Subgroups — C₁₃×#61578 #15747917

Order 3328.

2114 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3321	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3313	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3271	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3269	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3194	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3004	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3002	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
20	C₁₃×#559	—	2	2	no	—
21	C₁₃×#556	C₂²	1	2	yes	complemented
22	C₁₃×#555	C₂²	1	2	yes	complemented
23	C₁₃×#553	—	2	2	no	—
24	C₁₃×#550	C₂²	1	2	yes	complemented
25	C₁₃×#548	—	2	2	no	—
26	C₁₃×#548	—	2	2	no	—
27	C₁₃×#548	C₂²	1	4	yes	—
28	C₁₃×#548	C₂²	1	4	yes	—
29	C₁₃×#547	C₂²	1	2	yes	complemented
30	C₁₃×#538	—	2	1	no	—
31	C₁₃×#538	—	2	1	no	—
32	C₁₃×#535	—	2	1	no	—
33	C₁₃×#533	C₂²	1	1	yes	characteristic
34	C₁₃×#532	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#124	—	2	1	no	—
36	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
37	C₁₃×#525	C₂²	1	2	yes	—
38	C₁₃×#525	C₂²	1	2	yes	—
39	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
40	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#121	—	2	1	no	—
42	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
43	C₁₃×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₁₃	—	2	1	no	—
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₁₃×#497	C₂²	1	2	yes	complemented
48	C₁₃×#496	C₂²	1	2	yes	complemented
49	C₁₃×#489	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	2	yes	complemented
51	C₁₃×#485	C₂²	1	4	yes	complemented
52	C₁₃×#483	C₂²	1	2	yes	—
53	C₁₃×#482	C₂²	1	4	yes	complemented
54	C₁₃×#480	C₂²	1	2	yes	—
55	C₁₃×#477	C₂²	1	2	yes	complemented
56	C₁₃×#475	C₂²	1	2	yes	complemented
57	C₁₃×#469	C₂²	1	4	yes	complemented
58	C₁₃×#468	C₂²	1	4	yes	complemented
59	C₁₃×#467	C₂²	1	4	yes	complemented
60	C₁₃×#465	C₂²	1	4	yes	complemented
61	C₁₃×#464	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	complemented
63	C₁₃×#462	C₂²	1	2	yes	complemented
64	C₁₃×#460	C₂²	1	2	yes	complemented
65	C₁₃×#452	C₂²	1	4	yes	complemented
66	C₁₃×#452	C₂²	1	4	yes	complemented
67	C₁₃×#451	C₂²	1	2	yes	—
68	C₁₃×#451	C₂²	1	2	yes	—
69	C₁₃×#451	C₂²	1	4	yes	complemented
70	C₁₃×#450	C₂²	1	2	yes	—
71	C₁₃×#449	C₂²	1	4	yes	complemented
72	C₁₃×#449	C₂²	1	4	yes	complemented
73	C₁₃×#448	C₂²	1	2	yes	—
74	C₁₃×#448	C₂²	1	2	yes	—
75	C₁₃×#448	C₂²	1	4	yes	complemented
76	C₁₃×#447	C₂²	1	2	yes	—
77	C₁₃×#441	C₂²	1	4	yes	complemented
78	C₁₃×#440	C₂²	1	4	yes	complemented
79	C₁₃×#435	C₂²	1	4	yes	complemented
80	C₁₃×#435	C₂²	1	4	yes	complemented
81	C₁₃×#432	C₂²	1	1	yes	characteristic
82	C₁₃×#432	C₂²	1	1	yes	characteristic
83	C₁₃×#419	C₂²	1	4	yes	complemented
84	C₁₃×#416	C₂²	1	4	yes	complemented
85	C₁₃×#407	C₂²	1	2	yes	—
86	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
87	C₂×C₁₃×#41	—	2	1	no	—
88	C₂×C₁₃×#41	—	2	2	no	—
89	C₂×C₁₃×#41	—	4	4	no	—
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂×C₁₃×#41	C₂³	1	2	yes	—
93	C₂²×Q₈×C₁₃	—	2	1	no	—
94	C₂²×Q₈×C₁₃	—	2	2	no	—
95	C₂²×Q₈×C₁₃	—	4	4	no	—
96	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
98	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₃	—	2	1	no	—
104	C₂³×C₄×C₁₃	—	2	1	no	—
105	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#137	—	4	8	no	—
