Subgroups — C₇₃×#59652 #32969056

Order 18688.

2444 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#554×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2730	C₂	1	4	yes	maximal, complemented
4	C₇₃×#2540	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2537	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2490	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2441	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2428	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2426	C₂	1	4	yes	maximal, complemented
11	C₇₃×#2416	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2415	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2363	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2352	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#555×C₇₃	—	2	8	no	—
19	#554×C₇₃	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#125×C₇₃	C₂²	1	2	yes	—
23	C₂×#124×C₇₃	C₂²	1	4	yes	—
24	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
28	C₂×#121×C₇₃	C₂²	1	2	yes	—
29	C₂×#121×C₇₃	C₂²	1	2	yes	—
30	C₂×#121×C₇₃	C₂²	1	2	yes	—
31	C₂×#121×C₇₃	C₂²	1	2	yes	—
32	C₂×#121×C₇₃	C₂²	1	4	yes	—
33	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
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	C₂×#117×C₇₃	C₂²	1	2	yes	—
43	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
44	#399×C₇₃	C₂²	1	4	yes	—
45	#397×C₇₃	C₂²	1	4	yes	—
46	#396×C₇₃	C₂²	1	4	yes	—
47	#396×C₇₃	C₂²	1	4	yes	—
48	#394×C₇₃	C₂²	1	4	yes	—
49	#394×C₇₃	C₂²	1	4	yes	—
50	#394×C₇₃	C₂²	1	4	yes	—
51	#392×C₇₃	C₂²	1	4	yes	—
52	#391×C₇₃	C₂²	1	2	yes	—
53	#391×C₇₃	C₂²	1	1	yes	characteristic
54	#390×C₇₃	C₂²	1	2	yes	—
55	#390×C₇₃	C₂²	1	1	yes	characteristic
56	#390×C₇₃	C₂²	1	2	yes	—
57	#390×C₇₃	C₂²	1	4	yes	—
58	#390×C₇₃	C₂²	1	4	yes	—
59	#390×C₇₃	C₂²	1	1	yes	characteristic
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	2	yes	—
64	#389×C₇₃	C₂²	1	4	yes	—
65	#389×C₇₃	C₂²	1	2	yes	—
66	#388×C₇₃	C₂²	1	2	yes	—
67	#388×C₇₃	C₂²	1	4	yes	—
68	#388×C₇₃	C₂²	1	4	yes	—
69	#388×C₇₃	C₂²	1	2	yes	—
70	#387×C₇₃	C₂²	1	4	yes	—
71	#386×C₇₃	C₂²	1	4	yes	—
72	#386×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	#380×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×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
84	C₄³×C₇₃	C₂²	1	1	yes	characteristic
85	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
93	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₇₃	C₂³	1	2	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	C₄⋊Q₈×C₇₃	D₄	1	8	yes	complemented
99	#127×C₇₃	—	2	4	no	—
100	#125×C₇₃	—	2	8	no	—
101	#124×C₇₃	—	2	16	no	—
102	#124×C₇₃	—	2	4	no	—
103	C₂²⋊Q₈×C₇₃	—	2	16	no	—
104	C₂²⋊Q₈×C₇₃	—	2	8	no	—
105	C₂²⋊Q₈×C₇₃	—	4	4	no	—
106	#121×C₇₃	—	2	8	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	C₄×Q₈×C₇₃	—	2	4	no	—
112	C₄×Q₈×C₇₃	—	4	4	no	—
113	C₄×D₄×C₇₃	—	2	8	no	—
114	C₄×D₄×C₇₃	—	2	4	no	—
115	C₄×D₄×C₇₃	—	2	4	no	—
116	C₄×D₄×C₇₃	—	2	4	no	—
117	C₄×D₄×C₇₃	—	2	8	no	—
118	C₄×D₄×C₇₃	—	4	4	no	—
119	#117×C₇₃	—	2	8	no	—
120	#117×C₇₃	—	2	8	no	—
121	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
122	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
127	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
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	4	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	4	yes	—
136	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	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	2	yes	—
