Subgroups — C₇₃×#59815 #32969219

Order 18688.

3292 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₂×#547×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2682	C₂	1	4	yes	maximal, complemented
4	C₇₃×#2541	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2538	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2537	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2445	C₂	1	4	yes	maximal, complemented
8	C₇₃×#2416	C₂	1	4	yes	maximal, complemented
9	C₇₃×#2407	C₂	1	4	yes	maximal, complemented
10	D₄×C₄⋊C₄×C₇₃	C₂	1	2	yes	maximal, complemented
11	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₇₃	C₂²	1	4	yes	—
15	#550×C₇₃	—	2	16	no	—
16	#547×C₇₃	—	2	16	no	—
17	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#127×C₇₃	C₂²	1	4	yes	—
19	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#123×C₇₃	C₂²	1	8	yes	—
22	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	—
23	C₂×#121×C₇₃	C₂²	1	4	yes	—
24	C₂×#121×C₇₃	C₂²	1	4	yes	—
25	C₂×#121×C₇₃	C₂²	1	8	yes	—
26	C₂×#121×C₇₃	C₂²	1	4	yes	—
27	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₇₃	C₂²	1	4	yes	—
36	#396×C₇₃	C₂²	1	8	yes	—
37	#394×C₇₃	C₂²	1	8	yes	—
38	#394×C₇₃	C₂²	1	8	yes	—
39	#392×C₇₃	C₂²	1	8	yes	—
40	#391×C₇₃	C₂²	1	2	yes	—
41	#390×C₇₃	C₂²	1	2	yes	—
42	#390×C₇₃	C₂²	1	2	yes	—
43	#390×C₇₃	C₂²	1	4	yes	—
44	#390×C₇₃	C₂²	1	2	yes	—
45	#390×C₇₃	C₂²	1	2	yes	—
46	#390×C₇₃	C₂²	1	2	yes	—
47	#390×C₇₃	C₂²	1	2	yes	—
48	#389×C₇₃	C₂²	1	4	yes	—
49	#389×C₇₃	C₂²	1	2	yes	—
50	#389×C₇₃	C₂²	1	2	yes	—
51	#386×C₇₃	C₂²	1	8	yes	—
52	#385×C₇₃	C₂²	1	8	yes	—
53	#384×C₇₃	C₂²	1	1	yes	characteristic
54	#384×C₇₃	C₂²	1	1	yes	characteristic
55	#384×C₇₃	C₂²	1	1	yes	characteristic
56	#380×C₇₃	C₂²	1	4	yes	—
57	#380×C₇₃	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
60	C₄³×C₇₃	C₂²	1	1	yes	characteristic
61	C₂×#41×C₇₃	—	2	16	no	—
62	C₂×#41×C₇₃	—	2	16	no	—
63	C₂×#41×C₇₃	—	4	8	no	—
64	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
66	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
67	C₂²×D₄×C₇₃	C₂³	1	8	yes	—
68	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
70	C₂²×D₄×C₇₃	C₂³	1	8	yes	—
71	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
75	C₂³×C₄×C₇₃	C₂³	1	8	yes	—
76	C₄⋊Q₈×C₇₃	D₄	1	8	yes	complemented
77	#127×C₇₃	—	2	16	no	—
78	#127×C₇₃	—	2	4	no	—
79	#127×C₇₃	D₄	1	8	yes	complemented
80	#123×C₇₃	—	2	32	no	—
81	C₂²⋊Q₈×C₇₃	—	2	16	no	—
82	#121×C₇₃	—	2	16	no	—
83	#121×C₇₃	—	2	32	no	—
84	#121×C₇₃	—	2	16	no	—
85	#121×C₇₃	—	4	8	no	—
86	C₄×Q₈×C₇₃	—	2	8	no	—
87	C₄×D₄×C₇₃	—	2	16	no	—
88	C₄×D₄×C₇₃	—	2	8	no	—
89	C₄×D₄×C₇₃	—	2	8	no	—
90	C₄×D₄×C₇₃	—	2	8	no	—
91	C₄×D₄×C₇₃	—	2	8	no	—
92	C₄×D₄×C₇₃	—	4	4	no	—
93	C₄×D₄×C₇₃	—	4	4	no	—
94	C₂×C₄⋊C₄×C₇₃	—	2	16	no	—
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	2	yes	—
100	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₇₃	C₂³	1	8	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	8	yes	—