108	C₁₃×#135	—	4	8	no	—
109	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×D₈	C₂³	1	4	yes	—
115	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
116	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×#127	—	2	2	no	—
121	C₁₃×#127	C₂³	1	1	yes	characteristic
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#125	—	2	1	no	—
125	C₁₃×#124	—	2	2	no	—
126	C₁₃×#124	—	2	4	no	—
127	C₁₃×#124	—	2	4	no	—
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	1	no	—
132	C₁₃×#124	—	2	1	no	—
133	C₁₃×#124	C₂³	1	2	yes	—
134	C₁₃×#124	C₂³	1	2	yes	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₁₃×#121	—	2	4	no	—
148	C₁₃×#121	—	2	4	no	—
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	—	2	2	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	C₂³	1	2	yes	—
156	C₁₃×#121	C₂³	1	2	yes	—
157	C₁₃×#121	C₂³	1	2	yes	—
158	C₁₃×#121	C₂³	1	4	yes	—
159	C₁₃×#120	—	2	2	no	—
160	C₁₃×#120	—	2	2	no	—
161	C₄×Q₈×C₁₃	—	2	2	no	—
162	C₄×Q₈×C₁₃	—	2	1	no	—
163	C₄×Q₈×C₁₃	—	2	1	no	—
164	C₄×Q₈×C₁₃	—	2	1	no	—
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	4	no	—
174	C₄×D₄×C₁₃	—	2	4	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	D₄	1	2	yes	—
177	C₄×D₄×C₁₃	D₄	1	2	yes	—
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₁₃×#117	—	2	1	no	—
182	C₁₃×#117	—	2	2	no	—
183	C₁₃×#117	C₂³	1	2	yes	—
184	C₁₃×#117	C₂³	1	2	yes	—
185	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
195	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₄²×C₁₃	—	2	1	no	—
197	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
198	C₁₃×#107	C₂³	1	4	yes	—
199	C₁₃×#106	C₂³	1	4	yes	—
200	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
201	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₁₃×#103	C₂³	1	4	yes	—
203	C₁₃×#103	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#103	C₂³	1	4	yes	—
206	C₁₃×#103	C₂³	1	4	yes	—
207	C₁₃×#102	C₂³	1	4	yes	—
208	C₁₃×#102	C₂³	1	4	yes	—
209	C₁₃×#102	C₂³	1	4	yes	—
210	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
214	C₁₃×#97	C₂³	1	2	yes	—
215	C₁₃×#97	C₂³	1	2	yes	—
216	#61578	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂⁴×C₁₃	—	2	1	no	—
218	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₁₃×#41	—	2	8	no	—
221	C₁₃×#41	—	4	4	no	—
222	C₁₃×#41	—	4	4	no	—
223	C₁₃×#41	—	4	4	no	—
224	C₁₃×#41	—	4	4	no	—
225	C₁₃×#41	—	4	8	no	—
226	C₂×Q₈×C₁₃	—	2	4	no	—
227	C₂×Q₈×C₁₃	—	2	1	no	—
228	C₂×Q₈×C₁₃	—	2	1	no	—
229	C₂×Q₈×C₁₃	—	2	4	no	—
230	C₂×Q₈×C₁₃	—	2	1	no	—
231	C₂×Q₈×C₁₃	—	2	1	no	—
232	C₂×Q₈×C₁₃	—	2	8	no	—
233	C₂×Q₈×C₁₃	—	4	4	no	—
234	C₂×Q₈×C₁₃	—	4	2	no	—
235	C₂×Q₈×C₁₃	—	4	4	no	—
236	C₂×Q₈×C₁₃	—	4	8	no	—
237	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₁₃	—	2	2	no	—
241	C₂×D₄×C₁₃	—	2	4	no	—
242	C₂×D₄×C₁₃	—	2	4	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	4	2	no	—
251	C₂×D₄×C₁₃	—	4	2	no	—
252	C₂×D₄×C₁₃	—	4	4	no	—
253	C₂×D₄×C₁₃	—	4	4	no	—
254	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	4	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	4	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	4	2	no	—
267	C₂²×C₄×C₁₃	—	4	2	no	—
268	C₂²×C₄×C₁₃	—	4	4	no	—
269	C₂²×C₄×C₁₃	—	4	4	no	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
279	C₁₃×Q₁₆	—	2	8	no	—
280	C₁₃×Q₁₆	—	4	4	no	—
281	C₁₃×SD₁₆	—	2	8	no	—
282	C₁₃×SD₁₆	—	4	4	no	—
283	C₁₃×SD₁₆	—	4	4	no	—
284	C₁₃×D₈	—	4	4	no	—
285	C₁₃×M₁₆	—	4	4	no	—
