Subgroups — C₇₃×#62586 #32971990

Order 18688.

1782 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3372	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3366	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3309	C₂	1	4	yes	maximal, complemented
6	C₇₃×#3307	C₂	1	4	yes	maximal, complemented
7	C₇₃×#3305	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3303	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3240	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#3214	C₂	1	2	yes	maximal, complemented
13	C₇₃×#3180	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3171	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3141	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	#557×C₇₃	C₂²	1	1	yes	characteristic
19	#556×C₇₃	—	2	1	no	—
20	#555×C₇₃	C₂²	1	2	yes	—
21	#554×C₇₃	C₂²	1	2	yes	—
22	#553×C₇₃	—	2	1	no	—
23	#553×C₇₃	—	2	2	no	—
24	#553×C₇₃	C₂²	1	4	yes	—
25	#550×C₇₃	—	2	1	no	—
26	#550×C₇₃	C₂²	1	1	yes	characteristic
27	#550×C₇₃	C₂²	1	2	yes	—
28	#550×C₇₃	C₂²	1	1	yes	characteristic
29	#548×C₇₃	—	2	2	no	—
30	#547×C₇₃	—	2	1	no	—
31	#547×C₇₃	C₂²	1	1	yes	characteristic
32	#547×C₇₃	C₂²	1	2	yes	—
33	#542×C₇₃	—	2	2	no	—
34	#540×C₇₃	—	2	1	no	—
35	#540×C₇₃	—	2	2	no	—
36	#537×C₇₃	—	2	1	no	—
37	#533×C₇₃	C₂²	1	2	yes	—
38	#532×C₇₃	C₂²	1	2	yes	—
39	#532×C₇₃	C₂²	1	1	yes	characteristic
40	#532×C₇₃	C₂²	1	1	yes	characteristic
41	#532×C₇₃	C₂²	1	2	yes	—
42	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
43	#529×C₇₃	C₂²	1	1	yes	characteristic
44	#529×C₇₃	C₂²	1	2	yes	—
45	#520×C₇₃	—	2	1	no	—
46	#520×C₇₃	—	2	1	no	—
47	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
48	#501×C₇₃	C₂²	1	2	yes	—
49	#501×C₇₃	C₂²	1	1	yes	characteristic
50	#496×C₇₃	C₂²	1	1	yes	characteristic
51	#496×C₇₃	C₂²	1	2	yes	—
52	#491×C₇₃	C₂²	1	4	yes	—
53	#490×C₇₃	C₂²	1	4	yes	—
54	#490×C₇₃	C₂²	1	1	yes	characteristic
55	#489×C₇₃	C₂²	1	2	yes	—
56	#489×C₇₃	C₂²	1	2	yes	—
57	#489×C₇₃	C₂²	1	2	yes	—
58	#489×C₇₃	C₂²	1	1	yes	characteristic
59	#489×C₇₃	C₂²	1	2	yes	—
60	#487×C₇₃	C₂²	1	2	yes	—
61	#486×C₇₃	C₂²	1	2	yes	—
62	#485×C₇₃	C₂²	1	4	yes	—
63	#483×C₇₃	C₂²	1	2	yes	—
64	#482×C₇₃	C₂²	1	4	yes	—
65	#480×C₇₃	C₂²	1	2	yes	—
66	#479×C₇₃	C₂²	1	4	yes	—
67	#478×C₇₃	C₂²	1	4	yes	—
68	#477×C₇₃	C₂²	1	2	yes	—
69	#476×C₇₃	C₂²	1	2	yes	—
70	#469×C₇₃	C₂²	1	2	yes	—
71	#468×C₇₃	C₂²	1	2	yes	—
72	#466×C₇₃	C₂²	1	4	yes	—
73	#465×C₇₃	C₂²	1	4	yes	—
74	#461×C₇₃	C₂²	1	2	yes	—
75	#461×C₇₃	C₂²	1	4	yes	—
76	#459×C₇₃	C₂²	1	2	yes	—
77	#459×C₇₃	C₂²	1	4	yes	—
78	#449×C₇₃	C₂²	1	4	yes	—
79	#449×C₇₃	C₂²	1	4	yes	—
80	#449×C₇₃	C₂²	1	4	yes	—
81	#446×C₇₃	C₂²	1	2	yes	—
82	#442×C₇₃	C₂²	1	4	yes	—
83	#440×C₇₃	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	—
85	C₄×D₈×C₇₃	C₂²	1	2	yes	—
86	#435×C₇₃	C₂²	1	4	yes	—
87	C₈×D₄×C₇₃	C₂²	1	2	yes	—
