Subgroups — C₂×C₇₃×#3175 #32970083

Order 18688.

1970 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#3175	C₂	1	16	yes	maximal, direct product factor
3	C₂×#500×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#495×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#489×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₂×#468×C₇₃	C₂	1	2	yes	maximal, complemented
7	C₂×#467×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#466×C₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂×#440×C₇₃	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×Q₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#405×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
15	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
18	#542×C₇₃	—	2	8	no	—
19	#542×C₇₃	C₂²	1	16	yes	complemented
20	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
21	C₂×#126×C₇₃	—	2	2	no	—
22	C₂×#124×C₇₃	—	2	2	no	—
23	C₂×#124×C₇₃	C₂²	1	2	yes	—
24	C₂×#123×C₇₃	—	2	2	no	—
25	C₂×C₂²⋊Q₈×C₇₃	—	2	2	no	—
26	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
27	C₂×#121×C₇₃	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
30	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
31	#500×C₇₃	C₂²	1	8	yes	complemented
32	#495×C₇₃	C₂²	1	8	yes	complemented
33	#489×C₇₃	C₂²	1	16	yes	complemented
34	#468×C₇₃	C₂²	1	16	yes	complemented
35	#467×C₇₃	C₂²	1	8	yes	complemented
36	#466×C₇₃	C₂²	1	8	yes	—
37	#440×C₇₃	C₂²	1	16	yes	complemented
38	C₄×Q₁₆×C₇₃	C₂²	1	8	yes	complemented
39	C₄×D₈×C₇₃	C₂²	1	8	yes	complemented
40	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×#107×C₇₃	C₂²	1	2	yes	—
43	C₂×#103×C₇₃	C₂²	1	2	yes	—
44	C₂×#103×C₇₃	C₂²	1	2	yes	—
45	C₂×#102×C₇₃	C₂²	1	2	yes	—
46	C₂×#102×C₇₃	C₂²	1	2	yes	—
47	#405×C₇₃	C₂²	1	8	yes	complemented
48	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
49	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₇₃	—	2	2	no	—
53	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₇₃	—	2	2	no	—
55	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₇₃	—	2	2	no	—
57	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
58	C₂×Q₁₆×C₇₃	—	2	4	no	—
59	C₂×Q₁₆×C₇₃	C₂³	1	4	yes	—
60	C₂×SD₁₆×C₇₃	—	2	8	no	—
61	C₂×SD₁₆×C₇₃	C₂³	1	8	yes	—
62	C₂×D₈×C₇₃	—	2	4	no	—
63	C₂×D₈×C₇₃	C₂³	1	4	yes	—
64	C₂×M₁₆×C₇₃	—	2	4	no	—
65	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
66	C₂²×C₈×C₇₃	—	2	4	no	—
67	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
70	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
72	C₄⋊Q₈×C₇₃	—	2	4	no	—
73	C₄⋊Q₈×C₇₃	C₂³	1	8	yes	—
74	#126×C₇₃	—	2	16	no	—
75	#124×C₇₃	—	2	16	no	—
76	#124×C₇₃	—	2	4	no	—
77	#124×C₇₃	C₂³	1	8	yes	—
78	#123×C₇₃	—	2	16	no	—
79	C₂²⋊Q₈×C₇₃	—	2	4	no	—
80	C₂²⋊Q₈×C₇₃	—	2	16	no	—
81	C₂²⋊Q₈×C₇₃	C₂³	1	8	yes	—
82	#121×C₇₃	—	2	4	no	—
83	#121×C₇₃	C₂³	1	8	yes	—
84	C₄×Q₈×C₇₃	—	2	4	no	—
85	C₄×Q₈×C₇₃	C₂³	1	8	yes	—
86	C₄×D₄×C₇₃	—	2	4	no	—
87	C₄×D₄×C₇₃	C₂³	1	8	yes	—
88	#117×C₇₃	D₄	1	4	yes	—
89	#117×C₇₃	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
92	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
