Subgroups — C₇₃×#59841 #32969245

Order 18688.

2368 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2731	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2699	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2609	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2491	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2476	C₂	1	4	yes	maximal, complemented
9	C₇₃×#2459	C₂	1	4	yes	maximal, complemented
10	C₇₃×#2428	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2416	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2361	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2344	C₂	1	2	yes	maximal, complemented
14	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2293	C₂	1	2	yes	maximal, complemented
16	#555×C₇₃	—	2	16	no	—
17	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#124×C₇₃	C₂²	1	4	yes	—
21	C₂×#124×C₇₃	C₂²	1	2	yes	—
22	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×#121×C₇₃	C₂²	1	4	yes	—
24	C₂×#121×C₇₃	C₂²	1	4	yes	—
25	C₂×#121×C₇₃	C₂²	1	2	yes	—
26	C₂×#121×C₇₃	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₇₃	C₂²	1	4	yes	—
32	C₂×#117×C₇₃	C₂²	1	4	yes	—
33	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
34	#398×C₇₃	C₂²	1	2	yes	—
35	#398×C₇₃	C₂²	1	2	yes	—
36	#396×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	#394×C₇₃	C₂²	1	4	yes	—
41	#394×C₇₃	C₂²	1	4	yes	—
42	#393×C₇₃	C₂²	1	4	yes	—
43	#392×C₇₃	C₂²	1	4	yes	—
44	#391×C₇₃	C₂²	1	2	yes	—
45	#391×C₇₃	C₂²	1	1	yes	characteristic
46	#390×C₇₃	C₂²	1	1	yes	characteristic
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	#389×C₇₃	C₂²	1	2	yes	—
52	#389×C₇₃	C₂²	1	2	yes	—
53	#389×C₇₃	C₂²	1	2	yes	—
54	#388×C₇₃	C₂²	1	4	yes	—
55	#388×C₇₃	C₂²	1	2	yes	—
56	#388×C₇₃	C₂²	1	4	yes	—
57	#388×C₇₃	C₂²	1	4	yes	—
58	#388×C₇₃	C₂²	1	2	yes	—
59	#388×C₇₃	C₂²	1	4	yes	—
60	#387×C₇₃	C₂²	1	4	yes	—
61	#387×C₇₃	C₂²	1	4	yes	—
62	#386×C₇₃	C₂²	1	4	yes	—
63	#386×C₇₃	C₂²	1	4	yes	—
64	#386×C₇₃	C₂²	1	4	yes	—
65	#385×C₇₃	C₂²	1	4	yes	—
66	#382×C₇₃	C₂²	1	1	yes	characteristic
67	#381×C₇₃	C₂²	1	4	yes	—
68	#380×C₇₃	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
73	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
75	C₄³×C₇₃	C₂²	1	1	yes	characteristic
76	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
77	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
79	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
80	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
81	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
86	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
87	C₄⋊Q₈×C₇₃	—	2	8	no	—
88	C₄⋊Q₈×C₇₃	—	4	2	no	—
89	#127×C₇₃	—	4	2	no	—
90	#124×C₇₃	—	2	8	no	—
91	#124×C₇₃	—	2	16	no	—
92	#124×C₇₃	D₄	1	8	yes	complemented
93	#121×C₇₃	—	2	16	no	—
94	#121×C₇₃	—	2	8	no	—
95	#121×C₇₃	—	2	16	no	—
96	#121×C₇₃	—	4	4	no	—
97	C₄×Q₈×C₇₃	—	4	2	no	—
98	C₄×D₄×C₇₃	—	2	8	no	—
99	C₄×D₄×C₇₃	—	2	16	no	—
100	C₄×D₄×C₇₃	—	4	2	no	—
101	#117×C₇₃	—	2	16	no	—
102	#117×C₇₃	—	2	16	no	—
