	2	2	no	—
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	2	no	—
660	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
662	#107	C₂³×C₁₃	1	2	yes	—
663	#107	C₂³×C₁₃	1	4	yes	—
664	#107	C₂³×C₁₃	1	2	yes	—
665	#106	C₂³×C₁₃	1	4	yes	—
666	#106	C₂³×C₁₃	1	4	yes	—
667	#106	C₂³×C₁₃	1	4	yes	—
668	#106	C₂³×C₁₃	1	4	yes	—
669	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
670	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
671	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
672	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
673	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
674	#102	C₂³×C₁₃	1	4	yes	—
675	#102	C₂³×C₁₃	1	4	yes	—
676	#102	C₂³×C₁₃	1	2	yes	—
677	#102	C₂³×C₁₃	1	4	yes	—
678	#102	C₂³×C₁₃	1	4	yes	—
679	#102	C₂³×C₁₃	1	2	yes	—
680	#102	C₂³×C₁₃	1	2	yes	—
681	#102	C₂³×C₁₃	1	2	yes	—
682	#102	C₂³×C₁₃	1	4	yes	—
683	#102	C₂³×C₁₃	1	4	yes	—
684	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
685	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
686	#97	C₂³×C₁₃	1	4	yes	—
687	C₄×C₈	C₂³×C₁₃	1	2	yes	—
688	C₂×C₁₃	—	2	2	no	—
689	C₂×C₁₃	—	4	2	no	—
690	C₂×C₁₃	—	4	2	no	—
691	C₂×C₁₃	—	8	2	no	—
692	C₂×C₁₃	—	8	1	no	—
693	C₂×C₁₃	—	8	2	no	—
694	C₂×C₁₃	#3489	1	1	yes	characteristic
695	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
696	C₂×C₁₃	#3585	1	1	yes	characteristic
697	C₂⁴	—	2	2	no	—
698	C₂⁴	—	2	1	no	—
699	#41	—	2	4	no	—
700	#41	—	4	8	no	—
701	#41	—	4	8	no	—
702	#41	—	4	4	no	—
703	#41	—	4	4	no	—
704	#41	—	4	4	no	—
705	#41	—	4	4	no	—
706	#41	—	8	4	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	4	4	no	—
713	C₂×Q₈	—	8	2	no	—
714	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	4	1	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	8	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
736	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
738	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
739	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	4	8	no	—
753	C₂²×C₄	—	4	4	no	—
754	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
757	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
760	D₈	—	2	4	no	—
761	D₈	—	4	4	no	—
762	D₈	—	4	2	no	—
763	M₁₆	—	4	4	no	—
764	C₂×C₈	—	4	2	no	—
765	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
766	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
767	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
781	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
782	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
783	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
784	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
786	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
803	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
804	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
805	C₄²	—	2	4	no	—
806	C₄²	C₂×D₄×C₁₃	1	2	yes	—
807	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₄²	C₂×D₄×C₁₃	1	2	yes	—
810	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₄²	C₂⁴×C₁₃	1	2	yes	—
812	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
813	C₁₃	#62110	1	1	yes	characteristic, direct product factor, Sylow
814	C₂³	—	2	1	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	4	2	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	8	1	no	—
823	C₂³	—	8	2	no	—
824	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
825	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
826	Q₈	—	2	2	no	—
827	Q₈	—	4	4	no	—
828	Q₈	—	4	4	no	—
829	Q₈	—	4	2	no	—
830	Q₈	—	4	2	no	—
831	Q₈	—	8	2	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	1	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	1	no	—
838	D₄	—	2	2	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	1	no	—
841	D₄	—	4	2	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	2	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	2	no	—
851	D₄	—	8	2	no	—
852	D₄	—	8	1	no	—
853	D₄	—	8	4	no	—
854	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	4	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	4	2	no	—
874	C₂×C₄	—	4	4	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	4	no	—
877	C₂×C₄	—	8	4	no	—
878	C₂×C₄	—	8	2	no	—
879	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
880	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
881	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
883	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
884	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
886	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
888	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
889	C₈	—	2	2	no	—
890	C₈	—	2	4	no	—
891	C₈	—	2	2	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	8	4	no	—
910	C₂²	—	8	8	no	—