93	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₇₃	—	2	2	no	—
105	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
107	#107×C₇₃	C₂³	1	4	yes	—
108	#107×C₇₃	C₂³	1	4	yes	—
109	#107×C₇₃	C₂³	1	8	yes	—
110	#103×C₇₃	C₂³	1	8	yes	—
111	#103×C₇₃	C₂³	1	8	yes	—
112	#102×C₇₃	C₂³	1	8	yes	—
113	#102×C₇₃	C₂³	1	8	yes	—
114	#97×C₇₃	C₂³	1	4	yes	—
115	#97×C₇₃	C₂³	1	4	yes	—
116	C₄×C₈×C₇₃	C₂³	1	4	yes	—
117	C₄×C₈×C₇₃	C₂³	1	4	yes	—
118	C₂⁴×C₇₃	—	2	2	no	—
119	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₇₃	—	2	2	no	—
121	C₂×Q₈×C₇₃	—	2	8	no	—
122	C₂×Q₈×C₇₃	—	2	4	no	—
123	C₂×Q₈×C₇₃	—	2	4	no	—
124	C₂×Q₈×C₇₃	—	8	4	no	—
125	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
126	C₂×D₄×C₇₃	—	2	8	no	—
127	C₂×D₄×C₇₃	—	2	2	no	—
128	C₂×D₄×C₇₃	—	2	4	no	—
129	C₂×D₄×C₇₃	—	2	4	no	—
130	C₂×D₄×C₇₃	—	8	4	no	—
131	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₇₃	—	2	2	no	—
133	C₂²×C₄×C₇₃	—	2	2	no	—
134	C₂²×C₄×C₇₃	—	2	2	no	—
135	C₂²×C₄×C₇₃	—	2	2	no	—
136	C₂²×C₄×C₇₃	—	2	2	no	—
137	C₂²×C₄×C₇₃	—	2	8	no	—
138	C₂²×C₄×C₇₃	—	8	4	no	—
139	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
147	Q₁₆×C₇₃	—	2	8	no	—
148	SD₁₆×C₇₃	—	2	16	no	—
149	D₈×C₇₃	—	2	8	no	—
150	M₁₆×C₇₃	—	2	8	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×C₇₃	—	2	8	no	—
154	C₂×C₈×C₇₃	#41	1	4	yes	—
155	C₂×C₈×C₇₃	#41	1	4	yes	—
156	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
157	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
158	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
159	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
160	C₄⋊C₄×C₇₃	—	2	8	no	—
161	C₄⋊C₄×C₇₃	—	2	8	no	—
162	C₄⋊C₄×C₇₃	—	2	8	no	—
163	C₄⋊C₄×C₇₃	—	2	2	no	—
164	C₄⋊C₄×C₇₃	—	2	2	no	—
165	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
166	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
167	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
169	C₂²⋊C₄×C₇₃	—	2	8	no	—
170	C₂²⋊C₄×C₇₃	—	2	8	no	—
171	C₂²⋊C₄×C₇₃	—	2	8	no	—
172	C₂²⋊C₄×C₇₃	—	2	8	no	—
173	C₂²⋊C₄×C₇₃	—	2	8	no	—
174	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
175	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
176	C₄²×C₇₃	—	2	8	no	—
177	C₄²×C₇₃	C₂×D₄	1	2	yes	—
178	C₄²×C₇₃	C₂×D₄	1	2	yes	—
179	C₄²×C₇₃	C₂⁴	1	2	yes	—
180	C₄²×C₇₃	C₂⁴	1	2	yes	—
181	C₂³×C₇₃	—	2	2	no	—
182	C₂³×C₇₃	—	2	2	no	—
183	C₂³×C₇₃	—	2	2	no	—
184	C₂³×C₇₃	—	2	4	no	—
185	C₂³×C₇₃	—	4	4	no	—
186	C₂³×C₇₃	—	4	4	no	—
187	C₂³×C₇₃	—	4	4	no	—
188	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
189	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₇₃	—	2	4	no	—
191	Q₈×C₇₃	—	2	4	no	—
192	Q₈×C₇₃	—	4	4	no	—
193	Q₈×C₇₃	—	8	8	no	—
194	D₄×C₇₃	—	2	4	no	—
195	D₄×C₇₃	—	2	4	no	—
196	D₄×C₇₃	—	4	4	no	—
197	D₄×C₇₃	—	8	8	no	—
198	C₂×C₄×C₇₃	—	2	2	no	—
199	C₂×C₄×C₇₃	—	2	2	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	2	2	no	—
202	C₂×C₄×C₇₃	—	2	2	no	—
203	C₂×C₄×C₇₃	—	2	4	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	2	no	—
206	C₂×C₄×C₇₃	—	2	4	no	—
207	C₂×C₄×C₇₃	—	2	4	no	—
208	C₂×C₄×C₇₃	—	2	4	no	—
209	C₂×C₄×C₇₃	—	4	4	no	—
210	C₂×C₄×C₇₃	—	4	4	no	—
