Subgroups — C₇₃×#59836 #32969240

Order 18688.

2464 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2732	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2724	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2679	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2609	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2553	C₂	1	4	yes	maximal, complemented
7	C₇₃×#2536	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2534	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2468	C₂	1	4	yes	maximal, complemented
10	C₇₃×#2418	C₂	1	4	yes	maximal, complemented
11	C₇₃×#2358	C₂	1	4	yes	maximal, complemented
12	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#2293	C₂	1	2	yes	maximal, complemented
14	#551×C₇₃	—	2	16	no	—
15	C₂×#126×C₇₃	C₂²	1	4	yes	complemented
16	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#123×C₇₃	C₂²	1	2	yes	—
18	C₂×#123×C₇₃	C₂²	1	4	yes	—
19	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	complemented
20	C₂×#120×C₇₃	C₂²	1	2	yes	—
21	C₂×#120×C₇₃	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
27	C₂×#117×C₇₃	C₂²	1	4	yes	complemented
28	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	complemented
29	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
30	#399×C₇₃	C₂²	1	4	yes	complemented
31	#398×C₇₃	C₂²	1	2	yes	complemented
32	#398×C₇₃	C₂²	1	4	yes	complemented
33	#398×C₇₃	C₂²	1	2	yes	complemented
34	#397×C₇₃	C₂²	1	4	yes	complemented
35	#396×C₇₃	C₂²	1	4	yes	complemented
36	#394×C₇₃	C₂²	1	4	yes	—
37	#394×C₇₃	C₂²	1	4	yes	—
38	#394×C₇₃	C₂²	1	2	yes	—
39	#394×C₇₃	C₂²	1	2	yes	—
40	#391×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	#390×C₇₃	C₂²	1	1	yes	characteristic
42	#390×C₇₃	C₂²	1	2	yes	—
43	#390×C₇₃	C₂²	1	2	yes	—
44	#389×C₇₃	C₂²	1	2	yes	complemented
45	#389×C₇₃	C₂²	1	2	yes	complemented
46	#388×C₇₃	C₂²	1	4	yes	complemented
47	#388×C₇₃	C₂²	1	4	yes	complemented
48	#388×C₇₃	C₂²	1	4	yes	complemented
49	#388×C₇₃	C₂²	1	4	yes	complemented
50	#388×C₇₃	C₂²	1	4	yes	complemented
51	#387×C₇₃	C₂²	1	4	yes	complemented
52	#386×C₇₃	C₂²	1	4	yes	—
53	#386×C₇₃	C₂²	1	4	yes	—
54	#386×C₇₃	C₂²	1	4	yes	—
55	#385×C₇₃	C₂²	1	4	yes	complemented
56	#385×C₇₃	C₂²	1	4	yes	complemented
57	#385×C₇₃	C₂²	1	4	yes	complemented
58	#382×C₇₃	C₂²	1	2	yes	complemented
59	#382×C₇₃	C₂²	1	1	yes	characteristic, complemented
60	#381×C₇₃	C₂²	1	2	yes	complemented
61	#380×C₇₃	C₂²	1	4	yes	complemented
62	#380×C₇₃	C₂²	1	2	yes	complemented
63	#379×C₇₃	C₂²	1	2	yes	complemented
64	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	complemented
66	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	complemented
67	C₄³×C₇₃	C₂²	1	1	yes	characteristic, complemented
68	C₂⁵×C₇₃	C₂³	1	2	yes	—
69	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
72	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
