Subgroups — C₇₃×#59680 #32969084

Order 18688.

2640 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2714	C₂	1	4	yes	maximal, complemented
3	C₇₃×#2541	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2541	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2541	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2535	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2512	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2456	C₂	1	4	yes	maximal, complemented
9	C₇₃×#2445	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2416	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2414	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2366	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#125×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#553×C₇₃	—	2	16	no	—
19	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#127×C₇₃	C₂²	1	2	yes	—
22	C₂×#127×C₇₃	C₂²	1	2	yes	—
23	C₂×#126×C₇₃	C₂²	1	4	yes	—
24	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#123×C₇₃	C₂²	1	4	yes	—
26	C₂×#121×C₇₃	C₂²	1	4	yes	—
27	C₂×#121×C₇₃	C₂²	1	2	yes	—
28	C₂×#121×C₇₃	C₂²	1	2	yes	—
29	C₂×#121×C₇₃	C₂²	1	4	yes	—
30	C₂×#121×C₇₃	C₂²	1	2	yes	—
31	C₂×#121×C₇₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
33	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
41	C₂×#117×C₇₃	C₂²	1	2	yes	—
42	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
43	#397×C₇₃	C₂²	1	4	yes	—
44	#396×C₇₃	C₂²	1	4	yes	—
45	#394×C₇₃	C₂²	1	4	yes	—
46	#394×C₇₃	C₂²	1	4	yes	—
47	#392×C₇₃	C₂²	1	4	yes	—
48	#392×C₇₃	C₂²	1	4	yes	—
49	#392×C₇₃	C₂²	1	4	yes	—
50	#392×C₇₃	C₂²	1	4	yes	—
51	#390×C₇₃	C₂²	1	1	yes	characteristic
52	#390×C₇₃	C₂²	1	2	yes	—
53	#390×C₇₃	C₂²	1	2	yes	—
54	#390×C₇₃	C₂²	1	2	yes	—
55	#390×C₇₃	C₂²	1	2	yes	—
56	#390×C₇₃	C₂²	1	2	yes	—
57	#390×C₇₃	C₂²	1	4	yes	—
58	#390×C₇₃	C₂²	1	2	yes	—
59	#390×C₇₃	C₂²	1	2	yes	—
60	#390×C₇₃	C₂²	1	1	yes	characteristic
61	#390×C₇₃	C₂²	1	2	yes	—
62	#389×C₇₃	C₂²	1	2	yes	—
63	#389×C₇₃	C₂²	1	1	yes	characteristic
64	#389×C₇₃	C₂²	1	1	yes	characteristic
65	#388×C₇₃	C₂²	1	4	yes	—
66	#388×C₇₃	C₂²	1	4	yes	—
67	#387×C₇₃	C₂²	1	2	yes	—
68	#387×C₇₃	C₂²	1	2	yes	—
69	#386×C₇₃	C₂²	1	4	yes	—
70	#386×C₇₃	C₂²	1	4	yes	—
71	#386×C₇₃	C₂²	1	4	yes	—
72	#385×C₇₃	C₂²	1	4	yes	—
73	#384×C₇₃	C₂²	1	1	yes	characteristic
74	#384×C₇₃	C₂²	1	1	yes	characteristic
75	#382×C₇₃	C₂²	1	1	yes	characteristic
76	#380×C₇₃	C₂²	1	2	yes	—
77	#380×C₇₃	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
83	C₄³×C₇₃	C₂²	1	1	yes	characteristic
84	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
89	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
92	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
94	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
95	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
97	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
98	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
99	#127×C₇₃	—	2	4	no	—
100	#127×C₇₃	—	2	8	no	—
101	#127×C₇₃	—	2	4	no	—
102	#127×C₇₃	—	4	4	no	—
103	#126×C₇₃	—	2	16	no	—
