Subgroups — C₇₃×#59418 #32968822

Order 18688.

2368 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2707	C₂	1	4	yes	maximal, complemented
4	C₇₃×#2558	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2490	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2442	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2432	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2429	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2426	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2421	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2360	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2341	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₇₃	C₂²	1	2	yes	—
19	#557×C₇₃	—	2	8	no	—
20	#547×C₇₃	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×#125×C₇₃	C₂²	1	2	yes	—
24	C₂×#125×C₇₃	C₂²	1	4	yes	—
25	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#123×C₇₃	C₂²	1	4	yes	—
28	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
31	C₂×#121×C₇₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×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	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
40	#400×C₇₃	C₂²	1	4	yes	—
41	#398×C₇₃	C₂²	1	4	yes	—
42	#397×C₇₃	C₂²	1	4	yes	—
43	#396×C₇₃	C₂²	1	4	yes	—
44	#396×C₇₃	C₂²	1	4	yes	—
45	#396×C₇₃	C₂²	1	4	yes	—
46	#394×C₇₃	C₂²	1	4	yes	—
47	#394×C₇₃	C₂²	1	4	yes	—
48	#391×C₇₃	C₂²	1	1	yes	characteristic
49	#391×C₇₃	C₂²	1	1	yes	characteristic
50	#391×C₇₃	C₂²	1	2	yes	—
51	#390×C₇₃	C₂²	1	4	yes	—
52	#390×C₇₃	C₂²	1	1	yes	characteristic
53	#390×C₇₃	C₂²	1	2	yes	—
54	#390×C₇₃	C₂²	1	4	yes	—
55	#390×C₇₃	C₂²	1	2	yes	—
56	#390×C₇₃	C₂²	1	1	yes	characteristic
57	#389×C₇₃	C₂²	1	2	yes	—
58	#389×C₇₃	C₂²	1	2	yes	—
59	#389×C₇₃	C₂²	1	2	yes	—
60	#389×C₇₃	C₂²	1	2	yes	—
61	#389×C₇₃	C₂²	1	4	yes	—
62	#388×C₇₃	C₂²	1	2	yes	—
63	#388×C₇₃	C₂²	1	2	yes	—
64	#388×C₇₃	C₂²	1	4	yes	—
65	#388×C₇₃	C₂²	1	2	yes	—
66	#388×C₇₃	C₂²	1	2	yes	—
67	#388×C₇₃	C₂²	1	4	yes	—
68	#387×C₇₃	C₂²	1	4	yes	—
69	#385×C₇₃	C₂²	1	4	yes	—
70	#385×C₇₃	C₂²	1	4	yes	—
71	#384×C₇₃	C₂²	1	1	yes	characteristic
72	#382×C₇₃	C₂²	1	1	yes	characteristic
73	#382×C₇₃	C₂²	1	1	yes	characteristic
74	#380×C₇₃	C₂²	1	4	yes	—
75	#380×C₇₃	C₂²	1	2	yes	—
76	#380×C₇₃	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
84	C₄³×C₇₃	C₂²	1	1	yes	characteristic
85	C₂×#41×C₇₃	—	2	8	no	—
86	C₂×#41×C₇₃	—	2	8	no	—
87	C₂×#41×C₇₃	—	4	4	no	—
88	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
90	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
93	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
97	C₄⋊Q₈×C₇₃	—	2	8	no	—
98	C₄⋊Q₈×C₇₃	D₄	1	8	yes	—
99	#125×C₇₃	—	2	16	no	—
100	#125×C₇₃	—	2	8	no	—
101	#124×C₇₃	—	2	4	no	—
102	#124×C₇₃	—	2	4	no	—
103	#123×C₇₃	—	2	16	no	—
104	C₂²⋊Q₈×C₇₃	—	2	8	no	—
105	C₂²⋊Q₈×C₇₃	—	2	8	no	—
106	C₂²⋊Q₈×C₇₃	—	4	4	no	—
107	#121×C₇₃	—	2	8	no	—
108	C₄×Q₈×C₇₃	—	2	8	no	—
109	C₄×Q₈×C₇₃	—	2	8	no	—
110	C₄×Q₈×C₇₃	—	2	4	no	—
111	C₄×Q₈×C₇₃	—	2	4	no	—
112	C₄×Q₈×C₇₃	—	4	4	no	—
113	C₄×D₄×C₇₃	—	2	4	no	—
114	C₄×D₄×C₇₃	—	2	4	no	—
115	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
