Subgroups — C₇₃×#62580 #32971984

Order 18688.

1790 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3375	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3373	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3319	C₂	1	4	yes	maximal, complemented
6	C₇₃×#3311	C₂	1	4	yes	maximal, complemented
7	C₇₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3304	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#3235	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3219	C₂	1	2	yes	maximal, complemented
12	C₇₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#3180	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#3135	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	#559×C₇₃	—	2	1	no	—
19	#559×C₇₃	C₂²	1	2	yes	—
20	Q₈²×C₇₃	C₂²	1	1	yes	characteristic, complemented
21	#556×C₇₃	—	2	2	no	—
22	#556×C₇₃	—	2	1	no	—
23	#556×C₇₃	C₂²	1	2	yes	—
24	#556×C₇₃	C₂²	1	1	yes	characteristic, complemented
25	#555×C₇₃	C₂²	1	2	yes	—
26	#555×C₇₃	C₂²	1	1	yes	characteristic, complemented
27	#550×C₇₃	—	2	1	no	—
28	#550×C₇₃	C₂²	1	2	yes	—
29	D₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
30	#548×C₇₃	—	2	1	no	—
31	#546×C₇₃	—	2	2	no	—
32	#546×C₇₃	C₂²	1	4	yes	—
33	#542×C₇₃	—	2	1	no	—
34	#542×C₇₃	—	2	2	no	—
35	#540×C₇₃	—	2	2	no	—
36	#535×C₇₃	—	2	1	no	—
37	#533×C₇₃	C₂²	1	1	yes	characteristic
38	#533×C₇₃	C₂²	1	1	yes	characteristic
39	#533×C₇₃	C₂²	1	2	yes	complemented
40	#532×C₇₃	C₂²	1	2	yes	—
41	#532×C₇₃	C₂²	1	2	yes	—
42	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
43	#529×C₇₃	C₂²	1	1	yes	characteristic
44	#529×C₇₃	C₂²	1	2	yes	complemented
45	#519×C₇₃	—	2	1	no	—
46	#518×C₇₃	—	2	1	no	—
47	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
48	#501×C₇₃	C₂²	1	1	yes	characteristic, complemented
49	#501×C₇₃	C₂²	1	2	yes	complemented
50	#497×C₇₃	C₂²	1	1	yes	characteristic, complemented
51	#496×C₇₃	C₂²	1	2	yes	—
52	#491×C₇₃	C₂²	1	2	yes	complemented
53	#491×C₇₃	C₂²	1	1	yes	characteristic, complemented
54	#490×C₇₃	C₂²	1	2	yes	—
55	#490×C₇₃	C₂²	1	2	yes	—
56	#490×C₇₃	C₂²	1	2	yes	—
57	#489×C₇₃	C₂²	1	4	yes	complemented
58	#489×C₇₃	C₂²	1	4	yes	complemented
59	#489×C₇₃	C₂²	1	1	yes	characteristic, complemented
60	#486×C₇₃	C₂²	1	2	yes	—
61	#486×C₇₃	C₂²	1	2	yes	—
62	#485×C₇₃	C₂²	1	4	yes	—
63	#482×C₇₃	C₂²	1	4	yes	complemented
64	#482×C₇₃	C₂²	1	4	yes	complemented
65	#477×C₇₃	C₂²	1	2	yes	complemented
66	#476×C₇₃	C₂²	1	4	yes	complemented
67	#475×C₇₃	C₂²	1	2	yes	complemented
68	#474×C₇₃	C₂²	1	4	yes	complemented
69	#470×C₇₃	C₂²	1	2	yes	—
70	#468×C₇₃	C₂²	1	2	yes	—
71	#466×C₇₃	C₂²	1	4	yes	complemented
72	#465×C₇₃	C₂²	1	4	yes	complemented
73	#464×C₇₃	C₂²	1	4	yes	complemented
74	#463×C₇₃	C₂²	1	4	yes	complemented
75	#460×C₇₃	C₂²	1	2	yes	—
76	#459×C₇₃	C₂²	1	2	yes	—
77	#452×C₇₃	C₂²	1	4	yes	complemented
78	#450×C₇₃	C₂²	1	2	yes	—
79	#449×C₇₃	C₂²	1	4	yes	complemented
80	#447×C₇₃	C₂²	1	2	yes	—
81	#446×C₇₃	C₂²	1	2	yes	complemented
82	#442×C₇₃	C₂²	1	4	yes	complemented
83	#440×C₇₃	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₇₃	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
86	#435×C₇₃	C₂²	1	4	yes	—