143	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	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	2	yes	—
154	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
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	4	yes	—
163	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
166	#95×C₇₃	C₂³	1	2	yes	—
167	#95×C₇₃	C₂³	1	4	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	4	yes	—
172	#95×C₇₃	C₂³	1	4	yes	—
173	#95×C₇₃	C₂³	1	4	yes	—
174	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
175	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
176	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
177	C₂×Q₈×C₇₃	—	2	2	no	—
178	C₂×Q₈×C₇₃	—	2	2	no	—
179	C₂×Q₈×C₇₃	—	2	2	no	—
180	C₂×Q₈×C₇₃	—	4	2	no	—
181	C₂×Q₈×C₇₃	—	4	2	no	—
182	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
183	C₂×D₄×C₇₃	—	2	4	no	—
184	C₂×D₄×C₇₃	—	2	4	no	—
185	C₂×D₄×C₇₃	—	2	8	no	—
186	C₂×D₄×C₇₃	—	2	2	no	—
187	C₂×D₄×C₇₃	—	2	2	no	—
188	C₂×D₄×C₇₃	—	2	2	no	—
189	C₂×D₄×C₇₃	—	2	8	no	—
190	C₂×D₄×C₇₃	—	2	4	no	—
191	C₂×D₄×C₇₃	—	2	2	no	—
192	C₂×D₄×C₇₃	—	2	2	no	—
193	C₂×D₄×C₇₃	—	2	4	no	—
194	C₂×D₄×C₇₃	—	2	2	no	—
195	C₂×D₄×C₇₃	—	2	2	no	—
196	C₂×D₄×C₇₃	—	2	2	no	—
197	C₂×D₄×C₇₃	—	4	2	no	—
198	C₂×D₄×C₇₃	—	4	2	no	—
199	C₂×D₄×C₇₃	—	4	4	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	#41	1	4	yes	—
204	C₂²×C₄×C₇₃	—	2	4	no	—
205	C₂²×C₄×C₇₃	—	2	4	no	—
206	C₂²×C₄×C₇₃	—	2	4	no	—
207	C₂²×C₄×C₇₃	—	2	4	no	—
208	C₂²×C₄×C₇₃	—	2	4	no	—
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	8	no	—
214	C₂²×C₄×C₇₃	—	4	4	no	—
215	C₂²×C₄×C₇₃	—	4	4	no	—
216	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
230	C₄⋊C₄×C₇₃	—	2	2	no	—
231	C₄⋊C₄×C₇₃	—	2	8	no	—
232	C₄⋊C₄×C₇₃	—	2	2	no	—
233	C₄⋊C₄×C₇₃	—	2	2	no	—
234	C₄⋊C₄×C₇₃	—	2	2	no	—
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	4	no	—
239	C₄⋊C₄×C₇₃	—	2	8	no	—
240	C₄⋊C₄×C₇₃	—	2	4	no	—
241	C₄⋊C₄×C₇₃	—	4	2	no	—
242	C₄⋊C₄×C₇₃	—	4	2	no	—
243	C₄⋊C₄×C₇₃	—	4	4	no	—
244	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
245	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
246	C₂²⋊C₄×C₇₃	—	2	8	no	—
247	C₂²⋊C₄×C₇₃	—	2	8	no	—
248	C₂²⋊C₄×C₇₃	—	2	8	no	—
249	C₂²⋊C₄×C₇₃	—	2	8	no	—
250	C₂²⋊C₄×C₇₃	—	2	4	no	—
251	C₂²⋊C₄×C₇₃	—	2	4	no	—
252	C₂²⋊C₄×C₇₃	—	2	4	no	—
253	C₂²⋊C₄×C₇₃	—	2	4	no	—
254	C₂²⋊C₄×C₇₃	—	2	4	no	—
255	C₂²⋊C₄×C₇₃	—	2	4	no	—
256	C₂²⋊C₄×C₇₃	—	2	4	no	—
257	C₂²⋊C₄×C₇₃	—	2	4	no	—
258	C₂²⋊C₄×C₇₃	—	4	2	no	—
259	C₂²⋊C₄×C₇₃	—	4	2	no	—
260	C₂²⋊C₄×C₇₃	—	4	2	no	—
261	C₂²⋊C₄×C₇₃	—	4	4	no	—
262	C₂²⋊C₄×C₇₃	—	4	4	no	—
263	C₂²⋊C₄×C₇₃	—	4	4	no	—
264	C₄²×C₇₃	—	2	8	no	—
265	C₄²×C₇₃	—	2	4	no	—
266	C₄²×C₇₃	—	2	2	no	—
267	C₄²×C₇₃	—	2	2	no	—
268	C₄²×C₇₃	—	2	2	no	—
269	C₄²×C₇₃	—	2	2	no	—
270	C₄²×C₇₃	—	4	1	no	—
271	C₄²×C₇₃	—	4	4	no	—
272	C₄²×C₇₃	C₂×D₄	1	4	yes	—
273	C₄²×C₇₃	#41	1	4	yes	—
274	C₂³×C₇₃	—	2	2	no	—
275	C₂³×C₇₃	—	2	2	no	—
276	C₂³×C₇₃	—	2	2	no	—
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	2	no	—
285	C₂³×C₇₃	—	2	2	no	—
286	C₂³×C₇₃	—	2	2	no	—
287	C₂³×C₇₃	—	2	2	no	—
288	C₂³×C₇₃	—	2	2	no	—
289	C₂³×C₇₃	—	2	2	no	—
290	C₂³×C₇₃	—	2	2	no	—
291	C₂³×C₇₃	—	2	2	no	—
292	C₂³×C₇₃	—	2	2	no	—
293	C₂³×C₇₃	—	2	2	no	—
294	C₂³×C₇₃	C₂×#41	1	4	yes	—
295	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
296	Q₈×C₇₃	—	4	8	no	—
297	Q₈×C₇₃	—	4	4	no	—
298	D₄×C₇₃	—	2	8	no	—
299	D₄×C₇₃	—	4	8	no	—
300	D₄×C₇₃	—	4	8	no	—
