Subgroups — C₂×C₆₇×#3119 #30739799

Order 17152.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3119	C₂	1	16	yes	maximal, direct product factor
4	C₂×#481×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#480×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#479×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#478×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#460×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#459×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#449×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#449×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#442×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#433×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
22	#540×C₆₇	—	2	4	no	—
23	#540×C₆₇	C₂²	1	8	yes	complemented
24	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#123×C₆₇	—	2	1	no	—
27	C₂×#123×C₆₇	—	2	1	no	—
28	C₂×#121×C₆₇	—	2	1	no	—
29	C₂×#121×C₆₇	—	2	1	no	—
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
32	#520×C₆₇	—	2	4	no	—
33	#520×C₆₇	C₂²	1	8	yes	complemented
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	—	2	1	no	—
37	C₂×C₄×D₄×C₆₇	—	2	1	no	—
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#117×C₆₇	—	2	1	no	—
43	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
45	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
46	#481×C₆₇	C₂²	1	8	yes	complemented
47	#480×C₆₇	C₂²	1	8	yes	complemented
48	#479×C₆₇	C₂²	1	8	yes	complemented
49	#478×C₆₇	C₂²	1	8	yes	complemented
50	#460×C₆₇	C₂²	1	8	yes	complemented
51	#459×C₆₇	C₂²	1	8	yes	complemented
52	#449×C₆₇	C₂²	1	8	yes	complemented
53	#449×C₆₇	C₂²	1	8	yes	complemented
54	#442×C₆₇	C₂²	1	8	yes	complemented
55	#440×C₆₇	C₂²	1	8	yes	complemented
56	C₄×SD₁₆×C₆₇	C₂²	1	8	yes	complemented
57	C₄×D₈×C₆₇	C₂²	1	8	yes	complemented
58	#433×C₆₇	C₂²	1	8	yes	complemented
59	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
61	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
67	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
69	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
70	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
71	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
72	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
74	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
75	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
77	C₂×#41×C₆₇	—	2	4	no	—
78	C₂×#41×C₆₇	—	2	4	no	—
79	C₂×#41×C₆₇	—	2	2	no	—
80	C₂×#41×C₆₇	C₂³	1	4	yes	—
81	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₆₇	—	2	1	no	—
83	C₂²×D₄×C₆₇	—	2	1	no	—
84	C₂²×D₄×C₆₇	—	2	1	no	—
85	C₂²×D₄×C₆₇	—	2	1	no	—
86	C₂²×D₄×C₆₇	—	2	1	no	—
87	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₆₇	—	2	1	no	—
91	C₂³×C₄×C₆₇	—	2	1	no	—
92	C₂³×C₄×C₆₇	—	2	1	no	—
93	C₂³×C₄×C₆₇	—	2	1	no	—
94	C₂³×C₄×C₆₇	—	2	1	no	—
95	C₂³×C₄×C₆₇	—	2	1	no	—
96	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂×SD₁₆×C₆₇	—	2	4	no	—
98	C₂×SD₁₆×C₆₇	—	2	4	no	—
99	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
101	C₂×D₈×C₆₇	—	2	4	no	—
102	C₂×D₈×C₆₇	—	2	4	no	—
103	C₂×D₈×C₆₇	C₂³	1	4	yes	—
104	C₂×D₈×C₆₇	C₂³	1	4	yes	—
105	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
109	#127×C₆₇	—	2	2	no	—
110	#127×C₆₇	C₂³	1	4	yes	—
111	#125×C₆₇	—	2	2	no	—