87	C₈×D₄×C₇₃	C₂²	1	2	yes	complemented
88	#432×C₇₃	C₂²	1	1	yes	characteristic
89	#432×C₇₃	C₂²	1	2	yes	complemented
90	#418×C₇₃	C₂²	1	4	yes	—
91	#416×C₇₃	C₂²	1	4	yes	complemented
92	#416×C₇₃	C₂²	1	4	yes	complemented
93	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
94	C₂×#97×C₇₃	C₂²	1	2	yes	complemented
95	C₂×#41×C₇₃	—	2	2	no	—
96	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
97	C₂×#41×C₇₃	C₂³	1	4	yes	—
98	C₂²×Q₈×C₇₃	—	2	1	no	—
99	C₂²×D₄×C₇₃	—	2	1	no	—
100	C₂²×D₄×C₇₃	—	2	1	no	—
101	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
102	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
105	C₂×D₈×C₇₃	C₂³	1	4	yes	—
106	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
108	C₄⋊Q₈×C₇₃	—	2	1	no	—
109	C₄⋊Q₈×C₇₃	—	2	2	no	—
110	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
116	#127×C₇₃	—	2	2	no	—
117	#127×C₇₃	—	2	1	no	—
118	#127×C₇₃	—	2	1	no	—
119	#127×C₇₃	C₂³	1	2	yes	—
120	#127×C₇₃	C₂³	1	2	yes	—
121	#126×C₇₃	—	2	2	no	—
122	#126×C₇₃	—	2	2	no	—
123	#126×C₇₃	—	2	2	no	—
124	#126×C₇₃	—	2	1	no	—
125	#126×C₇₃	—	2	2	no	—
126	#125×C₇₃	—	2	1	no	—
127	#125×C₇₃	C₂³	1	1	yes	characteristic
128	#125×C₇₃	C₂³	1	2	yes	—
129	#124×C₇₃	—	2	2	no	—
130	#124×C₇₃	—	2	2	no	—
131	#124×C₇₃	—	2	1	no	—
132	#124×C₇₃	—	2	2	no	—
133	#124×C₇₃	—	2	2	no	—
134	#124×C₇₃	—	2	2	no	—
135	#124×C₇₃	—	2	2	no	—
136	#124×C₇₃	C₂³	1	4	yes	—
137	#124×C₇₃	C₂³	1	1	yes	characteristic
138	#123×C₇₃	—	2	1	no	—
139	#123×C₇₃	—	2	2	no	—
140	#123×C₇₃	—	2	4	no	—
141	#123×C₇₃	—	2	4	no	—
142	C₂²⋊Q₈×C₇₃	—	2	1	no	—
143	C₂²⋊Q₈×C₇₃	—	2	1	no	—
144	C₂²⋊Q₈×C₇₃	—	2	1	no	—
145	C₂²⋊Q₈×C₇₃	—	2	2	no	—
146	C₂²⋊Q₈×C₇₃	—	2	2	no	—
147	C₂²⋊Q₈×C₇₃	—	2	1	no	—
148	C₂²⋊Q₈×C₇₃	—	2	2	no	—
149	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
150	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
151	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
152	#121×C₇₃	—	2	2	no	—
153	#121×C₇₃	—	2	1	no	—
154	#121×C₇₃	—	2	2	no	—
155	#121×C₇₃	—	2	2	no	—
156	#121×C₇₃	—	2	2	no	—
157	#121×C₇₃	—	2	4	no	—
158	#121×C₇₃	—	2	4	no	—
159	#121×C₇₃	C₂³	1	1	yes	characteristic
160	#121×C₇₃	C₂³	1	2	yes	—
161	#121×C₇₃	C₂³	1	4	yes	—
162	#120×C₇₃	—	2	4	no	—
163	C₄×Q₈×C₇₃	—	2	1	no	—
164	C₄×Q₈×C₇₃	—	2	2	no	—
165	C₄×Q₈×C₇₃	—	2	1	no	—
166	C₄×Q₈×C₇₃	—	2	1	no	—
167	C₄×Q₈×C₇₃	—	2	2	no	—
168	C₄×Q₈×C₇₃	—	2	1	no	—
169	C₄×Q₈×C₇₃	—	2	1	no	—
170	C₄×Q₈×C₇₃	—	2	2	no	—
171	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
172	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₇₃	—	2	1	no	—
177	C₄×D₄×C₇₃	—	2	2	no	—
178	C₄×D₄×C₇₃	—	2	2	no	—
179	C₄×D₄×C₇₃	—	2	2	no	—
180	C₄×D₄×C₇₃	—	2	2	no	—
181	C₄×D₄×C₇₃	—	2	2	no	—
182	C₄×D₄×C₇₃	—	2	2	no	—
183	C₄×D₄×C₇₃	D₄	1	2	yes	—
184	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₇₃	C₂³	1	4	yes	—
187	C₄×D₄×C₇₃	C₂³	1	2	yes	—
188	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₇₃	C₂³	1	2	yes	—
190	#117×C₇₃	—	2	1	no	—
191	#117×C₇₃	—	2	2	no	—
192	#117×C₇₃	—	2	1	no	—
193	#117×C₇₃	—	2	1	no	—
194	#117×C₇₃	—	2	2	no	—
195	#117×C₇₃	D₄	1	1	yes	characteristic
196	#117×C₇₃	D₄	1	2	yes	—
197	#117×C₇₃	C₂³	1	2	yes	—
198	#117×C₇₃	C₂³	1	2	yes	—
