Subgroups — C₇₃×#59425 #32968829

Order 18688.

1750 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2789	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2758	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2605	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2588	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2514	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2503	C₂	1	1	yes	maximal, characteristic
10	C₇₃×#2493	C₂	1	2	yes	maximal
11	C₇₃×#2493	C₂	1	2	yes	maximal
12	C₇₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#2446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2438	C₂	1	2	yes	maximal
15	C₇₃×#2434	C₂	1	1	yes	maximal, characteristic
16	C₇₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2356	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#2344	C₂	1	1	yes	maximal, characteristic
19	C₇₃×#2343	C₂	1	2	yes	maximal
20	Q₈×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic
21	C₄×C₂²⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
22	C₄×C₂²⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
23	C₂×#391×C₇₃	C₂	1	1	yes	maximal, characteristic
24	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×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×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#117×C₇₃	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
36	#401×C₇₃	C₂²	1	2	yes	—
37	#401×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	#400×C₇₃	C₂²	1	2	yes	—
42	#400×C₇₃	C₂²	1	2	yes	—
43	#400×C₇₃	C₂²	1	2	yes	—
44	#400×C₇₃	C₂²	1	2	yes	—
45	#400×C₇₃	C₂²	1	2	yes	—
46	#400×C₇₃	C₂²	1	2	yes	—
47	#398×C₇₃	C₂²	1	2	yes	—
48	#398×C₇₃	C₂²	1	2	yes	—
49	#395×C₇₃	C₂²	1	2	yes	—
50	#395×C₇₃	C₂²	1	2	yes	—
51	#395×C₇₃	C₂²	1	2	yes	—
52	#391×C₇₃	C₂²	1	1	yes	characteristic
53	#391×C₇₃	C₂²	1	1	yes	characteristic
54	#391×C₇₃	C₂²	1	1	yes	characteristic
55	#391×C₇₃	C₂²	1	1	yes	characteristic
56	#391×C₇₃	C₂²	1	1	yes	characteristic
57	#391×C₇₃	C₂²	1	2	yes	—
58	#391×C₇₃	C₂²	1	2	yes	—
59	#391×C₇₃	C₂²	1	1	yes	characteristic
60	#391×C₇₃	C₂²	1	1	yes	characteristic
61	#391×C₇₃	C₂²	1	1	yes	characteristic
62	#391×C₇₃	C₂²	1	1	yes	characteristic
63	#391×C₇₃	C₂²	1	2	yes	—
64	#391×C₇₃	C₂²	1	2	yes	—
65	#391×C₇₃	C₂²	1	1	yes	characteristic
66	#391×C₇₃	C₂²	1	1	yes	characteristic
67	#391×C₇₃	C₂²	1	2	yes	—
68	#391×C₇₃	C₂²	1	1	yes	characteristic
69	#389×C₇₃	C₂²	1	1	yes	characteristic
70	#389×C₇₃	C₂²	1	1	yes	characteristic
71	#389×C₇₃	C₂²	1	2	yes	—
72	#389×C₇₃	C₂²	1	1	yes	characteristic
73	#389×C₇₃	C₂²	1	1	yes	characteristic
74	#387×C₇₃	C₂²	1	2	yes	—
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	1	yes	characteristic