115	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
117	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
118	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
125	#95×C₇₃	C₂³	1	4	yes	—
126	#95×C₇₃	C₂³	1	4	yes	—
127	#95×C₇₃	C₂³	1	8	yes	—
128	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
129	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
130	#41×C₇₃	—	4	64	no	—
131	C₂×Q₈×C₇₃	—	2	4	no	—
132	C₂×Q₈×C₇₃	—	2	4	no	—
133	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
134	C₂×D₄×C₇₃	—	2	16	no	—
135	C₂×D₄×C₇₃	—	2	16	no	—
136	C₂×D₄×C₇₃	—	2	4	no	—
137	C₂×D₄×C₇₃	—	2	4	no	—
138	C₂×D₄×C₇₃	—	2	4	no	—
139	C₂×D₄×C₇₃	—	2	16	no	—
140	C₂×D₄×C₇₃	—	2	4	no	—
141	C₂×D₄×C₇₃	—	2	4	no	—
142	C₂×D₄×C₇₃	—	2	4	no	—
143	C₂×D₄×C₇₃	—	2	4	no	—
144	C₂×D₄×C₇₃	—	2	4	no	—
145	C₂×D₄×C₇₃	—	2	4	no	—
146	C₂×D₄×C₇₃	—	2	4	no	—
147	C₂×D₄×C₇₃	—	2	4	no	—
148	C₂×D₄×C₇₃	—	4	2	no	—
149	C₂×D₄×C₇₃	—	4	2	no	—
150	C₂×D₄×C₇₃	—	4	2	no	—
151	C₂×D₄×C₇₃	—	4	2	no	—
152	C₂×D₄×C₇₃	—	4	8	no	—
153	C₂×D₄×C₇₃	—	4	8	no	—
154	C₂×D₄×C₇₃	—	4	8	no	—
155	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
156	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
157	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
158	C₂²×C₄×C₇₃	—	2	16	no	—
159	C₂²×C₄×C₇₃	—	2	8	no	—
160	C₂²×C₄×C₇₃	—	2	16	no	—
161	C₂²×C₄×C₇₃	—	2	8	no	—
162	C₂²×C₄×C₇₃	—	2	8	no	—
163	C₂²×C₄×C₇₃	—	2	8	no	—
164	C₂²×C₄×C₇₃	—	2	8	no	—
165	C₂²×C₄×C₇₃	—	2	8	no	—
166	C₂²×C₄×C₇₃	—	4	8	no	—
167	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
178	C₄⋊C₄×C₇₃	—	2	4	no	—
179	C₄⋊C₄×C₇₃	—	2	16	no	—
180	C₄⋊C₄×C₇₃	—	2	4	no	—
181	C₄⋊C₄×C₇₃	—	2	4	no	—
182	C₄⋊C₄×C₇₃	—	2	8	no	—
183	C₄⋊C₄×C₇₃	—	2	4	no	—
184	C₄⋊C₄×C₇₃	—	2	4	no	—
185	C₄⋊C₄×C₇₃	—	2	4	no	—
186	C₄⋊C₄×C₇₃	—	4	2	no	—
187	C₄⋊C₄×C₇₃	—	4	2	no	—
188	C₄⋊C₄×C₇₃	—	4	2	no	—
189	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
190	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
191	C₂²⋊C₄×C₇₃	—	2	16	no	—
192	C₂²⋊C₄×C₇₃	—	2	8	no	—
193	C₂²⋊C₄×C₇₃	—	2	8	no	—
194	C₂²⋊C₄×C₇₃	—	2	8	no	—
195	C₂²⋊C₄×C₇₃	—	2	16	no	—
196	C₂²⋊C₄×C₇₃	—	2	8	no	—
197	C₂²⋊C₄×C₇₃	—	4	4	no	—
198	C₂²⋊C₄×C₇₃	—	4	4	no	—
199	C₂²⋊C₄×C₇₃	—	4	8	no	—
200	C₄²×C₇₃	—	2	8	no	—
201	C₄²×C₇₃	—	2	2	no	—
202	C₄²×C₇₃	—	2	2	no	—
203	C₄²×C₇₃	—	2	2	no	—
204	C₄²×C₇₃	—	4	1	no	—
205	C₄²×C₇₃	C₂×D₄	1	4	yes	—
206	C₄²×C₇₃	C₂×D₄	1	4	yes	—
207	C₄²×C₇₃	#41	1	4	yes	complemented
208	C₂³×C₇₃	—	2	4	no	—
209	C₂³×C₇₃	—	2	4	no	—
210	C₂³×C₇₃	—	2	4	no	—
211	C₂³×C₇₃	—	2	4	no	—
212	C₂³×C₇₃	—	2	4	no	—
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	4	no	—
218	C₂³×C₇₃	—	2	4	no	—
219	C₂³×C₇₃	—	2	4	no	—
220	C₂³×C₇₃	—	2	4	no	—
221	C₂³×C₇₃	C₂²×D₄	1	8	yes	—
222	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
223	Q₈×C₇₃	—	2	16	no	—
224	D₄×C₇₃	—	2	16	no	—
225	D₄×C₇₃	—	2	16	no	—
226	D₄×C₇₃	—	4	8	no	—
227	D₄×C₇₃	—	4	32	no	—
228	D₄×C₇₃	—	4	8	no	—
229	D₄×C₇₃	—	4	8	no	—
230	D₄×C₇₃	—	4	8	no	—
231	D₄×C₇₃	—	8	16	no	—
232	C₂×C₄×C₇₃	—	2	4	no	—
