Subgroups — C₇₃×#59444 #32968848

Order 18688.

2264 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2694	C₂	1	4	yes	maximal, complemented
3	C₇₃×#2552	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2536	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2512	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2479	C₂	1	4	yes	maximal, complemented
9	C₇₃×#2445	C₂	1	2	yes	maximal
10	C₇₃×#2417	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2415	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2354	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×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic
17	C₄×#125×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#552×C₇₃	—	2	16	no	—
19	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#126×C₇₃	C₂²	1	4	yes	—
22	C₂×#125×C₇₃	C₂²	1	4	yes	—
23	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#123×C₇₃	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
35	C₂×#117×C₇₃	C₂²	1	4	yes	—
36	C₂×#117×C₇₃	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
38	#399×C₇₃	C₂²	1	4	yes	—
39	#399×C₇₃	C₂²	1	4	yes	—
40	#398×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	#394×C₇₃	C₂²	1	4	yes	—
45	#394×C₇₃	C₂²	1	4	yes	—
46	#391×C₇₃	C₂²	1	2	yes	—
47	#390×C₇₃	C₂²	1	2	yes	—
48	#390×C₇₃	C₂²	1	2	yes	—
49	#390×C₇₃	C₂²	1	2	yes	—
50	#390×C₇₃	C₂²	1	2	yes	—
51	#390×C₇₃	C₂²	1	1	yes	characteristic
52	#390×C₇₃	C₂²	1	1	yes	characteristic
53	#390×C₇₃	C₂²	1	2	yes	—
54	#389×C₇₃	C₂²	1	2	yes	—
55	#389×C₇₃	C₂²	1	4	yes	—
56	#389×C₇₃	C₂²	1	2	yes	—
57	#389×C₇₃	C₂²	1	1	yes	characteristic
58	#389×C₇₃	C₂²	1	1	yes	characteristic
59	#389×C₇₃	C₂²	1	2	yes	—
60	#388×C₇₃	C₂²	1	4	yes	—
61	#388×C₇₃	C₂²	1	4	yes	—
62	#388×C₇₃	C₂²	1	4	yes	—
63	#388×C₇₃	C₂²	1	4	yes	—
64	#387×C₇₃	C₂²	1	2	yes	—
65	#387×C₇₃	C₂²	1	2	yes	—
66	#386×C₇₃	C₂²	1	4	yes	—
67	#385×C₇₃	C₂²	1	4	yes	—
68	#384×C₇₃	C₂²	1	2	yes	—
69	#384×C₇₃	C₂²	1	2	yes	—
70	#384×C₇₃	C₂²	1	1	yes	characteristic
71	#384×C₇₃	C₂²	1	1	yes	characteristic
72	#382×C₇₃	C₂²	1	1	yes	characteristic
73	#380×C₇₃	C₂²	1	2	yes	—
74	#380×C₇₃	C₂²	1	2	yes	—
75	#380×C₇₃	C₂²	1	4	yes	—
76	C₄×C₄⋊C₄×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×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
83	C₄³×C₇₃	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
90	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
92	C₄⋊Q₈×C₇₃	—	2	4	no	—
93	#127×C₇₃	—	2	4	no	—
94	#126×C₇₃	—	2	16	no	—
95	#125×C₇₃	—	2	16	no	—
96	#125×C₇₃	D₄	1	8	yes	complemented
97	#123×C₇₃	—	2	16	no	—
98	C₂²⋊Q₈×C₇₃	—	2	8	no	—
99	C₂²⋊Q₈×C₇₃	—	2	8	no	—
100	C₂²⋊Q₈×C₇₃	—	4	4	no	—
101	C₂²⋊Q₈×C₇₃	—	4	4	no	—
102	C₄×Q₈×C₇₃	—	2	8	no	—
103	C₄×D₄×C₇₃	—	2	8	no	—
104	C₄×D₄×C₇₃	—	2	8	no	—
105	C₄×D₄×C₇₃	—	2	4	no	—
106	C₄×D₄×C₇₃	—	2	4	no	—
107	C₄×D₄×C₇₃	—	4	4	no	—
108	#117×C₇₃	—	2	8	no	—
109	#117×C₇₃	—	2	16	no	—
110	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
111	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
126	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	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	4	yes	—