104	#125×C₇₃	D₄	1	8	yes	complemented
105	#123×C₇₃	—	2	16	no	—
106	#121×C₇₃	—	2	16	no	—
107	#121×C₇₃	—	2	8	no	—
108	#121×C₇₃	—	2	8	no	—
109	#121×C₇₃	—	4	8	no	—
110	#121×C₇₃	—	4	4	no	—
111	#121×C₇₃	—	4	4	no	—
112	C₄×D₄×C₇₃	—	2	16	no	—
113	C₄×D₄×C₇₃	—	2	8	no	—
114	C₄×D₄×C₇₃	—	2	8	no	—
115	C₄×D₄×C₇₃	—	2	4	no	—
116	C₄×D₄×C₇₃	—	2	4	no	—
117	C₄×D₄×C₇₃	—	4	4	no	—
118	C₄×D₄×C₇₃	—	4	4	no	—
119	C₄×D₄×C₇₃	—	4	4	no	—
120	C₄×D₄×C₇₃	—	4	4	no	—
121	#117×C₇₃	—	2	8	no	—
122	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
123	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
157	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
160	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
165	#95×C₇₃	C₂³	1	4	yes	—
166	#95×C₇₃	C₂³	1	2	yes	—
167	#95×C₇₃	C₂³	1	2	yes	—
168	#95×C₇₃	C₂³	1	2	yes	—
169	#95×C₇₃	C₂³	1	2	yes	—
170	#95×C₇₃	C₂³	1	2	yes	—
171	#95×C₇₃	C₂³	1	2	yes	—
172	#95×C₇₃	C₂³	1	4	yes	—
173	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
174	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
175	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
176	C₂×D₄×C₇₃	—	2	4	no	—
177	C₂×D₄×C₇₃	—	2	8	no	—
178	C₂×D₄×C₇₃	—	2	4	no	—
179	C₂×D₄×C₇₃	—	2	8	no	—
180	C₂×D₄×C₇₃	—	2	8	no	—
181	C₂×D₄×C₇₃	—	2	4	no	—
182	C₂×D₄×C₇₃	—	2	4	no	—
183	C₂×D₄×C₇₃	—	2	8	no	—
184	C₂×D₄×C₇₃	—	2	2	no	—
185	C₂×D₄×C₇₃	—	2	2	no	—
186	C₂×D₄×C₇₃	—	2	4	no	—
187	C₂×D₄×C₇₃	—	2	4	no	—
188	C₂×D₄×C₇₃	—	2	2	no	—
189	C₂×D₄×C₇₃	—	2	4	no	—
190	C₂×D₄×C₇₃	—	2	4	no	—
191	C₂×D₄×C₇₃	—	2	2	no	—
192	C₂×D₄×C₇₃	—	2	4	no	—
193	C₂×D₄×C₇₃	—	2	4	no	—
194	C₂×D₄×C₇₃	—	2	4	no	—
195	C₂×D₄×C₇₃	—	2	2	no	—
196	C₂×D₄×C₇₃	—	4	2	no	—
197	C₂×D₄×C₇₃	—	4	2	no	—
198	C₂×D₄×C₇₃	—	4	2	no	—
199	C₂×D₄×C₇₃	—	4	2	no	—
200	C₂×D₄×C₇₃	—	4	4	no	—
201	C₂×D₄×C₇₃	—	4	4	no	—
202	C₂×D₄×C₇₃	—	4	4	no	—
203	C₂×D₄×C₇₃	—	4	4	no	—
204	C₂×D₄×C₇₃	—	4	4	no	—
205	C₂×D₄×C₇₃	—	4	4	no	—
206	C₂×D₄×C₇₃	—	4	4	no	—
207	C₂×D₄×C₇₃	—	4	4	no	—
208	C₂×D₄×C₇₃	#41	1	4	yes	—
209	C₂²×C₄×C₇₃	—	2	4	no	—
210	C₂²×C₄×C₇₃	—	2	4	no	—
211	C₂²×C₄×C₇₃	—	2	4	no	—
212	C₂²×C₄×C₇₃	—	2	4	no	—
213	C₂²×C₄×C₇₃	—	2	4	no	—
214	C₂²×C₄×C₇₃	—	2	4	no	—
215	C₂²×C₄×C₇₃	—	2	8	no	—
216	C₂²×C₄×C₇₃	—	2	8	no	—
217	C₂²×C₄×C₇₃	—	4	4	no	—
218	C₂²×C₄×C₇₃	—	4	4	no	—
219	C₂²×C₄×C₇₃	—	4	4	no	—
220	C₂²×C₄×C₇₃	—	4	4	no	—
221	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
226	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
235	C₄⋊C₄×C₇₃	—	2	4	no	—
236	C₄⋊C₄×C₇₃	—	2	8	no	—
237	C₄⋊C₄×C₇₃	—	2	4	no	—
238	C₄⋊C₄×C₇₃	—	2	2	no	—
239	C₄⋊C₄×C₇₃	—	2	2	no	—
240	C₄⋊C₄×C₇₃	—	2	4	no	—
241	C₄⋊C₄×C₇₃	—	2	4	no	—
242	C₄⋊C₄×C₇₃	—	2	2	no	—
243	C₄⋊C₄×C₇₃	—	2	2	no	—
244	C₄⋊C₄×C₇₃	—	4	2	no	—
245	C₄⋊C₄×C₇₃	—	4	2	no	—
246	C₄⋊C₄×C₇₃	—	4	2	no	—
247	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
248	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
249	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
250	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
251	C₂²⋊C₄×C₇₃	—	2	8	no	—
252	C₂²⋊C₄×C₇₃	—	2	4	no	—
253	C₂²⋊C₄×C₇₃	—	2	8	no	—
254	C₂²⋊C₄×C₇₃	—	2	8	no	—
