Subgroups — C₆₇×#61645 #30740896

Order 17152.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3326	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3320	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3312	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3278	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3276	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3271	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3269	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3223	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3221	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3201	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3197	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3013	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3004	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
21	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#137×C₆₇	C₂²	1	2	yes	—
23	C₂×#137×C₆₇	C₂²	1	2	yes	—
24	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
25	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
26	#560×C₆₇	—	2	2	no	—
27	#553×C₆₇	—	2	2	no	—
28	#553×C₆₇	C₂²	1	2	yes	—
29	#552×C₆₇	C₂²	1	2	yes	—
30	#550×C₆₇	C₂²	1	2	yes	—
31	D₄×Q₈×C₆₇	—	2	2	no	—
32	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
33	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
34	#548×C₆₇	—	2	2	no	—
35	#548×C₆₇	C₂²	1	2	yes	—
36	#548×C₆₇	C₂²	1	2	yes	—
37	#547×C₆₇	C₂²	1	2	yes	—
38	#541×C₆₇	C₂²	1	1	yes	characteristic
39	#540×C₆₇	—	2	2	no	—
40	#540×C₆₇	C₂²	1	1	yes	characteristic
41	#539×C₆₇	—	2	2	no	—
42	#537×C₆₇	C₂²	1	2	yes	—
43	#536×C₆₇	—	2	2	no	—
44	#536×C₆₇	C₂²	1	1	yes	characteristic
45	#536×C₆₇	C₂²	1	1	yes	characteristic
46	#525×C₆₇	—	2	2	no	—
47	#525×C₆₇	C₂²	1	2	yes	—
48	#525×C₆₇	C₂²	1	1	yes	characteristic
49	#525×C₆₇	C₂²	1	1	yes	characteristic
50	#519×C₆₇	C₂²	1	1	yes	characteristic
51	#497×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#496×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#491×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#491×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#488×C₆₇	C₂²	1	1	yes	characteristic, complemented
58	#488×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#485×C₆₇	C₂²	1	2	yes	—
60	#485×C₆₇	C₂²	1	2	yes	—
61	#484×C₆₇	C₂²	1	2	yes	complemented
62	#483×C₆₇	C₂²	1	2	yes	complemented
63	#482×C₆₇	C₂²	1	2	yes	—
64	#482×C₆₇	C₂²	1	2	yes	—
65	#479×C₆₇	C₂²	1	2	yes	complemented
66	#479×C₆₇	C₂²	1	2	yes	complemented
67	#470×C₆₇	C₂²	1	2	yes	—
68	#470×C₆₇	C₂²	1	2	yes	complemented
69	#469×C₆₇	C₂²	1	2	yes	—
70	#468×C₆₇	C₂²	1	2	yes	—
71	#468×C₆₇	C₂²	1	2	yes	—
72	#468×C₆₇	C₂²	1	2	yes	complemented
73	#467×C₆₇	C₂²	1	2	yes	complemented