83	#387×C₇₃	C₂²	1	2	yes	—
84	#387×C₇₃	C₂²	1	2	yes	—
85	#387×C₇₃	C₂²	1	2	yes	—
86	#387×C₇₃	C₂²	1	2	yes	—
87	#387×C₇₃	C₂²	1	1	yes	characteristic
88	#387×C₇₃	C₂²	1	2	yes	—
89	#387×C₇₃	C₂²	1	2	yes	—
90	#387×C₇₃	C₂²	1	2	yes	—
91	#385×C₇₃	C₂²	1	1	yes	characteristic
92	#385×C₇₃	C₂²	1	2	yes	—
93	#385×C₇₃	C₂²	1	2	yes	—
94	#385×C₇₃	C₂²	1	1	yes	characteristic
95	#385×C₇₃	C₂²	1	2	yes	—
96	#383×C₇₃	C₂²	1	2	yes	—
97	#383×C₇₃	C₂²	1	2	yes	—
98	#383×C₇₃	C₂²	1	2	yes	—
99	#382×C₇₃	C₂²	1	1	yes	characteristic
100	#382×C₇₃	C₂²	1	1	yes	characteristic
101	#382×C₇₃	C₂²	1	2	yes	—
102	#381×C₇₃	C₂²	1	2	yes	—
103	#381×C₇₃	C₂²	1	2	yes	—
104	#381×C₇₃	C₂²	1	2	yes	—
105	#380×C₇₃	C₂²	1	1	yes	characteristic
106	#380×C₇₃	C₂²	1	2	yes	—
107	#380×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	1	yes	characteristic
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×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
120	#376×C₇₃	C₂²	1	2	yes	—
121	C₂×#95×C₇₃	C₂²	1	2	yes	—
122	C₂×#95×C₇₃	C₂²	1	2	yes	—
123	C₂²×Q₈×C₇₃	—	2	4	no	—
124	C₂²×Q₈×C₇₃	—	2	4	no	—
125	C₂²×Q₈×C₇₃	—	4	2	no	—
126	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
129	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₇₃	—	2	4	no	—
137	C₄⋊Q₈×C₇₃	—	4	2	no	—
138	C₂²⋊Q₈×C₇₃	—	2	4	no	—
139	C₂²⋊Q₈×C₇₃	—	2	4	no	—
140	C₄×Q₈×C₇₃	—	2	4	no	—
141	C₄×Q₈×C₇₃	—	4	2	no	—
142	C₄×Q₈×C₇₃	—	4	2	no	—
143	C₄×Q₈×C₇₃	—	4	2	no	—
144	#117×C₇₃	—	2	8	no	—
145	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
156	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₇₃	—	4	2	no	—
179	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
193	#95×C₇₃	C₂³	1	2	yes	—
194	#95×C₇₃	C₂³	1	2	yes	—
195	#95×C₇₃	C₂³	1	2	yes	—
196	#95×C₇₃	C₂³	1	2	yes	—
197	#95×C₇₃	C₂³	1	1	yes	characteristic
198	#95×C₇₃	C₂³	1	1	yes	characteristic
199	#95×C₇₃	C₂³	1	1	yes	characteristic
200	#95×C₇₃	C₂³	1	1	yes	characteristic
201	#95×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
211	#95×C₇₃	C₂³	1	2	yes	—
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	#95×C₇₃	C₂³	1	2	yes	—
231	#95×C₇₃	C₂³	1	2	yes	—
232	#95×C₇₃	C₂³	1	2	yes	—
233	#95×C₇₃	C₂³	1	2	yes	—
234	#95×C₇₃	C₂³	1	2	yes	—
235	#95×C₇₃	C₂³	1	2	yes	—
236	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₇₃	—	2	2	no	—
238	C₂×Q₈×C₇₃	—	2	2	no	—
239	C₂×Q₈×C₇₃	—	2	2	no	—
240	C₂×Q₈×C₇₃	—	2	2	no	—
241	C₂×Q₈×C₇₃	—	2	4	no	—
242	C₂×Q₈×C₇₃	—	2	4	no	—
243	C₂×Q₈×C₇₃	—	2	2	no	—
244	C₂×Q₈×C₇₃	—	2	2	no	—
245	C₂×Q₈×C₇₃	—	2	2	no	—
246	C₂×Q₈×C₇₃	—	2	2	no	—
247	C₂×Q₈×C₇₃	—	2	2	no	—
248	C₂×Q₈×C₇₃	—	2	2	no	—
249	C₂×Q₈×C₇₃	—	4	1	no	—
250	C₂×Q₈×C₇₃	—	4	2	no	—
251	C₂×Q₈×C₇₃	—	4	16	no	—
