Subgroups — C₇₃×#23535 #32932939

Order 18688.

1352 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2896	C₂	1	2	yes	maximal, complemented
4	C₂×#410×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2053	C₂	1	8	yes	maximal, complemented
6	C₂×H(3,ℤ/4)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₇₃	C₂²	1	2	yes	—
8	#575×C₇₃	—	2	4	no	—
9	#575×C₇₃	—	2	2	no	—
10	#575×C₇₃	C₂²	1	4	yes	—
11	C₂×#137×C₇₃	—	2	2	no	—
12	C₂×AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
13	C₂×#135×C₇₃	—	2	2	no	—
14	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#117×C₇₃	C₂²	1	2	yes	—
17	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
18	#424×C₇₃	—	2	2	no	—
19	#424×C₇₃	C₂²	1	4	yes	complemented
20	#423×C₇₃	—	2	2	no	—
21	#419×C₇₃	—	2	2	no	—
22	#418×C₇₃	—	2	2	no	—
23	#417×C₇₃	—	2	4	no	—
24	#416×C₇₃	C₂²	1	8	yes	complemented
25	#410×C₇₃	—	2	4	no	—
26	#410×C₇₃	C₂²	1	8	yes	complemented
27	C₂×#99×C₇₃	—	2	4	no	—
28	H(3,ℤ/4)×C₇₃	C₂²	1	4	yes	complemented
29	C₂×#41×C₇₃	—	2	2	no	—
30	C₂×#41×C₇₃	—	2	2	no	—
31	C₂×#41×C₇₃	—	2	2	no	—
32	C₂×#41×C₇₃	—	2	2	no	—
33	C₂×#41×C₇₃	—	2	2	no	—
34	C₂×#41×C₇₃	—	2	2	no	—
35	C₂×#41×C₇₃	—	2	2	no	—
36	C₂×#41×C₇₃	—	2	2	no	—
37	C₂×#41×C₇₃	—	2	2	no	—
38	C₂×#41×C₇₃	—	2	2	no	—
39	C₂×#41×C₇₃	D₄	1	4	yes	—
40	C₂×#41×C₇₃	C₂³	1	4	yes	—
41	C₂²×Q₈×C₇₃	D₄	1	2	yes	—
42	C₂²×D₄×C₇₃	—	2	2	no	—
43	C₂²×D₄×C₇₃	D₄	1	2	yes	—
44	C₂³×C₄×C₇₃	—	2	2	no	—
45	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
46	#137×C₇₃	—	2	8	no	—
47	#137×C₇₃	—	2	8	no	—
48	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
49	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
50	#135×C₇₃	—	2	8	no	—
51	#135×C₇₃	—	2	8	no	—
52	C₂×Q₁₆×C₇₃	—	2	2	no	—
53	C₂×SD₁₆×C₇₃	—	2	4	no	—
54	C₂×D₈×C₇₃	—	2	2	no	—
55	C₂×M₁₆×C₇₃	—	2	2	no	—
56	C₂×M₁₆×C₇₃	—	2	2	no	—
57	C₂×M₁₆×C₇₃	—	2	2	no	—
58	C₂×M₁₆×C₇₃	—	2	2	no	—
59	C₂×M₁₆×C₇₃	—	2	1	no	—
60	C₂×M₁₆×C₇₃	—	2	1	no	—
61	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
62	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₇₃	D₄	1	2	yes	—
64	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
65	#117×C₇₃	—	2	1	no	—
66	#117×C₇₃	—	2	1	no	—
67	#117×C₇₃	—	2	2	no	—
68	#117×C₇₃	—	2	2	no	—
69	#117×C₇₃	—	2	2	no	—
70	#117×C₇₃	D₄	1	2	yes	—
71	#117×C₇₃	C₂³	1	4	yes	—
72	#117×C₇₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
77	C₂×C₄²×C₇₃	—	2	1	no	—
78	C₂×C₄²×C₇₃	—	2	2	no	—
79	C₄⋊C₈×C₇₃	—	2	8	no	—
80	#103×C₇₃	—	2	8	no	—
81	#102×C₇₃	—	2	8	no	—
82	#99×C₇₃	—	2	16	no	—
83	C₂⁴×C₇₃	—	2	2	no	—
84	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
85	#41×C₇₃	—	2	4	no	—
86	#41×C₇₃	—	2	4	no	—