233	C₂×C₄×C₇₃	—	2	1	no	—
234	C₂×C₄×C₇₃	—	2	1	no	—
235	C₂×C₄×C₇₃	—	2	4	no	—
236	C₂×C₄×C₇₃	—	2	1	no	—
237	C₂×C₄×C₇₃	—	2	1	no	—
238	C₂×C₄×C₇₃	—	2	1	no	—
239	C₂×C₄×C₇₃	—	2	1	no	—
240	C₂×C₄×C₇₃	—	2	4	no	—
241	C₂×C₄×C₇₃	—	2	4	no	—
242	C₂×C₄×C₇₃	—	2	4	no	—
243	C₂×C₄×C₇₃	—	2	4	no	—
244	C₂×C₄×C₇₃	—	2	4	no	—
245	C₂×C₄×C₇₃	—	2	1	no	—
246	C₂×C₄×C₇₃	—	2	1	no	—
247	C₂×C₄×C₇₃	—	2	4	no	—
248	C₂×C₄×C₇₃	—	2	4	no	—
249	C₂×C₄×C₇₃	—	2	4	no	—
250	C₂×C₄×C₇₃	—	2	1	no	—
251	C₂×C₄×C₇₃	—	2	4	no	—
252	C₂×C₄×C₇₃	—	4	32	no	—
253	C₂×C₄×C₇₃	—	4	16	no	—
254	C₂×C₄×C₇₃	—	4	16	no	—
255	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₇₃	C₂²×D₄	1	8	yes	—
258	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
263	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
264	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
265	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
266	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
267	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
268	C₂²×C₇₃	—	2	8	no	—
269	C₂²×C₇₃	—	2	8	no	—
270	C₂²×C₇₃	—	2	8	no	—
271	C₂²×C₇₃	—	4	4	no	—
272	C₂²×C₇₃	—	4	4	no	—
273	C₂²×C₇₃	—	4	4	no	—
274	C₂²×C₇₃	—	4	4	no	—
275	C₂²×C₇₃	—	4	4	no	—
276	C₂²×C₇₃	—	4	4	no	—
277	C₂²×C₇₃	—	4	4	no	—
278	C₂²×C₇₃	—	4	4	no	—
279	C₂²×C₇₃	—	4	4	no	—
280	C₂²×C₇₃	—	4	4	no	—
281	C₂²×C₇₃	—	4	4	no	—
282	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
283	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
284	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
285	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
286	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
287	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
288	C₂²×C₇₃	#585	1	1	yes	characteristic
289	C₄×C₇₃	—	2	8	no	—
290	C₄×C₇₃	—	2	2	no	—
291	C₄×C₇₃	—	2	2	no	—
292	C₄×C₇₃	—	2	2	no	—
293	C₄×C₇₃	—	4	4	no	—
294	C₄×C₇₃	—	4	4	no	—
295	C₄×C₇₃	—	4	4	no	—
296	C₄×C₇₃	—	4	1	no	—
297	C₄×C₇₃	D₄²	1	4	yes	—
298	C₄×C₇₃	#547	1	4	yes	complemented
299	C₄×C₇₃	#550	1	4	yes	complemented
300	#59815	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
301	C₂×C₇₃	—	4	8	no	—
302	C₂×C₇₃	—	8	4	no	—
303	C₂×C₇₃	C₂×D₄²	1	1	yes	characteristic
304	C₂×C₇₃	C₂×#547	1	1	yes	characteristic
305	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
306	C₂×C₇₃	#3496	1	1	yes	characteristic
307	C₂×C₇₃	#3497	1	1	yes	characteristic
308	C₂×C₇₃	#3506	1	1	yes	characteristic
309	C₂×C₇₃	#3548	1	1	yes	characteristic
310	C₂×#550	C₂×C₇₃	1	2	yes	complemented
311	C₂×#547	C₂×C₇₃	1	2	yes	complemented
312	#2682	C₂×C₇₃	1	4	yes	complemented
313	#2541	C₂×C₇₃	1	2	yes	complemented
314	#2538	C₂×C₇₃	1	2	yes	complemented
315	#2537	C₂×C₇₃	1	2	yes	complemented
316	#2445	C₂×C₇₃	1	4	yes	complemented
317	#2416	C₂×C₇₃	1	4	yes	complemented
318	#2407	C₂×C₇₃	1	4	yes	complemented
319	D₄×C₄⋊C₄	C₂×C₇₃	1	2	yes	complemented
320	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
321	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