252	C₂×Q₈×C₇₃	#41	1	4	yes	—
253	C₂²×C₄×C₇₃	—	2	2	no	—
254	C₂²×C₄×C₇₃	—	2	2	no	—
255	C₂²×C₄×C₇₃	—	2	4	no	—
256	C₂²×C₄×C₇₃	—	2	4	no	—
257	C₂²×C₄×C₇₃	—	2	2	no	—
258	C₂²×C₄×C₇₃	—	2	4	no	—
259	C₂²×C₄×C₇₃	—	2	2	no	—
260	C₂²×C₄×C₇₃	—	2	4	no	—
261	C₂²×C₄×C₇₃	—	2	4	no	—
262	C₂²×C₄×C₇₃	—	2	2	no	—
263	C₂²×C₄×C₇₃	—	2	2	no	—
264	C₂²×C₄×C₇₃	—	4	1	no	—
265	C₂²×C₄×C₇₃	—	4	1	no	—
266	C₂²×C₄×C₇₃	—	4	2	no	—
267	C₂²×C₄×C₇₃	#41	1	4	yes	—
268	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
290	C₄⋊C₄×C₇₃	—	2	4	no	—
291	C₄⋊C₄×C₇₃	—	2	2	no	—
292	C₄⋊C₄×C₇₃	—	2	2	no	—
293	C₄⋊C₄×C₇₃	—	2	4	no	—
294	C₄⋊C₄×C₇₃	—	2	4	no	—
295	C₄⋊C₄×C₇₃	—	2	4	no	—
296	C₄⋊C₄×C₇₃	—	2	2	no	—
297	C₄⋊C₄×C₇₃	—	2	2	no	—
298	C₄⋊C₄×C₇₃	—	2	2	no	—
299	C₄⋊C₄×C₇₃	—	2	4	no	—
300	C₄⋊C₄×C₇₃	—	2	2	no	—
301	C₄⋊C₄×C₇₃	—	2	2	no	—
302	C₄⋊C₄×C₇₃	—	2	4	no	—
303	C₄⋊C₄×C₇₃	—	2	4	no	—
304	C₄⋊C₄×C₇₃	—	2	2	no	—
305	C₄⋊C₄×C₇₃	—	2	2	no	—
306	C₄⋊C₄×C₇₃	—	2	2	no	—
307	C₄⋊C₄×C₇₃	—	2	2	no	—
308	C₄⋊C₄×C₇₃	—	2	4	no	—
309	C₄⋊C₄×C₇₃	—	4	1	no	—
310	C₄⋊C₄×C₇₃	—	4	1	no	—
311	C₄⋊C₄×C₇₃	—	4	2	no	—
312	C₄⋊C₄×C₇₃	—	4	1	no	—
313	C₄⋊C₄×C₇₃	—	4	2	no	—
314	C₄⋊C₄×C₇₃	—	4	2	no	—
315	C₄⋊C₄×C₇₃	—	4	2	no	—
316	C₂²⋊C₄×C₇₃	—	2	4	no	—
317	C₂²⋊C₄×C₇₃	—	2	2	no	—
318	C₂²⋊C₄×C₇₃	—	2	4	no	—
319	C₂²⋊C₄×C₇₃	—	2	2	no	—
320	C₂²⋊C₄×C₇₃	—	2	2	no	—
321	C₂²⋊C₄×C₇₃	#41	1	4	yes	—
322	C₄²×C₇₃	—	2	4	no	—
323	C₄²×C₇₃	—	2	4	no	—
324	C₄²×C₇₃	—	2	4	no	—
325	C₄²×C₇₃	—	2	2	no	—
326	C₄²×C₇₃	—	2	2	no	—
327	C₄²×C₇₃	—	2	2	no	—
328	C₄²×C₇₃	—	2	2	no	—
329	C₄²×C₇₃	—	2	2	no	—
330	C₄²×C₇₃	—	2	2	no	—
331	C₄²×C₇₃	—	2	4	no	—
332	C₄²×C₇₃	—	4	1	no	—
333	C₄²×C₇₃	—	4	1	no	—
334	C₄²×C₇₃	—	4	2	no	—
335	C₄²×C₇₃	—	4	2	no	—
336	C₂³×C₇₃	—	2	1	no	—
337	C₂³×C₇₃	—	2	1	no	—
338	C₂³×C₇₃	—	2	1	no	—
339	C₂³×C₇₃	—	2	1	no	—
340	C₂³×C₇₃	C₂×#41	1	2	yes	—
341	C₂³×C₇₃	C₂×#41	1	2	yes	—
342	C₂³×C₇₃	2₋¹⁺⁴	1	2	yes	—
343	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
344	Q₈×C₇₃	—	2	8	no	—
345	Q₈×C₇₃	—	4	4	no	—
346	Q₈×C₇₃	—	4	8	no	—
347	Q₈×C₇₃	—	4	4	no	—
348	Q₈×C₇₃	—	4	4	no	—
349	C₂×C₄×C₇₃	—	2	1	no	—
350	C₂×C₄×C₇₃	—	2	1	no	—
351	C₂×C₄×C₇₃	—	2	1	no	—
352	C₂×C₄×C₇₃	—	2	2	no	—
353	C₂×C₄×C₇₃	—	2	1	no	—
354	C₂×C₄×C₇₃	—	2	1	no	—
355	C₂×C₄×C₇₃	—	2	1	no	—
356	C₂×C₄×C₇₃	—	2	1	no	—
357	C₂×C₄×C₇₃	—	2	2	no	—
358	C₂×C₄×C₇₃	—	2	1	no	—
359	C₂×C₄×C₇₃	—	2	1	no	—
360	C₂×C₄×C₇₃	—	2	1	no	—
361	C₂×C₄×C₇₃	—	2	8	no	—
362	C₂×C₄×C₇₃	—	2	1	no	—
363	C₂×C₄×C₇₃	—	2	2	no	—
364	C₂×C₄×C₇₃	—	2	2	no	—
365	C₂×C₄×C₇₃	—	2	2	no	—
366	C₂×C₄×C₇₃	—	2	2	no	—
367	C₂×C₄×C₇₃	—	2	1	no	—
368	C₂×C₄×C₇₃	—	2	1	no	—
369	C₂×C₄×C₇₃	—	2	1	no	—
370	C₂×C₄×C₇₃	—	2	2	no	—
371	C₂×C₄×C₇₃	—	2	2	no	—
372	C₂×C₄×C₇₃	—	2	1	no	—
373	C₂×C₄×C₇₃	—	2	2	no	—
374	C₂×C₄×C₇₃	—	2	2	no	—
