Subgroups — C₇₃×#59574 #32968978

Order 18688.

1550 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2776	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2745	C₂	1	2	yes	maximal
3	C₇₃×#2588	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2528	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2527	C₂	1	2	yes	maximal
7	C₇₃×#2514	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2494	C₂	1	1	yes	maximal, characteristic
11	C₇₃×#2492	C₂	1	1	yes	maximal, characteristic
12	C₇₃×#2489	C₂	1	1	yes	maximal, characteristic
13	C₇₃×#2478	C₂	1	2	yes	maximal
14	C₇₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2442	C₂	1	1	yes	maximal, characteristic
16	C₇₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#2360	C₂	1	1	yes	maximal, characteristic
19	C₇₃×#2347	C₂	1	2	yes	maximal
20	C₇₃×#2344	C₂	1	1	yes	maximal, characteristic
21	C₄×#125×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#126×C₇₃	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#126×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#117×C₇₃	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
32	#401×C₇₃	C₂²	1	2	yes	—
33	#401×C₇₃	C₂²	1	2	yes	—
34	#401×C₇₃	C₂²	1	2	yes	—
35	#400×C₇₃	C₂²	1	2	yes	—
36	#400×C₇₃	C₂²	1	2	yes	—
37	#400×C₇₃	C₂²	1	2	yes	—
38	#400×C₇₃	C₂²	1	2	yes	—
39	#400×C₇₃	C₂²	1	2	yes	—
40	#400×C₇₃	C₂²	1	2	yes	—
41	#398×C₇₃	C₂²	1	2	yes	—
42	#398×C₇₃	C₂²	1	2	yes	—
43	#398×C₇₃	C₂²	1	2	yes	—
44	#397×C₇₃	C₂²	1	2	yes	—
45	#397×C₇₃	C₂²	1	2	yes	—
46	#395×C₇₃	C₂²	1	2	yes	—
47	#393×C₇₃	C₂²	1	2	yes	—
48	#391×C₇₃	C₂²	1	1	yes	characteristic
49	#391×C₇₃	C₂²	1	1	yes	characteristic
50	#391×C₇₃	C₂²	1	1	yes	characteristic
51	#391×C₇₃	C₂²	1	2	yes	—
52	#391×C₇₃	C₂²	1	1	yes	characteristic
53	#391×C₇₃	C₂²	1	2	yes	—
54	#391×C₇₃	C₂²	1	1	yes	characteristic
55	#391×C₇₃	C₂²	1	2	yes	—
56	#391×C₇₃	C₂²	1	2	yes	—
57	#389×C₇₃	C₂²	1	1	yes	characteristic
58	#389×C₇₃	C₂²	1	1	yes	characteristic
59	#389×C₇₃	C₂²	1	1	yes	characteristic
60	#389×C₇₃	C₂²	1	2	yes	—
61	#389×C₇₃	C₂²	1	1	yes	characteristic
62	#389×C₇₃	C₂²	1	2	yes	—
63	#389×C₇₃	C₂²	1	2	yes	—
64	#389×C₇₃	C₂²	1	1	yes	characteristic
65	#389×C₇₃	C₂²	1	2	yes	—
66	#389×C₇₃	C₂²	1	2	yes	—
67	#389×C₇₃	C₂²	1	1	yes	characteristic
68	#389×C₇₃	C₂²	1	1	yes	characteristic
69	#388×C₇₃	C₂²	1	2	yes	—
70	#388×C₇₃	C₂²	1	2	yes	—
71	#388×C₇₃	C₂²	1	1	yes	characteristic
72	#388×C₇₃	C₂²	1	2	yes	—
73	#388×C₇₃	C₂²	1	1	yes	characteristic
74	#388×C₇₃	C₂²	1	1	yes	characteristic
75	#387×C₇₃	C₂²	1	2	yes	—
76	#387×C₇₃	C₂²	1	2	yes	—
77	#387×C₇₃	C₂²	1	2	yes	—
78	#387×C₇₃	C₂²	1	2	yes	—
79	#387×C₇₃	C₂²	1	2	yes	—