74	#465×C₆₇	C₂²	1	2	yes	complemented
75	#464×C₆₇	C₂²	1	2	yes	complemented
76	#463×C₆₇	C₂²	1	2	yes	complemented
77	#462×C₆₇	C₂²	1	2	yes	complemented
78	#462×C₆₇	C₂²	1	2	yes	complemented
79	#461×C₆₇	C₂²	1	2	yes	complemented
80	#460×C₆₇	C₂²	1	2	yes	complemented
81	#452×C₆₇	C₂²	1	2	yes	—
82	#452×C₆₇	C₂²	1	2	yes	—
83	#452×C₆₇	C₂²	1	2	yes	complemented
84	#452×C₆₇	C₂²	1	2	yes	complemented
85	#452×C₆₇	C₂²	1	2	yes	complemented
86	#451×C₆₇	C₂²	1	2	yes	—
87	#451×C₆₇	C₂²	1	2	yes	—
88	#451×C₆₇	C₂²	1	2	yes	—
89	#451×C₆₇	C₂²	1	2	yes	—
90	#451×C₆₇	C₂²	1	2	yes	complemented
91	#449×C₆₇	C₂²	1	2	yes	—
92	#449×C₆₇	C₂²	1	2	yes	—
93	#449×C₆₇	C₂²	1	2	yes	complemented
94	#448×C₆₇	C₂²	1	2	yes	—
95	#448×C₆₇	C₂²	1	2	yes	—
96	#448×C₆₇	C₂²	1	2	yes	—
97	#448×C₆₇	C₂²	1	2	yes	—
98	#448×C₆₇	C₂²	1	2	yes	complemented
99	#441×C₆₇	C₂²	1	2	yes	complemented
100	#440×C₆₇	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
103	#436×C₆₇	C₂²	1	2	yes	—
104	#436×C₆₇	C₂²	1	2	yes	—
105	#435×C₆₇	C₂²	1	2	yes	—
106	#435×C₆₇	C₂²	1	2	yes	—
107	#433×C₆₇	C₂²	1	1	yes	characteristic
108	#433×C₆₇	C₂²	1	1	yes	characteristic
109	#419×C₆₇	C₂²	1	2	yes	—
110	#419×C₆₇	C₂²	1	2	yes	—
111	#417×C₆₇	C₂²	1	2	yes	complemented
112	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
113	#408×C₆₇	C₂²	1	2	yes	—
114	#407×C₆₇	C₂²	1	2	yes	—
115	2₋¹⁺⁴×C₆₇	—	4	4	no	—
116	C₂×#41×C₆₇	—	2	2	no	—
117	C₂×#41×C₆₇	—	2	1	no	—
118	C₂×#41×C₆₇	C₂³	1	2	yes	—
119	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
120	C₂×#41×C₆₇	C₂³	1	2	yes	—
121	C₂×#41×C₆₇	C₂³	1	2	yes	—
122	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₆₇	—	2	1	no	—
124	C₂²×Q₈×C₆₇	—	2	1	no	—
125	C₂²×Q₈×C₆₇	—	2	2	no	—
126	C₂²×Q₈×C₆₇	—	4	4	no	—
127	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
129	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
130	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
131	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	—	2	1	no	—
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	#137×C₆₇	—	4	4	no	—
135	#137×C₆₇	—	4	4	no	—
136	#137×C₆₇	—	4	4	no	—
137	#135×C₆₇	—	4	4	no	—
138	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×D₈×C₆₇	C₂³	1	2	yes	—
150	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₆₇	—	2	1	no	—
155	C₄⋊Q₈×C₆₇	—	2	2	no	—
156	C₄⋊Q₈×C₆₇	—	2	2	no	—
157	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	#127×C₆₇	—	2	2	no	—
161	#127×C₆₇	C₂³	1	1	yes	characteristic
162	#126×C₆₇	—	2	2	no	—
163	#126×C₆₇	—	2	2	no	—
164	#126×C₆₇	—	2	2	no	—
165	#125×C₆₇	—	2	2	no	—
166	#125×C₆₇	—	2	2	no	—
167	#125×C₆₇	C₂³	1	1	yes	characteristic
168	#125×C₆₇	C₂³	1	1	yes	characteristic
169	#124×C₆₇	—	2	1	no	—
170	#124×C₆₇	—	2	2	no	—
171	#124×C₆₇	—	2	2	no	—
172	#124×C₆₇	C₂³	1	1	yes	characteristic