322	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
323	C₇₃	#59815	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²×#41	C₂²×C₇₃	1	4	yes	—
325	#550	—	2	16	no	—
326	#547	—	2	16	no	—
327	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
328	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
329	C₂×#127	C₂²×C₇₃	1	4	yes	—
330	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
331	C₂×#123	C₂²×C₇₃	1	8	yes	—
332	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	—
333	C₂×#121	C₂²×C₇₃	1	4	yes	—
334	C₂×#121	C₂²×C₇₃	1	8	yes	—
335	C₂×#121	C₂²×C₇₃	1	4	yes	—
336	C₂×#121	C₂²×C₇₃	1	4	yes	—
337	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
338	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
339	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
340	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
341	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
342	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
343	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
344	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
345	C₂²×C₄⋊C₄	C₂²×C₇₃	1	4	yes	—
346	#396	C₂²×C₇₃	1	8	yes	—
347	#394	C₂²×C₇₃	1	8	yes	—
348	#394	C₂²×C₇₃	1	8	yes	—
349	#392	C₂²×C₇₃	1	8	yes	—
350	#391	C₂²×C₇₃	1	2	yes	—
351	#390	C₂²×C₇₃	1	2	yes	—
352	#390	C₂²×C₇₃	1	2	yes	—
353	#390	C₂²×C₇₃	1	2	yes	—
354	#390	C₂²×C₇₃	1	2	yes	—
355	#390	C₂²×C₇₃	1	2	yes	—
356	#390	C₂²×C₇₃	1	2	yes	—
357	#390	C₂²×C₇₃	1	4	yes	—
358	#389	C₂²×C₇₃	1	2	yes	—
359	#389	C₂²×C₇₃	1	2	yes	—
360	#389	C₂²×C₇₃	1	4	yes	—
361	#386	C₂²×C₇₃	1	8	yes	—
362	#385	C₂²×C₇₃	1	8	yes	—
363	#384	C₂²×C₇₃	1	1	yes	characteristic
364	#384	C₂²×C₇₃	1	1	yes	characteristic
365	#384	C₂²×C₇₃	1	1	yes	characteristic
366	#380	C₂²×C₇₃	1	4	yes	—
367	#380	C₂²×C₇₃	1	4	yes	—
368	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
369	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
370	C₄³	C₂²×C₇₃	1	1	yes	characteristic
371	C₂×#41	—	2	16	no	—
372	C₂×#41	—	2	16	no	—
373	C₂×#41	—	4	8	no	—
374	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
375	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
376	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
377	C₂²×D₄	C₂³×C₇₃	1	8	yes	—
378	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
379	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
380	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
381	C₂²×D₄	C₂³×C₇₃	1	8	yes	—
382	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
383	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
384	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
385	C₂³×C₄	C₂³×C₇₃	1	8	yes	—
386	C₄⋊Q₈	D₄×C₇₃	1	8	yes	complemented
387	#127	—	2	16	no	—
388	#127	—	2	4	no	—
389	#127	D₄×C₇₃	1	8	yes	complemented
390	#123	—	2	32	no	—
391	C₂²⋊Q₈	—	2	16	no	—
392	#121	—	2	16	no	—
393	#121	—	2	32	no	—
394	#121	—	2	16	no	—
395	#121	—	4	8	no	—
396	C₄×Q₈	—	2	8	no	—
397	C₄×D₄	—	2	16	no	—
398	C₄×D₄	—	2	8	no	—