301	D₄×C₇₃	—	4	4	no	—
302	D₄×C₇₃	—	4	4	no	—
303	D₄×C₇₃	—	8	8	no	—
304	D₄×C₇₃	—	8	8	no	—
305	C₂×C₄×C₇₃	—	2	1	no	—
306	C₂×C₄×C₇₃	—	2	1	no	—
307	C₂×C₄×C₇₃	—	2	1	no	—
308	C₂×C₄×C₇₃	—	2	1	no	—
309	C₂×C₄×C₇₃	—	2	1	no	—
310	C₂×C₄×C₇₃	—	2	4	no	—
311	C₂×C₄×C₇₃	—	2	1	no	—
312	C₂×C₄×C₇₃	—	2	1	no	—
313	C₂×C₄×C₇₃	—	2	1	no	—
314	C₂×C₄×C₇₃	—	2	4	no	—
315	C₂×C₄×C₇₃	—	2	2	no	—
316	C₂×C₄×C₇₃	—	2	2	no	—
317	C₂×C₄×C₇₃	—	2	2	no	—
318	C₂×C₄×C₇₃	—	2	2	no	—
319	C₂×C₄×C₇₃	—	2	2	no	—
320	C₂×C₄×C₇₃	—	2	2	no	—
321	C₂×C₄×C₇₃	—	2	2	no	—
322	C₂×C₄×C₇₃	—	2	2	no	—
323	C₂×C₄×C₇₃	—	2	2	no	—
324	C₂×C₄×C₇₃	—	2	4	no	—
325	C₂×C₄×C₇₃	—	2	1	no	—
326	C₂×C₄×C₇₃	—	2	4	no	—
327	C₂×C₄×C₇₃	—	2	2	no	—
328	C₂×C₄×C₇₃	—	2	2	no	—
329	C₂×C₄×C₇₃	—	2	4	no	—
330	C₂×C₄×C₇₃	—	2	2	no	—
331	C₂×C₄×C₇₃	—	2	2	no	—
332	C₂×C₄×C₇₃	—	2	1	no	—
333	C₂×C₄×C₇₃	—	2	2	no	—
334	C₂×C₄×C₇₃	—	2	1	no	—
335	C₂×C₄×C₇₃	—	2	2	no	—
336	C₂×C₄×C₇₃	—	4	8	no	—
337	C₂×C₄×C₇₃	—	4	8	no	—
338	C₂×C₄×C₇₃	—	4	8	no	—
339	C₂×C₄×C₇₃	—	8	8	no	—
340	C₂×C₄×C₇₃	C₂²×D₄	1	8	yes	—
341	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
345	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
346	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
347	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
348	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
349	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
350	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
351	C₂²×C₇₃	—	2	4	no	—
352	C₂²×C₇₃	—	2	4	no	—
353	C₂²×C₇₃	—	2	4	no	—
354	C₂²×C₇₃	—	4	2	no	—
355	C₂²×C₇₃	—	4	2	no	—
356	C₂²×C₇₃	—	4	2	no	—
357	C₂²×C₇₃	—	4	2	no	—
358	C₂²×C₇₃	—	4	2	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	2	no	—
365	C₂²×C₇₃	—	4	2	no	—
366	C₂²×C₇₃	—	4	2	no	—
367	C₂²×C₇₃	—	4	2	no	—
368	C₂²×C₇₃	—	4	2	no	—
369	C₂²×C₇₃	—	4	2	no	—
370	C₂²×C₇₃	—	4	2	no	—
371	C₂²×C₇₃	—	4	2	no	—
372	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
373	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
374	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
375	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂²×C₇₃	#585	1	1	yes	characteristic
379	C₄×C₇₃	—	2	2	no	—
380	C₄×C₇₃	—	2	8	no	—
381	C₄×C₇₃	—	2	2	no	—
382	C₄×C₇₃	—	2	2	no	—
383	C₄×C₇₃	—	2	2	no	—
384	C₄×C₇₃	—	4	2	no	—
385	C₄×C₇₃	—	4	2	no	—
386	C₄×C₇₃	—	4	2	no	—
387	C₄×C₇₃	—	4	2	no	—
388	C₄×C₇₃	—	4	2	no	—
389	C₄×C₇₃	—	4	4	no	—
390	C₄×C₇₃	—	4	1	no	—
391	C₄×C₇₃	#548	1	4	yes	—
392	C₄×C₇₃	#550	1	4	yes	—
393	#59652	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
394	C₂×C₇₃	—	4	4	no	—
395	C₂×C₇₃	—	8	2	no	—
396	C₂×C₇₃	—	8	2	no	—
397	C₂×C₇₃	C₂×#548	1	1	yes	characteristic
398	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
399	C₂×C₇₃	#3475	1	1	yes	characteristic
400	C₂×C₇₃	#3496	1	1	yes	characteristic
401	C₂×C₇₃	#3511	1	1	yes	characteristic
402	C₂×C₇₃	#3519	1	1	yes	characteristic
403	C₂×C₇₃	#3547	1	1	yes	characteristic
404	C₂×#555	C₂×C₇₃	1	1	yes	characteristic, complemented
405	C₂×#554	C₂×C₇₃	1	1	yes	characteristic, complemented
406	#2730	C₂×C₇₃	1	4	yes	complemented
407	#2540	C₂×C₇₃	1	2	yes	complemented
408	#2538	C₂×C₇₃	1	1	yes	characteristic, complemented
409	#2537	C₂×C₇₃	1	1	yes	characteristic, complemented
410	#2490	C₂×C₇₃	1	2	yes	complemented
411	#2441	C₂×C₇₃	1	2	yes	complemented
412	#2428	C₂×C₇₃	1	2	yes	complemented
413	#2426	C₂×C₇₃	1	4	yes	complemented
414	#2416	C₂×C₇₃	1	2	yes	complemented
415	#2415	C₂×C₇₃	1	2	yes	complemented