211	C₂×C₄×C₇₃	—	4	4	no	—
212	C₂×C₄×C₇₃	—	8	8	no	—
213	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
220	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
221	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
222	C₈×C₇₃	—	2	2	no	—
223	C₈×C₇₃	—	2	2	no	—
224	C₈×C₇₃	C₂×#41	1	4	yes	—
225	C₈×C₇₃	C₂×#41	1	4	yes	—
226	C₂²×C₇₃	—	2	2	no	—
227	C₂²×C₇₃	—	2	2	no	—
228	C₂²×C₇₃	—	2	2	no	—
229	C₂²×C₇₃	—	4	4	no	—
230	C₂²×C₇₃	—	4	4	no	—
231	C₂²×C₇₃	—	4	4	no	—
232	C₂²×C₇₃	—	4	4	no	—
233	C₂²×C₇₃	—	8	8	no	—
234	C₂²×C₇₃	#532	1	2	yes	—
235	C₂²×C₇₃	#576	1	2	yes	—
236	C₂²×C₇₃	#578	1	2	yes	—
237	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
238	C₄×C₇₃	—	2	2	no	—
239	C₄×C₇₃	—	2	2	no	—
240	C₄×C₇₃	—	2	2	no	—
241	C₄×C₇₃	—	2	2	no	—
242	C₄×C₇₃	—	2	2	no	—
243	C₄×C₇₃	—	4	4	no	—
244	C₄×C₇₃	—	4	4	no	—
245	C₄×C₇₃	—	4	4	no	—
246	C₄×C₇₃	#532	1	2	yes	—
247	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
248	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
249	C₂×#3175	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂×C₇₃	—	4	2	no	—
251	C₂×C₇₃	—	8	4	no	—
252	C₂×C₇₃	#3175	1	4	yes	direct product factor
253	C₂×C₇₃	C₂×#532	1	1	yes	characteristic
254	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
255	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
256	C₂×#542	C₂×C₇₃	1	2	yes	complemented
257	#3175	C₂×C₇₃	1	16	yes	direct product factor
258	C₂×#500	C₂×C₇₃	1	1	yes	characteristic, complemented
259	C₂×#495	C₂×C₇₃	1	1	yes	characteristic, complemented
260	C₂×#489	C₂×C₇₃	1	2	yes	complemented
261	C₂×#468	C₂×C₇₃	1	2	yes	complemented
262	C₂×#467	C₂×C₇₃	1	1	yes	characteristic, complemented
263	C₂×#466	C₂×C₇₃	1	1	yes	characteristic
264	C₂×#440	C₂×C₇₃	1	2	yes	complemented
265	C₂×C₄×Q₁₆	C₂×C₇₃	1	1	yes	characteristic, complemented
266	C₂×C₄×D₈	C₂×C₇₃	1	1	yes	characteristic, complemented
267	C₂×#405	C₂×C₇₃	1	1	yes	characteristic, complemented
268	C₇₃	C₂×#3175	1	1	yes	characteristic, direct product factor, Sylow
269	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
270	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
271	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
272	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
273	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
274	#542	—	2	8	no	—
275	#542	C₂²×C₇₃	1	16	yes	complemented
276	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
277	C₂×#126	—	2	2	no	—
278	C₂×#124	—	2	2	no	—
279	C₂×#124	C₂²×C₇₃	1	2	yes	—
280	C₂×#123	—	2	2	no	—
281	C₂×C₂²⋊Q₈	—	2	2	no	—
282	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
283	C₂×#121	C₂²×C₇₃	1	2	yes	—
284	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
285	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
286	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
287	#500	C₂²×C₇₃	1	8	yes	complemented
288	#495	C₂²×C₇₃	1	8	yes	complemented
289	#489	C₂²×C₇₃	1	16	yes	complemented
290	#468	C₂²×C₇₃	1	16	yes	complemented
291	#467	C₂²×C₇₃	1	8	yes	complemented
292	#466	C₂²×C₇₃	1	8	yes	—
293	#440	C₂²×C₇₃	1	16	yes	complemented