75	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
78	#126×C₇₃	—	2	16	no	—
79	#124×C₇₃	D₄	1	8	yes	complemented
80	#123×C₇₃	—	2	8	no	—
81	#123×C₇₃	—	2	16	no	—
82	C₂²⋊Q₈×C₇₃	—	2	16	no	—
83	#120×C₇₃	—	2	8	no	—
84	#120×C₇₃	—	2	16	no	—
85	C₄×Q₈×C₇₃	—	4	2	no	—
86	C₄×D₄×C₇₃	—	2	8	no	—
87	C₄×D₄×C₇₃	—	2	16	no	—
88	C₄×D₄×C₇₃	—	4	4	no	—
89	C₄×D₄×C₇₃	—	4	2	no	—
90	#117×C₇₃	—	2	16	no	—
91	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
103	C₂×C₂²⋊C₄×C₇₃	—	2	16	no	—
104	C₂×C₂²⋊C₄×C₇₃	—	4	4	no	—
105	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
120	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
122	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
123	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
125	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
127	#95×C₇₃	C₂³	1	4	yes	—
128	#95×C₇₃	C₂³	1	4	yes	—
129	#95×C₇₃	C₂³	1	4	yes	—
130	#95×C₇₃	C₂³	1	4	yes	—
131	#95×C₇₃	C₂³	1	4	yes	—
132	#95×C₇₃	C₂³	1	4	yes	—
133	#95×C₇₃	C₂³	1	4	yes	—
134	#95×C₇₃	C₂³	1	2	yes	—
135	#95×C₇₃	C₂³	1	2	yes	—
136	C₂⁴×C₇₃	—	2	4	no	—
137	C₂⁴×C₇₃	—	2	8	no	—
138	C₂⁴×C₇₃	—	4	2	no	—
139	C₂⁴×C₇₃	—	4	4	no	—
140	C₂⁴×C₇₃	—	4	2	no	—
141	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
142	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
143	C₂×Q₈×C₇₃	—	4	1	no	—
144	C₂×Q₈×C₇₃	—	4	1	no	—
145	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
146	C₂×D₄×C₇₃	—	2	8	no	—
147	C₂×D₄×C₇₃	—	2	8	no	—
148	C₂×D₄×C₇₃	—	2	8	no	—
149	C₂×D₄×C₇₃	—	4	1	no	—
150	C₂×D₄×C₇₃	—	4	2	no	—
151	C₂×D₄×C₇₃	—	4	2	no	—
152	C₂×D₄×C₇₃	—	4	2	no	—
153	C₂×D₄×C₇₃	—	4	1	no	—
154	C₂×D₄×C₇₃	—	4	4	no	—
155	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
156	C₂×D₄×C₇₃	#41	1	8	yes	—
157	C₂²×C₄×C₇₃	—	2	8	no	—
158	C₂²×C₄×C₇₃	—	2	4	no	—
159	C₂²×C₄×C₇₃	—	2	8	no	—
160	C₂²×C₄×C₇₃	—	2	8	no	—
161	C₂²×C₄×C₇₃	—	2	4	no	—
162	C₂²×C₄×C₇₃	—	4	4	no	—
163	C₂²×C₄×C₇₃	—	4	2	no	—
164	C₂²×C₄×C₇₃	—	4	4	no	—
165	C₂²×C₄×C₇₃	—	4	4	no	—
166	C₂²×C₄×C₇₃	—	4	4	no	—
167	C₂²×C₄×C₇₃	—	4	2	no	—
168	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
179	C₄⋊C₄×C₇₃	—	2	8	no	—
180	C₄⋊C₄×C₇₃	—	2	8	no	—
181	C₄⋊C₄×C₇₃	—	2	8	no	—
182	C₄⋊C₄×C₇₃	—	2	8	no	—
183	C₄⋊C₄×C₇₃	—	2	4	no	—
184	C₄⋊C₄×C₇₃	—	4	2	no	—
185	C₄⋊C₄×C₇₃	—	4	2	no	—
186	C₄⋊C₄×C₇₃	—	4	4	no	—
187	C₄⋊C₄×C₇₃	—	4	1	no	—
188	C₄⋊C₄×C₇₃	—	4	2	no	—
189	C₄⋊C₄×C₇₃	—	4	1	no	—
190	C₄⋊C₄×C₇₃	—	4	2	no	—
191	C₂²⋊C₄×C₇₃	—	2	8	no	—
192	C₂²⋊C₄×C₇₃	—	2	4	no	—
193	C₂²⋊C₄×C₇₃	—	2	4	no	—
194	C₂²⋊C₄×C₇₃	—	2	8	no	—
195	C₂²⋊C₄×C₇₃	—	2	8	no	—
196	C₂²⋊C₄×C₇₃	—	2	8	no	—
197	C₂²⋊C₄×C₇₃	—	2	8	no	—
198	C₂²⋊C₄×C₇₃	—	2	8	no	—
199	C₂²⋊C₄×C₇₃	—	2	8	no	—
200	C₂²⋊C₄×C₇₃	—	2	8	no	—
201	C₂²⋊C₄×C₇₃	—	2	8	no	—
202	C₂²⋊C₄×C₇₃	—	4	4	no	—
203	C₂²⋊C₄×C₇₃	—	4	4	no	—
204	C₂²⋊C₄×C₇₃	—	4	2	no	—
205	C₂²⋊C₄×C₇₃	C₂×D₄	1	16	yes	—