416	#2363	C₂×C₇₃	1	2	yes	complemented
417	#2352	C₂×C₇₃	1	2	yes	complemented
418	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
419	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
420	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
421	C₇₃	#59652	1	1	yes	characteristic, direct product factor, Sylow
422	#555	—	2	8	no	—
423	#554	—	2	8	no	—
424	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
425	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
426	C₂×#125	C₂²×C₇₃	1	2	yes	—
427	C₂×#124	C₂²×C₇₃	1	4	yes	—
428	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
429	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
430	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	—
431	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
432	C₂×#121	C₂²×C₇₃	1	2	yes	—
433	C₂×#121	C₂²×C₇₃	1	2	yes	—
434	C₂×#121	C₂²×C₇₃	1	2	yes	—
435	C₂×#121	C₂²×C₇₃	1	4	yes	—
436	C₂×#121	C₂²×C₇₃	1	2	yes	—
437	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
438	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
439	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
440	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
441	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
442	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
443	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
444	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
445	C₂×#117	C₂²×C₇₃	1	2	yes	—
446	C₂×#117	C₂²×C₇₃	1	2	yes	—
447	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
448	#399	C₂²×C₇₃	1	4	yes	—
449	#397	C₂²×C₇₃	1	4	yes	—
450	#396	C₂²×C₇₃	1	4	yes	—
451	#396	C₂²×C₇₃	1	4	yes	—
452	#394	C₂²×C₇₃	1	4	yes	—
453	#394	C₂²×C₇₃	1	4	yes	—
454	#394	C₂²×C₇₃	1	4	yes	—
455	#392	C₂²×C₇₃	1	4	yes	—
456	#391	C₂²×C₇₃	1	2	yes	—
457	#391	C₂²×C₇₃	1	1	yes	characteristic
458	#390	C₂²×C₇₃	1	1	yes	characteristic
459	#390	C₂²×C₇₃	1	2	yes	—
460	#390	C₂²×C₇₃	1	2	yes	—
461	#390	C₂²×C₇₃	1	1	yes	characteristic
462	#390	C₂²×C₇₃	1	4	yes	—
463	#390	C₂²×C₇₃	1	1	yes	characteristic
464	#390	C₂²×C₇₃	1	4	yes	—
465	#390	C₂²×C₇₃	1	2	yes	—
466	#389	C₂²×C₇₃	1	2	yes	—
467	#389	C₂²×C₇₃	1	2	yes	—
468	#389	C₂²×C₇₃	1	2	yes	—
469	#389	C₂²×C₇₃	1	4	yes	—
470	#388	C₂²×C₇₃	1	4	yes	—
471	#388	C₂²×C₇₃	1	4	yes	—
472	#388	C₂²×C₇₃	1	2	yes	—
473	#388	C₂²×C₇₃	1	2	yes	—
474	#387	C₂²×C₇₃	1	4	yes	—
475	#386	C₂²×C₇₃	1	4	yes	—
476	#386	C₂²×C₇₃	1	4	yes	—
477	#384	C₂²×C₇₃	1	1	yes	characteristic
478	#384	C₂²×C₇₃	1	1	yes	characteristic
479	#382	C₂²×C₇₃	1	1	yes	characteristic
480	#380	C₂²×C₇₃	1	2	yes	—
481	#380	C₂²×C₇₃	1	2	yes	—
482	#380	C₂²×C₇₃	1	2	yes	—
483	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
485	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
486	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
487	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
488	C₄³	C₂²×C₇₃	1	1	yes	characteristic
489	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
491	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
492	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
494	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
495	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
497	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
498	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
499	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