255	C₂²⋊C₄×C₇₃	—	2	4	no	—
256	C₂²⋊C₄×C₇₃	—	2	8	no	—
257	C₂²⋊C₄×C₇₃	—	2	4	no	—
258	C₂²⋊C₄×C₇₃	—	2	4	no	—
259	C₂²⋊C₄×C₇₃	—	2	8	no	—
260	C₂²⋊C₄×C₇₃	—	4	2	no	—
261	C₂²⋊C₄×C₇₃	—	4	2	no	—
262	C₂²⋊C₄×C₇₃	—	4	4	no	—
263	C₂²⋊C₄×C₇₃	—	4	4	no	—
264	C₂²⋊C₄×C₇₃	—	4	4	no	—
265	C₂²⋊C₄×C₇₃	—	4	4	no	—
266	C₂²⋊C₄×C₇₃	—	4	4	no	—
267	C₄²×C₇₃	—	2	8	no	—
268	C₄²×C₇₃	—	2	2	no	—
269	C₄²×C₇₃	—	2	4	no	—
270	C₄²×C₇₃	—	2	2	no	—
271	C₄²×C₇₃	—	2	2	no	—
272	C₄²×C₇₃	—	2	2	no	—
273	C₄²×C₇₃	—	2	4	no	—
274	C₄²×C₇₃	—	4	1	no	—
275	C₄²×C₇₃	C₂×D₄	1	4	yes	—
276	C₄²×C₇₃	#41	1	4	yes	—
277	C₂³×C₇₃	—	2	2	no	—
278	C₂³×C₇₃	—	2	2	no	—
279	C₂³×C₇₃	—	2	2	no	—
280	C₂³×C₇₃	—	2	2	no	—
281	C₂³×C₇₃	—	2	2	no	—
282	C₂³×C₇₃	—	2	2	no	—
283	C₂³×C₇₃	—	2	2	no	—
284	C₂³×C₇₃	—	2	4	no	—
285	C₂³×C₇₃	—	2	2	no	—
286	C₂³×C₇₃	—	2	4	no	—
287	C₂³×C₇₃	—	2	2	no	—
288	C₂³×C₇₃	—	2	4	no	—
289	C₂³×C₇₃	—	2	4	no	—
290	C₂³×C₇₃	—	2	4	no	—
291	C₂³×C₇₃	—	2	2	no	—
292	C₂³×C₇₃	—	2	2	no	—
293	C₂³×C₇₃	—	2	4	no	—
294	C₂³×C₇₃	—	2	2	no	—
295	C₂³×C₇₃	—	2	4	no	—
296	C₂³×C₇₃	—	2	2	no	—
297	C₂³×C₇₃	C₂×#41	1	4	yes	—
298	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
299	D₄×C₇₃	—	2	8	no	—
300	D₄×C₇₃	—	4	8	no	—
301	D₄×C₇₃	—	4	16	no	—
302	D₄×C₇₃	—	4	8	no	—
303	D₄×C₇₃	—	4	8	no	—
304	D₄×C₇₃	—	4	8	no	—
305	D₄×C₇₃	—	4	4	no	—
306	D₄×C₇₃	—	4	8	no	—
307	D₄×C₇₃	—	8	8	no	—
308	D₄×C₇₃	—	8	8	no	—
309	D₄×C₇₃	—	8	8	no	—
310	C₂×C₄×C₇₃	—	2	1	no	—
311	C₂×C₄×C₇₃	—	2	2	no	—
312	C₂×C₄×C₇₃	—	2	1	no	—
313	C₂×C₄×C₇₃	—	2	1	no	—
314	C₂×C₄×C₇₃	—	2	1	no	—
315	C₂×C₄×C₇₃	—	2	1	no	—
316	C₂×C₄×C₇₃	—	2	1	no	—
317	C₂×C₄×C₇₃	—	2	2	no	—
318	C₂×C₄×C₇₃	—	2	2	no	—
319	C₂×C₄×C₇₃	—	2	1	no	—
320	C₂×C₄×C₇₃	—	2	1	no	—
321	C₂×C₄×C₇₃	—	2	2	no	—
322	C₂×C₄×C₇₃	—	2	2	no	—
323	C₂×C₄×C₇₃	—	2	4	no	—
324	C₂×C₄×C₇₃	—	2	2	no	—
325	C₂×C₄×C₇₃	—	2	2	no	—
326	C₂×C₄×C₇₃	—	2	2	no	—
327	C₂×C₄×C₇₃	—	2	2	no	—
328	C₂×C₄×C₇₃	—	2	1	no	—
329	C₂×C₄×C₇₃	—	2	1	no	—
330	C₂×C₄×C₇₃	—	2	2	no	—
331	C₂×C₄×C₇₃	—	2	4	no	—
332	C₂×C₄×C₇₃	—	2	2	no	—
333	C₂×C₄×C₇₃	—	2	2	no	—
334	C₂×C₄×C₇₃	—	2	4	no	—
335	C₂×C₄×C₇₃	—	2	2	no	—
336	C₂×C₄×C₇₃	—	2	2	no	—
337	C₂×C₄×C₇₃	—	2	2	no	—
338	C₂×C₄×C₇₃	—	2	1	no	—
339	C₂×C₄×C₇₃	—	2	2	no	—
340	C₂×C₄×C₇₃	—	4	8	no	—
341	C₂×C₄×C₇₃	—	4	8	no	—
342	C₂×C₄×C₇₃	—	8	8	no	—
343	C₂×C₄×C₇₃	—	8	8	no	—
344	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
348	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
350	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
351	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
352	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
353	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
354	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
355	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
356	C₂²×C₇₃	—	2	4	no	—
357	C₂²×C₇₃	—	2	4	no	—
358	C₂²×C₇₃	—	2	4	no	—
359	C₂²×C₇₃	—	4	2	no	—
360	C₂²×C₇₃	—	4	2	no	—
361	C₂²×C₇₃	—	4	2	no	—
362	C₂²×C₇₃	—	4	2	no	—
363	C₂²×C₇₃	—	4	2	no	—
364	C₂²×C₇₃	—	4	4	no	—
365	C₂²×C₇₃	—	4	2	no	—
366	C₂²×C₇₃	—	4	4	no	—
367	C₂²×C₇₃	—	4	2	no	—
368	C₂²×C₇₃	—	4	4	no	—