286	C₂×C₈×C₁₃	—	4	4	no	—
287	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
288	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
289	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	—	2	1	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₁₃×C₂²⋊C₄	—	2	4	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
322	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
323	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
324	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	—	2	2	no	—
329	C₄²×C₁₃	—	2	2	no	—
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
334	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₂×#548	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3321	C₂×C₁₃	1	4	yes	complemented
337	#3313	C₂×C₁₃	1	4	yes	complemented
338	#3271	C₂×C₁₃	1	4	yes	complemented
339	#3269	C₂×C₁₃	1	4	yes	complemented
340	#3215	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#3213	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3194	C₂×C₁₃	1	2	yes	complemented
343	#3190	C₂×C₁₃	1	2	yes	complemented
344	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3004	C₂×C₁₃	1	2	yes	complemented
347	#3002	C₂×C₁₃	1	2	yes	complemented
348	#2973	C₂×C₁₃	1	1	yes	characteristic, complemented
349	C₂³×C₁₃	—	2	2	no	—
350	C₂³×C₁₃	—	2	2	no	—
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	2	2	no	—
353	C₂³×C₁₃	—	4	1	no	—
354	C₂³×C₁₃	—	4	1	no	—
355	C₂³×C₁₃	—	4	1	no	—
356	C₂³×C₁₃	—	4	1	no	—
357	C₂³×C₁₃	—	4	2	no	—
358	C₂³×C₁₃	—	4	2	no	—
359	C₂³×C₁₃	—	4	2	no	—
360	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
361	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
362	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
363	Q₈×C₁₃	—	2	4	no	—
364	Q₈×C₁₃	—	2	2	no	—
365	Q₈×C₁₃	—	2	4	no	—
366	Q₈×C₁₃	—	2	4	no	—
367	Q₈×C₁₃	—	4	8	no	—
368	Q₈×C₁₃	—	4	2	no	—
369	Q₈×C₁₃	—	4	2	no	—
370	Q₈×C₁₃	—	8	1	no	—
371	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
372	D₄×C₁₃	—	2	4	no	—
373	D₄×C₁₃	—	2	4	no	—
374	D₄×C₁₃	—	4	2	no	—
375	D₄×C₁₃	—	4	2	no	—
376	D₄×C₁₃	—	4	8	no	—
377	D₄×C₁₃	—	4	2	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	4	8	no	—
380	D₄×C₁₃	—	4	4	no	—
381	D₄×C₁₃	—	8	1	no	—
382	D₄×C₁₃	—	8	2	no	—
383	D₄×C₁₃	—	8	2	no	—
384	D₄×C₁₃	—	8	2	no	—
385	D₄×C₁₃	—	8	2	no	—
386	C₂×C₄×C₁₃	—	2	4	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	4	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	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	4	1	no	—
398	C₂×C₄×C₁₃	—	4	2	no	—
399	C₂×C₄×C₁₃	—	4	1	no	—
400	C₂×C₄×C₁₃	—	4	2	no	—
401	C₂×C₄×C₁₃	—	4	1	no	—
402	C₂×C₄×C₁₃	—	4	8	no	—
403	C₂×C₄×C₁₃	—	4	8	no	—
404	C₂×C₄×C₁₃	—	4	4	no	—
405	C₂×C₄×C₁₃	—	4	2	no	—
406	C₂×C₄×C₁₃	—	4	2	no	—
407	C₂×C₄×C₁₃	—	8	2	no	—
408	C₂×C₄×C₁₃	—	8	2	no	—
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
417	C₈×C₁₃	—	2	4	no	—
418	C₈×C₁₃	—	2	4	no	—
419	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
420	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
422	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
423	#559	—	2	2	no	—
424	#556	C₂²×C₁₃	1	2	yes	complemented
425	#555	C₂²×C₁₃	1	2	yes	complemented
426	#553	—	2	2	no	—
427	#550	C₂²×C₁₃	1	2	yes	complemented
428	#548	—	2	2	no	—
429	#548	—	2	2	no	—
430	#548	C₂²×C₁₃	1	4	yes	—
431	#548	C₂²×C₁₃	1	4	yes	—
432	#547	C₂²×C₁₃	1	2	yes	complemented
433	#538	—	2	1	no	—
434	#538	—	2	1	no	—