294	C₄×Q₁₆	C₂²×C₇₃	1	8	yes	complemented
295	C₄×D₈	C₂²×C₇₃	1	8	yes	complemented
296	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
297	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
298	C₂×#107	C₂²×C₇₃	1	2	yes	—
299	C₂×#103	C₂²×C₇₃	1	2	yes	—
300	C₂×#103	C₂²×C₇₃	1	2	yes	—
301	C₂×#102	C₂²×C₇₃	1	2	yes	—
302	C₂×#102	C₂²×C₇₃	1	2	yes	—
303	#405	C₂²×C₇₃	1	8	yes	complemented
304	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
305	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
306	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
307	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
308	C₂²×Q₈	—	2	2	no	—
309	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
312	C₂³×C₄	—	2	2	no	—
313	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
314	C₂×Q₁₆	—	2	4	no	—
315	C₂×Q₁₆	C₂³×C₇₃	1	4	yes	—
316	C₂×SD₁₆	—	2	8	no	—
317	C₂×SD₁₆	C₂³×C₇₃	1	8	yes	—
318	C₂×D₈	—	2	4	no	—
319	C₂×D₈	C₂³×C₇₃	1	4	yes	—
320	C₂×M₁₆	—	2	4	no	—
321	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
322	C₂²×C₈	—	2	4	no	—
323	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
325	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
328	C₄⋊Q₈	—	2	4	no	—
329	C₄⋊Q₈	C₂³×C₇₃	1	8	yes	—
330	#126	—	2	16	no	—
331	#124	—	2	16	no	—
332	#124	—	2	4	no	—
333	#124	C₂³×C₇₃	1	8	yes	—
334	#123	—	2	16	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	—	2	16	no	—
337	C₂²⋊Q₈	C₂³×C₇₃	1	8	yes	—
338	#121	—	2	4	no	—
339	#121	C₂³×C₇₃	1	8	yes	—
340	C₄×Q₈	—	2	4	no	—
341	C₄×Q₈	C₂³×C₇₃	1	8	yes	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	C₂³×C₇₃	1	8	yes	—
344	#117	D₄×C₇₃	1	4	yes	—
345	#117	C₂³×C₇₃	1	4	yes	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
363	#107	C₂³×C₇₃	1	4	yes	—
364	#107	C₂³×C₇₃	1	4	yes	—
365	#107	C₂³×C₇₃	1	8	yes	—
366	#103	C₂³×C₇₃	1	8	yes	—
367	#103	C₂³×C₇₃	1	8	yes	—
368	#102	C₂³×C₇₃	1	8	yes	—
369	#102	C₂³×C₇₃	1	8	yes	—
370	#97	C₂³×C₇₃	1	4	yes	—
371	#97	C₂³×C₇₃	1	4	yes	—
372	C₄×C₈	C₂³×C₇₃	1	4	yes	—
373	C₄×C₈	C₂³×C₇₃	1	4	yes	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	8	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	8	4	no	—
381	C₂×Q₈	C₂⁴×C₇₃	1	4	yes	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	8	4	no	—
387	C₂×D₄	C₂⁴×C₇₃	1	4	yes	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	8	4	no	—
395	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
403	Q₁₆	—	2	8	no	—
404	SD₁₆	—	2	16	no	—
405	D₈	—	2	8	no	—
406	M₁₆	—	2	8	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	8	no	—
410	C₂×C₈	#41×C₇₃	1	4	yes	—
411	C₂×C₈	#41×C₇₃	1	4	yes	—
412	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
413	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
414	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
415	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
422	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
423	C₄⋊C₄	C₂⁴×C₇₃	1	4	yes	—
424	C₄⋊C₄	C₂⁴×C₇₃	1	4	yes	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
431	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
432	C₄²	—	2	8	no	—