500	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
501	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
502	C₄⋊Q₈	D₄×C₇₃	1	8	yes	complemented
503	#127	—	2	4	no	—
504	#125	—	2	8	no	—
505	#124	—	2	16	no	—
506	#124	—	2	4	no	—
507	C₂²⋊Q₈	—	2	16	no	—
508	C₂²⋊Q₈	—	2	8	no	—
509	C₂²⋊Q₈	—	4	4	no	—
510	#121	—	2	8	no	—
511	#121	—	2	8	no	—
512	#121	—	2	8	no	—
513	#121	—	4	8	no	—
514	#121	—	4	4	no	—
515	C₄×Q₈	—	2	4	no	—
516	C₄×Q₈	—	4	4	no	—
517	C₄×D₄	—	2	8	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	—	2	8	no	—
522	C₄×D₄	—	4	4	no	—
523	#117	—	2	8	no	—
524	#117	—	2	8	no	—
525	C₂×C₄⋊C₄	—	2	8	no	—
526	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	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	4	yes	—
537	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
540	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	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	4	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
560	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
561	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
563	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
565	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
566	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
567	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
570	#95	C₂³×C₇₃	1	2	yes	—
571	#95	C₂³×C₇₃	1	4	yes	—
572	#95	C₂³×C₇₃	1	2	yes	—
573	#95	C₂³×C₇₃	1	2	yes	—
574	#95	C₂³×C₇₃	1	2	yes	—
575	#95	C₂³×C₇₃	1	4	yes	—
576	#95	C₂³×C₇₃	1	4	yes	—
577	#95	C₂³×C₇₃	1	4	yes	—
578	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
579	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
580	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	4	2	no	—
585	C₂×Q₈	—	4	2	no	—
586	C₂×Q₈	C₂×D₄×C₇₃	1	8	yes	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	8	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	4	2	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	#41×C₇₃	1	4	yes	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	8	no	—
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	—	4	4	no	—
620	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
623	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
628	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	8	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	8	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	8	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	4	no	—
648	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
649	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
650	C₂²⋊C₄	—	2	8	no	—
651	C₂²⋊C₄	—	2	8	no	—
652	C₂²⋊C₄	—	2	8	no	—
653	C₂²⋊C₄	—	2	8	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	4	no	—
666	C₂²⋊C₄	—	4	4	no	—
667	C₂²⋊C₄	—	4	4	no	—
668	C₄²	—	2	8	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	2	2	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	2	no	—
673	C₄²	—	2	2	no	—
674	C₄²	—	4	1	no	—
675	C₄²	—	4	4	no	—
676	C₄²	C₂×D₄×C₇₃	1	4	yes	—
677	C₄²	#41×C₇₃	1	4	yes	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
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	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	C₂×#41×C₇₃	1	4	yes	—
699	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
700	Q₈	—	4	8	no	—
701	Q₈	—	4	4	no	—
702	D₄	—	2	8	no	—
703	D₄	—	4	8	no	—
704	D₄	—	4	8	no	—
705	D₄	—	4	4	no	—
706	D₄	—	4	4	no	—
707	D₄	—	8	8	no	—