88	#432×C₇₃	C₂²	1	1	yes	characteristic
89	#432×C₇₃	C₂²	1	2	yes	—
90	#417×C₇₃	C₂²	1	4	yes	—
91	#416×C₇₃	C₂²	1	4	yes	—
92	#416×C₇₃	C₂²	1	4	yes	—
93	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
94	C₂×#97×C₇₃	C₂²	1	2	yes	—
95	C₂×#41×C₇₃	—	2	1	no	—
96	C₂×#41×C₇₃	—	2	1	no	—
97	C₂×#41×C₇₃	—	2	2	no	—
98	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
99	C₂×#41×C₇₃	C₂³	1	2	yes	—
100	C₂×#41×C₇₃	C₂³	1	2	yes	—
101	C₂×#41×C₇₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₇₃	—	2	1	no	—
103	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
105	C₂×D₈×C₇₃	C₂³	1	2	yes	—
106	C₂×D₈×C₇₃	C₂³	1	4	yes	—
107	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
108	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₇₃	—	2	1	no	—
110	C₄⋊Q₈×C₇₃	—	2	1	no	—
111	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
116	#127×C₇₃	—	2	1	no	—
117	#127×C₇₃	—	2	2	no	—
118	#127×C₇₃	C₂³	1	1	yes	characteristic
119	#127×C₇₃	C₂³	1	2	yes	—
120	#127×C₇₃	C₂³	1	1	yes	characteristic
121	#126×C₇₃	—	2	4	no	—
122	#126×C₇₃	—	2	2	no	—
123	#126×C₇₃	—	2	1	no	—
124	#125×C₇₃	—	2	1	no	—
125	#125×C₇₃	—	2	2	no	—
126	#125×C₇₃	C₂³	1	4	yes	—
127	#125×C₇₃	C₂³	1	1	yes	characteristic
128	#124×C₇₃	—	2	4	no	—
129	#124×C₇₃	—	2	1	no	—
130	#124×C₇₃	—	2	2	no	—
131	#124×C₇₃	C₂³	1	1	yes	characteristic
132	#124×C₇₃	C₂³	1	2	yes	—
133	#123×C₇₃	—	2	1	no	—
134	#123×C₇₃	—	2	2	no	—
135	#123×C₇₃	—	2	2	no	—
136	#123×C₇₃	—	2	2	no	—
137	#123×C₇₃	—	2	2	no	—
138	#123×C₇₃	—	2	4	no	—
139	C₂²⋊Q₈×C₇₃	—	2	2	no	—
140	C₂²⋊Q₈×C₇₃	—	2	2	no	—
141	C₂²⋊Q₈×C₇₃	—	2	2	no	—
142	C₂²⋊Q₈×C₇₃	—	2	4	no	—
143	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
144	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
145	#121×C₇₃	—	2	2	no	—
146	#121×C₇₃	—	2	4	no	—
147	#121×C₇₃	—	2	1	no	—
148	#121×C₇₃	—	2	2	no	—
149	#121×C₇₃	—	2	2	no	—
150	#121×C₇₃	—	2	1	no	—
151	#121×C₇₃	—	2	2	no	—
152	#121×C₇₃	—	2	1	no	—
153	#121×C₇₃	—	2	1	no	—
154	#121×C₇₃	—	2	2	no	—
155	#121×C₇₃	—	2	1	no	—
156	#121×C₇₃	—	2	2	no	—
157	#121×C₇₃	—	2	2	no	—
158	#121×C₇₃	—	2	2	no	—
159	#121×C₇₃	—	2	2	no	—
160	#121×C₇₃	C₂³	1	4	yes	—
161	#121×C₇₃	C₂³	1	2	yes	—
162	#121×C₇₃	C₂³	1	2	yes	—
163	#121×C₇₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₇₃	—	2	1	no	—
165	C₄×Q₈×C₇₃	—	2	2	no	—
166	C₄×Q₈×C₇₃	—	2	2	no	—
167	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
168	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
171	C₄×D₄×C₇₃	—	2	1	no	—
172	C₄×D₄×C₇₃	—	2	2	no	—
173	C₄×D₄×C₇₃	—	2	1	no	—
174	C₄×D₄×C₇₃	—	2	2	no	—
175	C₄×D₄×C₇₃	—	2	4	no	—
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	1	no	—
180	C₄×D₄×C₇₃	—	2	2	no	—
181	C₄×D₄×C₇₃	—	2	1	no	—
182	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
183	C₄×D₄×C₇₃	D₄	1	2	yes	—
184	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₇₃	C₂³	1	2	yes	—