103	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
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	4	yes	—
107	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	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×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
131	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
135	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
137	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
141	#95×C₇₃	C₂³	1	4	yes	—
142	#95×C₇₃	C₂³	1	2	yes	—
143	#95×C₇₃	C₂³	1	2	yes	—
144	#95×C₇₃	C₂³	1	4	yes	—
145	#95×C₇₃	C₂³	1	2	yes	—
146	#95×C₇₃	C₂³	1	2	yes	—
147	#95×C₇₃	C₂³	1	2	yes	—
148	#95×C₇₃	C₂³	1	4	yes	—
149	#95×C₇₃	C₂³	1	2	yes	—
150	#95×C₇₃	C₂³	1	4	yes	—
151	#95×C₇₃	C₂³	1	4	yes	—
152	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
153	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
154	C₂×Q₈×C₇₃	—	2	4	no	—
155	C₂×Q₈×C₇₃	—	4	1	no	—
156	C₂×Q₈×C₇₃	—	4	1	no	—
157	C₂×Q₈×C₇₃	—	4	2	no	—
158	C₂×Q₈×C₇₃	—	4	2	no	—
159	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
160	C₂×D₄×C₇₃	—	2	8	no	—
161	C₂×D₄×C₇₃	—	2	8	no	—
162	C₂×D₄×C₇₃	—	2	4	no	—
163	C₂×D₄×C₇₃	—	2	4	no	—
164	C₂×D₄×C₇₃	—	2	8	no	—
165	C₂×D₄×C₇₃	—	2	4	no	—
166	C₂×D₄×C₇₃	—	2	4	no	—
167	C₂×D₄×C₇₃	—	4	1	no	—
168	C₂×D₄×C₇₃	—	4	1	no	—
169	C₂×D₄×C₇₃	—	4	4	no	—
170	C₂×D₄×C₇₃	—	4	4	no	—
171	C₂×D₄×C₇₃	—	4	2	no	—
172	C₂×D₄×C₇₃	—	4	2	no	—
173	C₂×D₄×C₇₃	—	4	2	no	—
174	C₂×D₄×C₇₃	—	4	4	no	—
175	C₂×D₄×C₇₃	—	4	4	no	—
176	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₇₃	—	2	8	no	—
178	C₂²×C₄×C₇₃	—	2	8	no	—
179	C₂²×C₄×C₇₃	—	2	8	no	—
180	C₂²×C₄×C₇₃	—	2	4	no	—
181	C₂²×C₄×C₇₃	—	2	8	no	—
182	C₂²×C₄×C₇₃	—	2	4	no	—
183	C₂²×C₄×C₇₃	—	2	4	no	—
184	C₂²×C₄×C₇₃	—	4	4	no	—
185	C₂²×C₄×C₇₃	—	4	4	no	—
186	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
199	C₄⋊C₄×C₇₃	—	2	8	no	—
200	C₄⋊C₄×C₇₃	—	2	8	no	—
201	C₄⋊C₄×C₇₃	—	2	8	no	—
202	C₄⋊C₄×C₇₃	—	2	8	no	—
203	C₄⋊C₄×C₇₃	—	2	4	no	—
204	C₄⋊C₄×C₇₃	—	2	4	no	—
205	C₄⋊C₄×C₇₃	—	4	1	no	—
206	C₄⋊C₄×C₇₃	—	4	1	no	—
207	C₄⋊C₄×C₇₃	—	4	1	no	—
208	C₄⋊C₄×C₇₃	—	4	1	no	—
209	C₄⋊C₄×C₇₃	—	4	2	no	—
210	C₄⋊C₄×C₇₃	#41	1	8	yes	—
211	C₂²⋊C₄×C₇₃	—	2	8	no	—
212	C₂²⋊C₄×C₇₃	—	2	8	no	—
213	C₂²⋊C₄×C₇₃	—	2	8	no	—
214	C₂²⋊C₄×C₇₃	—	2	8	no	—
215	C₂²⋊C₄×C₇₃	—	2	8	no	—
216	C₂²⋊C₄×C₇₃	—	2	8	no	—
217	C₂²⋊C₄×C₇₃	—	4	2	no	—
218	C₂²⋊C₄×C₇₃	—	4	4	no	—
219	C₂²⋊C₄×C₇₃	—	4	2	no	—
220	C₂²⋊C₄×C₇₃	—	4	4	no	—
221	C₂²⋊C₄×C₇₃	—	4	4	no	—
222	C₂²⋊C₄×C₇₃	—	4	2	no	—
223	C₂²⋊C₄×C₇₃	—	4	4	no	—
224	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
225	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
226	C₄²×C₇₃	—	2	4	no	—
227	C₄²×C₇₃	—	2	8	no	—
228	C₄²×C₇₃	—	2	4	no	—
229	C₄²×C₇₃	—	2	4	no	—
230	C₄²×C₇₃	—	2	2	no	—
231	C₄²×C₇₃	—	2	2	no	—
232	C₄²×C₇₃	—	2	2	no	—
233	C₄²×C₇₃	—	4	2	no	—
234	C₄²×C₇₃	—	4	1	no	—
235	C₄²×C₇₃	C₂×D₄	1	4	yes	—
236	C₂³×C₇₃	—	2	2	no	—
237	C₂³×C₇₃	—	2	2	no	—
238	C₂³×C₇₃	—	2	2	no	—
239	C₂³×C₇₃	—	2	2	no	—
240	C₂³×C₇₃	—	2	2	no	—