911	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
912	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
913	C₄	—	2	2	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	4	no	—
924	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
925	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
926	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
927	C₄	C₁₃×#585	1	1	yes	characteristic
928	C₂	—	2	2	no	—
929	C₂	—	4	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	8	1	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₁₃×#3489	1	1	yes	characteristic
935	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
936	C₂	C₁₃×#3585	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. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3384	C₂	semidirect
4. C₁₃×#3366	C₂	semidirect
5. C₁₃×#3354	C₂	semidirect
6. C₁₃×#3345	C₂	semidirect
7. C₁₃×#3325	C₂	semidirect
8. C₁₃×#3318	C₂	semidirect
9. C₁₃×#3253	C₂	semidirect
10. C₁₃×#3245	C₂	semidirect
11. C₁₃×#3235	C₂	semidirect
12. C₁₃×#3227	C₂	semidirect
13. C₁₃×#3109	C₂	semidirect
14. C₁₃×#3100	C₂	semidirect
15. C₁₃×#3077	C₂	semidirect
16. C₂×C₁₃×#476	C₂	semidirect
17. C₁₃×#2989	C₂	semidirect
20. C₁₃×#555	C₂²	semidirect
21. C₁₃×#554	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
36. C₁₃×#533	C₂²	semidirect
39. C₁₃×#532	C₂²	semidirect
40. C₁₃×#532	C₂²	semidirect
41. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#498	C₂²	semidirect
50. C₁₃×#490	C₂²	semidirect
51. C₁₃×#486	C₂²	semidirect
52. C₁₃×#482	C₂²	semidirect
53. C₁₃×#482	C₂²	semidirect
54. C₁₃×#481	C₂²	semidirect
55. C₁₃×#481	C₂²	semidirect
56. C₁₃×#480	C₂²	semidirect
58. C₁₃×#478	C₂²	semidirect
61. C₁₃×#476	C₂²	semidirect
62. C₁₃×#476	C₂²	semidirect
63. C₁₃×#476	C₂²	semidirect
64. C₁₃×#476	C₂²	semidirect
65. C₁₃×#476	C₂²	semidirect
67. C₁₃×#474	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
69. C₁₃×#474	C₂²	semidirect
70. C₁₃×#469	C₂²	semidirect
71. C₁₃×#469	C₂²	semidirect
72. C₁₃×#466	C₂²	semidirect
74. C₁₃×#459	C₂²	semidirect
75. C₁₃×#459	C₂²	semidirect
76. C₁₃×#459	C₂²	semidirect
77. C₁₃×#459	C₂²	semidirect
80. C₁₃×#446	C₂²	semidirect
82. C₁₃×#442	C₂²	semidirect
84. C₄×C₁₃×D₈	C₂²	semidirect
85. C₁₃×#436	C₂²	semidirect
86. C₁₃×#435	C₂²	semidirect
87. C₁₃×#432	C₂²	semidirect
88. C₁₃×#431	C₂²	semidirect
89. C₁₃×#428	C₂²	semidirect
90. C₂×C₁₃×#106	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
92. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
229. #62110	C₁₃	direct (N × H)
346. #3511	C₂×C₁₃	semidirect
347. D₄×#41	C₂×C₁₃	semidirect
348. #3384	C₂×C₁₃	semidirect
349. #3366	C₂×C₁₃	semidirect
350. #3354	C₂×C₁₃	semidirect
351. #3345	C₂×C₁₃	semidirect
352. #3325	C₂×C₁₃	semidirect
353. #3318	C₂×C₁₃	semidirect
354. #3253	C₂×C₁₃	semidirect
355. #3245	C₂×C₁₃	semidirect
356. #3235	C₂×C₁₃	semidirect
357. #3227	C₂×C₁₃	semidirect
358. #3109	C₂×C₁₃	semidirect
359. #3100	C₂×C₁₃	semidirect
360. #3077	C₂×C₁₃	semidirect
361. C₂×#476	C₂×C₁₃	semidirect
362. #2989	C₂×C₁₃	semidirect
443. #555	C₂²×C₁₃	semidirect
444. #554	C₂²×C₁₃	semidirect
445. #553	C₂²×C₁₃	semidirect
459. #533	C₂²×C₁₃	semidirect
462. #532	C₂²×C₁₃	semidirect
463. #532	C₂²×C₁₃	semidirect
464. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
471. #501	C₂²×C₁₃	semidirect
472. #498	C₂²×C₁₃	semidirect
473. #490	C₂²×C₁₃	semidirect
474. #486	C₂²×C₁₃	semidirect
475. #482	C₂²×C₁₃	semidirect
476. #482	C₂²×C₁₃	semidirect
477. #481	C₂²×C₁₃	semidirect
478. #481	C₂²×C₁₃	semidirect
479. #480	C₂²×C₁₃	semidirect
481. #478	C₂²×C₁₃	semidirect
484. #476	C₂²×C₁₃	semidirect
485. #476	C₂²×C₁₃	semidirect
486. #476	C₂²×C₁₃	semidirect
487. #476	C₂²×C₁₃	semidirect
488. #476	C₂²×C₁₃	semidirect
490. #474	C₂²×C₁₃	semidirect
491. #474	C₂²×C₁₃	semidirect
492. #474	C₂²×C₁₃	semidirect
493. #469	C₂²×C₁₃	semidirect
494. #469	C₂²×C₁₃	semidirect
495. #466	C₂²×C₁₃	semidirect
497. #459	C₂²×C₁₃	semidirect
498. #459	C₂²×C₁₃	semidirect
499. #459	C₂²×C₁₃	semidirect
500. #459	C₂²×C₁₃	semidirect
503. #446	C₂²×C₁₃	semidirect
505. #442	C₂²×C₁₃	semidirect
507. C₄×D₈	C₂²×C₁₃	semidirect
508. #436	C₂²×C₁₃	semidirect
509. #435	C₂²×C₁₃	semidirect
510. #432	C₂²×C₁₃	semidirect
511. #431	C₂²×C₁₃	semidirect
512. #428	C₂²×C₁₃	semidirect
513. C₂×#106	C₂²×C₁₃	semidirect
514. #423	C₂²×C₁₃	semidirect
515. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
813. C₁₃	#62110	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
D₄×C₁₃×#41	2
C₁₃×#3384	2
C₁₃×#3366	2
C₁₃×#3354	2
C₁₃×#3345	2
C₁₃×#3325	2
C₁₃×#3318	2
C₁₃×#3253	2
C₁₃×#3245	2
C₁₃×#3235	2
C₁₃×#3227	2
C₁₃×#3109	2
C₁₃×#3100	2
C₁₃×#3077	2
C₂×C₁₃×#476	2
C₁₃×#2989	2
#62110	13

Subgroups — C13×#62110 #15748449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62110 #15748449