Subgroups — C₇₃×#59834 #32969238

Order 18688.

2360 conjugacy classes of subgroups.

The subgroup lattice has 604 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×#2734	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2733	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2682	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2609	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2555	C₂	1	4	yes	maximal, complemented
7	C₇₃×#2545	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2543	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2474	C₂	1	4	yes	maximal, complemented
10	C₇₃×#2456	C₂	1	4	yes	maximal, complemented
11	C₇₃×#2359	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	#555×C₇₃	—	2	16	no	—
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
16	C₂×#124×C₇₃	C₂²	1	4	yes	—
17	C₂×#124×C₇₃	C₂²	1	2	yes	—
18	C₂×#124×C₇₃	C₂²	1	2	yes	—
19	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#123×C₇₃	C₂²	1	4	yes	—
21	C₂×#121×C₇₃	C₂²	1	4	yes	—
22	C₂×#121×C₇₃	C₂²	1	4	yes	—
23	C₂×#121×C₇₃	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₇₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₇₃	C₂²	1	4	yes	—
29	C₂×#117×C₇₃	C₂²	1	4	yes	—
30	#398×C₇₃	C₂²	1	2	yes	—
31	#397×C₇₃	C₂²	1	2	yes	—
32	#396×C₇₃	C₂²	1	4	yes	—
33	#396×C₇₃	C₂²	1	4	yes	—
34	#395×C₇₃	C₂²	1	4	yes	—
35	#394×C₇₃	C₂²	1	4	yes	—
36	#394×C₇₃	C₂²	1	2	yes	—
37	#392×C₇₃	C₂²	1	2	yes	—
38	#392×C₇₃	C₂²	1	4	yes	—
39	#392×C₇₃	C₂²	1	4	yes	—
40	#391×C₇₃	C₂²	1	2	yes	—
41	#391×C₇₃	C₂²	1	1	yes	characteristic
42	#390×C₇₃	C₂²	1	2	yes	—
43	#390×C₇₃	C₂²	1	2	yes	—
44	#390×C₇₃	C₂²	1	2	yes	—
45	#390×C₇₃	C₂²	1	1	yes	characteristic
46	#389×C₇₃	C₂²	1	2	yes	—
47	#389×C₇₃	C₂²	1	2	yes	—
48	#388×C₇₃	C₂²	1	4	yes	—
49	#388×C₇₃	C₂²	1	4	yes	—
50	#388×C₇₃	C₂²	1	4	yes	—
51	#388×C₇₃	C₂²	1	4	yes	—
52	#388×C₇₃	C₂²	1	4	yes	—
53	#388×C₇₃	C₂²	1	4	yes	—
54	#387×C₇₃	C₂²	1	4	yes	—
55	#387×C₇₃	C₂²	1	4	yes	—
56	#386×C₇₃	C₂²	1	4	yes	—
57	#386×C₇₃	C₂²	1	4	yes	—
58	#386×C₇₃	C₂²	1	4	yes	—
59	#385×C₇₃	C₂²	1	4	yes	—
60	#385×C₇₃	C₂²	1	4	yes	—
61	#382×C₇₃	C₂²	1	1	yes	characteristic
62	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
65	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
66	C₂×#95×C₇₃	C₂²	1	2	yes	—
67	C₄³×C₇₃	C₂²	1	1	yes	characteristic
68	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
69	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
71	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
72	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
74	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₇₃	C₂³	1	4	yes	—
78	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
79	C₄⋊Q₈×C₇₃	—	2	8	no	—
80	#124×C₇₃	—	2	8	no	—
81	#124×C₇₃	—	2	16	no	—
82	#124×C₇₃	—	4	4	no	—
83	#124×C₇₃	D₄	1	8	yes	complemented
84	#123×C₇₃	—	2	16	no	—
85	#121×C₇₃	—	2	16	no	—
86	#121×C₇₃	—	2	16	no	—
87	#121×C₇₃	—	4	4	no	—
88	C₄×Q₈×C₇₃	—	4	2	no	—
89	C₄×D₄×C₇₃	—	2	8	no	—
90	C₄×D₄×C₇₃	—	2	16	no	—
91	C₄×D₄×C₇₃	—	4	2	no	—
92	#117×C₇₃	—	2	16	no	—
93	#117×C₇₃	—	2	16	no	—
94	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	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	1	yes	characteristic