80	#387×C₇₃	C₂²	1	2	yes	—
81	#387×C₇₃	C₂²	1	2	yes	—
82	#387×C₇₃	C₂²	1	2	yes	—
83	#387×C₇₃	C₂²	1	2	yes	—
84	#387×C₇₃	C₂²	1	1	yes	characteristic
85	#387×C₇₃	C₂²	1	2	yes	—
86	#387×C₇₃	C₂²	1	2	yes	—
87	#387×C₇₃	C₂²	1	2	yes	—
88	#387×C₇₃	C₂²	1	1	yes	characteristic
89	#387×C₇₃	C₂²	1	2	yes	—
90	#387×C₇₃	C₂²	1	1	yes	characteristic
91	#385×C₇₃	C₂²	1	2	yes	—
92	#385×C₇₃	C₂²	1	2	yes	—
93	#383×C₇₃	C₂²	1	1	yes	characteristic
94	#383×C₇₃	C₂²	1	2	yes	—
95	#383×C₇₃	C₂²	1	2	yes	—
96	#382×C₇₃	C₂²	1	1	yes	characteristic
97	#382×C₇₃	C₂²	1	2	yes	—
98	#382×C₇₃	C₂²	1	1	yes	characteristic
99	#381×C₇₃	C₂²	1	2	yes	—
100	#380×C₇₃	C₂²	1	2	yes	—
101	#380×C₇₃	C₂²	1	1	yes	characteristic
102	#380×C₇₃	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
121	#376×C₇₃	C₂²	1	2	yes	—
122	C₄³×C₇₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
127	C₄⋊Q₈×C₇₃	—	2	4	no	—
128	#126×C₇₃	—	2	4	no	—
129	#125×C₇₃	—	2	4	no	—
130	#125×C₇₃	—	2	4	no	—
131	C₂²⋊Q₈×C₇₃	—	2	4	no	—
132	C₄×Q₈×C₇₃	—	2	4	no	—
133	#117×C₇₃	—	2	8	no	—
134	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
135	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
188	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
189	#95×C₇₃	C₂³	1	2	yes	—
190	#95×C₇₃	C₂³	1	1	yes	characteristic
191	#95×C₇₃	C₂³	1	2	yes	—
192	#95×C₇₃	C₂³	1	1	yes	characteristic
193	#95×C₇₃	C₂³	1	1	yes	characteristic
194	#95×C₇₃	C₂³	1	1	yes	characteristic
195	#95×C₇₃	C₂³	1	1	yes	characteristic
196	#95×C₇₃	C₂³	1	1	yes	characteristic
197	#95×C₇₃	C₂³	1	1	yes	characteristic
198	#95×C₇₃	C₂³	1	2	yes	—
199	#95×C₇₃	C₂³	1	2	yes	—
200	#95×C₇₃	C₂³	1	2	yes	—
201	#95×C₇₃	C₂³	1	2	yes	—
202	#95×C₇₃	C₂³	1	2	yes	—
203	#95×C₇₃	C₂³	1	1	yes	characteristic
204	#95×C₇₃	C₂³	1	2	yes	—
205	#95×C₇₃	C₂³	1	2	yes	—
206	#95×C₇₃	C₂³	1	2	yes	—
207	#95×C₇₃	C₂³	1	1	yes	characteristic
208	#95×C₇₃	C₂³	1	1	yes	characteristic
209	#95×C₇₃	C₂³	1	2	yes	—
210	#95×C₇₃	C₂³	1	2	yes	—
211	#95×C₇₃	C₂³	1	1	yes	characteristic
212	#95×C₇₃	C₂³	1	1	yes	characteristic
213	#95×C₇₃	C₂³	1	2	yes	—
214	#95×C₇₃	C₂³	1	2	yes	—
215	#95×C₇₃	C₂³	1	2	yes	—
216	#95×C₇₃	C₂³	1	2	yes	—
217	#95×C₇₃	C₂³	1	2	yes	—
218	#95×C₇₃	C₂³	1	2	yes	—
219	#95×C₇₃	C₂³	1	2	yes	—
220	#95×C₇₃	C₂³	1	2	yes	—
221	#95×C₇₃	C₂³	1	2	yes	—
222	#95×C₇₃	C₂³	1	2	yes	—
223	#95×C₇₃	C₂³	1	2	yes	—
224	#95×C₇₃	C₂³	1	2	yes	—
225	#95×C₇₃	C₂³	1	2	yes	—
226	#95×C₇₃	C₂³	1	2	yes	—
227	#95×C₇₃	C₂³	1	2	yes	—
228	#95×C₇₃	C₂³	1	2	yes	—
229	#95×C₇₃	C₂³	1	2	yes	—
230	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
231	C₂×Q₈×C₇₃	—	2	2	no	—
232	C₂×Q₈×C₇₃	—	2	2	no	—
233	C₂×Q₈×C₇₃	—	2	4	no	—
234	C₂×Q₈×C₇₃	—	2	2	no	—