375	C₂×C₄×C₇₃	—	2	2	no	—
376	C₂×C₄×C₇₃	—	2	1	no	—
377	C₂×C₄×C₇₃	—	2	2	no	—
378	C₂×C₄×C₇₃	—	2	2	no	—
379	C₂×C₄×C₇₃	—	2	2	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	1	no	—
385	C₂×C₄×C₇₃	—	2	2	no	—
386	C₂×C₄×C₇₃	—	2	2	no	—
387	C₂×C₄×C₇₃	—	2	2	no	—
388	C₂×C₄×C₇₃	—	2	2	no	—
389	C₂×C₄×C₇₃	—	2	2	no	—
390	C₂×C₄×C₇₃	—	2	1	no	—
391	C₂×C₄×C₇₃	—	2	1	no	—
392	C₂×C₄×C₇₃	—	2	1	no	—
393	C₂×C₄×C₇₃	—	2	1	no	—
394	C₂×C₄×C₇₃	—	2	1	no	—
395	C₂×C₄×C₇₃	—	2	2	no	—
396	C₂×C₄×C₇₃	—	2	2	no	—
397	C₂×C₄×C₇₃	—	2	1	no	—
398	C₂×C₄×C₇₃	—	2	1	no	—
399	C₂×C₄×C₇₃	—	2	1	no	—
400	C₂×C₄×C₇₃	—	2	1	no	—
401	C₂×C₄×C₇₃	—	2	2	no	—
402	C₂×C₄×C₇₃	—	2	2	no	—
403	C₂×C₄×C₇₃	—	2	1	no	—
404	C₂×C₄×C₇₃	—	2	1	no	—
405	C₂×C₄×C₇₃	—	2	1	no	—
406	C₂×C₄×C₇₃	—	2	1	no	—
407	C₂×C₄×C₇₃	—	4	4	no	—
408	C₂×C₄×C₇₃	—	4	4	no	—
409	C₂×C₄×C₇₃	—	4	8	no	—
410	C₂×C₄×C₇₃	—	4	8	no	—
411	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
412	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
413	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
414	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
415	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
416	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
417	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
419	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
420	C₂²×C₇₃	—	2	2	no	—
421	C₂²×C₇₃	—	2	2	no	—
422	C₂²×C₇₃	—	2	2	no	—
423	C₂²×C₇₃	—	2	2	no	—
424	C₂²×C₇₃	—	2	2	no	—
425	C₂²×C₇₃	—	2	2	no	—
426	C₂²×C₇₃	#556	1	4	yes	—
427	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
428	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
429	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
430	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
432	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
434	C₄×C₇₃	—	2	2	no	—
435	C₄×C₇₃	—	2	4	no	—
436	C₄×C₇₃	—	2	2	no	—
437	C₄×C₇₃	—	2	2	no	—
438	C₄×C₇₃	—	2	2	no	—
439	C₄×C₇₃	—	2	2	no	—
440	C₄×C₇₃	—	4	2	no	—
441	C₄×C₇₃	—	4	2	no	—
442	C₄×C₇₃	—	4	2	no	—
443	C₄×C₇₃	—	4	2	no	—
444	C₄×C₇₃	—	4	2	no	—
445	C₄×C₇₃	—	4	1	no	—
446	C₄×C₇₃	—	4	2	no	—
447	C₄×C₇₃	—	4	2	no	—
448	C₄×C₇₃	—	4	1	no	—
449	C₄×C₇₃	—	4	1	no	—
450	C₄×C₇₃	—	4	1	no	—
451	C₄×C₇₃	—	4	1	no	—
452	C₄×C₇₃	—	4	1	no	—
453	C₄×C₇₃	—	4	1	no	—
454	C₄×C₇₃	—	4	1	no	—
455	C₄×C₇₃	#551	1	4	yes	—
456	#59425	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
457	C₂×C₇₃	—	2	4	no	—
458	C₂×C₇₃	C₂×#551	1	1	yes	characteristic
459	C₂×C₇₃	C₂×#556	1	1	yes	characteristic
460	C₂×C₇₃	#3482	1	1	yes	characteristic
461	C₂×C₇₃	#3509	1	1	yes	characteristic
462	C₂×C₇₃	#3520	1	1	yes	characteristic
463	C₂×C₇₃	#3523	1	1	yes	characteristic