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	2	no	—
191	#117×C₇₃	—	2	1	no	—
192	#117×C₇₃	—	2	2	no	—
193	#117×C₇₃	D₄	1	1	yes	characteristic
194	#117×C₇₃	D₄	1	2	yes	—
195	#117×C₇₃	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
197	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
198	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
199	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
200	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	4	yes	—
211	#103×C₇₃	C₂³	1	4	yes	—
212	#103×C₇₃	C₂³	1	4	yes	—
213	#103×C₇₃	C₂³	1	4	yes	—
214	#102×C₇₃	C₂³	1	2	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	2	yes	—
220	#102×C₇₃	C₂³	1	2	yes	—
221	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	—
222	C₂²⋊C₈×C₇₃	C₂³	1	2	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	#41×C₇₃	—	4	2	no	—
229	#41×C₇₃	—	4	4	no	—
230	#41×C₇₃	—	4	4	no	—
231	#41×C₇₃	—	4	4	no	—
232	#41×C₇₃	—	4	4	no	—
233	#41×C₇₃	—	4	4	no	—
234	#41×C₇₃	—	8	4	no	—
235	C₂×Q₈×C₇₃	—	2	1	no	—
236	C₂×Q₈×C₇₃	—	2	2	no	—
237	C₂×Q₈×C₇₃	—	2	2	no	—
238	C₂×Q₈×C₇₃	—	8	2	no	—
239	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₇₃	—	2	2	no	—
243	C₂×D₄×C₇₃	—	2	2	no	—
244	C₂×D₄×C₇₃	—	2	1	no	—
245	C₂×D₄×C₇₃	—	2	2	no	—
246	C₂×D₄×C₇₃	—	2	2	no	—
247	C₂×D₄×C₇₃	—	2	2	no	—
248	C₂×D₄×C₇₃	—	2	4	no	—
249	C₂×D₄×C₇₃	—	2	1	no	—
250	C₂×D₄×C₇₃	—	2	2	no	—
251	C₂×D₄×C₇₃	—	2	1	no	—
252	C₂×D₄×C₇₃	—	2	1	no	—
253	C₂×D₄×C₇₃	—	2	1	no	—
254	C₂×D₄×C₇₃	—	2	2	no	—
255	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇₃	—	2	2	no	—
261	C₂²×C₄×C₇₃	—	2	2	no	—
262	C₂²×C₄×C₇₃	—	2	1	no	—
263	C₂²×C₄×C₇₃	—	2	2	no	—
264	C₂²×C₄×C₇₃	—	2	2	no	—
265	C₂²×C₄×C₇₃	—	2	2	no	—
266	C₂²×C₄×C₇₃	—	2	2	no	—
267	C₂²×C₄×C₇₃	—	2	4	no	—
268	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
272	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
274	SD₁₆×C₇₃	—	4	4	no	—
275	SD₁₆×C₇₃	—	4	2	no	—
276	D₈×C₇₃	—	4	4	no	—
277	D₈×C₇₃	—	4	2	no	—
278	M₁₆×C₇₃	—	4	2	no	—
279	C₂×C₈×C₇₃	—	4	4	no	—
280	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
281	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
282	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
283	C₄⋊C₄×C₇₃	—	2	2	no	—
284	C₄⋊C₄×C₇₃	—	2	2	no	—
285	C₄⋊C₄×C₇₃	—	2	1	no	—
286	C₄⋊C₄×C₇₃	—	2	2	no	—
287	C₄⋊C₄×C₇₃	—	2	1	no	—
288	C₄⋊C₄×C₇₃	—	2	2	no	—
289	C₄⋊C₄×C₇₃	—	2	4	no	—
290	C₄⋊C₄×C₇₃	—	2	2	no	—
291	C₄⋊C₄×C₇₃	—	2	1	no	—
292	C₄⋊C₄×C₇₃	—	2	1	no	—
293	C₄⋊C₄×C₇₃	—	2	1	no	—
294	C₄⋊C₄×C₇₃	—	2	1	no	—
295	C₄⋊C₄×C₇₃	—	2	2	no	—
296	C₄⋊C₄×C₇₃	—	2	4	no	—
297	C₄⋊C₄×C₇₃	—	2	1	no	—
298	C₄⋊C₄×C₇₃	—	2	2	no	—
299	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
305	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
307	C₂²⋊C₄×C₇₃	—	2	4	no	—
308	C₂²⋊C₄×C₇₃	—	2	2	no	—