206	C₄²×C₇₃	—	2	8	no	—
207	C₄²×C₇₃	—	2	4	no	—
208	C₄²×C₇₃	—	2	2	no	—
209	C₄²×C₇₃	—	2	4	no	—
210	C₄²×C₇₃	—	4	1	no	—
211	C₄²×C₇₃	—	4	2	no	—
212	C₄²×C₇₃	C₂×D₄	1	4	yes	—
213	C₂³×C₇₃	—	2	4	no	—
214	C₂³×C₇₃	—	2	4	no	—
215	C₂³×C₇₃	—	2	4	no	—
216	C₂³×C₇₃	—	2	4	no	—
217	C₂³×C₇₃	—	2	2	no	—
218	C₂³×C₇₃	—	2	4	no	—
219	C₂³×C₇₃	—	2	4	no	—
220	C₂³×C₇₃	—	2	4	no	—
221	C₂³×C₇₃	—	2	4	no	—
222	C₂³×C₇₃	—	2	2	no	—
223	C₂³×C₇₃	—	4	16	no	—
224	C₂³×C₇₃	—	4	8	no	—
225	C₂³×C₇₃	—	8	8	no	—
226	C₂³×C₇₃	—	8	4	no	—
227	C₂³×C₇₃	—	8	4	no	—
228	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
229	C₂³×C₇₃	C₂×#41	1	8	yes	—
230	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
231	Q₈×C₇₃	—	4	4	no	—
232	D₄×C₇₃	—	4	4	no	—
233	D₄×C₇₃	—	4	8	no	—
234	D₄×C₇₃	—	4	16	no	—
235	D₄×C₇₃	—	4	8	no	—
236	C₂×C₄×C₇₃	—	2	2	no	—
237	C₂×C₄×C₇₃	—	2	1	no	—
238	C₂×C₄×C₇₃	—	2	2	no	—
239	C₂×C₄×C₇₃	—	2	2	no	—
240	C₂×C₄×C₇₃	—	2	2	no	—
241	C₂×C₄×C₇₃	—	2	2	no	—
242	C₂×C₄×C₇₃	—	2	2	no	—
243	C₂×C₄×C₇₃	—	2	1	no	—
244	C₂×C₄×C₇₃	—	2	2	no	—
245	C₂×C₄×C₇₃	—	2	4	no	—
246	C₂×C₄×C₇₃	—	2	4	no	—
247	C₂×C₄×C₇₃	—	2	4	no	—
248	C₂×C₄×C₇₃	—	2	2	no	—
249	C₂×C₄×C₇₃	—	2	4	no	—
250	C₂×C₄×C₇₃	—	2	4	no	—
251	C₂×C₄×C₇₃	—	2	4	no	—
252	C₂×C₄×C₇₃	—	2	1	no	—
253	C₂×C₄×C₇₃	—	2	2	no	—
254	C₂×C₄×C₇₃	—	2	4	no	—
255	C₂×C₄×C₇₃	—	2	2	no	—
256	C₂×C₄×C₇₃	—	2	4	no	—
257	C₂×C₄×C₇₃	—	2	4	no	—
258	C₂×C₄×C₇₃	—	2	4	no	—
259	C₂×C₄×C₇₃	—	2	4	no	—
260	C₂×C₄×C₇₃	—	4	16	no	—
261	C₂×C₄×C₇₃	—	8	8	no	—
262	C₂×C₄×C₇₃	—	8	4	no	—
263	C₂×C₄×C₇₃	—	8	4	no	—
264	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
265	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
267	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
268	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
269	C₂²×C₇₃	—	2	8	no	—
270	C₂²×C₇₃	—	2	8	no	—
271	C₂²×C₇₃	—	2	8	no	—
272	C₂²×C₇₃	—	2	8	no	—
273	C₂²×C₇₃	—	2	4	no	—
274	C₂²×C₇₃	—	4	4	no	—
275	C₂²×C₇₃	—	4	2	no	—
276	C₂²×C₇₃	—	4	4	no	—
277	C₂²×C₇₃	—	4	4	no	—
278	C₂²×C₇₃	—	4	4	no	—
279	C₂²×C₇₃	—	4	2	no	—
280	C₂²×C₇₃	—	4	4	no	—
281	C₂²×C₇₃	—	8	16	no	—
282	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
283	C₂²×C₇₃	C₂²×#41	1	2	yes	—
284	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
285	C₂²×C₇₃	#585	1	2	yes	—
286	C₂²×C₇₃	#585	1	1	yes	characteristic
287	C₄×C₇₃	—	2	4	no	—
288	C₄×C₇₃	—	2	4	no	—
289	C₄×C₇₃	—	2	4	no	—
290	C₄×C₇₃	—	2	2	no	—
291	C₄×C₇₃	—	2	2	no	—
292	C₄×C₇₃	—	4	4	no	—
293	C₄×C₇₃	—	4	4	no	—
294	C₄×C₇₃	—	4	1	no	—
295	C₄×C₇₃	—	4	2	no	—
296	C₄×C₇₃	—	4	4	no	—
297	C₄×C₇₃	—	4	2	no	—
298	#59836	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₂×C₇₃	—	4	8	no	—
300	C₂×C₇₃	—	4	4	no	—
301	C₂×C₇₃	D₄×#41	1	2	yes	—
302	C₂×C₇₃	#3481	1	1	yes	characteristic
303	C₂×C₇₃	#3491	1	2	yes	—
304	C₂×C₇₃	#3496	1	1	yes	characteristic
305	C₂×C₇₃	#3545	1	1	yes	characteristic