199	#117×C₇₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
201	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
203	#107×C₇₃	C₂³	1	2	yes	—
204	#107×C₇₃	C₂³	1	4	yes	—
205	#106×C₇₃	C₂³	1	2	yes	—
206	#106×C₇₃	C₂³	1	4	yes	—
207	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
208	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
209	#103×C₇₃	C₂³	1	2	yes	—
210	#103×C₇₃	C₂³	1	2	yes	—
211	#103×C₇₃	C₂³	1	4	yes	—
212	#103×C₇₃	C₂³	1	4	yes	—
213	#103×C₇₃	C₂³	1	2	yes	—
214	#102×C₇₃	C₂³	1	4	yes	—
215	#102×C₇₃	C₂³	1	4	yes	—
216	#102×C₇₃	C₂³	1	4	yes	—
217	#102×C₇₃	C₂³	1	4	yes	—
218	#102×C₇₃	C₂³	1	4	yes	—
219	#102×C₇₃	C₂³	1	4	yes	—
220	#102×C₇₃	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
222	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	—
223	#97×C₇₃	C₂³	1	1	yes	characteristic
224	#97×C₇₃	C₂³	1	2	yes	—
225	#97×C₇₃	C₂³	1	4	yes	—
226	#97×C₇₃	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₇₃	C₂³	1	2	yes	—
228	C₂⁴×C₇₃	—	2	2	no	—
229	#41×C₇₃	—	4	2	no	—
230	#41×C₇₃	—	4	4	no	—
231	#41×C₇₃	—	4	4	no	—
232	#41×C₇₃	—	8	4	no	—
233	C₂×Q₈×C₇₃	—	2	2	no	—
234	C₂×Q₈×C₇₃	—	2	1	no	—
235	C₂×Q₈×C₇₃	—	2	1	no	—
236	C₂×Q₈×C₇₃	—	2	2	no	—
237	C₂×Q₈×C₇₃	—	2	1	no	—
238	C₂×Q₈×C₇₃	—	4	4	no	—
239	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₇₃	—	2	1	no	—
243	C₂×D₄×C₇₃	—	2	2	no	—
244	C₂×D₄×C₇₃	—	2	4	no	—
245	C₂×D₄×C₇₃	—	2	4	no	—
246	C₂×D₄×C₇₃	—	2	2	no	—
247	C₂×D₄×C₇₃	—	2	2	no	—
248	C₂×D₄×C₇₃	—	2	2	no	—
249	C₂×D₄×C₇₃	—	2	2	no	—
250	C₂×D₄×C₇₃	—	2	2	no	—
251	C₂×D₄×C₇₃	—	4	4	no	—
252	C₂×D₄×C₇₃	—	4	4	no	—
253	C₂×D₄×C₇₃	—	8	2	no	—
254	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
257	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₇₃	—	2	2	no	—
259	C₂²×C₄×C₇₃	—	2	1	no	—
260	C₂²×C₄×C₇₃	—	2	4	no	—
261	C₂²×C₄×C₇₃	—	2	4	no	—
262	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₇₃	—	4	2	no	—
269	SD₁₆×C₇₃	—	4	4	no	—
270	SD₁₆×C₇₃	—	4	2	no	—
271	D₈×C₇₃	—	4	4	no	—
272	M₁₆×C₇₃	—	4	2	no	—
273	C₂×C₈×C₇₃	—	4	4	no	—
274	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₇₃	—	2	1	no	—
278	C₄⋊C₄×C₇₃	—	2	1	no	—
279	C₄⋊C₄×C₇₃	—	2	2	no	—
280	C₄⋊C₄×C₇₃	—	2	1	no	—
281	C₄⋊C₄×C₇₃	—	2	1	no	—
282	C₄⋊C₄×C₇₃	—	2	2	no	—
283	C₄⋊C₄×C₇₃	—	2	2	no	—
284	C₄⋊C₄×C₇₃	—	2	1	no	—
285	C₄⋊C₄×C₇₃	—	2	1	no	—
286	C₄⋊C₄×C₇₃	—	2	1	no	—
287	C₄⋊C₄×C₇₃	—	2	2	no	—
288	C₄⋊C₄×C₇₃	—	2	2	no	—
289	C₄⋊C₄×C₇₃	—	2	2	no	—
290	C₄⋊C₄×C₇₃	—	2	1	no	—
291	C₄⋊C₄×C₇₃	—	2	2	no	—
292	C₄⋊C₄×C₇₃	—	2	2	no	—
293	C₄⋊C₄×C₇₃	—	2	1	no	—
294	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
303	C₂²⋊C₄×C₇₃	—	2	2	no	—
304	C₂²⋊C₄×C₇₃	—	2	2	no	—
305	C₂²⋊C₄×C₇₃	—	2	2	no	—
306	C₂²⋊C₄×C₇₃	—	2	2	no	—
307	C₂²⋊C₄×C₇₃	—	2	1	no	—
308	C₂²⋊C₄×C₇₃	—	2	2	no	—
309	C₂²⋊C₄×C₇₃	—	2	4	no	—
310	C₂²⋊C₄×C₇₃	—	2	4	no	—
311	C₂²⋊C₄×C₇₃	—	2	2	no	—
312	C₂²⋊C₄×C₇₃	—	2	1	no	—
313	C₂²⋊C₄×C₇₃	—	2	1	no	—
314	C₂²⋊C₄×C₇₃	—	2	1	no	—
315	C₂²⋊C₄×C₇₃	—	2	4	no	—
316	C₂²⋊C₄×C₇₃	—	2	4	no	—
317	C₂²⋊C₄×C₇₃	—	2	2	no	—
318	C₂²⋊C₄×C₇₃	—	2	1	no	—
319	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
322	C₄²×C₇₃	—	2	2	no	—
323	C₄²×C₇₃	—	2	2	no	—
324	C₄²×C₇₃	—	2	2	no	—
325	C₄²×C₇₃	—	2	2	no	—