309	C₂²⋊C₄×C₇₃	—	2	1	no	—
310	C₂²⋊C₄×C₇₃	—	2	2	no	—
311	C₂²⋊C₄×C₇₃	—	2	1	no	—
312	C₂²⋊C₄×C₇₃	—	2	1	no	—
313	C₂²⋊C₄×C₇₃	—	2	2	no	—
314	C₂²⋊C₄×C₇₃	—	2	4	no	—
315	C₂²⋊C₄×C₇₃	—	2	1	no	—
316	C₂²⋊C₄×C₇₃	—	2	2	no	—
317	C₂²⋊C₄×C₇₃	—	2	2	no	—
318	C₂²⋊C₄×C₇₃	—	2	4	no	—
319	C₂²⋊C₄×C₇₃	—	2	1	no	—
320	C₂²⋊C₄×C₇₃	—	2	2	no	—
321	C₂²⋊C₄×C₇₃	—	2	2	no	—
322	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
325	C₄²×C₇₃	—	2	4	no	—
326	C₄²×C₇₃	—	2	2	no	—
327	C₄²×C₇₃	—	2	1	no	—
328	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₇₃	C₂×D₄	1	2	yes	—
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	2	no	—
336	C₂³×C₇₃	—	2	2	no	—
337	C₂³×C₇₃	—	2	1	no	—
338	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
339	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₇₃	—	2	2	no	—
341	Q₈×C₇₃	—	2	4	no	—
342	Q₈×C₇₃	—	2	2	no	—
343	Q₈×C₇₃	—	4	4	no	—
344	Q₈×C₇₃	—	4	2	no	—
345	Q₈×C₇₃	—	8	2	no	—
346	D₄×C₇₃	—	2	2	no	—
347	D₄×C₇₃	—	2	2	no	—
348	D₄×C₇₃	—	2	4	no	—
349	D₄×C₇₃	—	2	2	no	—
350	D₄×C₇₃	—	2	2	no	—
351	D₄×C₇₃	—	4	2	no	—
352	D₄×C₇₃	—	4	2	no	—
353	D₄×C₇₃	—	4	4	no	—
354	D₄×C₇₃	—	4	2	no	—
355	D₄×C₇₃	—	4	4	no	—
356	D₄×C₇₃	—	4	2	no	—
357	D₄×C₇₃	—	8	2	no	—
358	D₄×C₇₃	—	8	1	no	—
359	D₄×C₇₃	—	8	1	no	—
360	D₄×C₇₃	—	8	2	no	—
361	D₄×C₇₃	—	8	2	no	—
362	D₄×C₇₃	—	8	2	no	—
363	D₄×C₇₃	—	8	2	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	2	no	—
370	C₂×C₄×C₇₃	—	2	2	no	—
371	C₂×C₄×C₇₃	—	2	1	no	—
372	C₂×C₄×C₇₃	—	2	4	no	—
373	C₂×C₄×C₇₃	—	2	1	no	—
374	C₂×C₄×C₇₃	—	4	1	no	—
375	C₂×C₄×C₇₃	—	4	2	no	—
376	C₂×C₄×C₇₃	—	4	2	no	—
377	C₂×C₄×C₇₃	—	4	4	no	—
378	C₂×C₄×C₇₃	—	4	2	no	—
379	C₂×C₄×C₇₃	—	4	4	no	—
380	C₂×C₄×C₇₃	—	8	2	no	—
381	C₂×C₄×C₇₃	—	8	2	no	—
382	C₂×C₄×C₇₃	—	8	2	no	—
383	C₂×C₄×C₇₃	—	8	4	no	—
384	C₂×C₄×C₇₃	—	8	2	no	—
385	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
394	C₈×C₇₃	—	2	2	no	—
395	C₈×C₇₃	—	2	4	no	—
396	C₈×C₇₃	—	2	2	no	—
397	C₂²×C₇₃	—	2	1	no	—
398	C₂²×C₇₃	—	2	2	no	—
399	C₂²×C₇₃	—	2	2	no	—
400	C₂²×C₇₃	—	2	1	no	—
401	C₂²×C₇₃	—	2	1	no	—
402	C₂²×C₇₃	—	2	2	no	—
403	C₂²×C₇₃	—	4	2	no	—
404	C₂²×C₇₃	—	4	1	no	—
405	C₂²×C₇₃	—	4	2	no	—
406	C₂²×C₇₃	—	4	2	no	—
407	C₂²×C₇₃	—	4	1	no	—
408	C₂²×C₇₃	—	4	2	no	—
409	C₂²×C₇₃	—	4	2	no	—
410	C₂²×C₇₃	—	4	1	no	—
411	C₂²×C₇₃	—	4	2	no	—
412	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₇₃	—	2	1	no	—
414	C₄×C₇₃	—	2	2	no	—
415	C₄×C₇₃	—	2	1	no	—
416	C₄×C₇₃	—	2	2	no	—
417	C₄×C₇₃	—	2	1	no	—
418	C₄×C₇₃	—	2	1	no	—
419	C₄×C₇₃	—	2	2	no	—
420	C₄×C₇₃	—	4	4	no	—
421	C₄×C₇₃	—	4	1	no	—
422	C₄×C₇₃	—	4	2	no	—
423	C₄×C₇₃	—	4	1	no	—
424	C₄×C₇₃	—	4	1	no	—
425	C₄×C₇₃	—	4	2	no	—
426	C₄×C₇₃	#575	1	2	yes	—
427	C₄×C₇₃	#585	1	2	yes	—
428	#62586	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
429	C₂×C₇₃	—	4	1	no	—
430	C₂×C₇₃	—	4	2	no	—
431	C₂×C₇₃	—	8	2	no	—
432	C₂×C₇₃	—	8	2	no	—