464	C₂×C₇₃	#3538	1	1	yes	characteristic
465	#2789	C₂×C₇₃	1	2	yes	complemented
466	#2758	C₂×C₇₃	1	2	yes	complemented
467	#2605	C₂×C₇₃	1	2	yes	complemented
468	#2588	C₂×C₇₃	1	2	yes	complemented
469	#2581	C₂×C₇₃	1	1	yes	characteristic, complemented
470	#2568	C₂×C₇₃	1	1	yes	characteristic, complemented
471	#2514	C₂×C₇₃	1	1	yes	characteristic, complemented
472	#2514	C₂×C₇₃	1	1	yes	characteristic, complemented
473	#2503	C₂×C₇₃	1	1	yes	characteristic
474	#2493	C₂×C₇₃	1	2	yes	—
475	#2493	C₂×C₇₃	1	2	yes	—
476	#2446	C₂×C₇₃	1	1	yes	characteristic, complemented
477	#2446	C₂×C₇₃	1	1	yes	characteristic, complemented
478	#2438	C₂×C₇₃	1	2	yes	—
479	#2434	C₂×C₇₃	1	1	yes	characteristic
480	#2365	C₂×C₇₃	1	1	yes	characteristic, complemented
481	#2356	C₂×C₇₃	1	1	yes	characteristic, complemented
482	#2344	C₂×C₇₃	1	1	yes	characteristic
483	#2343	C₂×C₇₃	1	2	yes	—
484	Q₈×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic
485	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
486	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
487	C₂×#391	C₂×C₇₃	1	1	yes	characteristic
488	C₇₃	#59425	1	1	yes	characteristic, direct product factor, Sylow
489	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
490	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
491	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
492	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
493	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
494	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
495	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
496	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
497	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
498	C₂×#117	C₂²×C₇₃	1	2	yes	—
499	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
500	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
501	#401	C₂²×C₇₃	1	2	yes	—
502	#401	C₂²×C₇₃	1	2	yes	—
503	#400	C₂²×C₇₃	1	2	yes	—
504	#400	C₂²×C₇₃	1	2	yes	—
505	#400	C₂²×C₇₃	1	2	yes	—
506	#400	C₂²×C₇₃	1	2	yes	—
507	#400	C₂²×C₇₃	1	2	yes	—
508	#400	C₂²×C₇₃	1	2	yes	—
509	#400	C₂²×C₇₃	1	2	yes	—
510	#400	C₂²×C₇₃	1	2	yes	—
511	#400	C₂²×C₇₃	1	2	yes	—
512	#398	C₂²×C₇₃	1	2	yes	—
513	#398	C₂²×C₇₃	1	2	yes	—
514	#395	C₂²×C₇₃	1	2	yes	—
515	#395	C₂²×C₇₃	1	2	yes	—
516	#395	C₂²×C₇₃	1	2	yes	—
517	#391	C₂²×C₇₃	1	1	yes	characteristic
518	#391	C₂²×C₇₃	1	2	yes	—
519	#391	C₂²×C₇₃	1	1	yes	characteristic
520	#391	C₂²×C₇₃	1	1	yes	characteristic
521	#391	C₂²×C₇₃	1	1	yes	characteristic
522	#391	C₂²×C₇₃	1	1	yes	characteristic
523	#391	C₂²×C₇₃	1	1	yes	characteristic
524	#391	C₂²×C₇₃	1	2	yes	—
525	#391	C₂²×C₇₃	1	2	yes	—
526	#391	C₂²×C₇₃	1	2	yes	—