112	#125×C₆₇	C₂³	1	4	yes	—
113	#123×C₆₇	—	2	8	no	—
114	#123×C₆₇	—	2	8	no	—
115	#121×C₆₇	—	2	2	no	—
116	#121×C₆₇	—	2	2	no	—
117	#121×C₆₇	—	2	8	no	—
118	#121×C₆₇	—	2	8	no	—
119	#121×C₆₇	C₂³	1	4	yes	—
120	#121×C₆₇	C₂³	1	4	yes	—
121	C₄×Q₈×C₆₇	—	2	2	no	—
122	C₄×Q₈×C₆₇	—	2	2	no	—
123	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
124	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
125	C₄×D₄×C₆₇	—	2	8	no	—
126	C₄×D₄×C₆₇	—	2	8	no	—
127	C₄×D₄×C₆₇	—	2	2	no	—
128	C₄×D₄×C₆₇	—	2	2	no	—
129	C₄×D₄×C₆₇	—	2	2	no	—
130	C₄×D₄×C₆₇	—	2	2	no	—
131	C₄×D₄×C₆₇	C₂³	1	4	yes	—
132	C₄×D₄×C₆₇	C₂³	1	4	yes	—
133	C₄×D₄×C₆₇	C₂³	1	4	yes	—
134	C₄×D₄×C₆₇	C₂³	1	4	yes	—
135	#117×C₆₇	—	2	8	no	—
136	#117×C₆₇	D₄	1	4	yes	—
137	#117×C₆₇	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
139	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
140	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
141	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
142	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
143	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
144	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
145	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₆₇	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₆₇	—	2	1	no	—
161	C₂×C₄²×C₆₇	—	2	1	no	—
162	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
164	#107×C₆₇	C₂³	1	4	yes	—
165	#107×C₆₇	C₂³	1	4	yes	—
166	#106×C₆₇	C₂³	1	4	yes	—
167	#106×C₆₇	C₂³	1	4	yes	—
168	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
169	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
170	#103×C₆₇	C₂³	1	4	yes	—
171	#103×C₆₇	C₂³	1	4	yes	—
172	#102×C₆₇	C₂³	1	4	yes	—
173	#102×C₆₇	C₂³	1	4	yes	—
174	#102×C₆₇	C₂³	1	4	yes	—
175	#102×C₆₇	C₂³	1	4	yes	—
176	#102×C₆₇	C₂³	1	4	yes	—
177	#102×C₆₇	C₂³	1	4	yes	—
178	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
179	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
180	#97×C₆₇	C₂³	1	4	yes	—
181	C₄×C₈×C₆₇	C₂³	1	4	yes	—
182	C₂⁴×C₆₇	—	2	1	no	—
183	C₂⁴×C₆₇	—	2	1	no	—
184	C₂⁴×C₆₇	—	2	1	no	—
185	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
186	#41×C₆₇	—	2	16	no	—
187	#41×C₆₇	—	2	8	no	—
188	#41×C₆₇	—	2	8	no	—
189	C₂×Q₈×C₆₇	—	2	1	no	—
190	C₂×Q₈×C₆₇	—	2	2	no	—
191	C₂×Q₈×C₆₇	#41	1	4	yes	—
192	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
193	C₂×D₄×C₆₇	—	2	8	no	—
194	C₂×D₄×C₆₇	—	2	4	no	—
195	C₂×D₄×C₆₇	—	2	4	no	—
196	C₂×D₄×C₆₇	—	2	4	no	—
197	C₂×D₄×C₆₇	—	2	1	no	—
198	C₂×D₄×C₆₇	—	2	1	no	—
199	C₂×D₄×C₆₇	—	2	1	no	—
200	C₂×D₄×C₆₇	—	2	4	no	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	2	2	no	—
203	C₂×D₄×C₆₇	—	2	2	no	—
204	C₂×D₄×C₆₇	—	2	2	no	—
205	C₂×D₄×C₆₇	—	2	2	no	—
206	C₂×D₄×C₆₇	—	2	2	no	—
207	C₂×D₄×C₆₇	—	8	2	no	—
208	C₂×D₄×C₆₇	—	8	2	no	—
209	C₂×D₄×C₆₇	—	8	2	no	—
210	C₂×D₄×C₆₇	—	8	2	no	—
211	C₂×D₄×C₆₇	#41	1	4	yes	—
212	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
213	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₇	—	2	8	no	—
216	C₂²×C₄×C₆₇	—	2	1	no	—
217	C₂²×C₄×C₆₇	—	2	4	no	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	1	no	—
221	C₂²×C₄×C₆₇	—	2	1	no	—
222	C₂²×C₄×C₆₇	—	2	1	no	—
223	C₂²×C₄×C₆₇	—	2	1	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	2	4	no	—
226	C₂²×C₄×C₆₇	—	2	4	no	—
227	C₂²×C₄×C₆₇	—	2	4	no	—
228	C₂²×C₄×C₆₇	—	2	4	no	—