433	C₂×C₇₃	—	8	1	no	—
434	C₂×C₇₃	#3500	1	1	yes	characteristic
435	C₂×C₇₃	C₂×#575	1	1	yes	characteristic
436	C₂×C₇₃	#3585	1	1	yes	characteristic
437	#3517	C₂×C₇₃	1	1	yes	characteristic, complemented
438	#3511	C₂×C₇₃	1	1	yes	characteristic, complemented
439	#3372	C₂×C₇₃	1	2	yes	complemented
440	#3366	C₂×C₇₃	1	2	yes	complemented
441	#3309	C₂×C₇₃	1	4	yes	complemented
442	#3307	C₂×C₇₃	1	4	yes	complemented
443	#3305	C₂×C₇₃	1	2	yes	complemented
444	#3303	C₂×C₇₃	1	2	yes	complemented
445	#3240	C₂×C₇₃	1	2	yes	complemented
446	#3238	C₂×C₇₃	1	1	yes	characteristic, complemented
447	#3214	C₂×C₇₃	1	2	yes	complemented
448	#3214	C₂×C₇₃	1	1	yes	characteristic, complemented
449	#3180	C₂×C₇₃	1	2	yes	complemented
450	#3171	C₂×C₇₃	1	1	yes	characteristic, complemented
451	#3141	C₂×C₇₃	1	1	yes	characteristic, complemented
452	#3135	C₂×C₇₃	1	2	yes	complemented
453	#2970	C₂×C₇₃	1	1	yes	characteristic, complemented
454	C₇₃	#62586	1	1	yes	characteristic, direct product factor, Sylow
455	#557	C₂²×C₇₃	1	1	yes	characteristic
456	#556	—	2	1	no	—
457	#555	C₂²×C₇₃	1	2	yes	—
458	#554	C₂²×C₇₃	1	2	yes	—
459	#553	—	2	1	no	—
460	#553	—	2	2	no	—
461	#553	C₂²×C₇₃	1	4	yes	—
462	#550	—	2	1	no	—
463	#550	C₂²×C₇₃	1	1	yes	characteristic
464	#550	C₂²×C₇₃	1	2	yes	—
465	#550	C₂²×C₇₃	1	1	yes	characteristic
466	#548	—	2	2	no	—
467	#547	—	2	1	no	—
468	#547	C₂²×C₇₃	1	1	yes	characteristic
469	#547	C₂²×C₇₃	1	2	yes	—
470	#542	—	2	2	no	—
471	#540	—	2	1	no	—
472	#540	—	2	2	no	—
473	#537	—	2	1	no	—
474	#533	C₂²×C₇₃	1	2	yes	—
475	#532	C₂²×C₇₃	1	2	yes	—
476	#532	C₂²×C₇₃	1	1	yes	characteristic
477	#532	C₂²×C₇₃	1	1	yes	characteristic
478	#532	C₂²×C₇₃	1	2	yes	—
479	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
480	#529	C₂²×C₇₃	1	1	yes	characteristic
481	#529	C₂²×C₇₃	1	2	yes	—
482	#520	—	2	1	no	—
483	#520	—	2	1	no	—
484	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
485	#501	C₂²×C₇₃	1	1	yes	characteristic
486	#501	C₂²×C₇₃	1	2	yes	—
487	#496	C₂²×C₇₃	1	1	yes	characteristic
488	#496	C₂²×C₇₃	1	2	yes	—
489	#491	C₂²×C₇₃	1	4	yes	—
490	#490	C₂²×C₇₃	1	4	yes	—
491	#490	C₂²×C₇₃	1	1	yes	characteristic
492	#489	C₂²×C₇₃	1	1	yes	characteristic
493	#489	C₂²×C₇₃	1	2	yes	—
494	#489	C₂²×C₇₃	1	2	yes	—
495	#489	C₂²×C₇₃	1	2	yes	—
496	#489	C₂²×C₇₃	1	2	yes	—
497	#487	C₂²×C₇₃	1	2	yes	—
498	#486	C₂²×C₇₃	1	2	yes	—
499	#485	C₂²×C₇₃	1	4	yes	—
500	#483	C₂²×C₇₃	1	2	yes	—
501	#482	C₂²×C₇₃	1	4	yes	—
502	#480	C₂²×C₇₃	1	2	yes	—
503	#479	C₂²×C₇₃	1	4	yes	—
504	#478	C₂²×C₇₃	1	4	yes	—
505	#477	C₂²×C₇₃	1	2	yes	—
506	#476	C₂²×C₇₃	1	2	yes	—
507	#469	C₂²×C₇₃	1	2	yes	—
508	#468	C₂²×C₇₃	1	2	yes	—
509	#466	C₂²×C₇₃	1	4	yes	—
510	#465	C₂²×C₇₃	1	4	yes	—
511	#461	C₂²×C₇₃	1	2	yes	—
512	#461	C₂²×C₇₃	1	4	yes	—
513	#459	C₂²×C₇₃	1	2	yes	—
514	#459	C₂²×C₇₃	1	4	yes	—