326	C₄²×C₇₃	—	2	2	no	—
327	C₄²×C₇₃	—	2	1	no	—
328	C₄²×C₇₃	C₂×D₄	1	2	yes	—
329	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₇₃	C₂×D₄	1	2	yes	—
331	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
334	C₄²×C₇₃	C₂⁴	1	2	yes	—
335	C₂³×C₇₃	—	2	1	no	—
336	C₂³×C₇₃	—	2	4	no	—
337	C₂³×C₇₃	—	4	4	no	—
338	C₂³×C₇₃	—	8	2	no	—
339	C₂³×C₇₃	—	8	2	no	—
340	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
341	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
342	Q₈×C₇₃	—	2	2	no	—
343	Q₈×C₇₃	—	2	2	no	—
344	Q₈×C₇₃	—	2	2	no	—
345	Q₈×C₇₃	—	2	2	no	—
346	Q₈×C₇₃	—	4	4	no	—
347	Q₈×C₇₃	—	4	2	no	—
348	Q₈×C₇₃	—	4	2	no	—
349	Q₈×C₇₃	—	8	2	no	—
350	Q₈×C₇₃	—	8	1	no	—
351	D₄×C₇₃	—	2	2	no	—
352	D₄×C₇₃	—	2	2	no	—
353	D₄×C₇₃	—	2	4	no	—
354	D₄×C₇₃	—	2	4	no	—
355	D₄×C₇₃	—	4	2	no	—
356	D₄×C₇₃	—	4	4	no	—
357	D₄×C₇₃	—	4	4	no	—
358	D₄×C₇₃	—	4	4	no	—
359	D₄×C₇₃	—	8	2	no	—
360	D₄×C₇₃	—	8	2	no	—
361	D₄×C₇₃	—	8	2	no	—
362	D₄×C₇₃	—	8	1	no	—
363	D₄×C₇₃	—	8	4	no	—
364	D₄×C₇₃	—	8	4	no	—
365	C₂×C₄×C₇₃	—	2	2	no	—
366	C₂×C₄×C₇₃	—	2	4	no	—
367	C₂×C₄×C₇₃	—	2	2	no	—
368	C₂×C₄×C₇₃	—	2	1	no	—
369	C₂×C₄×C₇₃	—	2	1	no	—
370	C₂×C₄×C₇₃	—	2	2	no	—
371	C₂×C₄×C₇₃	—	2	2	no	—
372	C₂×C₄×C₇₃	—	2	1	no	—
373	C₂×C₄×C₇₃	—	2	2	no	—
374	C₂×C₄×C₇₃	—	2	2	no	—
375	C₂×C₄×C₇₃	—	4	1	no	—
376	C₂×C₄×C₇₃	—	4	2	no	—
377	C₂×C₄×C₇₃	—	4	2	no	—
378	C₂×C₄×C₇₃	—	4	4	no	—
379	C₂×C₄×C₇₃	—	4	2	no	—
380	C₂×C₄×C₇₃	—	8	4	no	—
381	C₂×C₄×C₇₃	—	8	4	no	—
382	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
391	C₈×C₇₃	—	2	2	no	—
392	C₈×C₇₃	—	2	4	no	—
393	C₈×C₇₃	—	2	2	no	—
394	C₂²×C₇₃	—	2	2	no	—
395	C₂²×C₇₃	—	2	1	no	—
396	C₂²×C₇₃	—	2	2	no	—
397	C₂²×C₇₃	—	2	1	no	—
398	C₂²×C₇₃	—	2	1	no	—
399	C₂²×C₇₃	—	2	2	no	—
400	C₂²×C₇₃	—	4	4	no	—
401	C₂²×C₇₃	—	4	1	no	—
402	C₂²×C₇₃	—	4	4	no	—
403	C₂²×C₇₃	—	4	1	no	—
404	C₂²×C₇₃	—	4	1	no	—
405	C₂²×C₇₃	—	4	4	no	—
406	C₂²×C₇₃	—	16	4	no	—
407	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
408	C₄×C₇₃	—	2	1	no	—
409	C₄×C₇₃	—	2	2	no	—
410	C₄×C₇₃	—	2	1	no	—
411	C₄×C₇₃	—	2	2	no	—
412	C₄×C₇₃	—	2	1	no	—
413	C₄×C₇₃	—	2	1	no	—
414	C₄×C₇₃	—	2	2	no	—
415	C₄×C₇₃	—	4	2	no	—
416	C₄×C₇₃	—	4	2	no	—
417	C₄×C₇₃	—	4	1	no	—
418	C₄×C₇₃	—	4	2	no	—
419	C₄×C₇₃	—	4	1	no	—
420	C₄×C₇₃	—	4	2	no	—
421	C₄×C₇₃	—	4	1	no	—
422	C₄×C₇₃	#575	1	2	yes	—
423	C₄×C₇₃	#585	1	2	yes	—
424	#62580	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
425	C₂×C₇₃	—	4	2	no	—
426	C₂×C₇₃	—	4	1	no	—
427	C₂×C₇₃	—	8	1	no	—
428	C₂×C₇₃	—	8	4	no	—
429	C₂×C₇₃	#3500	1	1	yes	characteristic
430	C₂×C₇₃	C₂×#575	1	1	yes	characteristic
431	C₂×C₇₃	#3585	1	1	yes	characteristic
432	#3518	C₂×C₇₃	1	1	yes	characteristic, complemented
433	#3508	C₂×C₇₃	1	1	yes	characteristic, complemented
434	#3375	C₂×C₇₃	1	2	yes	complemented
435	#3373	C₂×C₇₃	1	2	yes	complemented
436	#3319	C₂×C₇₃	1	4	yes	complemented
437	#3311	C₂×C₇₃	1	4	yes	complemented
438	#3305	C₂×C₇₃	1	2	yes	complemented
439	#3304	C₂×C₇₃	1	2	yes	complemented
440	#3237	C₂×C₇₃	1	1	yes	characteristic, complemented
441	#3235	C₂×C₇₃	1	2	yes	complemented
442	#3219	C₂×C₇₃	1	2	yes	complemented
443	#3217	C₂×C₇₃	1	1	yes	characteristic, complemented