87	#41×C₇₃	—	2	4	no	—
88	#41×C₇₃	—	2	4	no	—
89	#41×C₇₃	—	2	4	no	—
90	#41×C₇₃	—	2	4	no	—
91	#41×C₇₃	—	2	4	no	—
92	#41×C₇₃	—	2	4	no	—
93	#41×C₇₃	—	4	2	no	—
94	#41×C₇₃	—	4	2	no	—
95	#41×C₇₃	—	4	2	no	—
96	#41×C₇₃	—	4	2	no	—
97	#41×C₇₃	—	4	2	no	—
98	#41×C₇₃	—	4	2	no	—
99	#41×C₇₃	—	4	2	no	—
100	#41×C₇₃	—	4	2	no	—
101	C₂×Q₈×C₇₃	—	2	2	no	—
102	C₂×Q₈×C₇₃	—	2	2	no	—
103	C₂×Q₈×C₇₃	—	2	2	no	—
104	C₂×Q₈×C₇₃	—	2	2	no	—
105	C₂×Q₈×C₇₃	—	2	2	no	—
106	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₇₃	—	2	4	no	—
108	C₂×D₄×C₇₃	—	2	4	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	2	no	—
113	C₂×D₄×C₇₃	—	2	2	no	—
114	C₂×D₄×C₇₃	—	4	2	no	—
115	C₂×D₄×C₇₃	—	4	2	no	—
116	C₂×D₄×C₇₃	—	4	2	no	—
117	C₂×D₄×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₇₃	—	2	2	no	—
120	C₂²×C₄×C₇₃	—	2	2	no	—
121	C₂²×C₄×C₇₃	—	2	4	no	—
122	C₂²×C₄×C₇₃	—	2	4	no	—
123	C₂²×C₄×C₇₃	—	4	2	no	—
124	C₂²×C₄×C₇₃	—	4	2	no	—
125	C₂²×C₄×C₇₃	—	4	2	no	—
126	C₂²×C₄×C₇₃	—	4	2	no	—
127	C₂²×C₄×C₇₃	—	4	2	no	—
128	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
134	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	#41	1	2	yes	—
136	C₂²×C₄×C₇₃	#41	1	2	yes	—
137	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
138	Q₁₆×C₇₃	—	2	8	no	—
139	SD₁₆×C₇₃	—	2	16	no	—
140	D₈×C₇₃	—	2	8	no	—
141	M₁₆×C₇₃	—	2	4	no	—
142	M₁₆×C₇₃	—	2	4	no	—
143	M₁₆×C₇₃	—	4	1	no	—
144	M₁₆×C₇₃	—	4	1	no	—
145	M₁₆×C₇₃	—	4	2	no	—
146	C₂×C₈×C₇₃	—	2	2	no	—
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	—	2	4	no	—
149	C₂×C₈×C₇₃	—	2	2	no	—
150	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₇₃	—	2	2	no	—
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	—	2	4	no	—
154	C₄⋊C₄×C₇₃	—	4	2	no	—
155	C₂²⋊C₄×C₇₃	—	2	2	no	—
156	C₂²⋊C₄×C₇₃	—	2	4	no	—
157	C₂²⋊C₄×C₇₃	—	4	2	no	—
158	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
159	C₄²×C₇₃	—	2	2	no	—
160	C₄²×C₇₃	—	2	2	no	—
161	C₄²×C₇₃	—	2	4	no	—
162	C₄²×C₇₃	—	4	2	no	—
163	C₂³×C₇₃	—	2	4	no	—
164	C₂³×C₇₃	—	4	2	no	—
165	C₂³×C₇₃	—	4	2	no	—
166	C₂³×C₇₃	—	8	1	no	—
167	C₂³×C₇₃	—	8	4	no	—
168	C₂³×C₇₃	#121	1	1	yes	characteristic
169	C₂³×C₇₃	#121	1	2	yes	—
170	C₂³×C₇₃	#121	1	1	yes	characteristic
171	C₂³×C₇₃	#121	1	2	yes	—
172	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₇₃	—	2	4	no	—
174	Q₈×C₇₃	—	2	4	no	—
175	Q₈×C₇₃	—	4	2	no	—
176	Q₈×C₇₃	—	4	2	no	—
177	D₄×C₇₃	—	2	4	no	—
178	D₄×C₇₃	—	2	4	no	—
179	D₄×C₇₃	—	4	4	no	—
180	D₄×C₇₃	—	4	4	no	—
181	D₄×C₇₃	—	4	4	no	—
182	D₄×C₇₃	—	4	4	no	—
183	D₄×C₇₃	—	4	2	no	—
184	D₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	—	2	4	no	—
186	C₂×C₄×C₇₃	—	2	4	no	—
187	C₂×C₄×C₇₃	—	4	2	no	—
188	C₂×C₄×C₇₃	—	4	2	no	—