173	#124×C₆₇	C₂³	1	1	yes	characteristic
174	#123×C₆₇	—	2	2	no	—
175	#123×C₆₇	—	2	2	no	—
176	#123×C₆₇	—	2	1	no	—
177	#123×C₆₇	—	2	2	no	—
178	#123×C₆₇	—	2	2	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	D₄	1	2	yes	—
184	C₂²⋊Q₈×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	—	2	2	no	—
186	C₂²⋊Q₈×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	2	no	—
188	C₂²⋊Q₈×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	—	2	2	no	—
192	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
193	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
199	#121×C₆₇	—	2	2	no	—
200	#121×C₆₇	—	2	2	no	—
201	#121×C₆₇	—	2	2	no	—
202	#121×C₆₇	—	2	2	no	—
203	#121×C₆₇	—	2	2	no	—
204	#121×C₆₇	—	2	2	no	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	—	2	2	no	—
207	#121×C₆₇	—	2	2	no	—
208	#121×C₆₇	—	2	2	no	—
209	#121×C₆₇	D₄	1	2	yes	—
210	#121×C₆₇	C₂³	1	2	yes	—
211	#121×C₆₇	C₂³	1	2	yes	—
212	#121×C₆₇	C₂³	1	2	yes	—
213	#121×C₆₇	C₂³	1	2	yes	—
214	#120×C₆₇	—	2	1	no	—
215	#120×C₆₇	—	2	2	no	—
216	#120×C₆₇	D₄	1	2	yes	—
217	C₄×Q₈×C₆₇	—	2	2	no	—
218	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
220	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
221	C₄×D₄×C₆₇	—	2	2	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	2	no	—
224	C₄×D₄×C₆₇	—	2	2	no	—
225	C₄×D₄×C₆₇	—	2	2	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	2	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	C₂³	1	2	yes	—
231	C₄×D₄×C₆₇	C₂³	1	2	yes	—
232	C₄×D₄×C₆₇	C₂³	1	2	yes	—
233	#117×C₆₇	—	2	2	no	—
234	#117×C₆₇	—	2	2	no	—
235	#117×C₆₇	C₂³	1	1	yes	characteristic
236	#117×C₆₇	C₂³	1	2	yes	—
237	#117×C₆₇	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
239	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
240	#107×C₆₇	C₂³	1	2	yes	—
241	#107×C₆₇	C₂³	1	2	yes	—
242	#106×C₆₇	C₂³	1	2	yes	—
243	#106×C₆₇	C₂³	1	2	yes	—
244	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
245	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
246	#103×C₆₇	C₂³	1	2	yes	—
247	#103×C₆₇	C₂³	1	2	yes	—
248	#103×C₆₇	C₂³	1	2	yes	—
249	#103×C₆₇	C₂³	1	2	yes	—
250	#103×C₆₇	C₂³	1	2	yes	—
251	#103×C₆₇	C₂³	1	2	yes	—
252	#103×C₆₇	C₂³	1	2	yes	—
253	#103×C₆₇	C₂³	1	2	yes	—
254	#103×C₆₇	C₂³	1	2	yes	—
255	#103×C₆₇	C₂³	1	2	yes	—
256	#103×C₆₇	C₂³	1	2	yes	—
257	#103×C₆₇	C₂³	1	2	yes	—
258	#102×C₆₇	C₂³	1	2	yes	—
259	#102×C₆₇	C₂³	1	2	yes	—
260	#102×C₆₇	C₂³	1	2	yes	—
261	#102×C₆₇	C₂³	1	2	yes	—
262	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
263	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
264	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
265	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
266	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
267	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