241	C₂³×C₇₃	—	2	2	no	—
242	C₂³×C₇₃	—	2	4	no	—
243	C₂³×C₇₃	—	2	4	no	—
244	C₂³×C₇₃	—	2	4	no	—
245	C₂³×C₇₃	—	2	4	no	—
246	C₂³×C₇₃	—	2	4	no	—
247	C₂³×C₇₃	—	2	4	no	—
248	C₂³×C₇₃	—	2	4	no	—
249	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
250	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
251	Q₈×C₇₃	—	4	4	no	—
252	Q₈×C₇₃	—	8	4	no	—
253	D₄×C₇₃	—	4	4	no	—
254	D₄×C₇₃	—	4	16	no	—
255	D₄×C₇₃	—	4	8	no	—
256	D₄×C₇₃	—	8	4	no	—
257	D₄×C₇₃	—	8	8	no	—
258	D₄×C₇₃	—	8	4	no	—
259	C₂×C₄×C₇₃	—	2	4	no	—
260	C₂×C₄×C₇₃	—	2	2	no	—
261	C₂×C₄×C₇₃	—	2	1	no	—
262	C₂×C₄×C₇₃	—	2	1	no	—
263	C₂×C₄×C₇₃	—	2	1	no	—
264	C₂×C₄×C₇₃	—	2	2	no	—
265	C₂×C₄×C₇₃	—	2	1	no	—
266	C₂×C₄×C₇₃	—	2	4	no	—
267	C₂×C₄×C₇₃	—	2	1	no	—
268	C₂×C₄×C₇₃	—	2	1	no	—
269	C₂×C₄×C₇₃	—	2	4	no	—
270	C₂×C₄×C₇₃	—	2	4	no	—
271	C₂×C₄×C₇₃	—	2	2	no	—
272	C₂×C₄×C₇₃	—	2	2	no	—
273	C₂×C₄×C₇₃	—	2	4	no	—
274	C₂×C₄×C₇₃	—	2	2	no	—
275	C₂×C₄×C₇₃	—	2	1	no	—
276	C₂×C₄×C₇₃	—	2	1	no	—
277	C₂×C₄×C₇₃	—	2	1	no	—
278	C₂×C₄×C₇₃	—	2	2	no	—
279	C₂×C₄×C₇₃	—	2	4	no	—
280	C₂×C₄×C₇₃	—	2	2	no	—
281	C₂×C₄×C₇₃	—	2	2	no	—
282	C₂×C₄×C₇₃	—	2	2	no	—
283	C₂×C₄×C₇₃	—	2	2	no	—
284	C₂×C₄×C₇₃	—	2	4	no	—
285	C₂×C₄×C₇₃	—	2	2	no	—
286	C₂×C₄×C₇₃	—	2	4	no	—
287	C₂×C₄×C₇₃	—	4	16	no	—
288	C₂×C₄×C₇₃	—	4	16	no	—
289	C₂×C₄×C₇₃	—	4	8	no	—
290	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
291	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₇₃	C₂×#41	1	8	yes	—
295	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
296	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
297	C₂²×C₇₃	—	2	4	no	—
298	C₂²×C₇₃	—	2	4	no	—
299	C₂²×C₇₃	—	2	4	no	—
300	C₂²×C₇₃	—	4	2	no	—
301	C₂²×C₇₃	—	4	2	no	—
302	C₂²×C₇₃	—	4	2	no	—
303	C₂²×C₇₃	—	4	2	no	—
304	C₂²×C₇₃	—	4	4	no	—
305	C₂²×C₇₃	—	4	4	no	—
306	C₂²×C₇₃	—	4	4	no	—
307	C₂²×C₇₃	—	4	4	no	—
308	C₂²×C₇₃	—	4	4	no	—
309	C₂²×C₇₃	—	4	4	no	—
310	C₂²×C₇₃	—	4	4	no	—
311	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
312	C₂²×C₇₃	C₂²×#41	1	2	yes	—
313	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂²×C₇₃	#585	1	2	yes	—
315	C₂²×C₇₃	#585	1	1	yes	characteristic
316	C₄×C₇₃	—	2	4	no	—
317	C₄×C₇₃	—	2	8	no	—
318	C₄×C₇₃	—	2	2	no	—
319	C₄×C₇₃	—	2	2	no	—
320	C₄×C₇₃	—	2	2	no	—
321	C₄×C₇₃	—	4	4	no	—
322	C₄×C₇₃	—	4	2	no	—
323	C₄×C₇₃	—	4	4	no	—
324	C₄×C₇₃	—	4	2	no	—
325	C₄×C₇₃	—	4	1	no	—
326	C₄×C₇₃	—	4	1	no	—
327	C₄×C₇₃	—	4	1	no	—
328	C₄×C₇₃	#555	1	4	yes	complemented
329	#59841	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂×C₇₃	—	4	4	no	—
331	C₂×C₇₃	—	8	4	no	—
332	C₂×C₇₃	D₄×#41	1	2	yes	—
333	C₂×C₇₃	C₂×#555	1	1	yes	characteristic
334	C₂×C₇₃	#3496	1	1	yes	characteristic
335	C₂×C₇₃	#3524	1	2	yes	—
336	C₂×C₇₃	#3551	1	1	yes	characteristic
337	C₂×#555	C₂×C₇₃	1	2	yes	complemented
338	#2731	C₂×C₇₃	1	2	yes	complemented
339	#2699	C₂×C₇₃	1	2	yes	complemented
340	#2609	C₂×C₇₃	1	2	yes	complemented
341	#2548	C₂×C₇₃	1	1	yes	characteristic, complemented
342	#2546	C₂×C₇₃	1	1	yes	characteristic, complemented
343	#2491	C₂×C₇₃	1	2	yes	complemented