515	#449	C₂²×C₇₃	1	4	yes	—
516	#449	C₂²×C₇₃	1	4	yes	—
517	#449	C₂²×C₇₃	1	4	yes	—
518	#446	C₂²×C₇₃	1	2	yes	—
519	#442	C₂²×C₇₃	1	4	yes	—
520	#440	C₂²×C₇₃	1	4	yes	—
521	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	—
522	C₄×D₈	C₂²×C₇₃	1	2	yes	—
523	#435	C₂²×C₇₃	1	4	yes	—
524	C₈×D₄	C₂²×C₇₃	1	2	yes	—
525	#432	C₂²×C₇₃	1	1	yes	characteristic
526	#432	C₂²×C₇₃	1	2	yes	—
527	#417	C₂²×C₇₃	1	4	yes	—
528	#416	C₂²×C₇₃	1	4	yes	—
529	#416	C₂²×C₇₃	1	4	yes	—
530	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
531	C₂×#97	C₂²×C₇₃	1	2	yes	—
532	C₂×#41	—	2	1	no	—
533	C₂×#41	—	2	1	no	—
534	C₂×#41	—	2	2	no	—
535	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
536	C₂×#41	C₂³×C₇₃	1	2	yes	—
537	C₂×#41	C₂³×C₇₃	1	2	yes	—
538	C₂×#41	C₂³×C₇₃	1	2	yes	—
539	C₂²×Q₈	—	2	1	no	—
540	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
541	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
542	C₂×D₈	C₂³×C₇₃	1	2	yes	—
543	C₂×D₈	C₂³×C₇₃	1	4	yes	—
544	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
545	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
553	#127	—	2	1	no	—
554	#127	—	2	2	no	—
555	#127	C₂³×C₇₃	1	1	yes	characteristic
556	#127	C₂³×C₇₃	1	1	yes	characteristic
557	#127	C₂³×C₇₃	1	2	yes	—
558	#126	—	2	4	no	—
559	#126	—	2	2	no	—
560	#126	—	2	1	no	—
561	#125	—	2	1	no	—
562	#125	—	2	2	no	—
563	#125	C₂³×C₇₃	1	1	yes	characteristic
564	#125	C₂³×C₇₃	1	4	yes	—
565	#124	—	2	4	no	—
566	#124	—	2	1	no	—
567	#124	—	2	2	no	—
568	#124	C₂³×C₇₃	1	1	yes	characteristic
569	#124	C₂³×C₇₃	1	2	yes	—
570	#123	—	2	1	no	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	#123	—	2	4	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	4	no	—
580	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
581	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
582	#121	—	2	2	no	—
583	#121	—	2	4	no	—
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	1	no	—
588	#121	—	2	2	no	—
589	#121	—	2	1	no	—
590	#121	—	2	1	no	—
591	#121	—	2	2	no	—
592	#121	—	2	1	no	—
593	#121	—	2	2	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	C₂³×C₇₃	1	2	yes	—
598	#121	C₂³×C₇₃	1	1	yes	characteristic
599	#121	C₂³×C₇₃	1	2	yes	—
600	#121	C₂³×C₇₃	1	4	yes	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
605	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
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	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
620	C₄×D₄	D₄×C₇₃	1	2	yes	—
621	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
622	C₄×D₄	C₂³×C₇₃	1	2	yes	—
623	C₄×D₄	C₂³×C₇₃	1	4	yes	—
624	C₄×D₄	C₂³×C₇₃	1	2	yes	—
625	C₄×D₄	C₂³×C₇₃	1	2	yes	—
626	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
627	#117	—	2	2	no	—
628	#117	—	2	1	no	—
629	#117	—	2	2	no	—
630	#117	D₄×C₇₃	1	1	yes	characteristic