369	C₂²×C₇₃	—	4	4	no	—
370	C₂²×C₇₃	—	4	2	no	—
371	C₂²×C₇₃	—	4	4	no	—
372	C₂²×C₇₃	—	4	2	no	—
373	C₂²×C₇₃	—	4	2	no	—
374	C₂²×C₇₃	—	4	4	no	—
375	C₂²×C₇₃	—	4	2	no	—
376	C₂²×C₇₃	—	4	4	no	—
377	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
378	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
379	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
380	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
381	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂²×C₇₃	#585	1	1	yes	characteristic
384	C₄×C₇₃	—	2	2	no	—
385	C₄×C₇₃	—	2	4	no	—
386	C₄×C₇₃	—	2	2	no	—
387	C₄×C₇₃	—	2	4	no	—
388	C₄×C₇₃	—	2	2	no	—
389	C₄×C₇₃	—	2	2	no	—
390	C₄×C₇₃	—	4	2	no	—
391	C₄×C₇₃	—	4	2	no	—
392	C₄×C₇₃	—	4	4	no	—
393	C₄×C₇₃	—	4	2	no	—
394	C₄×C₇₃	—	4	1	no	—
395	C₄×C₇₃	—	4	2	no	—
396	C₄×C₇₃	#550	1	4	yes	—
397	C₄×C₇₃	#553	1	4	yes	complemented
398	#59680	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂×C₇₃	—	4	4	no	—
400	C₂×C₇₃	—	8	2	no	—
401	C₂×C₇₃	—	8	4	no	—
402	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
403	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
404	C₂×C₇₃	C₂×#553	1	1	yes	characteristic
405	C₂×C₇₃	#3498	1	1	yes	characteristic
406	C₂×C₇₃	#3506	1	1	yes	characteristic
407	C₂×C₇₃	#3519	1	1	yes	characteristic
408	C₂×C₇₃	#3546	1	1	yes	characteristic
409	C₂×#553	C₂×C₇₃	1	2	yes	complemented
410	#2714	C₂×C₇₃	1	4	yes	complemented
411	#2541	C₂×C₇₃	1	1	yes	characteristic, complemented
412	#2541	C₂×C₇₃	1	1	yes	characteristic, complemented
413	#2541	C₂×C₇₃	1	2	yes	complemented
414	#2535	C₂×C₇₃	1	2	yes	complemented
415	#2512	C₂×C₇₃	1	2	yes	complemented
416	#2456	C₂×C₇₃	1	4	yes	complemented
417	#2445	C₂×C₇₃	1	2	yes	complemented
418	#2416	C₂×C₇₃	1	2	yes	complemented
419	#2414	C₂×C₇₃	1	2	yes	complemented
420	#2366	C₂×C₇₃	1	2	yes	complemented
421	#2354	C₂×C₇₃	1	1	yes	characteristic, complemented
422	D₄×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
423	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
424	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
425	C₄×#125	C₂×C₇₃	1	1	yes	characteristic, complemented
426	C₇₃	#59680	1	1	yes	characteristic, direct product factor, Sylow
427	#553	—	2	16	no	—
428	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
429	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
430	C₂×#127	C₂²×C₇₃	1	2	yes	—
431	C₂×#127	C₂²×C₇₃	1	2	yes	—
432	C₂×#126	C₂²×C₇₃	1	4	yes	—
433	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
434	C₂×#123	C₂²×C₇₃	1	4	yes	—
435	C₂×#121	C₂²×C₇₃	1	2	yes	—
436	C₂×#121	C₂²×C₇₃	1	2	yes	—
437	C₂×#121	C₂²×C₇₃	1	4	yes	—
438	C₂×#121	C₂²×C₇₃	1	2	yes	—
439	C₂×#121	C₂²×C₇₃	1	4	yes	—
440	C₂×#121	C₂²×C₇₃	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
442	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
443	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
444	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
445	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
446	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