235	C₂×Q₈×C₇₃	—	4	2	no	—
236	C₂×Q₈×C₇₃	—	4	2	no	—
237	C₂²×C₄×C₇₃	—	2	4	no	—
238	C₂²×C₄×C₇₃	—	2	4	no	—
239	C₂²×C₄×C₇₃	—	2	2	no	—
240	C₂²×C₄×C₇₃	—	2	2	no	—
241	C₂²×C₄×C₇₃	—	2	2	no	—
242	C₂²×C₄×C₇₃	—	4	2	no	—
243	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
265	C₄⋊C₄×C₇₃	—	2	4	no	—
266	C₄⋊C₄×C₇₃	—	2	2	no	—
267	C₄⋊C₄×C₇₃	—	2	4	no	—
268	C₄⋊C₄×C₇₃	—	2	4	no	—
269	C₄⋊C₄×C₇₃	—	2	4	no	—
270	C₄⋊C₄×C₇₃	—	2	4	no	—
271	C₄⋊C₄×C₇₃	—	2	4	no	—
272	C₄⋊C₄×C₇₃	—	2	4	no	—
273	C₄⋊C₄×C₇₃	—	2	4	no	—
274	C₄⋊C₄×C₇₃	—	2	4	no	—
275	C₄⋊C₄×C₇₃	—	2	2	no	—
276	C₄⋊C₄×C₇₃	—	2	2	no	—
277	C₄⋊C₄×C₇₃	—	2	2	no	—
278	C₄⋊C₄×C₇₃	—	2	2	no	—
279	C₄⋊C₄×C₇₃	—	2	2	no	—
280	C₄⋊C₄×C₇₃	—	2	4	no	—
281	C₄⋊C₄×C₇₃	—	2	2	no	—
282	C₄⋊C₄×C₇₃	—	2	2	no	—
283	C₄⋊C₄×C₇₃	—	2	4	no	—
284	C₄⋊C₄×C₇₃	—	2	2	no	—
285	C₄⋊C₄×C₇₃	—	4	2	no	—
286	C₄⋊C₄×C₇₃	—	4	2	no	—
287	C₄⋊C₄×C₇₃	—	4	1	no	—
288	C₄⋊C₄×C₇₃	—	4	2	no	—
289	C₄⋊C₄×C₇₃	—	4	1	no	—
290	C₄⋊C₄×C₇₃	—	4	2	no	—
291	C₄⋊C₄×C₇₃	#41	1	4	yes	—
292	C₄⋊C₄×C₇₃	#41	1	4	yes	—
293	C₂²⋊C₄×C₇₃	—	2	4	no	—
294	C₂²⋊C₄×C₇₃	—	2	2	no	—
295	C₂²⋊C₄×C₇₃	—	2	2	no	—
296	C₂²⋊C₄×C₇₃	—	2	4	no	—
297	C₂²⋊C₄×C₇₃	—	2	2	no	—
298	C₂²⋊C₄×C₇₃	—	4	1	no	—
299	C₂²⋊C₄×C₇₃	—	4	2	no	—
300	C₂²⋊C₄×C₇₃	—	4	1	no	—
301	C₂²⋊C₄×C₇₃	#41	1	4	yes	—
302	C₄²×C₇₃	—	2	4	no	—
303	C₄²×C₇₃	—	2	4	no	—
304	C₄²×C₇₃	—	2	2	no	—
305	C₄²×C₇₃	—	2	4	no	—
306	C₄²×C₇₃	—	2	2	no	—
307	C₄²×C₇₃	—	2	2	no	—
308	C₄²×C₇₃	—	2	2	no	—
309	C₄²×C₇₃	—	2	2	no	—
310	C₄²×C₇₃	—	2	2	no	—
311	C₄²×C₇₃	—	2	2	no	—
312	C₄²×C₇₃	—	2	2	no	—
313	C₄²×C₇₃	—	4	1	no	—
314	C₄²×C₇₃	—	4	2	no	—
315	C₄²×C₇₃	—	4	2	no	—
316	C₄²×C₇₃	—	4	2	no	—
317	C₄²×C₇₃	—	4	2	no	—
318	C₄²×C₇₃	—	4	1	no	—
319	C₂³×C₇₃	—	2	1	no	—
320	C₂³×C₇₃	—	2	1	no	—
321	C₂³×C₇₃	—	2	1	no	—
322	C₂³×C₇₃	—	2	1	no	—
323	C₂³×C₇₃	—	2	1	no	—
324	C₂³×C₇₃	—	2	1	no	—
325	C₂³×C₇₃	C₂×#41	1	2	yes	—
326	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
327	Q₈×C₇₃	—	4	4	no	—
328	Q₈×C₇₃	—	8	4	no	—
329	C₂×C₄×C₇₃	—	2	1	no	—
330	C₂×C₄×C₇₃	—	2	1	no	—
331	C₂×C₄×C₇₃	—	2	2	no	—
332	C₂×C₄×C₇₃	—	2	1	no	—
333	C₂×C₄×C₇₃	—	2	1	no	—
334	C₂×C₄×C₇₃	—	2	1	no	—
335	C₂×C₄×C₇₃	—	2	1	no	—
336	C₂×C₄×C₇₃	—	2	2	no	—
337	C₂×C₄×C₇₃	—	2	2	no	—
338	C₂×C₄×C₇₃	—	2	2	no	—
339	C₂×C₄×C₇₃	—	2	2	no	—
340	C₂×C₄×C₇₃	—	2	1	no	—
341	C₂×C₄×C₇₃	—	2	2	no	—
342	C₂×C₄×C₇₃	—	2	1	no	—
343	C₂×C₄×C₇₃	—	2	2	no	—
344	C₂×C₄×C₇₃	—	2	1	no	—
345	C₂×C₄×C₇₃	—	2	1	no	—
346	C₂×C₄×C₇₃	—	2	1	no	—
347	C₂×C₄×C₇₃	—	2	1	no	—
348	C₂×C₄×C₇₃	—	2	1	no	—
349	C₂×C₄×C₇₃	—	2	2	no	—
350	C₂×C₄×C₇₃	—	2	1	no	—
351	C₂×C₄×C₇₃	—	2	1	no	—
352	C₂×C₄×C₇₃	—	2	1	no	—
353	C₂×C₄×C₇₃	—	2	2	no	—
354	C₂×C₄×C₇₃	—	2	2	no	—
355	C₂×C₄×C₇₃	—	2	2	no	—