116	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	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	2	yes	—
130	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	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×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
143	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	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×C₄²×C₇₃	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
153	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
154	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
156	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
158	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
160	#95×C₇₃	C₂³	1	2	yes	—
161	#95×C₇₃	C₂³	1	2	yes	—
162	#95×C₇₃	C₂³	1	4	yes	—
163	#95×C₇₃	C₂³	1	2	yes	—
164	#95×C₇₃	C₂³	1	2	yes	—
165	#95×C₇₃	C₂³	1	2	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	4	yes	—
170	#95×C₇₃	C₂³	1	4	yes	—
171	#95×C₇₃	C₂³	1	4	yes	—
172	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
173	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
174	#41×C₇₃	—	4	32	no	—
175	C₂×Q₈×C₇₃	—	2	2	no	—
176	C₂×Q₈×C₇₃	—	2	2	no	—
177	C₂×Q₈×C₇₃	—	2	4	no	—
178	C₂×Q₈×C₇₃	—	2	2	no	—
179	C₂×Q₈×C₇₃	—	2	4	no	—
180	C₂×Q₈×C₇₃	—	2	2	no	—
181	C₂×Q₈×C₇₃	—	2	2	no	—
182	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
183	C₂×Q₈×C₇₃	#41	1	4	yes	complemented
184	C₂×D₄×C₇₃	—	2	8	no	—
185	C₂×D₄×C₇₃	—	2	2	no	—
186	C₂×D₄×C₇₃	—	2	2	no	—
187	C₂×D₄×C₇₃	—	2	8	no	—
188	C₂×D₄×C₇₃	—	2	2	no	—
189	C₂×D₄×C₇₃	—	2	2	no	—
190	C₂×D₄×C₇₃	—	2	2	no	—
191	C₂×D₄×C₇₃	—	4	4	no	—
192	C₂×D₄×C₇₃	#41	1	4	yes	—
193	C₂²×C₄×C₇₃	—	2	8	no	—
194	C₂²×C₄×C₇₃	—	2	4	no	—
195	C₂²×C₄×C₇₃	—	2	8	no	—
196	C₂²×C₄×C₇₃	—	2	4	no	—
197	C₂²×C₄×C₇₃	—	2	4	no	—
198	C₂²×C₄×C₇₃	—	2	4	no	—
199	C₂²×C₄×C₇₃	—	2	4	no	—
200	C₂²×C₄×C₇₃	—	2	4	no	—
201	C₂²×C₄×C₇₃	—	4	4	no	—
202	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
217	C₄⋊C₄×C₇₃	—	2	2	no	—
218	C₄⋊C₄×C₇₃	—	2	8	no	—
219	C₄⋊C₄×C₇₃	—	2	2	no	—
220	C₄⋊C₄×C₇₃	—	2	2	no	—
221	C₄⋊C₄×C₇₃	—	2	4	no	—
222	C₄⋊C₄×C₇₃	—	2	8	no	—
223	C₄⋊C₄×C₇₃	—	2	4	no	—
224	C₄⋊C₄×C₇₃	—	2	2	no	—
225	C₄⋊C₄×C₇₃	—	2	8	no	—
226	C₄⋊C₄×C₇₃	—	2	8	no	—
227	C₄⋊C₄×C₇₃	—	2	4	no	—
228	C₄⋊C₄×C₇₃	—	2	8	no	—
229	C₄⋊C₄×C₇₃	—	2	4	no	—
230	C₄⋊C₄×C₇₃	—	4	2	no	—
231	C₄⋊C₄×C₇₃	—	4	4	no	—
232	C₄⋊C₄×C₇₃	—	4	4	no	—
233	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
234	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
235	C₂²⋊C₄×C₇₃	—	2	4	no	—
236	C₂²⋊C₄×C₇₃	—	2	4	no	—
237	C₂²⋊C₄×C₇₃	—	2	4	no	—
238	C₂²⋊C₄×C₇₃	—	2	4	no	—
239	C₂²⋊C₄×C₇₃	—	2	8	no	—
240	C₂²⋊C₄×C₇₃	—	2	8	no	—
241	C₂²⋊C₄×C₇₃	—	2	4	no	—
242	C₂²⋊C₄×C₇₃	—	2	4	no	—
243	C₂²⋊C₄×C₇₃	—	2	4	no	—
244	C₂²⋊C₄×C₇₃	—	2	4	no	—
245	C₂²⋊C₄×C₇₃	—	4	2	no	—
246	C₂²⋊C₄×C₇₃	—	4	2	no	—
247	C₂²⋊C₄×C₇₃	—	4	4	no	—
248	C₂²⋊C₄×C₇₃	—	4	4	no	—
249	C₂²⋊C₄×C₇₃	—	4	4	no	—
250	C₄²×C₇₃	—	2	8	no	—
251	C₄²×C₇₃	—	2	4	no	—
252	C₄²×C₇₃	—	2	4	no	—
253	C₄²×C₇₃	—	2	2	no	—
254	C₄²×C₇₃	—	2	2	no	—
255	C₄²×C₇₃	—	2	2	no	—
256	C₄²×C₇₃	—	2	2	no	—
257	C₄²×C₇₃	—	2	2	no	—
258	C₄²×C₇₃	—	4	1	no	—
259	C₄²×C₇₃	—	4	4	no	—