101	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	4	yes	—
110	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	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	2	yes	—
116	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
118	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
119	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
120	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₇₃	C₂³	1	2	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	2	yes	—
133	#95×C₇₃	C₂³	1	4	yes	—
134	#95×C₇₃	C₂³	1	4	yes	—
135	#95×C₇₃	C₂³	1	2	yes	—
136	C₂⁴×C₇₃	C₂⁴	1	4	yes	—
137	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
138	C₂×Q₈×C₇₃	—	2	4	no	—
139	C₂×Q₈×C₇₃	—	4	1	no	—
140	C₂×Q₈×C₇₃	—	4	1	no	—
141	C₂×Q₈×C₇₃	—	4	2	no	—
142	C₂×Q₈×C₇₃	—	4	2	no	—
143	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
144	C₂×D₄×C₇₃	—	2	8	no	—
145	C₂×D₄×C₇₃	—	2	8	no	—
146	C₂×D₄×C₇₃	—	2	4	no	—
147	C₂×D₄×C₇₃	—	2	4	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	1	no	—
153	C₂×D₄×C₇₃	—	4	4	no	—
154	C₂×D₄×C₇₃	—	4	4	no	—
155	C₂×D₄×C₇₃	—	4	2	no	—
156	C₂×D₄×C₇₃	—	4	2	no	—
157	C₂×D₄×C₇₃	—	4	2	no	—
158	C₂×D₄×C₇₃	—	4	4	no	—
159	C₂×D₄×C₇₃	—	4	4	no	—
160	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
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	4	no	—
166	C₂²×C₄×C₇₃	—	4	4	no	—
167	C₂²×C₄×C₇₃	—	4	4	no	—
168	C₂²×C₄×C₇₃	—	4	4	no	—
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	2	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	4	yes	—
179	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
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	8	no	—
184	C₄⋊C₄×C₇₃	—	4	2	no	—
185	C₄⋊C₄×C₇₃	—	4	2	no	—
186	C₄⋊C₄×C₇₃	—	4	1	no	—
187	C₄⋊C₄×C₇₃	—	4	1	no	—
188	C₄⋊C₄×C₇₃	—	4	2	no	—
189	C₄⋊C₄×C₇₃	—	4	2	no	—
190	C₄⋊C₄×C₇₃	#41	1	8	yes	—
191	C₂²⋊C₄×C₇₃	—	2	8	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	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	—	4	4	no	—
201	C₂²⋊C₄×C₇₃	—	4	2	no	—
202	C₂²⋊C₄×C₇₃	—	4	4	no	—
203	C₂²⋊C₄×C₇₃	C₂×D₄	1	16	yes	—
204	C₄²×C₇₃	—	2	4	no	—
205	C₄²×C₇₃	—	2	8	no	—
206	C₄²×C₇₃	—	2	4	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	2	no	—
215	C₂³×C₇₃	—	2	4	no	—
216	C₂³×C₇₃	—	2	2	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	—	2	4	no	—
222	C₂³×C₇₃	—	2	4	no	—
223	C₂³×C₇₃	—	2	4	no	—
224	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
225	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
226	Q₈×C₇₃	—	4	4	no	—
227	Q₈×C₇₃	—	8	4	no	—
228	D₄×C₇₃	—	4	4	no	—
229	D₄×C₇₃	—	4	16	no	—
230	D₄×C₇₃	—	4	8	no	—
231	D₄×C₇₃	—	8	4	no	—
232	D₄×C₇₃	—	8	8	no	—
233	D₄×C₇₃	—	8	4	no	—
234	C₂×C₄×C₇₃	—	2	4	no	—
235	C₂×C₄×C₇₃	—	2	2	no	—
236	C₂×C₄×C₇₃	—	2	1	no	—
237	C₂×C₄×C₇₃	—	2	2	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	1	no	—
243	C₂×C₄×C₇₃	—	2	4	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	2	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	2	no	—
252	C₂×C₄×C₇₃	—	2	4	no	—
253	C₂×C₄×C₇₃	—	2	2	no	—
254	C₂×C₄×C₇₃	—	2	4	no	—
255	C₂×C₄×C₇₃	—	2	4	no	—
256	C₂×C₄×C₇₃	—	2	4	no	—
257	C₂×C₄×C₇₃	—	4	16	no	—
258	C₂×C₄×C₇₃	—	4	16	no	—
259	C₂×C₄×C₇₃	—	8	4	no	—