189	C₂×C₄×C₇₃	—	4	4	no	—
190	C₂×C₄×C₇₃	—	4	4	no	—
191	C₂×C₄×C₇₃	—	4	4	no	—
192	C₂×C₄×C₇₃	—	4	4	no	—
193	C₂×C₄×C₇₃	—	4	4	no	—
194	C₂×C₄×C₇₃	—	8	2	no	—
195	C₂×C₄×C₇₃	—	8	4	no	—
196	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
197	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
198	C₂×C₄×C₇₃	#120	1	2	yes	—
199	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
200	C₂×C₄×C₇₃	#121	1	2	yes	—
201	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
202	C₂×C₄×C₇₃	#121	1	2	yes	—
203	C₂×C₄×C₇₃	#123	1	2	yes	—
204	C₂×C₄×C₇₃	#123	1	2	yes	—
205	C₂×C₄×C₇₃	#123	1	2	yes	—
206	C₂×C₄×C₇₃	#123	1	2	yes	—
207	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
208	C₂×C₄×C₇₃	#124	1	2	yes	—
209	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
210	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
214	C₈×C₇₃	—	2	4	no	—
215	C₈×C₇₃	—	4	2	no	—
216	C₂²×C₇₃	—	4	1	no	—
217	C₂²×C₇₃	—	4	2	no	—
218	C₂²×C₇₃	—	4	2	no	—
219	C₂²×C₇₃	—	4	1	no	—
220	C₂²×C₇₃	—	4	1	no	—
221	C₂²×C₇₃	—	4	4	no	—
222	C₂²×C₇₃	—	8	4	no	—
223	C₂²×C₇₃	—	8	4	no	—
224	C₂²×C₇₃	—	8	4	no	—
225	C₂²×C₇₃	#394	1	1	yes	characteristic
226	C₂²×C₇₃	#394	1	2	yes	—
227	C₂²×C₇₃	#394	1	1	yes	characteristic
228	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
229	C₂²×C₇₃	C₂×#121	1	2	yes	—
230	C₄×C₇₃	—	4	4	no	—
231	C₄×C₇₃	—	4	4	no	—
232	C₄×C₇₃	—	8	4	no	—
233	C₄×C₇₃	#394	1	1	yes	characteristic
234	C₄×C₇₃	#394	1	2	yes	—
235	C₄×C₇₃	#394	1	1	yes	characteristic
236	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
237	C₄×C₇₃	C₂×#123	1	2	yes	—
238	C₄×C₇₃	C₂×#124	1	1	yes	characteristic
239	#23535	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂×C₇₃	—	2	1	no	—
241	C₂×C₇₃	—	2	2	no	—
242	C₂×C₇₃	—	2	1	no	—
243	C₂×C₇₃	—	2	2	no	—
244	C₂×C₇₃	—	2	1	no	—
245	C₂×C₇₃	—	8	4	no	—
246	C₂×C₇₃	C₂×#394	1	1	yes	characteristic
247	C₂×#575	C₂×C₇₃	1	1	yes	characteristic
248	#2905	C₂×C₇₃	1	1	yes	characteristic, complemented
249	#2896	C₂×C₇₃	1	2	yes	complemented
250	C₂×#410	C₂×C₇₃	1	2	yes	complemented
251	#2053	C₂×C₇₃	1	8	yes	complemented
252	C₂×H(3,ℤ/4)	C₂×C₇₃	1	1	yes	characteristic, complemented
253	C₇₃	#23535	1	1	yes	characteristic, direct product factor, Sylow
254	C₂²×#41	C₂²×C₇₃	1	2	yes	—
255	#575	—	2	4	no	—
256	#575	—	2	2	no	—
257	#575	C₂²×C₇₃	1	4	yes	—
258	C₂×#137	—	2	2	no	—
259	C₂×AGL(1,ℤ/8)	—	2	2	no	—
260	C₂×#135	—	2	2	no	—
261	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
262	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
263	C₂×#117	C₂²×C₇₃	1	2	yes	—
264	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
265	#424	—	2	2	no	—