447	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
448	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
449	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
450	C₂×#117	C₂²×C₇₃	1	2	yes	—
451	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
452	#397	C₂²×C₇₃	1	4	yes	—
453	#396	C₂²×C₇₃	1	4	yes	—
454	#394	C₂²×C₇₃	1	4	yes	—
455	#394	C₂²×C₇₃	1	4	yes	—
456	#392	C₂²×C₇₃	1	4	yes	—
457	#392	C₂²×C₇₃	1	4	yes	—
458	#392	C₂²×C₇₃	1	4	yes	—
459	#392	C₂²×C₇₃	1	4	yes	—
460	#390	C₂²×C₇₃	1	1	yes	characteristic
461	#390	C₂²×C₇₃	1	2	yes	—
462	#390	C₂²×C₇₃	1	1	yes	characteristic
463	#390	C₂²×C₇₃	1	2	yes	—
464	#390	C₂²×C₇₃	1	2	yes	—
465	#390	C₂²×C₇₃	1	2	yes	—
466	#390	C₂²×C₇₃	1	2	yes	—
467	#390	C₂²×C₇₃	1	2	yes	—
468	#390	C₂²×C₇₃	1	4	yes	—
469	#390	C₂²×C₇₃	1	2	yes	—
470	#390	C₂²×C₇₃	1	2	yes	—
471	#389	C₂²×C₇₃	1	1	yes	characteristic
472	#389	C₂²×C₇₃	1	1	yes	characteristic
473	#389	C₂²×C₇₃	1	2	yes	—
474	#388	C₂²×C₇₃	1	4	yes	—
475	#388	C₂²×C₇₃	1	4	yes	—
476	#387	C₂²×C₇₃	1	2	yes	—
477	#387	C₂²×C₇₃	1	2	yes	—
478	#386	C₂²×C₇₃	1	4	yes	—
479	#386	C₂²×C₇₃	1	4	yes	—
480	#386	C₂²×C₇₃	1	4	yes	—
481	#385	C₂²×C₇₃	1	4	yes	—
482	#384	C₂²×C₇₃	1	1	yes	characteristic
483	#384	C₂²×C₇₃	1	1	yes	characteristic
484	#382	C₂²×C₇₃	1	1	yes	characteristic
485	#380	C₂²×C₇₃	1	2	yes	—
486	#380	C₂²×C₇₃	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
488	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
489	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
492	C₄³	C₂²×C₇₃	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
494	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
495	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
496	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
497	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
498	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
499	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
501	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
502	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
503	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
504	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
505	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
506	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
507	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
508	#127	—	2	4	no	—
509	#127	—	2	8	no	—
510	#127	—	2	4	no	—
511	#127	—	4	4	no	—
512	#126	—	2	16	no	—
513	#125	D₄×C₇₃	1	8	yes	complemented
514	#123	—	2	16	no	—
515	#121	—	2	16	no	—
516	#121	—	2	8	no	—
517	#121	—	2	8	no	—
518	#121	—	4	8	no	—
519	#121	—	4	4	no	—
520	#121	—	4	4	no	—
521	C₄×D₄	—	2	16	no	—
522	C₄×D₄	—	2	8	no	—
523	C₄×D₄	—	2	8	no	—
524	C₄×D₄	—	2	4	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	4	4	no	—
527	C₄×D₄	—	4	4	no	—
528	C₄×D₄	—	4	4	no	—
529	C₄×D₄	—	4	4	no	—
530	#117	—	2	8	no	—
531	C₂×C₄⋊C₄	—	2	8	no	—
532	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
564	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
565	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