306	C₂×#551	C₂×C₇₃	1	2	yes	complemented
307	#2732	C₂×C₇₃	1	2	yes	complemented
308	#2724	C₂×C₇₃	1	1	yes	characteristic, complemented
309	#2679	C₂×C₇₃	1	1	yes	characteristic
310	#2609	C₂×C₇₃	1	2	yes	complemented
311	#2553	C₂×C₇₃	1	4	yes	complemented
312	#2536	C₂×C₇₃	1	2	yes	complemented
313	#2534	C₂×C₇₃	1	2	yes	complemented
314	#2468	C₂×C₇₃	1	4	yes	complemented
315	#2418	C₂×C₇₃	1	4	yes	complemented
316	#2358	C₂×C₇₃	1	4	yes	complemented
317	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
318	#2293	C₂×C₇₃	1	2	yes	complemented
319	C₇₃	#59836	1	1	yes	characteristic, direct product factor, Sylow
320	#551	—	2	16	no	—
321	C₂×#126	C₂²×C₇₃	1	4	yes	complemented
322	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
323	C₂×#123	C₂²×C₇₃	1	4	yes	—
324	C₂×#123	C₂²×C₇₃	1	2	yes	—
325	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	complemented
326	C₂×#120	C₂²×C₇₃	1	4	yes	—
327	C₂×#120	C₂²×C₇₃	1	2	yes	—
328	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
329	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
330	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
331	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
332	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
333	C₂×#117	C₂²×C₇₃	1	4	yes	complemented
334	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	complemented
335	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
336	#399	C₂²×C₇₃	1	4	yes	complemented
337	#398	C₂²×C₇₃	1	2	yes	complemented
338	#398	C₂²×C₇₃	1	2	yes	complemented
339	#398	C₂²×C₇₃	1	4	yes	complemented
340	#397	C₂²×C₇₃	1	4	yes	complemented
341	#396	C₂²×C₇₃	1	4	yes	complemented
342	#394	C₂²×C₇₃	1	2	yes	—
343	#394	C₂²×C₇₃	1	2	yes	—
344	#394	C₂²×C₇₃	1	4	yes	—
345	#394	C₂²×C₇₃	1	4	yes	—
346	#391	C₂²×C₇₃	1	1	yes	characteristic, complemented
347	#390	C₂²×C₇₃	1	2	yes	—
348	#390	C₂²×C₇₃	1	1	yes	characteristic
349	#390	C₂²×C₇₃	1	2	yes	—
350	#389	C₂²×C₇₃	1	2	yes	complemented
351	#389	C₂²×C₇₃	1	2	yes	complemented
352	#388	C₂²×C₇₃	1	4	yes	complemented
353	#388	C₂²×C₇₃	1	4	yes	complemented
354	#388	C₂²×C₇₃	1	4	yes	complemented
355	#388	C₂²×C₇₃	1	4	yes	complemented
356	#388	C₂²×C₇₃	1	4	yes	complemented
357	#387	C₂²×C₇₃	1	4	yes	complemented
358	#386	C₂²×C₇₃	1	4	yes	—
359	#386	C₂²×C₇₃	1	4	yes	—
360	#386	C₂²×C₇₃	1	4	yes	—
361	#385	C₂²×C₇₃	1	4	yes	complemented
362	#385	C₂²×C₇₃	1	4	yes	complemented
363	#385	C₂²×C₇₃	1	4	yes	complemented
364	#382	C₂²×C₇₃	1	1	yes	characteristic, complemented
365	#382	C₂²×C₇₃	1	2	yes	complemented
366	#381	C₂²×C₇₃	1	2	yes	complemented
367	#380	C₂²×C₇₃	1	4	yes	complemented
368	#380	C₂²×C₇₃	1	2	yes	complemented
369	#379	C₂²×C₇₃	1	2	yes	complemented
370	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	complemented
371	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	complemented