631	#117	D₄×C₇₃	1	2	yes	—
632	#117	C₂³×C₇₃	1	4	yes	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	2	no	—
637	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
640	#107	C₂³×C₇₃	1	2	yes	—
641	#107	C₂³×C₇₃	1	4	yes	—
642	#106	C₂³×C₇₃	1	2	yes	—
643	#106	C₂³×C₇₃	1	4	yes	—
644	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
646	#103	C₂³×C₇₃	1	2	yes	—
647	#103	C₂³×C₇₃	1	4	yes	—
648	#103	C₂³×C₇₃	1	4	yes	—
649	#103	C₂³×C₇₃	1	4	yes	—
650	#103	C₂³×C₇₃	1	4	yes	—
651	#102	C₂³×C₇₃	1	2	yes	—
652	#102	C₂³×C₇₃	1	4	yes	—
653	#102	C₂³×C₇₃	1	4	yes	—
654	#102	C₂³×C₇₃	1	4	yes	—
655	#102	C₂³×C₇₃	1	4	yes	—
656	#102	C₂³×C₇₃	1	2	yes	—
657	#102	C₂³×C₇₃	1	2	yes	—
658	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	—
659	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
660	#97	C₂³×C₇₃	1	1	yes	characteristic
661	#97	C₂³×C₇₃	1	2	yes	—
662	#97	C₂³×C₇₃	1	4	yes	—
663	#97	C₂³×C₇₃	1	1	yes	characteristic
664	C₄×C₈	C₂³×C₇₃	1	2	yes	—
665	#41	—	4	2	no	—
666	#41	—	4	4	no	—
667	#41	—	4	4	no	—
668	#41	—	4	4	no	—
669	#41	—	4	4	no	—
670	#41	—	4	4	no	—
671	#41	—	8	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	8	2	no	—
676	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
677	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
678	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	4	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
693	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
694	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
695	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
696	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
707	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
711	SD₁₆	—	4	4	no	—
712	SD₁₆	—	4	2	no	—
713	D₈	—	4	4	no	—
714	D₈	—	4	2	no	—
715	M₁₆	—	4	2	no	—
716	C₂×C₈	—	4	4	no	—
717	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
718	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
719	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
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	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
739	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
740	C₄⋊C₄	C₂⁴×C₇₃	1	4	yes	—
741	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
744	C₂²⋊C₄	—	2	4	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	1	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
760	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	1	no	—
765	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₇₃	1	2	yes	—
767	C₄²	C₂×D₄×C₇₃	1	2	yes	—
768	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
769	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
770	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
771	C₄²	C₂⁴×C₇₃	1	2	yes	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	1	no	—