435	#535	—	2	1	no	—
436	#533	C₂²×C₁₃	1	1	yes	characteristic
437	#532	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×#124	—	2	1	no	—
439	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
440	#525	C₂²×C₁₃	1	2	yes	—
441	#525	C₂²×C₁₃	1	2	yes	—
442	C₂×C₂²⋊Q₈	—	2	1	no	—
443	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×#121	—	2	1	no	—
445	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
446	#520	—	2	1	no	—
447	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
448	C₂×C₄×D₄	—	2	1	no	—
449	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
450	#497	C₂²×C₁₃	1	2	yes	complemented
451	#496	C₂²×C₁₃	1	2	yes	complemented
452	#489	C₂²×C₁₃	1	2	yes	complemented
453	#489	C₂²×C₁₃	1	2	yes	complemented
454	#485	C₂²×C₁₃	1	4	yes	complemented
455	#483	C₂²×C₁₃	1	2	yes	—
456	#482	C₂²×C₁₃	1	4	yes	complemented
457	#480	C₂²×C₁₃	1	2	yes	—
458	#477	C₂²×C₁₃	1	2	yes	complemented
459	#475	C₂²×C₁₃	1	2	yes	complemented
460	#469	C₂²×C₁₃	1	4	yes	complemented
461	#468	C₂²×C₁₃	1	4	yes	complemented
462	#467	C₂²×C₁₃	1	4	yes	complemented
463	#465	C₂²×C₁₃	1	4	yes	complemented
464	#464	C₂²×C₁₃	1	4	yes	complemented
465	#463	C₂²×C₁₃	1	4	yes	complemented
466	#462	C₂²×C₁₃	1	2	yes	complemented
467	#460	C₂²×C₁₃	1	2	yes	complemented
468	#452	C₂²×C₁₃	1	4	yes	complemented
469	#452	C₂²×C₁₃	1	4	yes	complemented
470	#451	C₂²×C₁₃	1	2	yes	—
471	#451	C₂²×C₁₃	1	2	yes	—
472	#451	C₂²×C₁₃	1	4	yes	complemented
473	#450	C₂²×C₁₃	1	2	yes	—
474	#449	C₂²×C₁₃	1	4	yes	complemented
475	#449	C₂²×C₁₃	1	4	yes	complemented
476	#448	C₂²×C₁₃	1	2	yes	—
477	#448	C₂²×C₁₃	1	2	yes	—
478	#448	C₂²×C₁₃	1	4	yes	complemented
479	#447	C₂²×C₁₃	1	2	yes	—
480	#441	C₂²×C₁₃	1	4	yes	complemented
481	#440	C₂²×C₁₃	1	4	yes	complemented
482	#435	C₂²×C₁₃	1	4	yes	complemented
483	#435	C₂²×C₁₃	1	4	yes	complemented
484	#432	C₂²×C₁₃	1	1	yes	characteristic
485	#432	C₂²×C₁₃	1	1	yes	characteristic
486	#419	C₂²×C₁₃	1	4	yes	complemented
487	#416	C₂²×C₁₃	1	4	yes	complemented
488	#407	C₂²×C₁₃	1	2	yes	—
489	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	2	1	no	—
492	C₂²×C₁₃	—	2	2	no	—
493	C₂²×C₁₃	—	2	2	no	—
494	C₂²×C₁₃	—	2	2	no	—
495	C₂²×C₁₃	—	2	2	no	—
496	C₂²×C₁₃	—	2	2	no	—
497	C₂²×C₁₃	—	2	2	no	—
498	C₂²×C₁₃	—	4	4	no	—
499	C₂²×C₁₃	—	4	2	no	—
500	C₂²×C₁₃	—	4	2	no	—
501	C₂²×C₁₃	—	4	2	no	—
502	C₂²×C₁₃	—	4	2	no	—
503	C₂²×C₁₃	—	4	2	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	8	2	no	—
506	C₂²×C₁₃	—	8	4	no	—
507	C₂²×C₁₃	#575	1	2	yes	—
508	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	1	no	—
511	C₄×C₁₃	—	2	4	no	—
512	C₄×C₁₃	—	2	2	no	—
513	C₄×C₁₃	—	2	1	no	—
514	C₄×C₁₃	—	2	2	no	—
515	C₄×C₁₃	—	2	1	no	—
516	C₄×C₁₃	—	2	1	no	—
517	C₄×C₁₃	—	4	2	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	2	no	—
520	C₄×C₁₃	—	4	2	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
523	C₂×#41	—	2	1	no	—
524	C₂×#41	—	2	2	no	—
525	C₂×#41	—	4	4	no	—
526	C₂×#41	C₂³×C₁₃	1	4	yes	—
527	C₂×#41	C₂³×C₁₃	1	2	yes	—
528	C₂×#41	C₂³×C₁₃	1	2	yes	—
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×Q₈	—	2	2	no	—
531	C₂²×Q₈	—	4	4	no	—
532	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
534	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	—	2	1	no	—
537	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
538	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂³×C₄	—	2	1	no	—
540	C₂³×C₄	—	2	1	no	—