372	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	complemented
373	C₄³	C₂²×C₇₃	1	1	yes	characteristic, complemented
374	C₂⁵	C₂³×C₇₃	1	2	yes	—
375	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
376	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
377	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
378	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
379	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
380	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
381	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
382	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
383	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
384	#126	—	2	16	no	—
385	#124	D₄×C₇₃	1	8	yes	complemented
386	#123	—	2	8	no	—
387	#123	—	2	16	no	—
388	C₂²⋊Q₈	—	2	16	no	—
389	#120	—	2	8	no	—
390	#120	—	2	16	no	—
391	C₄×Q₈	—	4	2	no	—
392	C₄×D₄	—	2	8	no	—
393	C₄×D₄	—	2	16	no	—
394	C₄×D₄	—	4	4	no	—
395	C₄×D₄	—	4	2	no	—
396	#117	—	2	16	no	—
397	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
398	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
399	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
409	C₂×C₂²⋊C₄	—	2	16	no	—
410	C₂×C₂²⋊C₄	—	4	4	no	—
411	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
426	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
427	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
429	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
430	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
431	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
433	#95	C₂³×C₇₃	1	4	yes	—
434	#95	C₂³×C₇₃	1	4	yes	—
435	#95	C₂³×C₇₃	1	4	yes	—
436	#95	C₂³×C₇₃	1	4	yes	—
437	#95	C₂³×C₇₃	1	4	yes	—
438	#95	C₂³×C₇₃	1	4	yes	—
439	#95	C₂³×C₇₃	1	4	yes	—
440	#95	C₂³×C₇₃	1	2	yes	—
441	#95	C₂³×C₇₃	1	2	yes	—
442	C₂⁴	—	2	4	no	—
443	C₂⁴	—	2	8	no	—
444	C₂⁴	—	4	2	no	—
445	C₂⁴	—	4	4	no	—
446	C₂⁴	—	4	2	no	—
447	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
448	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
449	C₂×Q₈	—	4	1	no	—
450	C₂×Q₈	—	4	1	no	—
451	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	2	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
462	C₂×D₄	#41×C₇₃	1	8	yes	—
463	C₂²×C₄	—	2	8	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	8	no	—
466	C₂²×C₄	—	2	8	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	4	4	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	4	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
479	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
481	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
482	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
485	C₄⋊C₄	—	2	8	no	—
486	C₄⋊C₄	—	2	8	no	—
487	C₄⋊C₄	—	2	8	no	—