141	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	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	4	yes	—
146	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
147	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
153	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
154	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
158	#95×C₇₃	C₂³	1	4	yes	—
159	#95×C₇₃	C₂³	1	4	yes	—
160	#95×C₇₃	C₂³	1	2	yes	—
161	#95×C₇₃	C₂³	1	2	yes	—
162	#95×C₇₃	C₂³	1	2	yes	—
163	#95×C₇₃	C₂³	1	2	yes	—
164	#95×C₇₃	C₂³	1	4	yes	—
165	#95×C₇₃	C₂³	1	2	yes	—
166	#95×C₇₃	C₂³	1	2	yes	—
167	#95×C₇₃	C₂³	1	4	yes	—
168	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
169	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
170	C₂×Q₈×C₇₃	—	2	4	no	—
171	C₂×Q₈×C₇₃	—	2	4	no	—
172	C₂×Q₈×C₇₃	—	2	4	no	—
173	C₂×D₄×C₇₃	—	2	4	no	—
174	C₂×D₄×C₇₃	—	2	4	no	—
175	C₂×D₄×C₇₃	—	2	4	no	—
176	C₂×D₄×C₇₃	—	2	2	no	—
177	C₂×D₄×C₇₃	—	2	2	no	—
178	C₂×D₄×C₇₃	—	2	2	no	—
179	C₂×D₄×C₇₃	—	2	2	no	—
180	C₂×D₄×C₇₃	—	2	4	no	—
181	C₂×D₄×C₇₃	—	2	2	no	—
182	C₂×D₄×C₇₃	—	4	2	no	—
183	C₂×D₄×C₇₃	—	4	2	no	—
184	C₂×D₄×C₇₃	#41	1	4	yes	—
185	C₂²×C₄×C₇₃	—	2	8	no	—
186	C₂²×C₄×C₇₃	—	2	8	no	—
187	C₂²×C₄×C₇₃	—	2	4	no	—
188	C₂²×C₄×C₇₃	—	2	4	no	—
189	C₂²×C₄×C₇₃	—	2	4	no	—
190	C₂²×C₄×C₇₃	—	2	4	no	—
191	C₂²×C₄×C₇₃	—	2	4	no	—
192	C₂²×C₄×C₇₃	—	2	4	no	—
193	C₂²×C₄×C₇₃	—	4	4	no	—
194	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
209	C₄⋊C₄×C₇₃	—	2	4	no	—
210	C₄⋊C₄×C₇₃	—	2	8	no	—
211	C₄⋊C₄×C₇₃	—	2	8	no	—
212	C₄⋊C₄×C₇₃	—	2	4	no	—
213	C₄⋊C₄×C₇₃	—	2	8	no	—
214	C₄⋊C₄×C₇₃	—	2	8	no	—
215	C₄⋊C₄×C₇₃	—	2	4	no	—
216	C₄⋊C₄×C₇₃	—	2	2	no	—
217	C₄⋊C₄×C₇₃	—	2	2	no	—
218	C₄⋊C₄×C₇₃	—	2	4	no	—
219	C₄⋊C₄×C₇₃	—	2	4	no	—
220	C₄⋊C₄×C₇₃	—	2	2	no	—
221	C₄⋊C₄×C₇₃	—	2	2	no	—
222	C₄⋊C₄×C₇₃	—	2	4	no	—
223	C₄⋊C₄×C₇₃	—	4	2	no	—
224	C₄⋊C₄×C₇₃	—	4	2	no	—
225	C₄⋊C₄×C₇₃	—	4	2	no	—
226	C₄⋊C₄×C₇₃	—	4	4	no	—
227	C₄⋊C₄×C₇₃	—	4	4	no	—
228	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
229	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
230	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
231	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
232	C₂²⋊C₄×C₇₃	—	2	8	no	—
233	C₂²⋊C₄×C₇₃	—	2	4	no	—
234	C₂²⋊C₄×C₇₃	—	2	8	no	—
235	C₂²⋊C₄×C₇₃	—	2	8	no	—
236	C₂²⋊C₄×C₇₃	—	2	4	no	—
237	C₂²⋊C₄×C₇₃	—	2	8	no	—
238	C₂²⋊C₄×C₇₃	—	2	4	no	—
239	C₂²⋊C₄×C₇₃	—	2	4	no	—
240	C₂²⋊C₄×C₇₃	—	4	4	no	—
241	C₂²⋊C₄×C₇₃	—	4	2	no	—
242	C₂²⋊C₄×C₇₃	—	4	2	no	—
243	C₂²⋊C₄×C₇₃	—	4	4	no	—
244	C₂²⋊C₄×C₇₃	—	4	4	no	—
245	C₄²×C₇₃	—	2	8	no	—
246	C₄²×C₇₃	—	2	8	no	—
247	C₄²×C₇₃	—	2	4	no	—
248	C₄²×C₇₃	—	2	2	no	—
249	C₄²×C₇₃	—	2	2	no	—
250	C₄²×C₇₃	—	2	2	no	—
251	C₄²×C₇₃	—	2	4	no	—
252	C₄²×C₇₃	—	2	2	no	—
253	C₄²×C₇₃	—	4	1	no	—
254	C₄²×C₇₃	C₂×D₄	1	4	yes	—
255	C₄²×C₇₃	#41	1	4	yes	—
256	C₂³×C₇₃	—	2	2	no	—
257	C₂³×C₇₃	—	2	2	no	—
258	C₂³×C₇₃	—	2	2	no	—
259	C₂³×C₇₃	—	2	2	no	—
260	C₂³×C₇₃	—	2	2	no	—
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	C₂×#41	1	4	yes	—
270	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
271	Q₈×C₇₃	—	4	8	no	—