260	C₄²×C₇₃	C₂×D₄	1	4	yes	—
261	C₂³×C₇₃	—	2	2	no	—
262	C₂³×C₇₃	—	2	2	no	—
263	C₂³×C₇₃	—	2	2	no	—
264	C₂³×C₇₃	—	2	2	no	—
265	C₂³×C₇₃	—	2	2	no	—
266	C₂³×C₇₃	—	2	2	no	—
267	C₂³×C₇₃	—	2	2	no	—
268	C₂³×C₇₃	—	2	2	no	—
269	C₂³×C₇₃	—	2	2	no	—
270	C₂³×C₇₃	—	2	2	no	—
271	C₂³×C₇₃	—	2	2	no	—
272	C₂³×C₇₃	—	2	2	no	—
273	C₂³×C₇₃	—	2	2	no	—
274	C₂³×C₇₃	C₂×#41	1	4	yes	—
275	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
276	Q₈×C₇₃	—	2	16	no	—
277	Q₈×C₇₃	—	2	8	no	—
278	Q₈×C₇₃	—	4	4	no	—
279	D₄×C₇₃	—	2	8	no	—
280	D₄×C₇₃	—	4	16	no	—
281	D₄×C₇₃	—	4	4	no	—
282	C₂×C₄×C₇₃	—	2	2	no	—
283	C₂×C₄×C₇₃	—	2	4	no	—
284	C₂×C₄×C₇₃	—	2	1	no	—
285	C₂×C₄×C₇₃	—	2	4	no	—
286	C₂×C₄×C₇₃	—	2	1	no	—
287	C₂×C₄×C₇₃	—	2	1	no	—
288	C₂×C₄×C₇₃	—	2	2	no	—
289	C₂×C₄×C₇₃	—	2	1	no	—
290	C₂×C₄×C₇₃	—	2	2	no	—
291	C₂×C₄×C₇₃	—	2	2	no	—
292	C₂×C₄×C₇₃	—	2	2	no	—
293	C₂×C₄×C₇₃	—	2	2	no	—
294	C₂×C₄×C₇₃	—	2	2	no	—
295	C₂×C₄×C₇₃	—	2	1	no	—
296	C₂×C₄×C₇₃	—	2	1	no	—
297	C₂×C₄×C₇₃	—	2	1	no	—
298	C₂×C₄×C₇₃	—	2	1	no	—
299	C₂×C₄×C₇₃	—	2	2	no	—
300	C₂×C₄×C₇₃	—	2	4	no	—
301	C₂×C₄×C₇₃	—	2	2	no	—
302	C₂×C₄×C₇₃	—	2	2	no	—
303	C₂×C₄×C₇₃	—	2	1	no	—
304	C₂×C₄×C₇₃	—	2	4	no	—
305	C₂×C₄×C₇₃	—	2	2	no	—
306	C₂×C₄×C₇₃	—	2	2	no	—
307	C₂×C₄×C₇₃	—	2	1	no	—
308	C₂×C₄×C₇₃	—	2	1	no	—
309	C₂×C₄×C₇₃	—	2	2	no	—
310	C₂×C₄×C₇₃	—	2	2	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	2	no	—
315	C₂×C₄×C₇₃	—	2	2	no	—
316	C₂×C₄×C₇₃	—	2	4	no	—
317	C₂×C₄×C₇₃	—	4	16	no	—
318	C₂×C₄×C₇₃	—	4	8	no	—
319	C₂×C₄×C₇₃	—	4	8	no	—
320	C₂×C₄×C₇₃	C₂²×D₄	1	8	yes	—
321	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
325	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
326	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
327	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
328	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
329	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
330	C₂²×C₇₃	—	2	4	no	—
331	C₂²×C₇₃	—	2	4	no	—
332	C₂²×C₇₃	—	2	4	no	—
333	C₂²×C₇₃	—	4	2	no	—
334	C₂²×C₇₃	—	4	2	no	—
335	C₂²×C₇₃	—	4	2	no	—
336	C₂²×C₇₃	—	4	2	no	—
337	C₂²×C₇₃	—	4	2	no	—
338	C₂²×C₇₃	—	4	2	no	—
339	C₂²×C₇₃	—	4	2	no	—
340	C₂²×C₇₃	—	4	2	no	—
341	C₂²×C₇₃	—	4	2	no	—
342	C₂²×C₇₃	—	4	2	no	—
343	C₂²×C₇₃	—	4	2	no	—
344	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
345	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
346	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
347	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
349	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
350	C₂²×C₇₃	#585	1	1	yes	characteristic
351	C₄×C₇₃	—	2	8	no	—
352	C₄×C₇₃	—	2	4	no	—
353	C₄×C₇₃	—	2	2	no	—
354	C₄×C₇₃	—	2	2	no	—
355	C₄×C₇₃	—	4	2	no	—
356	C₄×C₇₃	—	4	2	no	—
357	C₄×C₇₃	—	4	2	no	—
358	C₄×C₇₃	—	4	1	no	—
359	C₄×C₇₃	—	4	2	no	—
360	C₄×C₇₃	—	4	2	no	—
361	C₄×C₇₃	—	4	1	no	—
362	C₄×C₇₃	—	4	1	no	—
363	C₄×C₇₃	—	4	4	no	—
364	C₄×C₇₃	#546	1	4	yes	—
365	C₄×C₇₃	#548	1	4	yes	—
366	#59418	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₂×C₇₃	—	4	4	no	—
368	C₂×C₇₃	—	8	2	no	—
369	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
370	C₂×C₇₃	C₂×#548	1	1	yes	characteristic