541	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
543	#137	—	4	8	no	—
544	#135	—	4	8	no	—
545	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
546	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
547	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
548	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
549	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
550	C₂×D₈	C₂³×C₁₃	1	4	yes	—
551	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
552	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
553	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
554	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
556	#127	—	2	2	no	—
557	#127	C₂³×C₁₃	1	1	yes	characteristic
558	#126	—	2	2	no	—
559	#126	—	2	2	no	—
560	#125	—	2	1	no	—
561	#124	—	2	2	no	—
562	#124	—	2	4	no	—
563	#124	—	2	4	no	—
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	—	2	1	no	—
567	#124	—	2	1	no	—
568	#124	—	2	1	no	—
569	#124	C₂³×C₁₃	1	2	yes	—
570	#124	C₂³×C₁₃	1	2	yes	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	4	no	—
578	C₂²⋊Q₈	—	2	4	no	—
579	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
580	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
581	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
582	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
583	#121	—	2	4	no	—
584	#121	—	2	4	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	1	no	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	C₂³×C₁₃	1	4	yes	—
592	#121	C₂³×C₁₃	1	2	yes	—
593	#121	C₂³×C₁₃	1	2	yes	—
594	#121	C₂³×C₁₃	1	2	yes	—
595	#120	—	2	2	no	—
596	#120	—	2	2	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
602	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
603	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	4	no	—
610	C₄×D₄	—	2	4	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	D₄×C₁₃	1	2	yes	—
613	C₄×D₄	D₄×C₁₃	1	2	yes	—
614	C₄×D₄	C₂³×C₁₃	1	2	yes	—
615	C₄×D₄	C₂³×C₁₃	1	2	yes	—
616	C₄×D₄	C₂³×C₁₃	1	2	yes	—
617	#117	—	2	1	no	—
618	#117	—	2	2	no	—
619	#117	C₂³×C₁₃	1	2	yes	—
620	#117	C₂³×C₁₃	1	2	yes	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
632	C₂×C₄²	—	2	1	no	—
633	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
634	#107	C₂³×C₁₃	1	4	yes	—
635	#106	C₂³×C₁₃	1	4	yes	—
636	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
638	#103	C₂³×C₁₃	1	4	yes	—
639	#103	C₂³×C₁₃	1	4	yes	—
640	#103	C₂³×C₁₃	1	4	yes	—
641	#103	C₂³×C₁₃	1	4	yes	—
642	#103	C₂³×C₁₃	1	4	yes	—
643	#102	C₂³×C₁₃	1	4	yes	—
644	#102	C₂³×C₁₃	1	4	yes	—
645	#102	C₂³×C₁₃	1	4	yes	—
646	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
647	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
648	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
649	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
650	#97	C₂³×C₁₃	1	2	yes	—
651	#97	C₂³×C₁₃	1	2	yes	—
652	C₂×C₁₃	—	2	2	no	—
653	C₂×C₁₃	—	4	2	no	—
654	C₂×C₁₃	—	4	2	no	—
655	C₂×C₁₃	—	8	2	no	—
656	C₂×C₁₃	—	8	2	no	—
657	C₂×C₁₃	#3484	1	1	yes	characteristic
658	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
659	C₂×C₁₃	#3586	1	1	yes	characteristic
660	C₂⁴	—	2	1	no	—
661	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
663	#41	—	2	8	no	—
664	#41	—	4	4	no	—
665	#41	—	4	4	no	—
666	#41	—	4	4	no	—
667	#41	—	4	4	no	—
668	#41	—	4	8	no	—