272	D₄×C₇₃	—	2	8	no	—
273	D₄×C₇₃	—	4	8	no	—
274	D₄×C₇₃	—	4	8	no	—
275	D₄×C₇₃	—	4	4	no	—
276	C₂×C₄×C₇₃	—	2	2	no	—
277	C₂×C₄×C₇₃	—	2	1	no	—
278	C₂×C₄×C₇₃	—	2	1	no	—
279	C₂×C₄×C₇₃	—	2	1	no	—
280	C₂×C₄×C₇₃	—	2	1	no	—
281	C₂×C₄×C₇₃	—	2	2	no	—
282	C₂×C₄×C₇₃	—	2	1	no	—
283	C₂×C₄×C₇₃	—	2	1	no	—
284	C₂×C₄×C₇₃	—	2	2	no	—
285	C₂×C₄×C₇₃	—	2	1	no	—
286	C₂×C₄×C₇₃	—	2	1	no	—
287	C₂×C₄×C₇₃	—	2	2	no	—
288	C₂×C₄×C₇₃	—	2	2	no	—
289	C₂×C₄×C₇₃	—	2	4	no	—
290	C₂×C₄×C₇₃	—	2	4	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	4	no	—
296	C₂×C₄×C₇₃	—	2	4	no	—
297	C₂×C₄×C₇₃	—	2	1	no	—
298	C₂×C₄×C₇₃	—	2	2	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	2	no	—
305	C₂×C₄×C₇₃	—	2	2	no	—
306	C₂×C₄×C₇₃	—	2	1	no	—
307	C₂×C₄×C₇₃	—	2	2	no	—
308	C₂×C₄×C₇₃	—	2	4	no	—
309	C₂×C₄×C₇₃	—	4	16	no	—
310	C₂×C₄×C₇₃	—	4	8	no	—
311	C₂×C₄×C₇₃	—	4	8	no	—
312	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
314	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
318	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
319	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
320	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
321	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
322	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
323	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
324	C₂²×C₇₃	—	2	4	no	—
325	C₂²×C₇₃	—	2	4	no	—
326	C₂²×C₇₃	—	2	4	no	—
327	C₂²×C₇₃	—	4	2	no	—
328	C₂²×C₇₃	—	4	2	no	—
329	C₂²×C₇₃	—	4	2	no	—
330	C₂²×C₇₃	—	4	2	no	—
331	C₂²×C₇₃	—	4	2	no	—
332	C₂²×C₇₃	—	4	2	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	C₂³×D₄	1	1	yes	characteristic
339	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
340	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
341	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
343	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
344	C₂²×C₇₃	#585	1	1	yes	characteristic
345	C₄×C₇₃	—	2	4	no	—
346	C₄×C₇₃	—	2	2	no	—
347	C₄×C₇₃	—	2	2	no	—
348	C₄×C₇₃	—	2	4	no	—
349	C₄×C₇₃	—	2	2	no	—
350	C₄×C₇₃	—	2	2	no	—
351	C₄×C₇₃	—	4	2	no	—
352	C₄×C₇₃	—	4	2	no	—
353	C₄×C₇₃	—	4	4	no	—
354	C₄×C₇₃	—	4	4	no	—
355	C₄×C₇₃	—	4	2	no	—
356	C₄×C₇₃	—	4	1	no	—
357	C₄×C₇₃	—	4	2	no	—
358	C₄×C₇₃	#550	1	4	yes	—
359	C₄×C₇₃	#552	1	4	yes	complemented
360	#59444	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂×C₇₃	—	4	4	no	—
362	C₂×C₇₃	—	8	2	no	—
363	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
364	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
365	C₂×C₇₃	C₂×#552	1	1	yes	characteristic
366	C₂×C₇₃	#3499	1	1	yes	characteristic
367	C₂×C₇₃	#3507	1	1	yes	characteristic
368	C₂×C₇₃	#3520	1	1	yes	characteristic
369	C₂×C₇₃	#3547	1	1	yes	characteristic
370	C₂×#552	C₂×C₇₃	1	2	yes	complemented
371	#2694	C₂×C₇₃	1	4	yes	complemented
372	#2552	C₂×C₇₃	1	2	yes	complemented
373	#2542	C₂×C₇₃	1	1	yes	characteristic, complemented
374	#2542	C₂×C₇₃	1	1	yes	characteristic, complemented
375	#2536	C₂×C₇₃	1	2	yes	complemented
376	#2512	C₂×C₇₃	1	2	yes	complemented
377	#2479	C₂×C₇₃	1	4	yes	complemented
378	#2445	C₂×C₇₃	1	2	yes	—