356	C₂×C₄×C₇₃	—	2	1	no	—
357	C₂×C₄×C₇₃	—	2	1	no	—
358	C₂×C₄×C₇₃	—	2	2	no	—
359	C₂×C₄×C₇₃	—	2	2	no	—
360	C₂×C₄×C₇₃	—	2	1	no	—
361	C₂×C₄×C₇₃	—	2	1	no	—
362	C₂×C₄×C₇₃	—	2	1	no	—
363	C₂×C₄×C₇₃	—	2	1	no	—
364	C₂×C₄×C₇₃	—	2	1	no	—
365	C₂×C₄×C₇₃	—	2	1	no	—
366	C₂×C₄×C₇₃	—	2	2	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	1	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	1	no	—
375	C₂×C₄×C₇₃	—	2	2	no	—
376	C₂×C₄×C₇₃	—	2	1	no	—
377	C₂×C₄×C₇₃	—	2	1	no	—
378	C₂×C₄×C₇₃	—	2	2	no	—
379	C₂×C₄×C₇₃	—	2	1	no	—
380	C₂×C₄×C₇₃	—	2	1	no	—
381	C₂×C₄×C₇₃	—	2	1	no	—
382	C₂×C₄×C₇₃	—	2	1	no	—
383	C₂×C₄×C₇₃	—	2	1	no	—
384	C₂×C₄×C₇₃	—	2	2	no	—
385	C₂×C₄×C₇₃	—	2	2	no	—
386	C₂×C₄×C₇₃	—	2	1	no	—
387	C₂×C₄×C₇₃	—	4	8	no	—
388	C₂×C₄×C₇₃	—	4	4	no	—
389	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
390	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
391	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
392	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
393	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
394	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
395	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
396	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
397	C₂²×C₇₃	—	2	2	no	—
398	C₂²×C₇₃	—	2	2	no	—
399	C₂²×C₇₃	—	2	2	no	—
400	C₂²×C₇₃	—	4	1	no	—
401	C₂²×C₇₃	—	4	1	no	—
402	C₂²×C₇₃	—	4	1	no	—
403	C₂²×C₇₃	—	4	1	no	—
404	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
405	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
406	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
407	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
408	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
409	C₂²×C₇₃	#585	1	1	yes	characteristic
410	C₂²×C₇₃	#585	1	1	yes	characteristic
411	C₄×C₇₃	—	2	4	no	—
412	C₄×C₇₃	—	2	2	no	—
413	C₄×C₇₃	—	2	2	no	—
414	C₄×C₇₃	—	2	2	no	—
415	C₄×C₇₃	—	2	4	no	—
416	C₄×C₇₃	—	4	1	no	—
417	C₄×C₇₃	—	4	2	no	—
418	C₄×C₇₃	—	4	1	no	—
419	C₄×C₇₃	—	4	1	no	—
420	C₄×C₇₃	—	4	2	no	—
421	C₄×C₇₃	—	4	1	no	—
422	C₄×C₇₃	—	4	2	no	—
423	C₄×C₇₃	—	4	2	no	—
424	C₄×C₇₃	—	4	1	no	—
425	C₄×C₇₃	—	4	1	no	—
426	C₄×C₇₃	—	4	2	no	—
427	C₄×C₇₃	—	4	1	no	—
428	C₄×C₇₃	—	4	2	no	—
429	C₄×C₇₃	—	4	1	no	—
430	C₄×C₇₃	—	4	1	no	—
431	C₄×C₇₃	—	4	1	no	—
432	C₄×C₇₃	#556	1	4	yes	—
433	#59574	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
434	C₂×C₇₃	—	4	2	no	—
435	C₂×C₇₃	C₂×#556	1	1	yes	characteristic
436	C₂×C₇₃	#3475	1	1	yes	characteristic
437	C₂×C₇₃	#3482	1	1	yes	characteristic
438	C₂×C₇₃	#3515	1	1	yes	characteristic
439	C₂×C₇₃	#3516	1	1	yes	characteristic
440	C₂×C₇₃	#3521	1	1	yes	characteristic