527	#391	C₂²×C₇₃	1	1	yes	characteristic
528	#391	C₂²×C₇₃	1	1	yes	characteristic
529	#391	C₂²×C₇₃	1	1	yes	characteristic
530	#391	C₂²×C₇₃	1	1	yes	characteristic
531	#391	C₂²×C₇₃	1	1	yes	characteristic
532	#391	C₂²×C₇₃	1	1	yes	characteristic
533	#391	C₂²×C₇₃	1	2	yes	—
534	#389	C₂²×C₇₃	1	1	yes	characteristic
535	#389	C₂²×C₇₃	1	1	yes	characteristic
536	#389	C₂²×C₇₃	1	1	yes	characteristic
537	#389	C₂²×C₇₃	1	1	yes	characteristic
538	#389	C₂²×C₇₃	1	2	yes	—
539	#387	C₂²×C₇₃	1	2	yes	—
540	#387	C₂²×C₇₃	1	2	yes	—
541	#387	C₂²×C₇₃	1	2	yes	—
542	#387	C₂²×C₇₃	1	2	yes	—
543	#387	C₂²×C₇₃	1	2	yes	—
544	#387	C₂²×C₇₃	1	2	yes	—
545	#387	C₂²×C₇₃	1	2	yes	—
546	#387	C₂²×C₇₃	1	2	yes	—
547	#387	C₂²×C₇₃	1	2	yes	—
548	#387	C₂²×C₇₃	1	2	yes	—
549	#387	C₂²×C₇₃	1	2	yes	—
550	#387	C₂²×C₇₃	1	2	yes	—
551	#387	C₂²×C₇₃	1	2	yes	—
552	#387	C₂²×C₇₃	1	2	yes	—
553	#387	C₂²×C₇₃	1	1	yes	characteristic
554	#387	C₂²×C₇₃	1	2	yes	—
555	#387	C₂²×C₇₃	1	1	yes	characteristic
556	#385	C₂²×C₇₃	1	1	yes	characteristic
557	#385	C₂²×C₇₃	1	2	yes	—
558	#385	C₂²×C₇₃	1	2	yes	—
559	#385	C₂²×C₇₃	1	2	yes	—
560	#385	C₂²×C₇₃	1	1	yes	characteristic
561	#383	C₂²×C₇₃	1	2	yes	—
562	#383	C₂²×C₇₃	1	2	yes	—
563	#383	C₂²×C₇₃	1	2	yes	—
564	#382	C₂²×C₇₃	1	2	yes	—
565	#382	C₂²×C₇₃	1	1	yes	characteristic
566	#382	C₂²×C₇₃	1	1	yes	characteristic
567	#381	C₂²×C₇₃	1	2	yes	—
568	#381	C₂²×C₇₃	1	2	yes	—
569	#381	C₂²×C₇₃	1	2	yes	—
570	#380	C₂²×C₇₃	1	1	yes	characteristic
571	#380	C₂²×C₇₃	1	2	yes	—
572	#380	C₂²×C₇₃	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
575	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
576	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
581	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
583	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
584	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
585	#376	C₂²×C₇₃	1	2	yes	—
586	C₂×#95	C₂²×C₇₃	1	2	yes	—
587	C₂×#95	C₂²×C₇₃	1	2	yes	—
588	C₂²×Q₈	—	2	4	no	—
589	C₂²×Q₈	—	2	4	no	—
590	C₂²×Q₈	—	4	2	no	—
591	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
592	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
593	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
594	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
595	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
597	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
599	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
601	C₄⋊Q₈	—	2	4	no	—
602	C₄⋊Q₈	—	4	2	no	—
603	C₂²⋊Q₈	—	2	4	no	—
604	C₂²⋊Q₈	—	2	4	no	—
605	C₄×Q₈	—	2	4	no	—
606	C₄×Q₈	—	4	2	no	—
607	C₄×Q₈	—	4	2	no	—
608	C₄×Q₈	—	4	2	no	—
609	#117	—	2	8	no	—
610	C₂×C₄⋊C₄	—	2	4	no	—