371	C₂×C₇₃	#3482	1	1	yes	characteristic
372	C₂×C₇₃	#3497	1	1	yes	characteristic
373	C₂×C₇₃	#3515	1	1	yes	characteristic
374	C₂×C₇₃	#3517	1	1	yes	characteristic
375	C₂×C₇₃	#3552	1	1	yes	characteristic
376	C₂×#557	C₂×C₇₃	1	1	yes	characteristic, complemented
377	C₂×#547	C₂×C₇₃	1	1	yes	characteristic
378	#2707	C₂×C₇₃	1	4	yes	complemented
379	#2558	C₂×C₇₃	1	4	yes	complemented
380	#2538	C₂×C₇₃	1	1	yes	characteristic, complemented
381	#2538	C₂×C₇₃	1	1	yes	characteristic, complemented
382	#2490	C₂×C₇₃	1	2	yes	complemented
383	#2442	C₂×C₇₃	1	2	yes	complemented
384	#2432	C₂×C₇₃	1	2	yes	complemented
385	#2429	C₂×C₇₃	1	2	yes	complemented
386	#2426	C₂×C₇₃	1	2	yes	complemented
387	#2421	C₂×C₇₃	1	2	yes	complemented
388	#2360	C₂×C₇₃	1	2	yes	complemented
389	#2341	C₂×C₇₃	1	2	yes	complemented
390	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
391	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
392	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
393	C₇₃	#59418	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²×#41	C₂²×C₇₃	1	2	yes	—
395	#557	—	2	8	no	—
396	#547	—	2	8	no	—
397	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
398	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
399	C₂×#125	C₂²×C₇₃	1	2	yes	—
400	C₂×#125	C₂²×C₇₃	1	4	yes	—
401	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
402	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
403	C₂×#123	C₂²×C₇₃	1	4	yes	—
404	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
405	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
406	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
407	C₂×#121	C₂²×C₇₃	1	2	yes	—
408	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
409	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
410	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
412	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
414	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
416	#400	C₂²×C₇₃	1	4	yes	—
417	#398	C₂²×C₇₃	1	4	yes	—
418	#397	C₂²×C₇₃	1	4	yes	—
419	#396	C₂²×C₇₃	1	4	yes	—
420	#396	C₂²×C₇₃	1	4	yes	—
421	#396	C₂²×C₇₃	1	4	yes	—
422	#394	C₂²×C₇₃	1	4	yes	—
423	#394	C₂²×C₇₃	1	4	yes	—
424	#391	C₂²×C₇₃	1	2	yes	—
425	#391	C₂²×C₇₃	1	1	yes	characteristic
426	#391	C₂²×C₇₃	1	1	yes	characteristic
427	#390	C₂²×C₇₃	1	1	yes	characteristic
428	#390	C₂²×C₇₃	1	4	yes	—
429	#390	C₂²×C₇₃	1	2	yes	—
430	#390	C₂²×C₇₃	1	4	yes	—
431	#390	C₂²×C₇₃	1	2	yes	—
432	#390	C₂²×C₇₃	1	1	yes	characteristic
433	#389	C₂²×C₇₃	1	2	yes	—
434	#389	C₂²×C₇₃	1	2	yes	—
435	#389	C₂²×C₇₃	1	4	yes	—
436	#389	C₂²×C₇₃	1	2	yes	—
437	#389	C₂²×C₇₃	1	2	yes	—
438	#388	C₂²×C₇₃	1	4	yes	—
439	#388	C₂²×C₇₃	1	4	yes	—
440	#388	C₂²×C₇₃	1	2	yes	—
441	#388	C₂²×C₇₃	1	2	yes	—
442	#388	C₂²×C₇₃	1	2	yes	—
443	#388	C₂²×C₇₃	1	2	yes	—
444	#387	C₂²×C₇₃	1	4	yes	—
445	#385	C₂²×C₇₃	1	4	yes	—
446	#385	C₂²×C₇₃	1	4	yes	—
447	#384	C₂²×C₇₃	1	1	yes	characteristic
448	#382	C₂²×C₇₃	1	1	yes	characteristic
449	#382	C₂²×C₇₃	1	1	yes	characteristic
450	#380	C₂²×C₇₃	1	2	yes	—
451	#380	C₂²×C₇₃	1	4	yes	—
452	#380	C₂²×C₇₃	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