441	C₂×C₇₃	#3555	1	1	yes	characteristic
442	#2776	C₂×C₇₃	1	2	yes	complemented
443	#2745	C₂×C₇₃	1	2	yes	—
444	#2588	C₂×C₇₃	1	2	yes	complemented
445	#2550	C₂×C₇₃	1	1	yes	characteristic, complemented
446	#2528	C₂×C₇₃	1	2	yes	complemented
447	#2527	C₂×C₇₃	1	2	yes	—
448	#2514	C₂×C₇₃	1	1	yes	characteristic, complemented
449	#2514	C₂×C₇₃	1	1	yes	characteristic, complemented
450	#2514	C₂×C₇₃	1	2	yes	complemented
451	#2494	C₂×C₇₃	1	1	yes	characteristic
452	#2492	C₂×C₇₃	1	1	yes	characteristic
453	#2489	C₂×C₇₃	1	1	yes	characteristic
454	#2478	C₂×C₇₃	1	2	yes	—
455	#2453	C₂×C₇₃	1	1	yes	characteristic, complemented
456	#2442	C₂×C₇₃	1	1	yes	characteristic
457	#2370	C₂×C₇₃	1	1	yes	characteristic, complemented
458	#2369	C₂×C₇₃	1	1	yes	characteristic, complemented
459	#2360	C₂×C₇₃	1	1	yes	characteristic
460	#2347	C₂×C₇₃	1	2	yes	—
461	#2344	C₂×C₇₃	1	1	yes	characteristic
462	C₄×#125	C₂×C₇₃	1	1	yes	characteristic, complemented
463	C₄×#126	C₂×C₇₃	1	1	yes	characteristic
464	#2295	C₂×C₇₃	1	1	yes	characteristic, complemented
465	C₇₃	#59574	1	1	yes	characteristic, direct product factor, Sylow
466	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
467	C₂×#126	C₂²×C₇₃	1	1	yes	characteristic
468	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
469	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
470	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
471	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
472	C₂×#117	C₂²×C₇₃	1	2	yes	—
473	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
474	#401	C₂²×C₇₃	1	2	yes	—
475	#401	C₂²×C₇₃	1	2	yes	—
476	#401	C₂²×C₇₃	1	2	yes	—
477	#400	C₂²×C₇₃	1	2	yes	—
478	#400	C₂²×C₇₃	1	2	yes	—
479	#400	C₂²×C₇₃	1	2	yes	—
480	#400	C₂²×C₇₃	1	2	yes	—
481	#400	C₂²×C₇₃	1	2	yes	—
482	#400	C₂²×C₇₃	1	2	yes	—
483	#398	C₂²×C₇₃	1	2	yes	—
484	#398	C₂²×C₇₃	1	2	yes	—
485	#398	C₂²×C₇₃	1	2	yes	—
486	#397	C₂²×C₇₃	1	2	yes	—
487	#397	C₂²×C₇₃	1	2	yes	—
488	#395	C₂²×C₇₃	1	2	yes	—
489	#393	C₂²×C₇₃	1	2	yes	—
490	#391	C₂²×C₇₃	1	2	yes	—
491	#391	C₂²×C₇₃	1	2	yes	—
492	#391	C₂²×C₇₃	1	1	yes	characteristic
493	#391	C₂²×C₇₃	1	2	yes	—
494	#391	C₂²×C₇₃	1	1	yes	characteristic
495	#391	C₂²×C₇₃	1	1	yes	characteristic
496	#391	C₂²×C₇₃	1	1	yes	characteristic
497	#391	C₂²×C₇₃	1	1	yes	characteristic
498	#391	C₂²×C₇₃	1	2	yes	—
499	#389	C₂²×C₇₃	1	1	yes	characteristic
500	#389	C₂²×C₇₃	1	1	yes	characteristic
501	#389	C₂²×C₇₃	1	2	yes	—
502	#389	C₂²×C₇₃	1	1	yes	characteristic
503	#389	C₂²×C₇₃	1	1	yes	characteristic
504	#389	C₂²×C₇₃	1	2	yes	—
505	#389	C₂²×C₇₃	1	2	yes	—
506	#389	C₂²×C₇₃	1	2	yes	—
507	#389	C₂²×C₇₃	1	1	yes	characteristic