488	C₄⋊C₄	—	2	8	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	4	4	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	2	8	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	8	no	—
501	C₂²⋊C₄	—	2	8	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	2	8	no	—
505	C₂²⋊C₄	—	2	8	no	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	4	4	no	—
509	C₂²⋊C₄	—	4	4	no	—
510	C₂²⋊C₄	—	4	2	no	—
511	C₂²⋊C₄	C₂×D₄×C₇₃	1	16	yes	—
512	C₄²	—	2	8	no	—
513	C₄²	—	2	4	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	4	no	—
516	C₄²	—	4	1	no	—
517	C₄²	—	4	2	no	—
518	C₄²	C₂×D₄×C₇₃	1	4	yes	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	4	16	no	—
530	C₂³	—	4	8	no	—
531	C₂³	—	8	8	no	—
532	C₂³	—	8	4	no	—
533	C₂³	—	8	4	no	—
534	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
535	C₂³	C₂×#41×C₇₃	1	8	yes	—
536	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
537	Q₈	—	4	4	no	—
538	D₄	—	4	4	no	—
539	D₄	—	4	8	no	—
540	D₄	—	4	16	no	—
541	D₄	—	4	8	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	4	16	no	—
567	C₂×C₄	—	8	8	no	—
568	C₂×C₄	—	8	4	no	—
569	C₂×C₄	—	8	4	no	—
570	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
571	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
572	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
573	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
574	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	8	no	—
578	C₂²	—	2	8	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	8	16	no	—
588	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
589	C₂²	C₂²×#41×C₇₃	1	2	yes	—
590	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
591	C₂²	#585×C₇₃	1	2	yes	—
592	C₂²	#585×C₇₃	1	1	yes	characteristic
593	C₄	—	2	4	no	—
594	C₄	—	2	4	no	—
595	C₄	—	2	4	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	4	4	no	—
599	C₄	—	4	4	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	4	no	—
603	C₄	—	4	2	no	—
604	C₂	—	4	8	no	—
605	C₂	—	4	4	no	—
606	C₂	D₄×#41×C₇₃	1	2	yes	—
607	C₂	C₇₃×#3481	1	1	yes	characteristic
608	C₂	C₇₃×#3491	1	2	yes	—
609	C₂	C₇₃×#3496	1	1	yes	characteristic
610	C₂	C₇₃×#3545	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₇₃×#2679	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×#551×C₇₃	C₂	semidirect
2. C₇₃×#2732	C₂	semidirect
3. C₇₃×#2724	C₂	semidirect
5. C₇₃×#2609	C₂	semidirect
6. C₇₃×#2553	C₂	semidirect
7. C₇₃×#2536	C₂	semidirect
8. C₇₃×#2534	C₂	semidirect
9. C₇₃×#2468	C₂	semidirect
10. C₇₃×#2418	C₂	semidirect
11. C₇₃×#2358	C₂	semidirect
12. C₄×#124×C₇₃	C₂	semidirect
13. C₇₃×#2293	C₂	semidirect
15. C₂×#126×C₇₃	C₂²	semidirect
19. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
22. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
27. C₂×#117×C₇₃	C₂²	semidirect
28. C₂²×C₂²⋊C₄×C₇₃	C₂²	semidirect
29. C₂²×C₂²⋊C₄×C₇₃	C₂²	semidirect
30. #399×C₇₃	C₂²	semidirect