344	#2476	C₂×C₇₃	1	4	yes	complemented
345	#2459	C₂×C₇₃	1	4	yes	complemented
346	#2428	C₂×C₇₃	1	2	yes	complemented
347	#2416	C₂×C₇₃	1	2	yes	complemented
348	#2361	C₂×C₇₃	1	2	yes	complemented
349	#2344	C₂×C₇₃	1	2	yes	complemented
350	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
351	#2293	C₂×C₇₃	1	2	yes	complemented
352	C₇₃	#59841	1	1	yes	characteristic, direct product factor, Sylow
353	#555	—	2	16	no	—
354	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
355	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
356	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
357	C₂×#124	C₂²×C₇₃	1	4	yes	—
358	C₂×#124	C₂²×C₇₃	1	2	yes	—
359	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
360	C₂×#121	C₂²×C₇₃	1	2	yes	—
361	C₂×#121	C₂²×C₇₃	1	4	yes	—
362	C₂×#121	C₂²×C₇₃	1	4	yes	—
363	C₂×#121	C₂²×C₇₃	1	2	yes	—
364	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
365	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
366	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
367	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
368	C₂×#117	C₂²×C₇₃	1	4	yes	—
369	C₂×#117	C₂²×C₇₃	1	4	yes	—
370	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
371	#398	C₂²×C₇₃	1	2	yes	—
372	#398	C₂²×C₇₃	1	2	yes	—
373	#396	C₂²×C₇₃	1	4	yes	—
374	#394	C₂²×C₇₃	1	2	yes	—
375	#394	C₂²×C₇₃	1	4	yes	—
376	#394	C₂²×C₇₃	1	4	yes	—
377	#394	C₂²×C₇₃	1	4	yes	—
378	#394	C₂²×C₇₃	1	2	yes	—
379	#393	C₂²×C₇₃	1	4	yes	—
380	#392	C₂²×C₇₃	1	4	yes	—
381	#391	C₂²×C₇₃	1	2	yes	—
382	#391	C₂²×C₇₃	1	1	yes	characteristic
383	#390	C₂²×C₇₃	1	2	yes	—
384	#390	C₂²×C₇₃	1	2	yes	—
385	#390	C₂²×C₇₃	1	2	yes	—
386	#390	C₂²×C₇₃	1	1	yes	characteristic
387	#390	C₂²×C₇₃	1	2	yes	—
388	#389	C₂²×C₇₃	1	2	yes	—
389	#389	C₂²×C₇₃	1	2	yes	—
390	#389	C₂²×C₇₃	1	2	yes	—
391	#388	C₂²×C₇₃	1	4	yes	—
392	#388	C₂²×C₇₃	1	4	yes	—
393	#388	C₂²×C₇₃	1	4	yes	—
394	#388	C₂²×C₇₃	1	2	yes	—
395	#388	C₂²×C₇₃	1	4	yes	—
396	#388	C₂²×C₇₃	1	2	yes	—
397	#387	C₂²×C₇₃	1	4	yes	—
398	#387	C₂²×C₇₃	1	4	yes	—
399	#386	C₂²×C₇₃	1	4	yes	—
400	#386	C₂²×C₇₃	1	4	yes	—
401	#386	C₂²×C₇₃	1	4	yes	—
402	#385	C₂²×C₇₃	1	4	yes	—
403	#382	C₂²×C₇₃	1	1	yes	characteristic
404	#381	C₂²×C₇₃	1	4	yes	—
405	#380	C₂²×C₇₃	1	2	yes	—
406	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
407	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
409	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
410	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
412	C₄³	C₂²×C₇₃	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
414	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
415	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
416	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
417	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
418	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
419	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
420	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