775	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
776	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
777	Q₈	—	2	2	no	—
778	Q₈	—	2	4	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	4	4	no	—
781	Q₈	—	4	2	no	—
782	Q₈	—	8	2	no	—
783	D₄	—	2	2	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	2	no	—
788	D₄	—	4	2	no	—
789	D₄	—	4	2	no	—
790	D₄	—	4	4	no	—
791	D₄	—	4	2	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	8	2	no	—
795	D₄	—	8	1	no	—
796	D₄	—	8	2	no	—
797	D₄	—	8	2	no	—
798	D₄	—	8	2	no	—
799	D₄	—	8	4	no	—
800	D₄	—	8	1	no	—
801	D₄	—	8	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	—	8	2	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	—	8	4	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
830	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
831	C₈	—	2	2	no	—
832	C₈	—	2	4	no	—
833	C₈	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	2	no	—
849	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
850	C₄	—	2	2	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	4	no	—
862	C₄	—	4	1	no	—
863	C₄	#575×C₇₃	1	2	yes	—
864	C₄	#585×C₇₃	1	2	yes	—
865	C₂	—	4	1	no	—
866	C₂	—	4	2	no	—
867	C₂	—	8	2	no	—
868	C₂	—	8	1	no	—
869	C₂	—	8	2	no	—
870	C₂	C₇₃×#3500	1	1	yes	characteristic
871	C₂	C₂×#575×C₇₃	1	1	yes	characteristic
872	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×#3517	C₂	semidirect
2. C₇₃×#3511	C₂	semidirect
3. C₇₃×#3372	C₂	semidirect
4. C₇₃×#3366	C₂	semidirect
5. C₇₃×#3309	C₂	semidirect
6. C₇₃×#3307	C₂	semidirect
7. C₇₃×#3305	C₂	semidirect
8. C₇₃×#3303	C₂	semidirect
9. C₇₃×#3240	C₂	semidirect
10. C₇₃×#3238	C₂	semidirect
11. C₇₃×#3214	C₂	semidirect
12. C₇₃×#3214	C₂	semidirect
13. C₇₃×#3180	C₂	semidirect
14. C₇₃×#3171	C₂	semidirect
15. C₇₃×#3141	C₂	semidirect
16. C₇₃×#3135	C₂	semidirect
17. C₇₃×#2970	C₂	semidirect
428. #62586	C₇₃	direct (N × H)
437. #3517	C₂×C₇₃	semidirect
438. #3511	C₂×C₇₃	semidirect
439. #3372	C₂×C₇₃	semidirect
440. #3366	C₂×C₇₃	semidirect
441. #3309	C₂×C₇₃	semidirect
442. #3307	C₂×C₇₃	semidirect
443. #3305	C₂×C₇₃	semidirect
444. #3303	C₂×C₇₃	semidirect
445. #3240	C₂×C₇₃	semidirect
446. #3238	C₂×C₇₃	semidirect
447. #3214	C₂×C₇₃	semidirect
448. #3214	C₂×C₇₃	semidirect
449. #3180	C₂×C₇₃	semidirect
450. #3171	C₂×C₇₃	semidirect
451. #3141	C₂×C₇₃	semidirect
452. #3135	C₂×C₇₃	semidirect
453. #2970	C₂×C₇₃	semidirect
454. C₇₃	#62586	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#3517	2
C₇₃×#3511	2
C₇₃×#3372	2
C₇₃×#3366	2
C₇₃×#3309	2
C₇₃×#3307	2
C₇₃×#3305	2
C₇₃×#3303	2
C₇₃×#3240	2
C₇₃×#3238	2
C₇₃×#3214	2
C₇₃×#3180	2
C₇₃×#3171	2
C₇₃×#3141	2
C₇₃×#3135	2
C₇₃×#2970	2
#62586	73

Subgroups — C73×#62586 #32971990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62586 #32971990