31. #398×C₇₃	C₂²	semidirect
32. #398×C₇₃	C₂²	semidirect
33. #398×C₇₃	C₂²	semidirect
34. #397×C₇₃	C₂²	semidirect
35. #396×C₇₃	C₂²	semidirect
40. #391×C₇₃	C₂²	semidirect
44. #389×C₇₃	C₂²	semidirect
45. #389×C₇₃	C₂²	semidirect
46. #388×C₇₃	C₂²	semidirect
47. #388×C₇₃	C₂²	semidirect
48. #388×C₇₃	C₂²	semidirect
49. #388×C₇₃	C₂²	semidirect
50. #388×C₇₃	C₂²	semidirect
51. #387×C₇₃	C₂²	semidirect
55. #385×C₇₃	C₂²	semidirect
56. #385×C₇₃	C₂²	semidirect
57. #385×C₇₃	C₂²	semidirect
58. #382×C₇₃	C₂²	semidirect
59. #382×C₇₃	C₂²	semidirect
60. #381×C₇₃	C₂²	semidirect
61. #380×C₇₃	C₂²	semidirect
62. #380×C₇₃	C₂²	semidirect
63. #379×C₇₃	C₂²	semidirect
64. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
65. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
66. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
67. C₄³×C₇₃	C₂²	semidirect
79. #124×C₇₃	D₄	semidirect
298. #59836	C₇₃	direct (N × H)
306. C₂×#551	C₂×C₇₃	semidirect
307. #2732	C₂×C₇₃	semidirect
308. #2724	C₂×C₇₃	semidirect
310. #2609	C₂×C₇₃	semidirect
311. #2553	C₂×C₇₃	semidirect
312. #2536	C₂×C₇₃	semidirect
313. #2534	C₂×C₇₃	semidirect
314. #2468	C₂×C₇₃	semidirect
315. #2418	C₂×C₇₃	semidirect
316. #2358	C₂×C₇₃	semidirect
317. C₄×#124	C₂×C₇₃	semidirect
318. #2293	C₂×C₇₃	semidirect
319. C₇₃	#59836	direct (N × H)
321. C₂×#126	C₂²×C₇₃	semidirect
325. C₂×C₂²⋊Q₈	C₂²×C₇₃	semidirect
328. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
333. C₂×#117	C₂²×C₇₃	semidirect
334. C₂²×C₂²⋊C₄	C₂²×C₇₃	semidirect
335. C₂²×C₂²⋊C₄	C₂²×C₇₃	semidirect
336. #399	C₂²×C₇₃	semidirect
337. #398	C₂²×C₇₃	semidirect
338. #398	C₂²×C₇₃	semidirect
339. #398	C₂²×C₇₃	semidirect
340. #397	C₂²×C₇₃	semidirect
341. #396	C₂²×C₇₃	semidirect
346. #391	C₂²×C₇₃	semidirect
350. #389	C₂²×C₇₃	semidirect
351. #389	C₂²×C₇₃	semidirect
352. #388	C₂²×C₇₃	semidirect
353. #388	C₂²×C₇₃	semidirect
354. #388	C₂²×C₇₃	semidirect
355. #388	C₂²×C₇₃	semidirect
356. #388	C₂²×C₇₃	semidirect
357. #387	C₂²×C₇₃	semidirect
361. #385	C₂²×C₇₃	semidirect
362. #385	C₂²×C₇₃	semidirect
363. #385	C₂²×C₇₃	semidirect
364. #382	C₂²×C₇₃	semidirect
365. #382	C₂²×C₇₃	semidirect
366. #381	C₂²×C₇₃	semidirect
367. #380	C₂²×C₇₃	semidirect
368. #380	C₂²×C₇₃	semidirect
369. #379	C₂²×C₇₃	semidirect
370. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
371. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
372. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
373. C₄³	C₂²×C₇₃	semidirect
385. #124	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×#551×C₇₃	2
C₇₃×#2732	2
C₇₃×#2724	2
C₇₃×#2679	2
C₇₃×#2609	2
C₇₃×#2553	2
C₇₃×#2536	2
C₇₃×#2534	2
C₇₃×#2468	2
C₇₃×#2418	2
C₇₃×#2358	2
C₄×#124×C₇₃	2
C₇₃×#2293	2
#59836	73

Subgroups — C73×#59836 #32969240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59836 #32969240