229	C₂²×C₄×C₆₇	—	8	2	no	—
230	C₂²×C₄×C₆₇	—	8	2	no	—
231	C₂²×C₄×C₆₇	—	8	2	no	—
232	C₂²×C₄×C₆₇	—	8	2	no	—
233	C₂²×C₄×C₆₇	—	8	2	no	—
234	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	SD₁₆×C₆₇	—	2	8	no	—
243	SD₁₆×C₆₇	—	2	8	no	—
244	D₈×C₆₇	—	2	8	no	—
245	D₈×C₆₇	—	2	8	no	—
246	C₂×C₈×C₆₇	—	2	2	no	—
247	C₂×C₈×C₆₇	—	2	2	no	—
248	C₂×C₈×C₆₇	—	2	2	no	—
249	C₂×C₈×C₆₇	—	2	2	no	—
250	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
251	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
252	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
253	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₆₇	—	2	4	no	—
255	C₄⋊C₄×C₆₇	—	2	4	no	—
256	C₄⋊C₄×C₆₇	—	2	4	no	—
257	C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₄⋊C₄×C₆₇	—	2	4	no	—
260	C₄⋊C₄×C₆₇	—	2	4	no	—
261	C₄⋊C₄×C₆₇	—	2	1	no	—
262	C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
264	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
265	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	4	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	4	no	—
275	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
276	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
277	C₄²×C₆₇	—	2	4	no	—
278	C₄²×C₆₇	—	2	4	no	—
279	C₄²×C₆₇	C₂×D₄	1	2	yes	—
280	C₄²×C₆₇	C₂×D₄	1	2	yes	—
281	C₄²×C₆₇	C₂⁴	1	2	yes	—
282	C₄²×C₆₇	C₂⁴	1	2	yes	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	—	2	4	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	2	2	no	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	4	2	no	—
291	C₂³×C₆₇	—	4	2	no	—
292	C₂³×C₆₇	—	4	2	no	—
293	C₂³×C₆₇	—	4	2	no	—
294	C₂³×C₆₇	—	4	2	no	—
295	C₂³×C₆₇	—	4	2	no	—
296	C₂³×C₆₇	—	4	2	no	—
297	C₂³×C₆₇	—	4	2	no	—
298	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
299	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₆₇	—	2	4	no	—
301	Q₈×C₆₇	—	2	2	no	—
302	Q₈×C₆₇	C₂×#41	1	4	yes	—
303	D₄×C₆₇	—	2	16	no	—
304	D₄×C₆₇	—	2	4	no	—
305	D₄×C₆₇	—	2	2	no	—
306	D₄×C₆₇	—	2	2	no	—
307	D₄×C₆₇	—	2	2	no	—
308	D₄×C₆₇	—	2	2	no	—
309	D₄×C₆₇	—	2	2	no	—
310	D₄×C₆₇	—	4	2	no	—
311	D₄×C₆₇	—	4	2	no	—
312	D₄×C₆₇	—	8	4	no	—
313	D₄×C₆₇	—	8	4	no	—
314	D₄×C₆₇	—	8	4	no	—
315	D₄×C₆₇	—	8	4	no	—
316	D₄×C₆₇	C₂×#41	1	4	yes	—
317	C₂×C₄×C₆₇	—	2	16	no	—
318	C₂×C₄×C₆₇	—	2	2	no	—
319	C₂×C₄×C₆₇	—	2	4	no	—
320	C₂×C₄×C₆₇	—	2	2	no	—
321	C₂×C₄×C₆₇	—	2	2	no	—
322	C₂×C₄×C₆₇	—	2	2	no	—
323	C₂×C₄×C₆₇	—	2	2	no	—
324	C₂×C₄×C₆₇	—	2	2	no	—
325	C₂×C₄×C₆₇	—	2	4	no	—
326	C₂×C₄×C₆₇	—	2	2	no	—
327	C₂×C₄×C₆₇	—	2	2	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	4	2	no	—
333	C₂×C₄×C₆₇	—	4	2	no	—
334	C₂×C₄×C₆₇	—	4	2	no	—
335	C₂×C₄×C₆₇	—	4	2	no	—
336	C₂×C₄×C₆₇	—	8	4	no	—
337	C₂×C₄×C₆₇	—	8	4	no	—
338	C₂×C₄×C₆₇	—	8	4	no	—
339	C₂×C₄×C₆₇	—	8	4	no	—
340	C₂×C₄×C₆₇	—	8	4	no	—
341	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
346	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
347	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
348	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
349	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
350	C₈×C₆₇	—	2	2	no	—
351	C₈×C₆₇	—	2	2	no	—
352	C₈×C₆₇	—	2	2	no	—
353	C₈×C₆₇	—	2	2	no	—
354	C₂²×C₆₇	—	2	2	no	—
355	C₂²×C₆₇	—	2	4	no	—
356	C₂²×C₆₇	—	2	2	no	—
357	C₂²×C₆₇	—	2	2	no	—
358	C₂²×C₆₇	—	4	4	no	—
359	C₂²×C₆₇	—	4	8	no	—
360	C₂²×C₆₇	—	4	2	no	—