260	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
261	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
262	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
264	C₂×C₄×C₇₃	C₂×#41	1	8	yes	—
265	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
266	C₂²×C₇₃	—	2	8	no	—
267	C₂²×C₇₃	—	2	4	no	—
268	C₂²×C₇₃	—	4	2	no	—
269	C₂²×C₇₃	—	4	4	no	—
270	C₂²×C₇₃	—	4	2	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	C₂³×D₄	1	1	yes	characteristic
279	C₂²×C₇₃	C₂²×#41	1	2	yes	—
280	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
281	C₂²×C₇₃	#585	1	2	yes	—
282	C₂²×C₇₃	#585	1	1	yes	characteristic
283	C₄×C₇₃	—	2	4	no	—
284	C₄×C₇₃	—	2	8	no	—
285	C₄×C₇₃	—	2	4	no	—
286	C₄×C₇₃	—	2	2	no	—
287	C₄×C₇₃	—	2	4	no	—
288	C₄×C₇₃	—	2	2	no	—
289	C₄×C₇₃	—	4	4	no	—
290	C₄×C₇₃	—	4	1	no	—
291	C₄×C₇₃	—	4	2	no	—
292	C₄×C₇₃	—	4	4	no	—
293	C₄×C₇₃	—	4	2	no	—
294	#59834	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂×C₇₃	—	4	4	no	—
296	C₂×C₇₃	—	8	4	no	—
297	C₂×C₇₃	D₄×#41	1	2	yes	—
298	C₂×C₇₃	#3483	1	1	yes	characteristic
299	C₂×C₇₃	#3493	1	2	yes	—
300	C₂×C₇₃	#3496	1	1	yes	characteristic
301	C₂×C₇₃	#3545	1	1	yes	characteristic
302	C₂×#555	C₂×C₇₃	1	2	yes	complemented
303	#2734	C₂×C₇₃	1	1	yes	characteristic, complemented
304	#2733	C₂×C₇₃	1	1	yes	characteristic, complemented
305	#2682	C₂×C₇₃	1	2	yes	complemented
306	#2609	C₂×C₇₃	1	2	yes	complemented
307	#2555	C₂×C₇₃	1	4	yes	complemented
308	#2545	C₂×C₇₃	1	2	yes	complemented
309	#2543	C₂×C₇₃	1	2	yes	complemented
310	#2474	C₂×C₇₃	1	4	yes	complemented
311	#2456	C₂×C₇₃	1	4	yes	complemented
312	#2359	C₂×C₇₃	1	4	yes	complemented
313	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
314	#2293	C₂×C₇₃	1	2	yes	complemented
315	C₇₃	#59834	1	1	yes	characteristic, direct product factor, Sylow
316	#555	—	2	16	no	—
317	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
318	C₂×#124	C₂²×C₇₃	1	4	yes	—
319	C₂×#124	C₂²×C₇₃	1	2	yes	—
320	C₂×#124	C₂²×C₇₃	1	2	yes	—
321	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
322	C₂×#123	C₂²×C₇₃	1	4	yes	—
323	C₂×#121	C₂²×C₇₃	1	4	yes	—
324	C₂×#121	C₂²×C₇₃	1	4	yes	—
325	C₂×#121	C₂²×C₇₃	1	2	yes	—
326	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
327	C₂×C₄×D₄	C₂²×C₇₃	1	4	yes	—
328	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
329	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
330	C₂×#117	C₂²×C₇₃	1	4	yes	—
331	C₂×#117	C₂²×C₇₃	1	4	yes	—
332	#398	C₂²×C₇₃	1	2	yes	—
333	#397	C₂²×C₇₃	1	2	yes	—
334	#396	C₂²×C₇₃	1	4	yes	—
335	#396	C₂²×C₇₃	1	4	yes	—
336	#395	C₂²×C₇₃	1	4	yes	—
337	#394	C₂²×C₇₃	1	2	yes	—
338	#394	C₂²×C₇₃	1	4	yes	—
339	#392	C₂²×C₇₃	1	4	yes	—
340	#392	C₂²×C₇₃	1	2	yes	—
341	#392	C₂²×C₇₃	1	4	yes	—
342	#391	C₂²×C₇₃	1	2	yes	—
343	#391	C₂²×C₇₃	1	1	yes	characteristic
344	#390	C₂²×C₇₃	1	1	yes	characteristic
345	#390	C₂²×C₇₃	1	2	yes	—
346	#390	C₂²×C₇₃	1	2	yes	—
347	#390	C₂²×C₇₃	1	2	yes	—
348	#389	C₂²×C₇₃	1	2	yes	—
349	#389	C₂²×C₇₃	1	2	yes	—
350	#388	C₂²×C₇₃	1	4	yes	—
351	#388	C₂²×C₇₃	1	4	yes	—
352	#388	C₂²×C₇₃	1	4	yes	—
353	#388	C₂²×C₇₃	1	4	yes	—
354	#388	C₂²×C₇₃	1	4	yes	—
355	#388	C₂²×C₇₃	1	4	yes	—
356	#387	C₂²×C₇₃	1	4	yes	—
357	#387	C₂²×C₇₃	1	4	yes	—