399	C₄×D₄	—	2	8	no	—
400	C₄×D₄	—	2	8	no	—
401	C₄×D₄	—	2	8	no	—
402	C₄×D₄	—	4	4	no	—
403	C₄×D₄	—	4	4	no	—
404	C₂×C₄⋊C₄	—	2	16	no	—
405	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
407	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	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	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₇₃	1	8	yes	—
427	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
430	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
435	#95	C₂³×C₇₃	1	4	yes	—
436	#95	C₂³×C₇₃	1	4	yes	—
437	#95	C₂³×C₇₃	1	8	yes	—
438	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
439	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
440	#41	—	4	64	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	C₂×D₄×C₇₃	1	8	yes	—
444	C₂×D₄	—	2	16	no	—
445	C₂×D₄	—	2	16	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	16	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	8	no	—
463	C₂×D₄	—	4	8	no	—
464	C₂×D₄	—	4	8	no	—
465	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
466	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
467	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
468	C₂²×C₄	—	2	16	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	16	no	—
471	C₂²×C₄	—	2	8	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	8	no	—
474	C₂²×C₄	—	2	8	no	—
475	C₂²×C₄	—	2	8	no	—
476	C₂²×C₄	—	4	8	no	—
477	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
479	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	16	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	8	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	4	2	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
500	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
501	C₂²⋊C₄	—	2	16	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	2	8	no	—
505	C₂²⋊C₄	—	2	16	no	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	4	4	no	—
508	C₂²⋊C₄	—	4	4	no	—
509	C₂²⋊C₄	—	4	8	no	—
510	C₄²	—	2	8	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	2	no	—
514	C₄²	—	4	1	no	—
515	C₄²	C₂×D₄×C₇₃	1	4	yes	—
516	C₄²	C₂×D₄×C₇₃	1	4	yes	—
517	C₄²	#41×C₇₃	1	4	yes	complemented
518	C₂³	—	2	4	no	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	4	no	—
531	C₂³	C₂²×D₄×C₇₃	1	8	yes	—
532	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
533	Q₈	—	2	16	no	—
534	D₄	—	2	16	no	—
535	D₄	—	2	16	no	—
536	D₄	—	4	8	no	—
537	D₄	—	4	32	no	—
538	D₄	—	4	8	no	—
539	D₄	—	4	8	no	—
540	D₄	—	4	8	no	—
541	D₄	—	8	16	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	4	32	no	—
563	C₂×C₄	—	4	16	no	—
564	C₂×C₄	—	4	16	no	—
565	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
567	C₂×C₄	C₂²×D₄×C₇₃	1	8	yes	—
568	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
570	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
571	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
572	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