361	C₂²×C₆₇	—	4	2	no	—
362	C₂²×C₆₇	—	4	2	no	—
363	C₂²×C₆₇	—	4	2	no	—
364	C₂²×C₆₇	—	4	2	no	—
365	C₂²×C₆₇	—	4	2	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	4	2	no	—
368	C₂²×C₆₇	—	8	4	no	—
369	C₂²×C₆₇	—	8	4	no	—
370	C₂²×C₆₇	#525	1	2	yes	—
371	C₂²×C₆₇	#576	1	2	yes	—
372	C₂²×C₆₇	#577	1	2	yes	—
373	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
374	C₄×C₆₇	—	2	2	no	—
375	C₄×C₆₇	—	2	4	no	—
376	C₄×C₆₇	—	2	2	no	—
377	C₄×C₆₇	—	2	2	no	—
378	C₄×C₆₇	—	2	2	no	—
379	C₄×C₆₇	—	2	2	no	—
380	C₄×C₆₇	—	4	2	no	—
381	C₄×C₆₇	—	4	2	no	—
382	C₄×C₆₇	—	4	2	no	—
383	C₄×C₆₇	—	4	2	no	—
384	C₄×C₆₇	#525	1	2	yes	—
385	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
386	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
387	C₂×#3119	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂×C₆₇	—	4	2	no	—
389	C₂×C₆₇	—	4	4	no	—
390	C₂×C₆₇	—	8	2	no	—
391	C₂×C₆₇	—	8	2	no	—
392	C₂×C₆₇	#3119	1	4	yes	direct product factor
393	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
394	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
395	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
396	C₂×#540	C₂×C₆₇	1	1	yes	characteristic, complemented
397	C₂×#520	C₂×C₆₇	1	1	yes	characteristic, complemented
398	#3119	C₂×C₆₇	1	16	yes	direct product factor
399	C₂×#481	C₂×C₆₇	1	1	yes	characteristic, complemented
400	C₂×#480	C₂×C₆₇	1	1	yes	characteristic, complemented
401	C₂×#479	C₂×C₆₇	1	1	yes	characteristic, complemented
402	C₂×#478	C₂×C₆₇	1	1	yes	characteristic, complemented
403	C₂×#460	C₂×C₆₇	1	1	yes	characteristic, complemented
404	C₂×#459	C₂×C₆₇	1	1	yes	characteristic, complemented
405	C₂×#449	C₂×C₆₇	1	1	yes	characteristic, complemented
406	C₂×#449	C₂×C₆₇	1	1	yes	characteristic, complemented
407	C₂×#442	C₂×C₆₇	1	1	yes	characteristic, complemented
408	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
409	C₂×C₄×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
410	C₂×C₄×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
411	C₂×#433	C₂×C₆₇	1	1	yes	characteristic, complemented
412	C₆₇	C₂×#3119	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
414	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
415	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
416	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
417	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
418	#540	—	2	4	no	—
419	#540	C₂²×C₆₇	1	8	yes	complemented
420	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
421	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
422	C₂×#123	—	2	1	no	—
423	C₂×#123	—	2	1	no	—
424	C₂×#121	—	2	1	no	—
425	C₂×#121	—	2	1	no	—
426	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
427	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
428	#520	—	2	4	no	—
429	#520	C₂²×C₆₇	1	8	yes	complemented
430	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
431	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
432	C₂×C₄×D₄	—	2	1	no	—
433	C₂×C₄×D₄	—	2	1	no	—
434	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
435	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
438	C₂×#117	—	2	1	no	—
439	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
440	C₂²×C₄⋊C₄	—	2	1	no	—
441	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