268	#97×C₆₇	C₂³	1	1	yes	characteristic
269	#97×C₆₇	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
271	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
272	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
273	#41×C₆₇	—	2	4	no	—
274	#41×C₆₇	—	4	2	no	—
275	#41×C₆₇	—	4	2	no	—
276	#41×C₆₇	—	4	2	no	—
277	#41×C₆₇	—	4	8	no	—
278	#41×C₆₇	—	4	2	no	—
279	#41×C₆₇	—	4	2	no	—
280	#41×C₆₇	—	4	2	no	—
281	#41×C₆₇	—	4	2	no	—
282	#41×C₆₇	—	4	4	no	—
283	C₂×Q₈×C₆₇	—	2	4	no	—
284	C₂×Q₈×C₆₇	—	2	1	no	—
285	C₂×Q₈×C₆₇	—	2	2	no	—
286	C₂×Q₈×C₆₇	—	2	2	no	—
287	C₂×Q₈×C₆₇	—	2	1	no	—
288	C₂×Q₈×C₆₇	—	2	2	no	—
289	C₂×Q₈×C₆₇	—	2	4	no	—
290	C₂×Q₈×C₆₇	—	2	4	no	—
291	C₂×Q₈×C₆₇	—	2	4	no	—
292	C₂×Q₈×C₆₇	—	4	2	no	—
293	C₂×Q₈×C₆₇	—	4	2	no	—
294	C₂×Q₈×C₆₇	—	4	2	no	—
295	C₂×Q₈×C₆₇	—	4	2	no	—
296	C₂×Q₈×C₆₇	—	4	4	no	—
297	C₂×Q₈×C₆₇	—	4	8	no	—
298	C₂×Q₈×C₆₇	—	4	4	no	—
299	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
300	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
305	C₂×D₄×C₆₇	—	2	2	no	—
306	C₂×D₄×C₆₇	—	2	1	no	—
307	C₂×D₄×C₆₇	—	2	2	no	—
308	C₂×D₄×C₆₇	—	2	2	no	—
309	C₂×D₄×C₆₇	—	2	2	no	—
310	C₂×D₄×C₆₇	—	2	2	no	—
311	C₂×D₄×C₆₇	—	2	2	no	—
312	C₂×D₄×C₆₇	—	2	2	no	—
313	C₂×D₄×C₆₇	—	2	2	no	—
314	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
315	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
317	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
318	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₆₇	—	2	1	no	—
321	C₂²×C₄×C₆₇	—	2	2	no	—
322	C₂²×C₄×C₆₇	—	2	2	no	—
323	C₂²×C₄×C₆₇	—	2	2	no	—
324	C₂²×C₄×C₆₇	—	2	1	no	—
325	C₂²×C₄×C₆₇	—	2	2	no	—
326	C₂²×C₄×C₆₇	—	2	2	no	—
327	C₂²×C₄×C₆₇	—	2	1	no	—
328	C₂²×C₄×C₆₇	—	2	2	no	—
329	C₂²×C₄×C₆₇	—	2	2	no	—
330	C₂²×C₄×C₆₇	—	2	2	no	—
331	C₂²×C₄×C₆₇	—	4	2	no	—
332	C₂²×C₄×C₆₇	—	4	4	no	—
333	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
334	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
338	Q₁₆×C₆₇	—	2	4	no	—
339	Q₁₆×C₆₇	—	2	4	no	—
340	Q₁₆×C₆₇	—	4	2	no	—
341	Q₁₆×C₆₇	—	4	2	no	—
342	Q₁₆×C₆₇	—	4	2	no	—
343	SD₁₆×C₆₇	—	2	4	no	—
344	SD₁₆×C₆₇	—	2	4	no	—
345	SD₁₆×C₆₇	—	4	2	no	—
346	SD₁₆×C₆₇	—	4	2	no	—
347	SD₁₆×C₆₇	—	4	2	no	—
348	SD₁₆×C₆₇	—	4	2	no	—
349	D₈×C₆₇	—	4	2	no	—
350	M₁₆×C₆₇	—	4	2	no	—
351	M₁₆×C₆₇	—	4	2	no	—
352	M₁₆×C₆₇	—	4	2	no	—
353	C₂×C₈×C₆₇	—	4	2	no	—
354	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
355	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
356	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
357	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₆₇	—	2	2	no	—
359	C₄⋊C₄×C₆₇	—	2	2	no	—
360	C₄⋊C₄×C₆₇	—	2	2	no	—
361	C₄⋊C₄×C₆₇	—	2	2	no	—
362	C₄⋊C₄×C₆₇	—	2	2	no	—
363	C₄⋊C₄×C₆₇	—	2	2	no	—
364	C₄⋊C₄×C₆₇	—	2	2	no	—
365	C₄⋊C₄×C₆₇	—	2	2	no	—