573	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
574	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
575	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
576	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
577	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
578	C₂²	—	2	8	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	4	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	4	no	—
592	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
593	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
594	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
595	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
596	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
597	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
598	C₂²	#585×C₇₃	1	1	yes	characteristic
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	8	no	—
603	C₄	—	4	4	no	—
604	C₄	—	4	4	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	4	no	—
607	C₄	D₄²×C₇₃	1	4	yes	—
608	C₄	#547×C₇₃	1	4	yes	complemented
609	C₄	#550×C₇₃	1	4	yes	complemented
610	C₂	—	4	8	no	—
611	C₂	—	8	4	no	—
612	C₂	C₂×D₄²×C₇₃	1	1	yes	characteristic
613	C₂	C₂×#547×C₇₃	1	1	yes	characteristic
614	C₂	C₂×#550×C₇₃	1	1	yes	characteristic
615	C₂	C₇₃×#3496	1	1	yes	characteristic
616	C₂	C₇₃×#3497	1	1	yes	characteristic
617	C₂	C₇₃×#3506	1	1	yes	characteristic
618	C₂	C₇₃×#3548	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#550×C₇₃	C₂	semidirect
2. C₂×#547×C₇₃	C₂	semidirect
3. C₇₃×#2682	C₂	semidirect
4. C₇₃×#2541	C₂	semidirect
5. C₇₃×#2538	C₂	semidirect
6. C₇₃×#2537	C₂	semidirect
7. C₇₃×#2445	C₂	semidirect
8. C₇₃×#2416	C₂	semidirect
9. C₇₃×#2407	C₂	semidirect
10. D₄×C₄⋊C₄×C₇₃	C₂	semidirect
11. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
12. C₄×#127×C₇₃	C₂	semidirect
13. C₄×#127×C₇₃	C₂	semidirect
76. C₄⋊Q₈×C₇₃	D₄	semidirect
79. #127×C₇₃	D₄	semidirect
207. C₄²×C₇₃	#41	semidirect
298. C₄×C₇₃	#547	semidirect
299. C₄×C₇₃	#550	semidirect
300. #59815	C₇₃	direct (N × H)
310. C₂×#550	C₂×C₇₃	semidirect
311. C₂×#547	C₂×C₇₃	semidirect
312. #2682	C₂×C₇₃	semidirect
313. #2541	C₂×C₇₃	semidirect
314. #2538	C₂×C₇₃	semidirect
315. #2537	C₂×C₇₃	semidirect
316. #2445	C₂×C₇₃	semidirect
317. #2416	C₂×C₇₃	semidirect
318. #2407	C₂×C₇₃	semidirect
319. D₄×C₄⋊C₄	C₂×C₇₃	semidirect
320. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
321. C₄×#127	C₂×C₇₃	semidirect
322. C₄×#127	C₂×C₇₃	semidirect
323. C₇₃	#59815	direct (N × H)
386. C₄⋊Q₈	D₄×C₇₃	semidirect
389. #127	D₄×C₇₃	semidirect
517. C₄²	#41×C₇₃	semidirect
608. C₄	#547×C₇₃	semidirect
609. C₄	#550×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₇₃	2
C₂×#547×C₇₃	2
C₇₃×#2682	2
C₇₃×#2541	2
C₇₃×#2538	2
C₇₃×#2537	2
C₇₃×#2445	2
C₇₃×#2416	2
C₇₃×#2407	2
D₄×C₄⋊C₄×C₇₃	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#127×C₇₃	2
#59815	73

Subgroups — C73×#59815 #32969219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59815 #32969219