508	#389	C₂²×C₇₃	1	2	yes	—
509	#389	C₂²×C₇₃	1	1	yes	characteristic
510	#389	C₂²×C₇₃	1	1	yes	characteristic
511	#388	C₂²×C₇₃	1	1	yes	characteristic
512	#388	C₂²×C₇₃	1	1	yes	characteristic
513	#388	C₂²×C₇₃	1	1	yes	characteristic
514	#388	C₂²×C₇₃	1	2	yes	—
515	#388	C₂²×C₇₃	1	2	yes	—
516	#388	C₂²×C₇₃	1	2	yes	—
517	#387	C₂²×C₇₃	1	1	yes	characteristic
518	#387	C₂²×C₇₃	1	1	yes	characteristic
519	#387	C₂²×C₇₃	1	1	yes	characteristic
520	#387	C₂²×C₇₃	1	2	yes	—
521	#387	C₂²×C₇₃	1	2	yes	—
522	#387	C₂²×C₇₃	1	2	yes	—
523	#387	C₂²×C₇₃	1	2	yes	—
524	#387	C₂²×C₇₃	1	2	yes	—
525	#387	C₂²×C₇₃	1	2	yes	—
526	#387	C₂²×C₇₃	1	2	yes	—
527	#387	C₂²×C₇₃	1	2	yes	—
528	#387	C₂²×C₇₃	1	2	yes	—
529	#387	C₂²×C₇₃	1	2	yes	—
530	#387	C₂²×C₇₃	1	2	yes	—
531	#387	C₂²×C₇₃	1	2	yes	—
532	#387	C₂²×C₇₃	1	2	yes	—
533	#385	C₂²×C₇₃	1	2	yes	—
534	#385	C₂²×C₇₃	1	2	yes	—
535	#383	C₂²×C₇₃	1	1	yes	characteristic
536	#383	C₂²×C₇₃	1	2	yes	—
537	#383	C₂²×C₇₃	1	2	yes	—
538	#382	C₂²×C₇₃	1	1	yes	characteristic
539	#382	C₂²×C₇₃	1	2	yes	—
540	#382	C₂²×C₇₃	1	1	yes	characteristic
541	#381	C₂²×C₇₃	1	2	yes	—
542	#380	C₂²×C₇₃	1	1	yes	characteristic
543	#380	C₂²×C₇₃	1	2	yes	—
544	#380	C₂²×C₇₃	1	1	yes	characteristic
545	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
546	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
547	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
548	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
549	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
550	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
551	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
552	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
553	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
554	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
555	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
556	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
557	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
559	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
560	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
561	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
562	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
563	#376	C₂²×C₇₃	1	2	yes	—
564	C₄³	C₂²×C₇₃	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
567	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
568	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
569	C₄⋊Q₈	—	2	4	no	—
570	#126	—	2	4	no	—
571	#125	—	2	4	no	—
572	#125	—	2	4	no	—
573	C₂²⋊Q₈	—	2	4	no	—
574	C₄×Q₈	—	2	4	no	—
575	#117	—	2	8	no	—
576	C₂×C₄⋊C₄	—	2	4	no	—