266	#424	C₂²×C₇₃	1	4	yes	complemented
267	#423	—	2	2	no	—
268	#419	—	2	2	no	—
269	#418	—	2	2	no	—
270	#417	—	2	4	no	—
271	#416	C₂²×C₇₃	1	8	yes	complemented
272	#410	—	2	4	no	—
273	#410	C₂²×C₇₃	1	8	yes	complemented
274	C₂×#99	—	2	4	no	—
275	H(3,ℤ/4)	C₂²×C₇₃	1	4	yes	complemented
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	2	no	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	—	2	2	no	—
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	—	2	2	no	—
286	C₂×#41	D₄×C₇₃	1	4	yes	—
287	C₂×#41	C₂³×C₇₃	1	4	yes	—
288	C₂²×Q₈	D₄×C₇₃	1	2	yes	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	D₄×C₇₃	1	2	yes	—
291	C₂³×C₄	—	2	2	no	—
292	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
293	#137	—	2	8	no	—
294	#137	—	2	8	no	—
295	AGL(1,ℤ/8)	—	2	8	no	—
296	AGL(1,ℤ/8)	—	2	8	no	—
297	#135	—	2	8	no	—
298	#135	—	2	8	no	—
299	C₂×Q₁₆	—	2	2	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×D₈	—	2	2	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂×M₁₆	D₄×C₇₃	1	2	yes	—
309	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
310	C₂²×C₈	D₄×C₇₃	1	2	yes	—
311	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
312	#117	—	2	1	no	—
313	#117	—	2	1	no	—
314	#117	—	2	2	no	—
315	#117	—	2	2	no	—
316	#117	—	2	2	no	—
317	#117	D₄×C₇₃	1	2	yes	—
318	#117	C₂³×C₇₃	1	4	yes	—
319	#117	C₂³×C₇₃	1	2	yes	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	2	no	—
326	C₄⋊C₈	—	2	8	no	—
327	#103	—	2	8	no	—
328	#102	—	2	8	no	—
329	#99	—	2	16	no	—
330	C₂⁴	—	2	2	no	—
331	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
332	#41	—	2	4	no	—
333	#41	—	2	4	no	—
334	#41	—	2	4	no	—
335	#41	—	2	4	no	—
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	2	4	no	—
339	#41	—	2	4	no	—
340	#41	—	4	2	no	—
341	#41	—	4	2	no	—
342	#41	—	4	2	no	—
343	#41	—	4	2	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
380	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
381	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
382	C₂²×C₄	#41×C₇₃	1	2	yes	—
383	C₂²×C₄	#41×C₇₃	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
385	Q₁₆	—	2	8	no	—
386	SD₁₆	—	2	16	no	—
387	D₈	—	2	8	no	—
388	M₁₆	—	2	4	no	—
389	M₁₆	—	2	4	no	—
390	M₁₆	—	4	1	no	—
391	M₁₆	—	4	1	no	—
392	M₁₆	—	4	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	4	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	4	no	—
409	C₄²	—	4	2	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	8	1	no	—
414	C₂³	—	8	4	no	—
415	C₂³	#121×C₇₃	1	1	yes	characteristic
416	C₂³	#121×C₇₃	1	2	yes	—
417	C₂³	#121×C₇₃	1	1	yes	characteristic
418	C₂³	#121×C₇₃	1	2	yes	—
419	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