444	#3180	C₂×C₇₃	1	2	yes	complemented
445	#3172	C₂×C₇₃	1	1	yes	characteristic, complemented
446	#3138	C₂×C₇₃	1	1	yes	characteristic, complemented
447	#3135	C₂×C₇₃	1	2	yes	complemented
448	#2970	C₂×C₇₃	1	1	yes	characteristic, complemented
449	C₇₃	#62580	1	1	yes	characteristic, direct product factor, Sylow
450	#559	—	2	1	no	—
451	#559	C₂²×C₇₃	1	2	yes	—
452	Q₈²	C₂²×C₇₃	1	1	yes	characteristic, complemented
453	#556	—	2	2	no	—
454	#556	—	2	1	no	—
455	#556	C₂²×C₇₃	1	2	yes	—
456	#556	C₂²×C₇₃	1	1	yes	characteristic, complemented
457	#555	C₂²×C₇₃	1	2	yes	—
458	#555	C₂²×C₇₃	1	1	yes	characteristic, complemented
459	#550	—	2	1	no	—
460	#550	C₂²×C₇₃	1	2	yes	—
461	D₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
462	#548	—	2	1	no	—
463	#546	—	2	2	no	—
464	#546	C₂²×C₇₃	1	4	yes	—
465	#542	—	2	1	no	—
466	#542	—	2	2	no	—
467	#540	—	2	2	no	—
468	#535	—	2	1	no	—
469	#533	C₂²×C₇₃	1	1	yes	characteristic
470	#533	C₂²×C₇₃	1	1	yes	characteristic
471	#533	C₂²×C₇₃	1	2	yes	complemented
472	#532	C₂²×C₇₃	1	2	yes	—
473	#532	C₂²×C₇₃	1	2	yes	—
474	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
475	#529	C₂²×C₇₃	1	1	yes	characteristic
476	#529	C₂²×C₇₃	1	2	yes	complemented
477	#519	—	2	1	no	—
478	#518	—	2	1	no	—
479	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
480	#501	C₂²×C₇₃	1	1	yes	characteristic, complemented
481	#501	C₂²×C₇₃	1	2	yes	complemented
482	#497	C₂²×C₇₃	1	1	yes	characteristic, complemented
483	#496	C₂²×C₇₃	1	2	yes	—
484	#491	C₂²×C₇₃	1	1	yes	characteristic, complemented
485	#491	C₂²×C₇₃	1	2	yes	complemented
486	#490	C₂²×C₇₃	1	2	yes	—
487	#490	C₂²×C₇₃	1	2	yes	—
488	#490	C₂²×C₇₃	1	2	yes	—
489	#489	C₂²×C₇₃	1	4	yes	complemented
490	#489	C₂²×C₇₃	1	4	yes	complemented
491	#489	C₂²×C₇₃	1	1	yes	characteristic, complemented
492	#486	C₂²×C₇₃	1	2	yes	—
493	#486	C₂²×C₇₃	1	2	yes	—
494	#485	C₂²×C₇₃	1	4	yes	—
495	#482	C₂²×C₇₃	1	4	yes	complemented
496	#482	C₂²×C₇₃	1	4	yes	complemented
497	#477	C₂²×C₇₃	1	2	yes	complemented
498	#476	C₂²×C₇₃	1	4	yes	complemented
499	#475	C₂²×C₇₃	1	2	yes	complemented
500	#474	C₂²×C₇₃	1	4	yes	complemented
501	#470	C₂²×C₇₃	1	2	yes	—
502	#468	C₂²×C₇₃	1	2	yes	—
503	#466	C₂²×C₇₃	1	4	yes	complemented
504	#465	C₂²×C₇₃	1	4	yes	complemented
505	#464	C₂²×C₇₃	1	4	yes	complemented
506	#463	C₂²×C₇₃	1	4	yes	complemented
507	#460	C₂²×C₇₃	1	2	yes	—
508	#459	C₂²×C₇₃	1	2	yes	—
509	#452	C₂²×C₇₃	1	4	yes	complemented
510	#450	C₂²×C₇₃	1	2	yes	—
511	#449	C₂²×C₇₃	1	4	yes	complemented
512	#447	C₂²×C₇₃	1	2	yes	—
513	#446	C₂²×C₇₃	1	2	yes	complemented
514	#442	C₂²×C₇₃	1	4	yes	complemented
515	#440	C₂²×C₇₃	1	4	yes	complemented
516	C₄×Q₁₆	C₂²×C₇₃	1	2	yes	complemented
517	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
518	#435	C₂²×C₇₃	1	4	yes	—
519	C₈×D₄	C₂²×C₇₃	1	2	yes	complemented
520	#432	C₂²×C₇₃	1	1	yes	characteristic
521	#432	C₂²×C₇₃	1	2	yes	complemented
522	#418	C₂²×C₇₃	1	4	yes	—
523	#416	C₂²×C₇₃	1	4	yes	complemented
524	#416	C₂²×C₇₃	1	4	yes	complemented
525	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
526	C₂×#97	C₂²×C₇₃	1	2	yes	complemented
527	C₂×#41	—	2	2	no	—
528	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