379	#2417	C₂×C₇₃	1	2	yes	complemented
380	#2415	C₂×C₇₃	1	2	yes	complemented
381	#2354	C₂×C₇₃	1	1	yes	characteristic, complemented
382	#2354	C₂×C₇₃	1	2	yes	complemented
383	D₄×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
384	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
385	C₄×#127	C₂×C₇₃	1	1	yes	characteristic
386	C₄×#125	C₂×C₇₃	1	1	yes	characteristic, complemented
387	C₇₃	#59444	1	1	yes	characteristic, direct product factor, Sylow
388	#552	—	2	16	no	—
389	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
390	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
391	C₂×#126	C₂²×C₇₃	1	4	yes	—
392	C₂×#125	C₂²×C₇₃	1	4	yes	—
393	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
394	C₂×#123	C₂²×C₇₃	1	4	yes	—
395	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
397	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
398	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
399	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
400	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
402	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
403	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
404	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
405	C₂×#117	C₂²×C₇₃	1	2	yes	—
406	C₂×#117	C₂²×C₇₃	1	4	yes	—
407	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
408	#399	C₂²×C₇₃	1	4	yes	—
409	#399	C₂²×C₇₃	1	4	yes	—
410	#398	C₂²×C₇₃	1	4	yes	—
411	#398	C₂²×C₇₃	1	4	yes	—
412	#397	C₂²×C₇₃	1	4	yes	—
413	#396	C₂²×C₇₃	1	4	yes	—
414	#394	C₂²×C₇₃	1	4	yes	—
415	#394	C₂²×C₇₃	1	4	yes	—
416	#391	C₂²×C₇₃	1	2	yes	—
417	#390	C₂²×C₇₃	1	1	yes	characteristic
418	#390	C₂²×C₇₃	1	2	yes	—
419	#390	C₂²×C₇₃	1	2	yes	—
420	#390	C₂²×C₇₃	1	1	yes	characteristic
421	#390	C₂²×C₇₃	1	2	yes	—
422	#390	C₂²×C₇₃	1	2	yes	—
423	#390	C₂²×C₇₃	1	2	yes	—
424	#389	C₂²×C₇₃	1	1	yes	characteristic
425	#389	C₂²×C₇₃	1	1	yes	characteristic
426	#389	C₂²×C₇₃	1	2	yes	—
427	#389	C₂²×C₇₃	1	2	yes	—
428	#389	C₂²×C₇₃	1	2	yes	—
429	#389	C₂²×C₇₃	1	4	yes	—
430	#388	C₂²×C₇₃	1	4	yes	—
431	#388	C₂²×C₇₃	1	4	yes	—
432	#388	C₂²×C₇₃	1	4	yes	—
433	#388	C₂²×C₇₃	1	4	yes	—
434	#387	C₂²×C₇₃	1	2	yes	—
435	#387	C₂²×C₇₃	1	2	yes	—
436	#386	C₂²×C₇₃	1	4	yes	—
437	#385	C₂²×C₇₃	1	4	yes	—
438	#384	C₂²×C₇₃	1	1	yes	characteristic
439	#384	C₂²×C₇₃	1	1	yes	characteristic
440	#384	C₂²×C₇₃	1	2	yes	—
441	#384	C₂²×C₇₃	1	2	yes	—
442	#382	C₂²×C₇₃	1	1	yes	characteristic
443	#380	C₂²×C₇₃	1	2	yes	—
444	#380	C₂²×C₇₃	1	4	yes	—
445	#380	C₂²×C₇₃	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
451	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
452	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
453	C₄³	C₂²×C₇₃	1	1	yes	characteristic
454	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
455	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
456	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
457	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
458	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
460	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