611	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
643	C₂×C₄²	—	4	2	no	—
644	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
645	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
646	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
649	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
655	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
658	#95	C₂³×C₇₃	1	2	yes	—
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	1	yes	characteristic
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	#95	C₂³×C₇₃	1	2	yes	—
673	#95	C₂³×C₇₃	1	1	yes	characteristic
674	#95	C₂³×C₇₃	1	1	yes	characteristic
675	#95	C₂³×C₇₃	1	1	yes	characteristic
676	#95	C₂³×C₇₃	1	1	yes	characteristic
677	#95	C₂³×C₇₃	1	1	yes	characteristic
678	#95	C₂³×C₇₃	1	2	yes	—
679	#95	C₂³×C₇₃	1	1	yes	characteristic
680	#95	C₂³×C₇₃	1	2	yes	—
681	#95	C₂³×C₇₃	1	2	yes	—
682	#95	C₂³×C₇₃	1	2	yes	—
683	#95	C₂³×C₇₃	1	1	yes	characteristic
684	#95	C₂³×C₇₃	1	1	yes	characteristic
685	#95	C₂³×C₇₃	1	2	yes	—
686	#95	C₂³×C₇₃	1	2	yes	—
687	#95	C₂³×C₇₃	1	1	yes	characteristic
688	#95	C₂³×C₇₃	1	2	yes	—
689	#95	C₂³×C₇₃	1	2	yes	—
690	#95	C₂³×C₇₃	1	2	yes	—
691	#95	C₂³×C₇₃	1	2	yes	—
692	#95	C₂³×C₇₃	1	2	yes	—
693	#95	C₂³×C₇₃	1	2	yes	—
694	#95	C₂³×C₇₃	1	2	yes	—
695	#95	C₂³×C₇₃	1	2	yes	—
696	#95	C₂³×C₇₃	1	2	yes	—
697	#95	C₂³×C₇₃	1	2	yes	—
698	#95	C₂³×C₇₃	1	2	yes	—
699	#95	C₂³×C₇₃	1	2	yes	—
700	#95	C₂³×C₇₃	1	2	yes	—
701	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	2	4	no	—
707	C₂×Q₈	—	2	4	no	—
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	4	1	no	—
715	C₂×Q₈	—	4	2	no	—
716	C₂×Q₈	—	4	16	no	—
717	C₂×Q₈	#41×C₇₃	1	4	yes	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	#41×C₇₃	1	4	yes	—
733	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	4	1	no	—
775	C₄⋊C₄	—	4	1	no	—
776	C₄⋊C₄	—	4	2	no	—
777	C₄⋊C₄	—	4	1	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	#41×C₇₃	1	4	yes	—
787	C₄²	—	2	4	no	—
788	C₄²	—	2	4	no	—
789	C₄²	—	2	4	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	4	no	—
797	C₄²	—	4	1	no	—
798	C₄²	—	4	1	no	—
799	C₄²	—	4	2	no	—
800	C₄²	—	4	2	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	C₂×#41×C₇₃	1	2	yes	—
806	C₂³	C₂×#41×C₇₃	1	2	yes	—
807	C₂³	2₋¹⁺⁴×C₇₃	1	2	yes	—
808	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
809	Q₈	—	2	8	no	—
810	Q₈	—	4	8	no	—
811	Q₈	—	4	4	no	—
812	Q₈	—	4	4	no	—
813	Q₈	—	4	4	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	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	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	8	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	4	8	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	4	4	no	—