422	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
423	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
424	C₄⋊Q₈	—	2	8	no	—
425	C₄⋊Q₈	—	4	2	no	—
426	#127	—	4	2	no	—
427	#124	—	2	8	no	—
428	#124	—	2	16	no	—
429	#124	D₄×C₇₃	1	8	yes	complemented
430	#121	—	2	16	no	—
431	#121	—	2	8	no	—
432	#121	—	2	16	no	—
433	#121	—	4	4	no	—
434	C₄×Q₈	—	4	2	no	—
435	C₄×D₄	—	2	8	no	—
436	C₄×D₄	—	2	16	no	—
437	C₄×D₄	—	4	2	no	—
438	#117	—	2	16	no	—
439	#117	—	2	16	no	—
440	C₂×C₄⋊C₄	—	2	8	no	—
441	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
468	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
469	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
470	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
471	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
473	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
476	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
478	#95	C₂³×C₇₃	1	4	yes	—
479	#95	C₂³×C₇₃	1	2	yes	—
480	#95	C₂³×C₇₃	1	2	yes	—
481	#95	C₂³×C₇₃	1	4	yes	—
482	#95	C₂³×C₇₃	1	2	yes	—
483	#95	C₂³×C₇₃	1	2	yes	—
484	#95	C₂³×C₇₃	1	2	yes	—
485	#95	C₂³×C₇₃	1	4	yes	—
486	#95	C₂³×C₇₃	1	2	yes	—
487	#95	C₂³×C₇₃	1	4	yes	—
488	#95	C₂³×C₇₃	1	4	yes	—
489	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
490	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
491	C₂×Q₈	—	2	4	no	—
492	C₂×Q₈	—	4	1	no	—
493	C₂×Q₈	—	4	1	no	—
494	C₂×Q₈	—	4	2	no	—
495	C₂×Q₈	—	4	2	no	—
496	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
497	C₂×D₄	—	2	8	no	—
498	C₂×D₄	—	2	8	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	8	no	—
502	C₂×D₄	—	2	4	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	4	1	no	—
505	C₂×D₄	—	4	1	no	—
506	C₂×D₄	—	4	4	no	—
507	C₂×D₄	—	4	4	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	—	4	2	no	—
511	C₂×D₄	—	4	4	no	—
512	C₂×D₄	—	4	4	no	—
513	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
514	C₂²×C₄	—	2	8	no	—
515	C₂²×C₄	—	2	8	no	—
516	C₂²×C₄	—	2	8	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	8	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	4	4	no	—
522	C₂²×C₄	—	4	4	no	—
523	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
535	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
536	C₄⋊C₄	—	2	8	no	—
537	C₄⋊C₄	—	2	8	no	—
538	C₄⋊C₄	—	2	8	no	—
539	C₄⋊C₄	—	2	8	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	4	1	no	—
543	C₄⋊C₄	—	4	1	no	—
544	C₄⋊C₄	—	4	1	no	—
545	C₄⋊C₄	—	4	1	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	#41×C₇₃	1	8	yes	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	2	8	no	—
551	C₂²⋊C₄	—	2	8	no	—
552	C₂²⋊C₄	—	2	8	no	—
553	C₂²⋊C₄	—	2	8	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	—	4	4	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	—	4	4	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
562	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	8	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	2	no	—
570	C₄²	—	4	2	no	—
571	C₄²	—	4	1	no	—