461	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
462	C₄⋊Q₈	—	2	4	no	—
463	#127	—	2	4	no	—
464	#126	—	2	16	no	—
465	#125	—	2	16	no	—
466	#125	D₄×C₇₃	1	8	yes	complemented
467	#123	—	2	16	no	—
468	C₂²⋊Q₈	—	2	8	no	—
469	C₂²⋊Q₈	—	2	8	no	—
470	C₂²⋊Q₈	—	4	4	no	—
471	C₂²⋊Q₈	—	4	4	no	—
472	C₄×Q₈	—	2	8	no	—
473	C₄×D₄	—	2	8	no	—
474	C₄×D₄	—	2	8	no	—
475	C₄×D₄	—	2	4	no	—
476	C₄×D₄	—	2	4	no	—
477	C₄×D₄	—	4	4	no	—
478	#117	—	2	8	no	—
479	#117	—	2	16	no	—
480	C₂×C₄⋊C₄	—	2	8	no	—
481	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
483	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
484	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
517	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
518	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
519	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
521	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
525	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
528	#95	C₂³×C₇₃	1	4	yes	—
529	#95	C₂³×C₇₃	1	4	yes	—
530	#95	C₂³×C₇₃	1	2	yes	—
531	#95	C₂³×C₇₃	1	2	yes	—
532	#95	C₂³×C₇₃	1	2	yes	—
533	#95	C₂³×C₇₃	1	2	yes	—
534	#95	C₂³×C₇₃	1	4	yes	—
535	#95	C₂³×C₇₃	1	2	yes	—
536	#95	C₂³×C₇₃	1	2	yes	—
537	#95	C₂³×C₇₃	1	4	yes	—
538	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
539	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
540	C₂×Q₈	—	2	4	no	—
541	C₂×Q₈	—	2	4	no	—
542	C₂×Q₈	—	2	4	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	4	2	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	#41×C₇₃	1	4	yes	—
555	C₂²×C₄	—	2	8	no	—
556	C₂²×C₄	—	2	8	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	4	4	no	—
564	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
568	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	8	no	—
581	C₄⋊C₄	—	2	8	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	2	8	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₄⋊C₄	—	4	2	no	—
596	C₄⋊C₄	—	4	4	no	—
597	C₄⋊C₄	—	4	4	no	—
598	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
599	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
600	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
601	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	4	4	no	—
611	C₂²⋊C₄	—	4	2	no	—
612	C₂²⋊C₄	—	4	2	no	—
613	C₂²⋊C₄	—	4	4	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₄²	—	2	8	no	—
616	C₄²	—	2	8	no	—
617	C₄²	—	2	4	no	—
618	C₄²	—	2	2	no	—
619	C₄²	—	2	2	no	—
620	C₄²	—	2	2	no	—
621	C₄²	—	2	2	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	4	1	no	—
624	C₄²	C₂×D₄×C₇₃	1	4	yes	—
625	C₄²	#41×C₇₃	1	4	yes	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	C₂×#41×C₇₃	1	4	yes	—
640	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
641	Q₈	—	4	8	no	—
642	D₄	—	2	8	no	—
643	D₄	—	4	8	no	—
644	D₄	—	4	8	no	—
645	D₄	—	4	4	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	4	16	no	—
680	C₂×C₄	—	4	8	no	—
681	C₂×C₄	—	4	8	no	—
682	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
683	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
684	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