457	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
460	C₄³	C₂²×C₇₃	1	1	yes	characteristic
461	C₂×#41	—	2	8	no	—
462	C₂×#41	—	2	8	no	—
463	C₂×#41	—	4	4	no	—
464	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
465	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
466	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
469	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
471	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
472	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
473	C₄⋊Q₈	—	2	8	no	—
474	C₄⋊Q₈	D₄×C₇₃	1	8	yes	—
475	#125	—	2	16	no	—
476	#125	—	2	8	no	—
477	#124	—	2	4	no	—
478	#124	—	2	4	no	—
479	#123	—	2	16	no	—
480	C₂²⋊Q₈	—	2	8	no	—
481	C₂²⋊Q₈	—	2	8	no	—
482	C₂²⋊Q₈	—	4	4	no	—
483	#121	—	2	8	no	—
484	C₄×Q₈	—	2	8	no	—
485	C₄×Q₈	—	2	8	no	—
486	C₄×Q₈	—	2	4	no	—
487	C₄×Q₈	—	2	4	no	—
488	C₄×Q₈	—	4	4	no	—
489	C₄×D₄	—	2	4	no	—
490	C₄×D₄	—	2	4	no	—
491	C₂×C₄⋊C₄	—	2	8	no	—
492	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
525	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
526	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
527	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
534	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
536	#95	C₂³×C₇₃	1	2	yes	—
537	#95	C₂³×C₇₃	1	2	yes	—
538	#95	C₂³×C₇₃	1	4	yes	—
539	#95	C₂³×C₇₃	1	2	yes	—
540	#95	C₂³×C₇₃	1	2	yes	—
541	#95	C₂³×C₇₃	1	2	yes	—
542	#95	C₂³×C₇₃	1	2	yes	—
543	#95	C₂³×C₇₃	1	2	yes	—
544	#95	C₂³×C₇₃	1	2	yes	—
545	#95	C₂³×C₇₃	1	4	yes	—
546	#95	C₂³×C₇₃	1	4	yes	—
547	#95	C₂³×C₇₃	1	4	yes	—
548	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
549	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
550	#41	—	4	32	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	4	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	2	4	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	C₂×D₄×C₇₃	1	8	yes	—
559	C₂×Q₈	#41×C₇₃	1	4	yes	complemented
560	C₂×D₄	—	2	8	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	#41×C₇₃	1	4	yes	—
569	C₂²×C₄	—	2	8	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	8	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	4	4	no	—
578	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
586	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
588	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	8	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	8	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	4	no	—
608	C₄⋊C₄	—	4	4	no	—
609	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
610	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
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	8	no	—
616	C₂²⋊C₄	—	2	8	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₄²	—	2	8	no	—
627	C₄²	—	2	4	no	—
628	C₄²	—	2	4	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	4	1	no	—
635	C₄²	—	4	4	no	—
636	C₄²	C₂×D₄×C₇₃	1	4	yes	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	C₂×#41×C₇₃	1	4	yes	—
651	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
652	Q₈	—	2	16	no	—
653	Q₈	—	2	8	no	—
654	Q₈	—	4	4	no	—
655	D₄	—	2	8	no	—