572	C₄²	C₂×D₄×C₇₃	1	4	yes	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	4	no	—
582	C₂³	—	2	4	no	—
583	C₂³	—	2	4	no	—
584	C₂³	—	2	4	no	—
585	C₂³	—	2	4	no	—
586	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
587	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
588	Q₈	—	4	4	no	—
589	Q₈	—	8	4	no	—
590	D₄	—	4	4	no	—
591	D₄	—	4	16	no	—
592	D₄	—	4	8	no	—
593	D₄	—	8	4	no	—
594	D₄	—	8	8	no	—
595	D₄	—	8	4	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	4	16	no	—
625	C₂×C₄	—	4	16	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
628	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
629	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
630	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
631	C₂×C₄	C₂×#41×C₇₃	1	8	yes	—
632	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
633	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	4	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
649	C₂²	C₂²×#41×C₇₃	1	2	yes	—
650	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
651	C₂²	#585×C₇₃	1	2	yes	—
652	C₂²	#585×C₇₃	1	1	yes	characteristic
653	C₄	—	2	4	no	—
654	C₄	—	2	8	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	4	4	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	4	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	#555×C₇₃	1	4	yes	complemented
666	C₂	—	4	4	no	—
667	C₂	—	8	4	no	—
668	C₂	D₄×#41×C₇₃	1	2	yes	—
669	C₂	C₂×#555×C₇₃	1	1	yes	characteristic
670	C₂	C₇₃×#3496	1	1	yes	characteristic
671	C₂	C₇₃×#3524	1	2	yes	—
672	C₂	C₇₃×#3551	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×#555×C₇₃	C₂	semidirect
2. C₇₃×#2731	C₂	semidirect
3. C₇₃×#2699	C₂	semidirect
4. C₇₃×#2609	C₂	semidirect
5. C₇₃×#2548	C₂	semidirect
6. C₇₃×#2546	C₂	semidirect
7. C₇₃×#2491	C₂	semidirect
8. C₇₃×#2476	C₂	semidirect
9. C₇₃×#2459	C₂	semidirect
10. C₇₃×#2428	C₂	semidirect
11. C₇₃×#2416	C₂	semidirect
12. C₇₃×#2361	C₂	semidirect
13. C₇₃×#2344	C₂	semidirect
14. C₄×#124×C₇₃	C₂	semidirect
15. C₇₃×#2293	C₂	semidirect
92. #124×C₇₃	D₄	semidirect
328. C₄×C₇₃	#555	semidirect
329. #59841	C₇₃	direct (N × H)
337. C₂×#555	C₂×C₇₃	semidirect
338. #2731	C₂×C₇₃	semidirect
339. #2699	C₂×C₇₃	semidirect
340. #2609	C₂×C₇₃	semidirect
341. #2548	C₂×C₇₃	semidirect
342. #2546	C₂×C₇₃	semidirect
343. #2491	C₂×C₇₃	semidirect
344. #2476	C₂×C₇₃	semidirect
345. #2459	C₂×C₇₃	semidirect
346. #2428	C₂×C₇₃	semidirect
347. #2416	C₂×C₇₃	semidirect
348. #2361	C₂×C₇₃	semidirect
349. #2344	C₂×C₇₃	semidirect
350. C₄×#124	C₂×C₇₃	semidirect
351. #2293	C₂×C₇₃	semidirect
352. C₇₃	#59841	direct (N × H)
429. #124	D₄×C₇₃	semidirect
665. C₄	#555×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#555×C₇₃	2
C₇₃×#2731	2
C₇₃×#2699	2
C₇₃×#2609	2
C₇₃×#2548	2
C₇₃×#2546	2
C₇₃×#2491	2
C₇₃×#2476	2
C₇₃×#2459	2
C₇₃×#2428	2
C₇₃×#2416	2
C₇₃×#2361	2
C₇₃×#2344	2
C₄×#124×C₇₃	2
C₇₃×#2293	2
#59841	73

Subgroups — C73×#59841 #32969245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59841 #32969245