577	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
615	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
616	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
618	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
627	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
628	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
629	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
630	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
631	#95	C₂³×C₇₃	1	2	yes	—
632	#95	C₂³×C₇₃	1	2	yes	—
633	#95	C₂³×C₇₃	1	2	yes	—
634	#95	C₂³×C₇₃	1	2	yes	—
635	#95	C₂³×C₇₃	1	2	yes	—
636	#95	C₂³×C₇₃	1	1	yes	characteristic
637	#95	C₂³×C₇₃	1	2	yes	—
638	#95	C₂³×C₇₃	1	1	yes	characteristic
639	#95	C₂³×C₇₃	1	1	yes	characteristic
640	#95	C₂³×C₇₃	1	1	yes	characteristic
641	#95	C₂³×C₇₃	1	1	yes	characteristic
642	#95	C₂³×C₇₃	1	1	yes	characteristic
643	#95	C₂³×C₇₃	1	1	yes	characteristic
644	#95	C₂³×C₇₃	1	2	yes	—
645	#95	C₂³×C₇₃	1	2	yes	—
646	#95	C₂³×C₇₃	1	2	yes	—
647	#95	C₂³×C₇₃	1	2	yes	—
648	#95	C₂³×C₇₃	1	2	yes	—
649	#95	C₂³×C₇₃	1	1	yes	characteristic
650	#95	C₂³×C₇₃	1	2	yes	—
651	#95	C₂³×C₇₃	1	2	yes	—
652	#95	C₂³×C₇₃	1	2	yes	—
653	#95	C₂³×C₇₃	1	1	yes	characteristic
654	#95	C₂³×C₇₃	1	1	yes	characteristic
655	#95	C₂³×C₇₃	1	2	yes	—
656	#95	C₂³×C₇₃	1	2	yes	—
657	#95	C₂³×C₇₃	1	1	yes	characteristic
658	#95	C₂³×C₇₃	1	1	yes	characteristic
659	#95	C₂³×C₇₃	1	2	yes	—
660	#95	C₂³×C₇₃	1	2	yes	—
661	#95	C₂³×C₇₃	1	2	yes	—
662	#95	C₂³×C₇₃	1	2	yes	—
663	#95	C₂³×C₇₃	1	2	yes	—
664	#95	C₂³×C₇₃	1	2	yes	—
665	#95	C₂³×C₇₃	1	2	yes	—
666	#95	C₂³×C₇₃	1	2	yes	—
667	#95	C₂³×C₇₃	1	2	yes	—
668	#95	C₂³×C₇₃	1	2	yes	—
669	#95	C₂³×C₇₃	1	2	yes	—
670	#95	C₂³×C₇₃	1	2	yes	—
671	#95	C₂³×C₇₃	1	2	yes	—
672	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	2	4	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	4	2	no	—
678	C₂×Q₈	—	4	2	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
691	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₄⋊C₄	—	4	2	no	—
731	C₄⋊C₄	—	4	1	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	#41×C₇₃	1	4	yes	—
734	C₄⋊C₄	#41×C₇₃	1	4	yes	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	4	1	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	1	no	—
743	C₂²⋊C₄	#41×C₇₃	1	4	yes	—
744	C₄²	—	2	4	no	—
745	C₄²	—	2	4	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	2	no	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	2	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	4	1	no	—
756	C₄²	—	4	2	no	—
757	C₄²	—	4	2	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	C₂×#41×C₇₃	1	2	yes	—