433	C₄²	C₂×D₄×C₇₃	1	2	yes	—
434	C₄²	C₂×D₄×C₇₃	1	2	yes	—
435	C₄²	C₂⁴×C₇₃	1	2	yes	—
436	C₄²	C₂⁴×C₇₃	1	2	yes	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
445	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
446	Q₈	—	2	4	no	—
447	Q₈	—	2	4	no	—
448	Q₈	—	4	4	no	—
449	Q₈	—	8	8	no	—
450	D₄	—	2	4	no	—
451	D₄	—	2	4	no	—
452	D₄	—	4	4	no	—
453	D₄	—	8	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	8	8	no	—
469	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
476	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
477	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	C₂×#41×C₇₃	1	4	yes	—
481	C₈	C₂×#41×C₇₃	1	4	yes	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	8	no	—
490	C₂²	#532×C₇₃	1	2	yes	—
491	C₂²	#576×C₇₃	1	2	yes	—
492	C₂²	#578×C₇₃	1	2	yes	—
493	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	4	no	—
502	C₄	#532×C₇₃	1	2	yes	—
503	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
504	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
505	C₂	—	4	2	no	—
506	C₂	—	8	4	no	—
507	C₂	C₇₃×#3175	1	4	yes	direct product factor
508	C₂	C₂×#532×C₇₃	1	1	yes	characteristic
509	C₂	C₂×#576×C₇₃	1	1	yes	characteristic
510	C₂	C₂×#578×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
prime radical	C₂×#466×C₇₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#542×C₇₃	C₂	semidirect
2. C₇₃×#3175	C₂	direct (N × H)
3. C₂×#500×C₇₃	C₂	semidirect
4. C₂×#495×C₇₃	C₂	semidirect
5. C₂×#489×C₇₃	C₂	semidirect
6. C₂×#468×C₇₃	C₂	semidirect
7. C₂×#467×C₇₃	C₂	semidirect
9. C₂×#440×C₇₃	C₂	semidirect
10. C₂×C₄×Q₁₆×C₇₃	C₂	semidirect
11. C₂×C₄×D₈×C₇₃	C₂	semidirect
12. C₂×#405×C₇₃	C₂	semidirect
19. #542×C₇₃	C₂²	semidirect
31. #500×C₇₃	C₂²	semidirect
32. #495×C₇₃	C₂²	semidirect
33. #489×C₇₃	C₂²	semidirect
34. #468×C₇₃	C₂²	semidirect
35. #467×C₇₃	C₂²	semidirect
37. #440×C₇₃	C₂²	semidirect
38. C₄×Q₁₆×C₇₃	C₂²	semidirect
39. C₄×D₈×C₇₃	C₂²	semidirect
47. #405×C₇₃	C₂²	semidirect
249. C₂×#3175	C₇₃	direct (N × H)
252. C₂×C₇₃	#3175	direct (N × H)
256. C₂×#542	C₂×C₇₃	semidirect
257. #3175	C₂×C₇₃	direct (N × H)
258. C₂×#500	C₂×C₇₃	semidirect
259. C₂×#495	C₂×C₇₃	semidirect
260. C₂×#489	C₂×C₇₃	semidirect
261. C₂×#468	C₂×C₇₃	semidirect
262. C₂×#467	C₂×C₇₃	semidirect
264. C₂×#440	C₂×C₇₃	semidirect
265. C₂×C₄×Q₁₆	C₂×C₇₃	semidirect
266. C₂×C₄×D₈	C₂×C₇₃	semidirect
267. C₂×#405	C₂×C₇₃	semidirect
268. C₇₃	C₂×#3175	direct (N × H)
275. #542	C₂²×C₇₃	semidirect
287. #500	C₂²×C₇₃	semidirect
288. #495	C₂²×C₇₃	semidirect
289. #489	C₂²×C₇₃	semidirect
290. #468	C₂²×C₇₃	semidirect
291. #467	C₂²×C₇₃	semidirect
293. #440	C₂²×C₇₃	semidirect
294. C₄×Q₁₆	C₂²×C₇₃	semidirect
295. C₄×D₈	C₂²×C₇₃	semidirect
303. #405	C₂²×C₇₃	semidirect
507. C₂	C₇₃×#3175	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#542×C₇₃	2
C₇₃×#3175	2
C₂×#500×C₇₃	2
C₂×#495×C₇₃	2
C₂×#489×C₇₃	2
C₂×#468×C₇₃	2
C₂×#467×C₇₃	2
C₂×#466×C₇₃	2
C₂×#440×C₇₃	2
C₂×C₄×Q₁₆×C₇₃	2
C₂×C₄×D₈×C₇₃	2
C₂×#405×C₇₃	2
C₂×#3175	73

Subgroups — C2×C73×#3175 #32970083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#3175 #32970083