420	Q₈	—	2	4	no	—
421	Q₈	—	2	4	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	D₄	—	2	4	no	—
425	D₄	—	2	4	no	—
426	D₄	—	4	4	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	—	8	4	no	—
443	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
444	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
445	C₂×C₄	#120×C₇₃	1	2	yes	—
446	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
447	C₂×C₄	#121×C₇₃	1	2	yes	—
448	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
449	C₂×C₄	#121×C₇₃	1	2	yes	—
450	C₂×C₄	#123×C₇₃	1	2	yes	—
451	C₂×C₄	#123×C₇₃	1	2	yes	—
452	C₂×C₄	#123×C₇₃	1	2	yes	—
453	C₂×C₄	#123×C₇₃	1	2	yes	—
454	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
455	C₂×C₄	#124×C₇₃	1	2	yes	—
456	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
461	C₈	—	2	4	no	—
462	C₈	—	4	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	8	4	no	—
470	C₂²	—	8	4	no	—
471	C₂²	—	8	4	no	—
472	C₂²	#394×C₇₃	1	1	yes	characteristic
473	C₂²	#394×C₇₃	1	2	yes	—
474	C₂²	#394×C₇₃	1	1	yes	characteristic
475	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
476	C₂²	C₂×#121×C₇₃	1	2	yes	—
477	C₄	—	4	4	no	—
478	C₄	—	4	4	no	—
479	C₄	—	8	4	no	—
480	C₄	#394×C₇₃	1	1	yes	characteristic
481	C₄	#394×C₇₃	1	2	yes	—
482	C₄	#394×C₇₃	1	1	yes	characteristic
483	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
484	C₄	C₂×#123×C₇₃	1	2	yes	—
485	C₄	C₂×#124×C₇₃	1	1	yes	characteristic
486	C₂	—	2	1	no	—
487	C₂	—	2	2	no	—
488	C₂	—	2	1	no	—
489	C₂	—	2	2	no	—
490	C₂	—	2	1	no	—
491	C₂	—	8	4	no	—
492	C₂	C₂×#394×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇₃	C₂×#124
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
socle	C₂×C₇₃	C₂×#394
prime radical	C₂×#575×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₃×#2905	C₂	semidirect
3. C₇₃×#2896	C₂	semidirect
4. C₂×#410×C₇₃	C₂	semidirect
5. C₇₃×#2053	C₂	semidirect
6. C₂×H(3,ℤ/4)×C₇₃	C₂	semidirect
19. #424×C₇₃	C₂²	semidirect
24. #416×C₇₃	C₂²	semidirect
26. #410×C₇₃	C₂²	semidirect
28. H(3,ℤ/4)×C₇₃	C₂²	semidirect
239. #23535	C₇₃	direct (N × H)
248. #2905	C₂×C₇₃	semidirect
249. #2896	C₂×C₇₃	semidirect
250. C₂×#410	C₂×C₇₃	semidirect
251. #2053	C₂×C₇₃	semidirect
252. C₂×H(3,ℤ/4)	C₂×C₇₃	semidirect
253. C₇₃	#23535	direct (N × H)
266. #424	C₂²×C₇₃	semidirect
271. #416	C₂²×C₇₃	semidirect
273. #410	C₂²×C₇₃	semidirect
275. H(3,ℤ/4)	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₇₃	2
C₇₃×#2905	2
C₇₃×#2896	2
C₂×#410×C₇₃	2
C₇₃×#2053	2
C₂×H(3,ℤ/4)×C₇₃	2
#23535	73

Subgroups — C73×#23535 #32932939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23535 #32932939