442	#481	C₂²×C₆₇	1	8	yes	complemented
443	#480	C₂²×C₆₇	1	8	yes	complemented
444	#479	C₂²×C₆₇	1	8	yes	complemented
445	#478	C₂²×C₆₇	1	8	yes	complemented
446	#460	C₂²×C₆₇	1	8	yes	complemented
447	#459	C₂²×C₆₇	1	8	yes	complemented
448	#449	C₂²×C₆₇	1	8	yes	complemented
449	#449	C₂²×C₆₇	1	8	yes	complemented
450	#442	C₂²×C₆₇	1	8	yes	complemented
451	#440	C₂²×C₆₇	1	8	yes	complemented
452	C₄×SD₁₆	C₂²×C₆₇	1	8	yes	complemented
453	C₄×D₈	C₂²×C₆₇	1	8	yes	complemented
454	#433	C₂²×C₆₇	1	8	yes	complemented
455	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
456	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
457	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
458	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
459	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
460	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
461	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
462	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
463	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
464	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
465	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
467	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
470	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
471	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
472	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
473	C₂×#41	—	2	4	no	—
474	C₂×#41	—	2	4	no	—
475	C₂×#41	—	2	2	no	—
476	C₂×#41	C₂³×C₆₇	1	4	yes	—
477	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
478	C₂²×D₄	—	2	1	no	—
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	2	1	no	—
483	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
484	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	—	2	1	no	—
491	C₂³×C₄	—	2	1	no	—
492	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
493	C₂×SD₁₆	—	2	4	no	—
494	C₂×SD₁₆	—	2	4	no	—
495	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
496	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
497	C₂×D₈	—	2	4	no	—
498	C₂×D₈	—	2	4	no	—
499	C₂×D₈	C₂³×C₆₇	1	4	yes	—
500	C₂×D₈	C₂³×C₆₇	1	4	yes	—
501	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
505	#127	—	2	2	no	—
506	#127	C₂³×C₆₇	1	4	yes	—
507	#125	—	2	2	no	—
508	#125	C₂³×C₆₇	1	4	yes	—
509	#123	—	2	8	no	—
510	#123	—	2	8	no	—
511	#121	—	2	2	no	—
512	#121	—	2	2	no	—
513	#121	—	2	8	no	—
514	#121	—	2	8	no	—
515	#121	C₂³×C₆₇	1	4	yes	—
516	#121	C₂³×C₆₇	1	4	yes	—
517	C₄×Q₈	—	2	2	no	—
518	C₄×Q₈	—	2	2	no	—
519	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
520	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
521	C₄×D₄	—	2	8	no	—
522	C₄×D₄	—	2	8	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	C₂³×C₆₇	1	4	yes	—
528	C₄×D₄	C₂³×C₆₇	1	4	yes	—
529	C₄×D₄	C₂³×C₆₇	1	4	yes	—
530	C₄×D₄	C₂³×C₆₇	1	4	yes	—
531	#117	—	2	8	no	—
532	#117	D₄×C₆₇	1	4	yes	—
533	#117	C₂³×C₆₇	1	4	yes	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	—	2	8	no	—
541	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
542	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	D₄×C₆₇	1	1	yes	characteristic
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
560	#107	C₂³×C₆₇	1	4	yes	—
561	#107	C₂³×C₆₇	1	4	yes	—
562	#106	C₂³×C₆₇	1	4	yes	—
563	#106	C₂³×C₆₇	1	4	yes	—
564	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