686	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
687	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
688	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
689	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
690	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
691	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
692	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
693	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
694	C₂²	—	2	4	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
709	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
710	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
711	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
712	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
713	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
714	C₂²	#585×C₇₃	1	1	yes	characteristic
715	C₄	—	2	4	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	4	no	—
724	C₄	—	4	4	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	2	no	—
728	C₄	#550×C₇₃	1	4	yes	—
729	C₄	#552×C₇₃	1	4	yes	complemented
730	C₂	—	4	4	no	—
731	C₂	—	8	2	no	—
732	C₂	C₂×#550×C₇₃	1	1	yes	characteristic
733	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
734	C₂	C₂×#552×C₇₃	1	1	yes	characteristic
735	C₂	C₇₃×#3499	1	1	yes	characteristic
736	C₂	C₇₃×#3507	1	1	yes	characteristic
737	C₂	C₇₃×#3520	1	1	yes	characteristic
738	C₂	C₇₃×#3547	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂×#127×C₇₃	C₂²
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×#552×C₇₃	C₂	semidirect
2. C₇₃×#2694	C₂	semidirect
3. C₇₃×#2552	C₂	semidirect
4. C₇₃×#2542	C₂	semidirect
5. C₇₃×#2542	C₂	semidirect
6. C₇₃×#2536	C₂	semidirect
7. C₇₃×#2512	C₂	semidirect
8. C₇₃×#2479	C₂	semidirect
10. C₇₃×#2417	C₂	semidirect
11. C₇₃×#2415	C₂	semidirect
12. C₇₃×#2354	C₂	semidirect
13. C₇₃×#2354	C₂	semidirect
14. D₄×C₄⋊C₄×C₇₃	C₂	semidirect
15. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
17. C₄×#125×C₇₃	C₂	semidirect
96. #125×C₇₃	D₄	semidirect
359. C₄×C₇₃	#552	semidirect
360. #59444	C₇₃	direct (N × H)
370. C₂×#552	C₂×C₇₃	semidirect
371. #2694	C₂×C₇₃	semidirect
372. #2552	C₂×C₇₃	semidirect
373. #2542	C₂×C₇₃	semidirect
374. #2542	C₂×C₇₃	semidirect
375. #2536	C₂×C₇₃	semidirect
376. #2512	C₂×C₇₃	semidirect
377. #2479	C₂×C₇₃	semidirect
379. #2417	C₂×C₇₃	semidirect
380. #2415	C₂×C₇₃	semidirect
381. #2354	C₂×C₇₃	semidirect
382. #2354	C₂×C₇₃	semidirect
383. D₄×C₄⋊C₄	C₂×C₇₃	semidirect
384. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
386. C₄×#125	C₂×C₇₃	semidirect
387. C₇₃	#59444	direct (N × H)
466. #125	D₄×C₇₃	semidirect
729. C₄	#552×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₇₃	2
C₇₃×#2694	2
C₇₃×#2552	2
C₇₃×#2542	2
C₇₃×#2536	2
C₇₃×#2512	2
C₇₃×#2479	2
C₇₃×#2445	2
C₇₃×#2417	2
C₇₃×#2415	2
C₇₃×#2354	2
D₄×C₄⋊C₄×C₇₃	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#127×C₇₃	2
C₄×#125×C₇₃	2
#59444	73

Subgroups — C73×#59444 #32968848

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59444 #32968848