529	C₂×#41	C₂³×C₇₃	1	4	yes	—
530	C₂²×Q₈	—	2	1	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
534	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
537	C₂×D₈	C₂³×C₇₃	1	4	yes	—
538	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
539	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
544	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
545	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
546	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
548	#127	—	2	2	no	—
549	#127	—	2	1	no	—
550	#127	—	2	1	no	—
551	#127	C₂³×C₇₃	1	2	yes	—
552	#127	C₂³×C₇₃	1	2	yes	—
553	#126	—	2	2	no	—
554	#126	—	2	2	no	—
555	#126	—	2	2	no	—
556	#126	—	2	1	no	—
557	#126	—	2	2	no	—
558	#125	—	2	1	no	—
559	#125	C₂³×C₇₃	1	1	yes	characteristic
560	#125	C₂³×C₇₃	1	2	yes	—
561	#124	—	2	2	no	—
562	#124	—	2	2	no	—
563	#124	—	2	1	no	—
564	#124	—	2	2	no	—
565	#124	—	2	2	no	—
566	#124	—	2	2	no	—
567	#124	—	2	2	no	—
568	#124	C₂³×C₇₃	1	1	yes	characteristic
569	#124	C₂³×C₇₃	1	4	yes	—
570	#123	—	2	1	no	—
571	#123	—	2	2	no	—
572	#123	—	2	4	no	—
573	#123	—	2	4	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	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	2	no	—
581	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
582	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
583	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
584	#121	—	2	2	no	—
585	#121	—	2	1	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	2	no	—
589	#121	—	2	4	no	—
590	#121	—	2	4	no	—
591	#121	C₂³×C₇₃	1	1	yes	characteristic
592	#121	C₂³×C₇₃	1	2	yes	—
593	#121	C₂³×C₇₃	1	4	yes	—
594	#120	—	2	4	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
605	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
606	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
607	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	D₄×C₇₃	1	2	yes	—
616	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₇₃	1	2	yes	—
619	C₄×D₄	C₂³×C₇₃	1	4	yes	—
620	C₄×D₄	C₂³×C₇₃	1	2	yes	—
621	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
622	#117	—	2	1	no	—
623	#117	—	2	2	no	—
624	#117	—	2	1	no	—
625	#117	—	2	1	no	—
626	#117	—	2	2	no	—
627	#117	D₄×C₇₃	1	1	yes	characteristic
628	#117	D₄×C₇₃	1	2	yes	—
629	#117	C₂³×C₇₃	1	2	yes	—
630	#117	C₂³×C₇₃	1	2	yes	—
631	#117	C₂³×C₇₃	1	2	yes	—
632	C₂×C₂²⋊C₄	—	2	4	no	—
633	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
635	#107	C₂³×C₇₃	1	2	yes	—
636	#107	C₂³×C₇₃	1	4	yes	—
637	#106	C₂³×C₇₃	1	2	yes	—
638	#106	C₂³×C₇₃	1	4	yes	—
639	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
640	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
641	#103	C₂³×C₇₃	1	2	yes	—
642	#103	C₂³×C₇₃	1	2	yes	—
643	#103	C₂³×C₇₃	1	4	yes	—
644	#103	C₂³×C₇₃	1	4	yes	—
645	#103	C₂³×C₇₃	1	2	yes	—
646	#102	C₂³×C₇₃	1	4	yes	—
647	#102	C₂³×C₇₃	1	4	yes	—
648	#102	C₂³×C₇₃	1	4	yes	—
649	#102	C₂³×C₇₃	1	4	yes	—
650	#102	C₂³×C₇₃	1	4	yes	—
651	#102	C₂³×C₇₃	1	4	yes	—
652	#102	C₂³×C₇₃	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
654	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	—
655	#97	C₂³×C₇₃	1	1	yes	characteristic