768	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
769	Q₈	—	4	4	no	—
770	Q₈	—	8	4	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
832	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
833	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
834	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
835	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
836	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
837	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
838	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
847	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
848	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
849	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
850	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
851	C₂²	#585×C₇₃	1	1	yes	characteristic
852	C₂²	#585×C₇₃	1	1	yes	characteristic
853	C₄	—	2	4	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	4	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	1	no	—
874	C₄	#556×C₇₃	1	4	yes	—
875	C₂	—	4	2	no	—
876	C₂	C₂×#556×C₇₃	1	1	yes	characteristic
877	C₂	C₇₃×#3475	1	1	yes	characteristic
878	C₂	C₇₃×#3482	1	1	yes	characteristic
879	C₂	C₇₃×#3515	1	1	yes	characteristic
880	C₂	C₇₃×#3516	1	1	yes	characteristic
881	C₂	C₇₃×#3521	1	1	yes	characteristic
882	C₂	C₇₃×#3555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂⁴×C₇₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2776	C₂	semidirect
3. C₇₃×#2588	C₂	semidirect
4. C₇₃×#2550	C₂	semidirect
5. C₇₃×#2528	C₂	semidirect
7. C₇₃×#2514	C₂	semidirect
8. C₇₃×#2514	C₂	semidirect
9. C₇₃×#2514	C₂	semidirect
14. C₇₃×#2453	C₂	semidirect
16. C₇₃×#2370	C₂	semidirect
17. C₇₃×#2369	C₂	semidirect
21. C₄×#125×C₇₃	C₂	semidirect
23. C₇₃×#2295	C₂	semidirect
433. #59574	C₇₃	direct (N × H)
442. #2776	C₂×C₇₃	semidirect
444. #2588	C₂×C₇₃	semidirect
445. #2550	C₂×C₇₃	semidirect
446. #2528	C₂×C₇₃	semidirect
448. #2514	C₂×C₇₃	semidirect
449. #2514	C₂×C₇₃	semidirect
450. #2514	C₂×C₇₃	semidirect
455. #2453	C₂×C₇₃	semidirect
457. #2370	C₂×C₇₃	semidirect
458. #2369	C₂×C₇₃	semidirect
462. C₄×#125	C₂×C₇₃	semidirect
464. #2295	C₂×C₇₃	semidirect
465. C₇₃	#59574	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×#2776	2
C₇₃×#2745	2
C₇₃×#2588	2
C₇₃×#2550	2
C₇₃×#2528	2
C₇₃×#2527	2
C₇₃×#2514	2
C₇₃×#2494	2
C₇₃×#2492	2
C₇₃×#2489	2
C₇₃×#2478	2
C₇₃×#2453	2
C₇₃×#2442	2
C₇₃×#2370	2
C₇₃×#2369	2
C₇₃×#2360	2
C₇₃×#2347	2
C₇₃×#2344	2
C₄×#125×C₇₃	2
C₄×#126×C₇₃	2
C₇₃×#2295	2
#59574	73

Subgroups — C73×#59574 #32968978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59574 #32968978