656	D₄	—	4	16	no	—
657	D₄	—	4	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	4	16	no	—
694	C₂×C₄	—	4	8	no	—
695	C₂×C₄	—	4	8	no	—
696	C₂×C₄	C₂²×D₄×C₇₃	1	8	yes	—
697	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
700	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
701	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
702	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
703	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
704	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
705	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	4	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
721	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
722	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
723	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
724	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
725	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
726	C₂²	#585×C₇₃	1	1	yes	characteristic
727	C₄	—	2	8	no	—
728	C₄	—	2	4	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	1	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	4	no	—
740	C₄	#546×C₇₃	1	4	yes	—
741	C₄	#548×C₇₃	1	4	yes	—
742	C₂	—	4	4	no	—
743	C₂	—	8	2	no	—
744	C₂	C₂×#546×C₇₃	1	1	yes	characteristic
745	C₂	C₂×#548×C₇₃	1	1	yes	characteristic
746	C₂	C₇₃×#3482	1	1	yes	characteristic
747	C₂	C₇₃×#3497	1	1	yes	characteristic
748	C₂	C₇₃×#3515	1	1	yes	characteristic
749	C₂	C₇₃×#3517	1	1	yes	characteristic
750	C₂	C₇₃×#3552	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂×#547×C₇₃	C₂
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×#557×C₇₃	C₂	semidirect
3. C₇₃×#2707	C₂	semidirect
4. C₇₃×#2558	C₂	semidirect
5. C₇₃×#2538	C₂	semidirect
6. C₇₃×#2538	C₂	semidirect
7. C₇₃×#2490	C₂	semidirect
8. C₇₃×#2442	C₂	semidirect
9. C₇₃×#2432	C₂	semidirect
10. C₇₃×#2429	C₂	semidirect
11. C₇₃×#2426	C₂	semidirect
12. C₇₃×#2421	C₂	semidirect
13. C₇₃×#2360	C₂	semidirect
14. C₇₃×#2341	C₂	semidirect
15. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
16. C₄×#124×C₇₃	C₂	semidirect
17. C₄×#124×C₇₃	C₂	semidirect
183. C₂×Q₈×C₇₃	#41	semidirect
366. #59418	C₇₃	direct (N × H)
376. C₂×#557	C₂×C₇₃	semidirect
378. #2707	C₂×C₇₃	semidirect
379. #2558	C₂×C₇₃	semidirect
380. #2538	C₂×C₇₃	semidirect
381. #2538	C₂×C₇₃	semidirect
382. #2490	C₂×C₇₃	semidirect
383. #2442	C₂×C₇₃	semidirect
384. #2432	C₂×C₇₃	semidirect
385. #2429	C₂×C₇₃	semidirect
386. #2426	C₂×C₇₃	semidirect
387. #2421	C₂×C₇₃	semidirect
388. #2360	C₂×C₇₃	semidirect
389. #2341	C₂×C₇₃	semidirect
390. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
391. C₄×#124	C₂×C₇₃	semidirect
392. C₄×#124	C₂×C₇₃	semidirect
393. C₇₃	#59418	direct (N × H)
559. C₂×Q₈	#41×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#557×C₇₃	2
C₂×#547×C₇₃	2
C₇₃×#2707	2
C₇₃×#2558	2
C₇₃×#2538	2
C₇₃×#2490	2
C₇₃×#2442	2
C₇₃×#2432	2
C₇₃×#2429	2
C₇₃×#2426	2
C₇₃×#2421	2
C₇₃×#2360	2
C₇₃×#2341	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#124×C₇₃	2
#59418	73

Subgroups — C73×#59418 #32968822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59418 #32968822