569	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
571	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
574	#95	C₂³×C₇₃	1	4	yes	—
575	#95	C₂³×C₇₃	1	2	yes	—
576	#95	C₂³×C₇₃	1	2	yes	—
577	#95	C₂³×C₇₃	1	2	yes	—
578	#95	C₂³×C₇₃	1	2	yes	—
579	#95	C₂³×C₇₃	1	2	yes	—
580	#95	C₂³×C₇₃	1	2	yes	—
581	#95	C₂³×C₇₃	1	4	yes	—
582	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
583	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
584	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	8	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	4	4	no	—
610	C₂×D₄	—	4	4	no	—
611	C₂×D₄	—	4	4	no	—
612	C₂×D₄	—	4	4	no	—
613	C₂×D₄	—	4	4	no	—
614	C₂×D₄	—	4	4	no	—
615	C₂×D₄	—	4	4	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	#41×C₇₃	1	4	yes	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	8	no	—
625	C₂²×C₄	—	2	8	no	—
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	—	4	4	no	—
630	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
635	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	8	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
657	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
658	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
659	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	8	no	—
663	C₂²⋊C₄	—	2	8	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	8	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	8	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	4	4	no	—
672	C₂²⋊C₄	—	4	4	no	—
673	C₂²⋊C₄	—	4	4	no	—
674	C₂²⋊C₄	—	4	4	no	—
675	C₂²⋊C₄	—	4	4	no	—
676	C₄²	—	2	8	no	—
677	C₄²	—	2	2	no	—
678	C₄²	—	2	4	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	4	1	no	—
684	C₄²	C₂×D₄×C₇₃	1	4	yes	—
685	C₄²	#41×C₇₃	1	4	yes	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	4	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	4	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	4	no	—
698	C₂³	—	2	4	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	4	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	2	2	no	—
706	C₂³	C₂×#41×C₇₃	1	4	yes	—
707	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
708	D₄	—	2	8	no	—
709	D₄	—	4	8	no	—
710	D₄	—	4	16	no	—
711	D₄	—	4	8	no	—
712	D₄	—	4	8	no	—
713	D₄	—	4	8	no	—
714	D₄	—	4	4	no	—
715	D₄	—	4	8	no	—
716	D₄	—	8	8	no	—
717	D₄	—	8	8	no	—
718	D₄	—	8	8	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	8	8	no	—
752	C₂×C₄	—	8	8	no	—
753	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
754	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
755	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
756	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
757	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
758	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
759	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
760	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
761	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
762	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