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	—
362	#385	C₂²×C₇₃	1	4	yes	—
363	#382	C₂²×C₇₃	1	1	yes	characteristic
364	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
365	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
366	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
367	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
368	C₂×#95	C₂²×C₇₃	1	2	yes	—
369	C₄³	C₂²×C₇₃	1	1	yes	characteristic
370	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
371	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
372	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
373	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
374	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
375	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
376	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
377	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
379	C₂³×C₄	C₂³×C₇₃	1	4	yes	—
380	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
381	C₄⋊Q₈	—	2	8	no	—
382	#124	—	2	8	no	—
383	#124	—	2	16	no	—
384	#124	—	4	4	no	—
385	#124	D₄×C₇₃	1	8	yes	complemented
386	#123	—	2	16	no	—
387	#121	—	2	16	no	—
388	#121	—	2	16	no	—
389	#121	—	4	4	no	—
390	C₄×Q₈	—	4	2	no	—
391	C₄×D₄	—	2	8	no	—
392	C₄×D₄	—	2	16	no	—
393	C₄×D₄	—	4	2	no	—
394	#117	—	2	16	no	—
395	#117	—	2	16	no	—
396	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
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	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
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	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
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	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
420	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
421	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
422	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
423	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
425	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
426	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
427	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
429	#95	C₂³×C₇₃	1	4	yes	—
430	#95	C₂³×C₇₃	1	2	yes	—
431	#95	C₂³×C₇₃	1	2	yes	—
432	#95	C₂³×C₇₃	1	4	yes	—
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	C₂⁴	C₂⁴×C₇₃	1	4	yes	—
439	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
440	C₂×Q₈	—	2	4	no	—
441	C₂×Q₈	—	4	1	no	—
442	C₂×Q₈	—	4	1	no	—
443	C₂×Q₈	—	4	2	no	—
444	C₂×Q₈	—	4	2	no	—
445	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	8	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	—	4	4	no	—
462	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
463	C₂²×C₄	—	2	8	no	—
464	C₂²×C₄	—	2	8	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	4	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
474	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
476	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
480	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
482	C₄⋊C₄	—	2	8	no	—
483	C₄⋊C₄	—	2	8	no	—
484	C₄⋊C₄	—	2	8	no	—
485	C₄⋊C₄	—	2	8	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	#41×C₇₃	1	8	yes	—
493	C₂²⋊C₄	—	2	8	no	—