565	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
566	#103	C₂³×C₆₇	1	4	yes	—
567	#103	C₂³×C₆₇	1	4	yes	—
568	#102	C₂³×C₆₇	1	4	yes	—
569	#102	C₂³×C₆₇	1	4	yes	—
570	#102	C₂³×C₆₇	1	4	yes	—
571	#102	C₂³×C₆₇	1	4	yes	—
572	#102	C₂³×C₆₇	1	4	yes	—
573	#102	C₂³×C₆₇	1	4	yes	—
574	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
575	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
576	#97	C₂³×C₆₇	1	4	yes	—
577	C₄×C₈	C₂³×C₆₇	1	4	yes	—
578	C₂⁴	—	2	1	no	—
579	C₂⁴	—	2	1	no	—
580	C₂⁴	—	2	1	no	—
581	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
582	#41	—	2	16	no	—
583	#41	—	2	8	no	—
584	#41	—	2	8	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	#41×C₆₇	1	4	yes	—
588	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	8	2	no	—
604	C₂×D₄	—	8	2	no	—
605	C₂×D₄	—	8	2	no	—
606	C₂×D₄	—	8	2	no	—
607	C₂×D₄	#41×C₆₇	1	4	yes	—
608	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
609	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
610	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
611	C₂²×C₄	—	2	8	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	8	2	no	—
626	C₂²×C₄	—	8	2	no	—
627	C₂²×C₄	—	8	2	no	—
628	C₂²×C₄	—	8	2	no	—
629	C₂²×C₄	—	8	2	no	—
630	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
638	SD₁₆	—	2	8	no	—
639	SD₁₆	—	2	8	no	—
640	D₈	—	2	8	no	—
641	D₈	—	2	8	no	—
642	C₂×C₈	—	2	2	no	—
643	C₂×C₈	—	2	2	no	—
644	C₂×C₈	—	2	2	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
647	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
648	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
649	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
660	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
661	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
662	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
663	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
664	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
672	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
673	C₄²	—	2	4	no	—
674	C₄²	—	2	4	no	—
675	C₄²	C₂×D₄×C₆₇	1	2	yes	—
676	C₄²	C₂×D₄×C₆₇	1	2	yes	—
677	C₄²	C₂⁴×C₆₇	1	2	yes	—
678	C₄²	C₂⁴×C₆₇	1	2	yes	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	—	4	2	no	—
688	C₂³	—	4	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	2	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
695	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
696	Q₈	—	2	4	no	—
697	Q₈	—	2	2	no	—
698	Q₈	C₂×#41×C₆₇	1	4	yes	—
699	D₄	—	2	16	no	—
700	D₄	—	2	4	no	—
701	D₄	—	2	2	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	2	no	—
705	D₄	—	2	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	8	4	no	—
709	D₄	—	8	4	no	—
710	D₄	—	8	4	no	—
711	D₄	—	8	4	no	—
712	D₄	C₂×#41×C₆₇	1	4	yes	—
713	C₂×C₄	—	2	16	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	8	4	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	—	8	4	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
738	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
740	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
742	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
743	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
744	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
745	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