656	#97	C₂³×C₇₃	1	2	yes	—
657	#97	C₂³×C₇₃	1	4	yes	—
658	#97	C₂³×C₇₃	1	1	yes	characteristic
659	C₄×C₈	C₂³×C₇₃	1	2	yes	—
660	C₂⁴	—	2	2	no	—
661	#41	—	4	2	no	—
662	#41	—	4	4	no	—
663	#41	—	4	4	no	—
664	#41	—	8	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	4	4	no	—
671	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
672	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	4	4	no	—
684	C₂×D₄	—	4	4	no	—
685	C₂×D₄	—	8	2	no	—
686	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
687	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
688	C₂×D₄	C₂⁴×C₇₃	1	4	yes	—
689	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
695	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
697	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
700	Q₁₆	—	4	2	no	—
701	SD₁₆	—	4	4	no	—
702	SD₁₆	—	4	2	no	—
703	D₈	—	4	4	no	—
704	M₁₆	—	4	2	no	—
705	C₂×C₈	—	4	4	no	—
706	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
707	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
708	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
728	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
752	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	C₂×D₄×C₇₃	1	2	yes	—
761	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₇₃	1	2	yes	—
763	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
764	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
765	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
766	C₄²	C₂⁴×C₇₃	1	2	yes	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	8	2	no	—
771	C₂³	—	8	2	no	—
772	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
773	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	4	4	no	—
779	Q₈	—	4	2	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	8	2	no	—
782	Q₈	—	8	1	no	—
783	D₄	—	2	2	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	4	no	—
787	D₄	—	4	2	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	4	no	—
791	D₄	—	8	2	no	—
792	D₄	—	8	2	no	—
793	D₄	—	8	4	no	—
794	D₄	—	8	4	no	—
795	D₄	—	8	2	no	—
796	D₄	—	8	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	8	4	no	—
813	C₂×C₄	—	8	4	no	—
814	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
822	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₈	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	16	4	no	—
839	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	#575×C₇₃	1	2	yes	—
855	C₄	#585×C₇₃	1	2	yes	—
856	C₂	—	4	1	no	—
857	C₂	—	4	2	no	—
858	C₂	—	8	4	no	—
859	C₂	—	8	1	no	—
860	C₂	C₇₃×#3500	1	1	yes	characteristic
861	C₂	C₂×#575×C₇₃	1	1	yes	characteristic
862	C₂	C₇₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₄×#41×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3518	C₂	semidirect
2. C₇₃×#3508	C₂	semidirect
3. C₇₃×#3375	C₂	semidirect
4. C₇₃×#3373	C₂	semidirect
5. C₇₃×#3319	C₂	semidirect
6. C₇₃×#3311	C₂	semidirect
7. C₇₃×#3305	C₂	semidirect
8. C₇₃×#3304	C₂	semidirect
9. C₇₃×#3237	C₂	semidirect
10. C₇₃×#3235	C₂	semidirect
11. C₇₃×#3219	C₂	semidirect
12. C₇₃×#3217	C₂	semidirect
13. C₇₃×#3180	C₂	semidirect
14. C₇₃×#3172	C₂	semidirect