494	C₂²⋊C₄	—	2	8	no	—
495	C₂²⋊C₄	—	2	8	no	—
496	C₂²⋊C₄	—	2	8	no	—
497	C₂²⋊C₄	—	2	8	no	—
498	C₂²⋊C₄	—	2	8	no	—
499	C₂²⋊C₄	—	2	8	no	—
500	C₂²⋊C₄	—	2	8	no	—
501	C₂²⋊C₄	—	2	8	no	—
502	C₂²⋊C₄	—	4	4	no	—
503	C₂²⋊C₄	—	4	2	no	—
504	C₂²⋊C₄	—	4	4	no	—
505	C₂²⋊C₄	C₂×D₄×C₇₃	1	16	yes	—
506	C₄²	—	2	4	no	—
507	C₄²	—	2	8	no	—
508	C₄²	—	2	4	no	—
509	C₄²	—	2	4	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	4	no	—
512	C₄²	—	4	1	no	—
513	C₄²	—	4	2	no	—
514	C₄²	C₂×D₄×C₇₃	1	4	yes	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	2	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	C₂²×D₄×C₇₃	1	4	yes	—
527	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
528	Q₈	—	4	4	no	—
529	Q₈	—	8	4	no	—
530	D₄	—	4	4	no	—
531	D₄	—	4	16	no	—
532	D₄	—	4	8	no	—
533	D₄	—	8	4	no	—
534	D₄	—	8	8	no	—
535	D₄	—	8	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	4	16	no	—
560	C₂×C₄	—	4	16	no	—
561	C₂×C₄	—	8	4	no	—
562	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
563	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
564	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
565	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
566	C₂×C₄	C₂×#41×C₇₃	1	8	yes	—
567	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
568	C₂²	—	2	8	no	—
569	C₂²	—	2	4	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	4	no	—
580	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
581	C₂²	C₂²×#41×C₇₃	1	2	yes	—
582	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
583	C₂²	#585×C₇₃	1	2	yes	—
584	C₂²	#585×C₇₃	1	1	yes	characteristic
585	C₄	—	2	4	no	—
586	C₄	—	2	8	no	—
587	C₄	—	2	4	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	4	no	—
590	C₄	—	2	2	no	—
591	C₄	—	4	4	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	2	no	—
596	C₂	—	4	4	no	—
597	C₂	—	8	4	no	—
598	C₂	D₄×#41×C₇₃	1	2	yes	—
599	C₂	C₇₃×#3483	1	1	yes	characteristic
600	C₂	C₇₃×#3493	1	2	yes	—
601	C₂	C₇₃×#3496	1	1	yes	characteristic
602	C₂	C₇₃×#3545	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×#2734	C₂	semidirect
3. C₇₃×#2733	C₂	semidirect
4. C₇₃×#2682	C₂	semidirect
5. C₇₃×#2609	C₂	semidirect
6. C₇₃×#2555	C₂	semidirect
7. C₇₃×#2545	C₂	semidirect
8. C₇₃×#2543	C₂	semidirect
9. C₇₃×#2474	C₂	semidirect
10. C₇₃×#2456	C₂	semidirect
11. C₇₃×#2359	C₂	semidirect
12. C₄×#124×C₇₃	C₂	semidirect
13. C₇₃×#2293	C₂	semidirect
83. #124×C₇₃	D₄	semidirect
294. #59834	C₇₃	direct (N × H)
302. C₂×#555	C₂×C₇₃	semidirect
303. #2734	C₂×C₇₃	semidirect
304. #2733	C₂×C₇₃	semidirect
305. #2682	C₂×C₇₃	semidirect
306. #2609	C₂×C₇₃	semidirect
307. #2555	C₂×C₇₃	semidirect
308. #2545	C₂×C₇₃	semidirect
309. #2543	C₂×C₇₃	semidirect
310. #2474	C₂×C₇₃	semidirect
311. #2456	C₂×C₇₃	semidirect
312. #2359	C₂×C₇₃	semidirect
313. C₄×#124	C₂×C₇₃	semidirect
314. #2293	C₂×C₇₃	semidirect
315. C₇₃	#59834	direct (N × H)
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×#555×C₇₃	2
C₇₃×#2734	2
C₇₃×#2733	2
C₇₃×#2682	2
C₇₃×#2609	2
C₇₃×#2555	2
C₇₃×#2545	2
C₇₃×#2543	2
C₇₃×#2474	2
C₇₃×#2456	2
C₇₃×#2359	2
C₄×#124×C₇₃	2
C₇₃×#2293	2
#59834	73

Subgroups — C73×#59834 #32969238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59834 #32969238