746	C₈	—	2	2	no	—
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	8	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	8	4	no	—
765	C₂²	—	8	4	no	—
766	C₂²	#525×C₆₇	1	2	yes	—
767	C₂²	#576×C₆₇	1	2	yes	—
768	C₂²	#577×C₆₇	1	2	yes	—
769	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	2	2	no	—
773	C₄	—	2	2	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	4	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₄	#525×C₆₇	1	2	yes	—
781	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
782	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
783	C₂	—	4	2	no	—
784	C₂	—	4	4	no	—
785	C₂	—	8	2	no	—
786	C₂	—	8	2	no	—
787	C₂	C₆₇×#3119	1	4	yes	direct product factor
788	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
789	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
790	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#540×C₆₇	C₂	semidirect
2. C₂×#520×C₆₇	C₂	semidirect
3. C₆₇×#3119	C₂	direct (N × H)
4. C₂×#481×C₆₇	C₂	semidirect
5. C₂×#480×C₆₇	C₂	semidirect
6. C₂×#479×C₆₇	C₂	semidirect
7. C₂×#478×C₆₇	C₂	semidirect
8. C₂×#460×C₆₇	C₂	semidirect
9. C₂×#459×C₆₇	C₂	semidirect
10. C₂×#449×C₆₇	C₂	semidirect
11. C₂×#449×C₆₇	C₂	semidirect
12. C₂×#442×C₆₇	C₂	semidirect
13. C₂×#440×C₆₇	C₂	semidirect
14. C₂×C₄×SD₁₆×C₆₇	C₂	semidirect
15. C₂×C₄×D₈×C₆₇	C₂	semidirect
16. C₂×#433×C₆₇	C₂	semidirect
23. #540×C₆₇	C₂²	semidirect
33. #520×C₆₇	C₂²	semidirect
46. #481×C₆₇	C₂²	semidirect
47. #480×C₆₇	C₂²	semidirect
48. #479×C₆₇	C₂²	semidirect
49. #478×C₆₇	C₂²	semidirect
50. #460×C₆₇	C₂²	semidirect
51. #459×C₆₇	C₂²	semidirect
52. #449×C₆₇	C₂²	semidirect
53. #449×C₆₇	C₂²	semidirect
54. #442×C₆₇	C₂²	semidirect
55. #440×C₆₇	C₂²	semidirect
56. C₄×SD₁₆×C₆₇	C₂²	semidirect
57. C₄×D₈×C₆₇	C₂²	semidirect
58. #433×C₆₇	C₂²	semidirect
387. C₂×#3119	C₆₇	direct (N × H)
392. C₂×C₆₇	#3119	direct (N × H)
396. C₂×#540	C₂×C₆₇	semidirect
397. C₂×#520	C₂×C₆₇	semidirect
398. #3119	C₂×C₆₇	direct (N × H)
399. C₂×#481	C₂×C₆₇	semidirect
400. C₂×#480	C₂×C₆₇	semidirect
401. C₂×#479	C₂×C₆₇	semidirect
402. C₂×#478	C₂×C₆₇	semidirect
403. C₂×#460	C₂×C₆₇	semidirect
404. C₂×#459	C₂×C₆₇	semidirect
405. C₂×#449	C₂×C₆₇	semidirect
406. C₂×#449	C₂×C₆₇	semidirect
407. C₂×#442	C₂×C₆₇	semidirect
408. C₂×#440	C₂×C₆₇	semidirect
409. C₂×C₄×SD₁₆	C₂×C₆₇	semidirect
410. C₂×C₄×D₈	C₂×C₆₇	semidirect
411. C₂×#433	C₂×C₆₇	semidirect
412. C₆₇	C₂×#3119	direct (N × H)
419. #540	C₂²×C₆₇	semidirect
429. #520	C₂²×C₆₇	semidirect
442. #481	C₂²×C₆₇	semidirect
443. #480	C₂²×C₆₇	semidirect
444. #479	C₂²×C₆₇	semidirect
445. #478	C₂²×C₆₇	semidirect
446. #460	C₂²×C₆₇	semidirect
447. #459	C₂²×C₆₇	semidirect
448. #449	C₂²×C₆₇	semidirect
449. #449	C₂²×C₆₇	semidirect
450. #442	C₂²×C₆₇	semidirect
451. #440	C₂²×C₆₇	semidirect
452. C₄×SD₁₆	C₂²×C₆₇	semidirect
453. C₄×D₈	C₂²×C₆₇	semidirect
454. #433	C₂²×C₆₇	semidirect
787. C₂	C₆₇×#3119	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×#540×C₆₇	2
C₂×#520×C₆₇	2
C₆₇×#3119	2
C₂×#481×C₆₇	2
C₂×#480×C₆₇	2
C₂×#479×C₆₇	2
C₂×#478×C₆₇	2
C₂×#460×C₆₇	2
C₂×#459×C₆₇	2
C₂×#449×C₆₇	2
C₂×#442×C₆₇	2
C₂×#440×C₆₇	2
C₂×C₄×SD₁₆×C₆₇	2
C₂×C₄×D₈×C₆₇	2
C₂×#433×C₆₇	2
C₂×#3119	67

Subgroups — C2×C67×#3119 #30739799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3119 #30739799