669	C₂×Q₈	—	2	4	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	4	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	8	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	—	4	2	no	—
678	C₂×Q₈	—	4	4	no	—
679	C₂×Q₈	—	4	8	no	—
680	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
681	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
682	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	4	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
698	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
699	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
700	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	4	no	—
712	C₂²×C₄	—	4	4	no	—
713	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
715	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
722	Q₁₆	—	2	8	no	—
723	Q₁₆	—	4	4	no	—
724	SD₁₆	—	2	8	no	—
725	SD₁₆	—	4	4	no	—
726	SD₁₆	—	4	4	no	—
727	D₈	—	4	4	no	—
728	M₁₆	—	4	4	no	—
729	C₂×C₈	—	4	4	no	—
730	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
731	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	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	C₂×D₄×C₁₃	1	2	yes	—
745	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
747	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
765	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
766	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
767	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
768	C₄²	—	2	2	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	2	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
774	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
775	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
776	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
777	C₁₃	#61578	1	1	yes	characteristic, direct product factor, Sylow
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	4	1	no	—
783	C₂³	—	4	1	no	—
784	C₂³	—	4	1	no	—
785	C₂³	—	4	1	no	—
786	C₂³	—	4	2	no	—
787	C₂³	—	4	2	no	—
788	C₂³	—	4	2	no	—
789	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
790	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
791	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
792	Q₈	—	2	4	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	4	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	4	8	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	2	no	—
799	Q₈	—	8	1	no	—
800	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
801	D₄	—	2	4	no	—
802	D₄	—	2	4	no	—
803	D₄	—	4	2	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	8	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	8	no	—
809	D₄	—	4	4	no	—
810	D₄	—	8	1	no	—
811	D₄	—	8	2	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	2	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	1	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	2	yes	—
843	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
846	C₈	—	2	4	no	—
847	C₈	—	2	4	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	8	2	no	—
864	C₂²	—	8	4	no	—
865	C₂²	C₁₃×#575	1	2	yes	—
866	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
867	C₄	—	2	1	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	4	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
881	C₂	—	2	2	no	—
882	C₂	—	4	2	no	—
883	C₂	—	4	2	no	—
884	C₂	—	8	2	no	—
885	C₂	—	8	2	no	—
886	C₂	C₁₃×#3484	1	1	yes	characteristic
887	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