763	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
764	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	4	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	4	no	—
778	C₂²	—	4	4	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	4	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	4	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	4	no	—
786	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
787	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
788	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
789	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
790	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
791	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
792	C₂²	#585×C₇₃	1	1	yes	characteristic
793	C₄	—	2	2	no	—
794	C₄	—	2	4	no	—
795	C₄	—	2	2	no	—
796	C₄	—	2	4	no	—
797	C₄	—	2	2	no	—
798	C₄	—	2	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	4	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	1	no	—
805	C₄	#550×C₇₃	1	4	yes	—
806	C₄	#553×C₇₃	1	4	yes	complemented
807	C₂	—	4	4	no	—
808	C₂	—	8	2	no	—
809	C₂	—	8	4	no	—
810	C₂	C₂×#550×C₇₃	1	1	yes	characteristic
811	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
812	C₂	C₂×#553×C₇₃	1	1	yes	characteristic
813	C₂	C₇₃×#3498	1	1	yes	characteristic
814	C₂	C₇₃×#3506	1	1	yes	characteristic
815	C₂	C₇₃×#3519	1	1	yes	characteristic
816	C₂	C₇₃×#3546	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
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. C₂×#553×C₇₃	C₂	semidirect
2. C₇₃×#2714	C₂	semidirect
3. C₇₃×#2541	C₂	semidirect
4. C₇₃×#2541	C₂	semidirect
5. C₇₃×#2541	C₂	semidirect
6. C₇₃×#2535	C₂	semidirect
7. C₇₃×#2512	C₂	semidirect
8. C₇₃×#2456	C₂	semidirect
9. C₇₃×#2445	C₂	semidirect
10. C₇₃×#2416	C₂	semidirect
11. C₇₃×#2414	C₂	semidirect
12. C₇₃×#2366	C₂	semidirect
13. C₇₃×#2354	C₂	semidirect
14. D₄×C₄⋊C₄×C₇₃	C₂	semidirect
15. C₄×#127×C₇₃	C₂	semidirect
16. C₄×#127×C₇₃	C₂	semidirect
17. C₄×#125×C₇₃	C₂	semidirect
104. #125×C₇₃	D₄	semidirect
397. C₄×C₇₃	#553	semidirect
398. #59680	C₇₃	direct (N × H)
409. C₂×#553	C₂×C₇₃	semidirect
410. #2714	C₂×C₇₃	semidirect
411. #2541	C₂×C₇₃	semidirect
412. #2541	C₂×C₇₃	semidirect
413. #2541	C₂×C₇₃	semidirect
414. #2535	C₂×C₇₃	semidirect
415. #2512	C₂×C₇₃	semidirect
416. #2456	C₂×C₇₃	semidirect
417. #2445	C₂×C₇₃	semidirect
418. #2416	C₂×C₇₃	semidirect
419. #2414	C₂×C₇₃	semidirect
420. #2366	C₂×C₇₃	semidirect
421. #2354	C₂×C₇₃	semidirect
422. D₄×C₄⋊C₄	C₂×C₇₃	semidirect
423. C₄×#127	C₂×C₇₃	semidirect
424. C₄×#127	C₂×C₇₃	semidirect
425. C₄×#125	C₂×C₇₃	semidirect
426. C₇₃	#59680	direct (N × H)
513. #125	D₄×C₇₃	semidirect
806. C₄	#553×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₇₃	2
C₇₃×#2714	2
C₇₃×#2541	2
C₇₃×#2535	2
C₇₃×#2512	2
C₇₃×#2456	2
C₇₃×#2445	2
C₇₃×#2416	2
C₇₃×#2414	2
C₇₃×#2366	2
C₇₃×#2354	2
D₄×C₄⋊C₄×C₇₃	2
C₄×#127×C₇₃	2
C₄×#125×C₇₃	2
#59680	73

Subgroups — C73×#59680 #32969084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59680 #32969084