875	C₂×C₄	—	4	8	no	—
876	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
877	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
878	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
879	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
880	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
881	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
882	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
883	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
884	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	#556×C₇₃	1	4	yes	—
892	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
893	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
894	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
895	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
896	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
897	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
898	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
899	C₄	—	2	2	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	2	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	#551×C₇₃	1	4	yes	—
921	C₂	—	2	4	no	—
922	C₂	C₂×#551×C₇₃	1	1	yes	characteristic
923	C₂	C₂×#556×C₇₃	1	1	yes	characteristic
924	C₂	C₇₃×#3482	1	1	yes	characteristic
925	C₂	C₇₃×#3509	1	1	yes	characteristic
926	C₂	C₇₃×#3520	1	1	yes	characteristic
927	C₂	C₇₃×#3523	1	1	yes	characteristic
928	C₂	C₇₃×#3538	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×#2789	C₂	semidirect
2. C₇₃×#2758	C₂	semidirect
3. C₇₃×#2605	C₂	semidirect
4. C₇₃×#2588	C₂	semidirect
5. C₇₃×#2581	C₂	semidirect
6. C₇₃×#2568	C₂	semidirect
7. C₇₃×#2514	C₂	semidirect
8. C₇₃×#2514	C₂	semidirect
12. C₇₃×#2446	C₂	semidirect
13. C₇₃×#2446	C₂	semidirect
16. C₇₃×#2365	C₂	semidirect
17. C₇₃×#2356	C₂	semidirect
456. #59425	C₇₃	direct (N × H)
465. #2789	C₂×C₇₃	semidirect
466. #2758	C₂×C₇₃	semidirect
467. #2605	C₂×C₇₃	semidirect
468. #2588	C₂×C₇₃	semidirect
469. #2581	C₂×C₇₃	semidirect
470. #2568	C₂×C₇₃	semidirect
471. #2514	C₂×C₇₃	semidirect
472. #2514	C₂×C₇₃	semidirect
476. #2446	C₂×C₇₃	semidirect
477. #2446	C₂×C₇₃	semidirect
480. #2365	C₂×C₇₃	semidirect
481. #2356	C₂×C₇₃	semidirect
488. C₇₃	#59425	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×#2789	2
C₇₃×#2758	2
C₇₃×#2605	2
C₇₃×#2588	2
C₇₃×#2581	2
C₇₃×#2568	2
C₇₃×#2514	2
C₇₃×#2503	2
C₇₃×#2493	2
C₇₃×#2446	2
C₇₃×#2438	2
C₇₃×#2434	2
C₇₃×#2365	2
C₇₃×#2356	2
C₇₃×#2344	2
C₇₃×#2343	2
Q₈×C₂²⋊C₄×C₇₃	2
C₄×C₂²⋊Q₈×C₇₃	2
C₂×#391×C₇₃	2
#59425	73

Subgroups — C73×#59425 #32968829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59425 #32968829