888	C₂	C₁₃×#3586	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3506	C₂	semidirect
2. C₂×C₁₃×#548	C₂	semidirect
3. C₁₃×#3321	C₂	semidirect
4. C₁₃×#3313	C₂	semidirect
5. C₁₃×#3271	C₂	semidirect
6. C₁₃×#3269	C₂	semidirect
7. C₁₃×#3215	C₂	semidirect
8. C₁₃×#3213	C₂	semidirect
9. C₁₃×#3194	C₂	semidirect
10. C₁₃×#3190	C₂	semidirect
11. C₁₃×#3113	C₂	semidirect
12. C₁₃×#3112	C₂	semidirect
13. C₁₃×#3004	C₂	semidirect
14. C₁₃×#3002	C₂	semidirect
15. C₁₃×#2973	C₂	semidirect
18. C₂×C₁₃×#137	C₂²	semidirect
19. C₂×C₁₃×#135	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
22. C₁₃×#555	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
29. C₁₃×#547	C₂²	semidirect
47. C₁₃×#497	C₂²	semidirect
48. C₁₃×#496	C₂²	semidirect
49. C₁₃×#489	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#485	C₂²	semidirect
53. C₁₃×#482	C₂²	semidirect
55. C₁₃×#477	C₂²	semidirect
56. C₁₃×#475	C₂²	semidirect
57. C₁₃×#469	C₂²	semidirect
58. C₁₃×#468	C₂²	semidirect
59. C₁₃×#467	C₂²	semidirect
60. C₁₃×#465	C₂²	semidirect
61. C₁₃×#464	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#462	C₂²	semidirect
64. C₁₃×#460	C₂²	semidirect
65. C₁₃×#452	C₂²	semidirect
66. C₁₃×#452	C₂²	semidirect
69. C₁₃×#451	C₂²	semidirect
71. C₁₃×#449	C₂²	semidirect
72. C₁₃×#449	C₂²	semidirect
75. C₁₃×#448	C₂²	semidirect
77. C₁₃×#441	C₂²	semidirect
78. C₁₃×#440	C₂²	semidirect
79. C₁₃×#435	C₂²	semidirect
80. C₁₃×#435	C₂²	semidirect
83. C₁₃×#419	C₂²	semidirect
84. C₁₃×#416	C₂²	semidirect
216. #61578	C₁₃	direct (N × H)
334. #3506	C₂×C₁₃	semidirect
335. C₂×#548	C₂×C₁₃	semidirect
336. #3321	C₂×C₁₃	semidirect
337. #3313	C₂×C₁₃	semidirect
338. #3271	C₂×C₁₃	semidirect
339. #3269	C₂×C₁₃	semidirect
340. #3215	C₂×C₁₃	semidirect
341. #3213	C₂×C₁₃	semidirect
342. #3194	C₂×C₁₃	semidirect
343. #3190	C₂×C₁₃	semidirect
344. #3113	C₂×C₁₃	semidirect
345. #3112	C₂×C₁₃	semidirect
346. #3004	C₂×C₁₃	semidirect
347. #3002	C₂×C₁₃	semidirect
348. #2973	C₂×C₁₃	semidirect
421. C₂×#137	C₂²×C₁₃	semidirect
422. C₂×#135	C₂²×C₁₃	semidirect
424. #556	C₂²×C₁₃	semidirect
425. #555	C₂²×C₁₃	semidirect
427. #550	C₂²×C₁₃	semidirect
432. #547	C₂²×C₁₃	semidirect
450. #497	C₂²×C₁₃	semidirect
451. #496	C₂²×C₁₃	semidirect
452. #489	C₂²×C₁₃	semidirect
453. #489	C₂²×C₁₃	semidirect
454. #485	C₂²×C₁₃	semidirect
456. #482	C₂²×C₁₃	semidirect
458. #477	C₂²×C₁₃	semidirect
459. #475	C₂²×C₁₃	semidirect
460. #469	C₂²×C₁₃	semidirect
461. #468	C₂²×C₁₃	semidirect
462. #467	C₂²×C₁₃	semidirect
463. #465	C₂²×C₁₃	semidirect
464. #464	C₂²×C₁₃	semidirect
465. #463	C₂²×C₁₃	semidirect
466. #462	C₂²×C₁₃	semidirect
467. #460	C₂²×C₁₃	semidirect
468. #452	C₂²×C₁₃	semidirect
469. #452	C₂²×C₁₃	semidirect
472. #451	C₂²×C₁₃	semidirect
474. #449	C₂²×C₁₃	semidirect
475. #449	C₂²×C₁₃	semidirect
478. #448	C₂²×C₁₃	semidirect
480. #441	C₂²×C₁₃	semidirect
481. #440	C₂²×C₁₃	semidirect
482. #435	C₂²×C₁₃	semidirect
483. #435	C₂²×C₁₃	semidirect
486. #419	C₂²×C₁₃	semidirect
487. #416	C₂²×C₁₃	semidirect
777. C₁₃	#61578	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×#3506	2
C₂×C₁₃×#548	2
C₁₃×#3321	2
C₁₃×#3313	2
C₁₃×#3271	2
C₁₃×#3269	2
C₁₃×#3215	2
C₁₃×#3213	2
C₁₃×#3194	2
C₁₃×#3190	2
C₁₃×#3113	2
C₁₃×#3112	2
C₁₃×#3004	2
C₁₃×#3002	2
C₁₃×#2973	2
#61578	13

Subgroups — C13×#61578 #15747917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61578 #15747917