708	D₄	—	8	8	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	4	8	no	—
741	C₂×C₄	—	4	8	no	—
742	C₂×C₄	—	4	8	no	—
743	C₂×C₄	—	8	8	no	—
744	C₂×C₄	C₂²×D₄×C₇₃	1	8	yes	—
745	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
746	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
747	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
748	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
749	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
750	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
751	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
752	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
753	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
754	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	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	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
777	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
778	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
779	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
780	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
781	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
782	C₂²	#585×C₇₃	1	1	yes	characteristic
783	C₄	—	2	2	no	—
784	C₄	—	2	8	no	—
785	C₄	—	2	2	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	2	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	4	no	—
794	C₄	—	4	1	no	—
795	C₄	#548×C₇₃	1	4	yes	—
796	C₄	#550×C₇₃	1	4	yes	—
797	C₂	—	4	4	no	—
798	C₂	—	8	2	no	—
799	C₂	—	8	2	no	—
800	C₂	C₂×#548×C₇₃	1	1	yes	characteristic
801	C₂	C₂×#550×C₇₃	1	1	yes	characteristic
802	C₂	C₇₃×#3475	1	1	yes	characteristic
803	C₂	C₇₃×#3496	1	1	yes	characteristic
804	C₂	C₇₃×#3511	1	1	yes	characteristic
805	C₂	C₇₃×#3519	1	1	yes	characteristic
806	C₂	C₇₃×#3547	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×#555×C₇₃	C₂	semidirect
2. C₂×#554×C₇₃	C₂	semidirect
3. C₇₃×#2730	C₂	semidirect
4. C₇₃×#2540	C₂	semidirect
5. C₇₃×#2538	C₂	semidirect
6. C₇₃×#2537	C₂	semidirect
7. C₇₃×#2490	C₂	semidirect
8. C₇₃×#2441	C₂	semidirect
9. C₇₃×#2428	C₂	semidirect
10. C₇₃×#2426	C₂	semidirect
11. C₇₃×#2416	C₂	semidirect
12. C₇₃×#2415	C₂	semidirect
13. C₇₃×#2363	C₂	semidirect
14. C₇₃×#2352	C₂	semidirect
15. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
16. C₄×#127×C₇₃	C₂	semidirect
17. C₄×#124×C₇₃	C₂	semidirect
98. C₄⋊Q₈×C₇₃	D₄	semidirect
393. #59652	C₇₃	direct (N × H)
404. C₂×#555	C₂×C₇₃	semidirect
405. C₂×#554	C₂×C₇₃	semidirect
406. #2730	C₂×C₇₃	semidirect
407. #2540	C₂×C₇₃	semidirect
408. #2538	C₂×C₇₃	semidirect
409. #2537	C₂×C₇₃	semidirect
410. #2490	C₂×C₇₃	semidirect
411. #2441	C₂×C₇₃	semidirect
412. #2428	C₂×C₇₃	semidirect
413. #2426	C₂×C₇₃	semidirect
414. #2416	C₂×C₇₃	semidirect
415. #2415	C₂×C₇₃	semidirect
416. #2363	C₂×C₇₃	semidirect
417. #2352	C₂×C₇₃	semidirect
418. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
419. C₄×#127	C₂×C₇₃	semidirect
420. C₄×#124	C₂×C₇₃	semidirect
421. C₇₃	#59652	direct (N × H)
502. C₄⋊Q₈	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#555×C₇₃	2
C₂×#554×C₇₃	2
C₇₃×#2730	2
C₇₃×#2540	2
C₇₃×#2538	2
C₇₃×#2537	2
C₇₃×#2490	2
C₇₃×#2441	2
C₇₃×#2428	2
C₇₃×#2426	2
C₇₃×#2416	2
C₇₃×#2415	2
C₇₃×#2363	2
C₇₃×#2352	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#127×C₇₃	2
C₄×#124×C₇₃	2
#59652	73

Subgroups — C73×#59652 #32969056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59652 #32969056