15. C₇₃×#3138	C₂	semidirect
16. C₇₃×#3135	C₂	semidirect
17. C₇₃×#2970	C₂	semidirect
20. Q₈²×C₇₃	C₂²	semidirect
24. #556×C₇₃	C₂²	semidirect
26. #555×C₇₃	C₂²	semidirect
29. D₄×Q₈×C₇₃	C₂²	semidirect
39. #533×C₇₃	C₂²	semidirect
44. #529×C₇₃	C₂²	semidirect
48. #501×C₇₃	C₂²	semidirect
49. #501×C₇₃	C₂²	semidirect
50. #497×C₇₃	C₂²	semidirect
52. #491×C₇₃	C₂²	semidirect
53. #491×C₇₃	C₂²	semidirect
57. #489×C₇₃	C₂²	semidirect
58. #489×C₇₃	C₂²	semidirect
59. #489×C₇₃	C₂²	semidirect
63. #482×C₇₃	C₂²	semidirect
64. #482×C₇₃	C₂²	semidirect
65. #477×C₇₃	C₂²	semidirect
66. #476×C₇₃	C₂²	semidirect
67. #475×C₇₃	C₂²	semidirect
68. #474×C₇₃	C₂²	semidirect
71. #466×C₇₃	C₂²	semidirect
72. #465×C₇₃	C₂²	semidirect
73. #464×C₇₃	C₂²	semidirect
74. #463×C₇₃	C₂²	semidirect
77. #452×C₇₃	C₂²	semidirect
79. #449×C₇₃	C₂²	semidirect
81. #446×C₇₃	C₂²	semidirect
82. #442×C₇₃	C₂²	semidirect
83. #440×C₇₃	C₂²	semidirect
84. C₄×Q₁₆×C₇₃	C₂²	semidirect
85. C₄×SD₁₆×C₇₃	C₂²	semidirect
87. C₈×D₄×C₇₃	C₂²	semidirect
89. #432×C₇₃	C₂²	semidirect
91. #416×C₇₃	C₂²	semidirect
92. #416×C₇₃	C₂²	semidirect
94. C₂×#97×C₇₃	C₂²	semidirect
424. #62580	C₇₃	direct (N × H)
432. #3518	C₂×C₇₃	semidirect
433. #3508	C₂×C₇₃	semidirect
434. #3375	C₂×C₇₃	semidirect
435. #3373	C₂×C₇₃	semidirect
436. #3319	C₂×C₇₃	semidirect
437. #3311	C₂×C₇₃	semidirect
438. #3305	C₂×C₇₃	semidirect
439. #3304	C₂×C₇₃	semidirect
440. #3237	C₂×C₇₃	semidirect
441. #3235	C₂×C₇₃	semidirect
442. #3219	C₂×C₇₃	semidirect
443. #3217	C₂×C₇₃	semidirect
444. #3180	C₂×C₇₃	semidirect
445. #3172	C₂×C₇₃	semidirect
446. #3138	C₂×C₇₃	semidirect
447. #3135	C₂×C₇₃	semidirect
448. #2970	C₂×C₇₃	semidirect
449. C₇₃	#62580	direct (N × H)
452. Q₈²	C₂²×C₇₃	semidirect
456. #556	C₂²×C₇₃	semidirect
458. #555	C₂²×C₇₃	semidirect
461. D₄×Q₈	C₂²×C₇₃	semidirect
471. #533	C₂²×C₇₃	semidirect
476. #529	C₂²×C₇₃	semidirect
480. #501	C₂²×C₇₃	semidirect
481. #501	C₂²×C₇₃	semidirect
482. #497	C₂²×C₇₃	semidirect
484. #491	C₂²×C₇₃	semidirect
485. #491	C₂²×C₇₃	semidirect
489. #489	C₂²×C₇₃	semidirect
490. #489	C₂²×C₇₃	semidirect
491. #489	C₂²×C₇₃	semidirect
495. #482	C₂²×C₇₃	semidirect
496. #482	C₂²×C₇₃	semidirect
497. #477	C₂²×C₇₃	semidirect
498. #476	C₂²×C₇₃	semidirect
499. #475	C₂²×C₇₃	semidirect
500. #474	C₂²×C₇₃	semidirect
503. #466	C₂²×C₇₃	semidirect
504. #465	C₂²×C₇₃	semidirect
505. #464	C₂²×C₇₃	semidirect
506. #463	C₂²×C₇₃	semidirect
509. #452	C₂²×C₇₃	semidirect
511. #449	C₂²×C₇₃	semidirect
513. #446	C₂²×C₇₃	semidirect
514. #442	C₂²×C₇₃	semidirect
515. #440	C₂²×C₇₃	semidirect
516. C₄×Q₁₆	C₂²×C₇₃	semidirect
517. C₄×SD₁₆	C₂²×C₇₃	semidirect
519. C₈×D₄	C₂²×C₇₃	semidirect
521. #432	C₂²×C₇₃	semidirect
523. #416	C₂²×C₇₃	semidirect
524. #416	C₂²×C₇₃	semidirect
526. C₂×#97	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3518	2
C₇₃×#3508	2
C₇₃×#3375	2
C₇₃×#3373	2
C₇₃×#3319	2
C₇₃×#3311	2
C₇₃×#3305	2
C₇₃×#3304	2
C₇₃×#3237	2
C₇₃×#3235	2
C₇₃×#3219	2
C₇₃×#3217	2
C₇₃×#3180	2
C₇₃×#3172	2
C₇₃×#3138	2
C₇₃×#3135	2
C₇₃×#2970	2
#62580	73

Subgroups — C73×#62580 #32971984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62580 #32971984