366	C₄⋊C₄×C₆₇	—	2	2	no	—
367	C₄⋊C₄×C₆₇	—	2	2	no	—
368	C₄⋊C₄×C₆₇	—	2	2	no	—
369	C₄⋊C₄×C₆₇	—	2	2	no	—
370	C₄⋊C₄×C₆₇	—	2	2	no	—
371	C₄⋊C₄×C₆₇	—	2	2	no	—
372	C₄⋊C₄×C₆₇	—	2	2	no	—
373	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
379	C₂²⋊C₄×C₆₇	—	2	1	no	—
380	C₂²⋊C₄×C₆₇	—	2	2	no	—
381	C₂²⋊C₄×C₆₇	—	2	2	no	—
382	C₂²⋊C₄×C₆₇	—	2	2	no	—
383	C₂²⋊C₄×C₆₇	—	2	2	no	—
384	C₂²⋊C₄×C₆₇	—	2	2	no	—
385	C₂²⋊C₄×C₆₇	—	2	2	no	—
386	C₂²⋊C₄×C₆₇	—	2	2	no	—
387	C₂²⋊C₄×C₆₇	—	2	2	no	—
388	C₂²⋊C₄×C₆₇	—	2	2	no	—
389	C₂²⋊C₄×C₆₇	—	2	2	no	—
390	C₂²⋊C₄×C₆₇	—	2	2	no	—
391	C₂²⋊C₄×C₆₇	—	2	2	no	—
392	C₂²⋊C₄×C₆₇	—	2	2	no	—
393	C₂²⋊C₄×C₆₇	—	2	2	no	—
394	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
399	C₄²×C₆₇	—	2	2	no	—
400	C₄²×C₆₇	—	2	2	no	—
401	C₄²×C₆₇	—	2	2	no	—
402	C₄²×C₆₇	—	2	2	no	—
403	C₄²×C₆₇	—	2	1	no	—
404	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
406	C₂³×C₆₇	—	2	1	no	—
407	C₂³×C₆₇	—	2	2	no	—
408	C₂³×C₆₇	—	4	1	no	—
409	C₂³×C₆₇	—	4	2	no	—
410	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
411	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
412	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
413	Q₈×C₆₇	—	2	4	no	—
414	Q₈×C₆₇	—	2	2	no	—
415	Q₈×C₆₇	—	2	2	no	—
416	Q₈×C₆₇	—	2	2	no	—
417	Q₈×C₆₇	—	2	2	no	—
418	Q₈×C₆₇	—	2	2	no	—
419	Q₈×C₆₇	—	2	2	no	—
420	Q₈×C₆₇	—	4	1	no	—
421	Q₈×C₆₇	—	4	4	no	—
422	Q₈×C₆₇	—	4	4	no	—
423	Q₈×C₆₇	—	4	4	no	—
424	Q₈×C₆₇	—	4	2	no	—
425	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
426	D₄×C₆₇	—	2	2	no	—
427	D₄×C₆₇	—	2	2	no	—
428	D₄×C₆₇	—	2	2	no	—
429	D₄×C₆₇	—	4	2	no	—
430	D₄×C₆₇	—	4	2	no	—
431	D₄×C₆₇	—	4	1	no	—
432	D₄×C₆₇	—	4	2	no	—
433	D₄×C₆₇	—	4	4	no	—
434	D₄×C₆₇	—	4	4	no	—
435	D₄×C₆₇	—	4	2	no	—
436	D₄×C₆₇	—	8	2	no	—
437	D₄×C₆₇	—	8	2	no	—
438	D₄×C₆₇	—	8	2	no	—
439	D₄×C₆₇	—	8	2	no	—
440	D₄×C₆₇	—	8	2	no	—
441	D₄×C₆₇	—	8	2	no	—
442	C₂×C₄×C₆₇	—	2	4	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	2	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	4	2	no	—
457	C₂×C₄×C₆₇	—	4	1	no	—
458	C₂×C₄×C₆₇	—	4	4	no	—
459	C₂×C₄×C₆₇	—	4	4	no	—
460	C₂×C₄×C₆₇	—	4	4	no	—
461	C₂×C₄×C₆₇	—	4	4	no	—
462	C₂×C₄×C₆₇	—	4	2	no	—
463	C₂×C₄×C₆₇	—	4	2	no	—
464	C₂×C₄×C₆₇	—	8	2	no	—
465	C₂×C₄×C₆₇	—	8	2	no	—
466	C₂×C₄×C₆₇	—	8	2	no	—
467	C₂×C₄×C₆₇	—	8	2	no	—
468	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
474	C₈×C₆₇	—	2	2	no	—
475	C₈×C₆₇	—	2	2	no	—
476	C₈×C₆₇	—	2	2	no	—
477	C₈×C₆₇	—	2	2	no	—
478	C₂²×C₆₇	—	2	2	no	—
479	C₂²×C₆₇	—	2	2	no	—
480	C₂²×C₆₇	—	2	2	no	—
481	C₂²×C₆₇	—	2	2	no	—
482	C₂²×C₆₇	—	2	2	no	—
483	C₂²×C₆₇	—	2	1	no	—
484	C₂²×C₆₇	—	2	2	no	—
485	C₂²×C₆₇	—	2	2	no	—
486	C₂²×C₆₇	—	4	4	no	—
487	C₂²×C₆₇	—	4	2	no	—
488	C₂²×C₆₇	—	4	2	no	—
489	C₂²×C₆₇	—	4	2	no	—
490	C₂²×C₆₇	—	4	1	no	—
491	C₂²×C₆₇	—	4	2	no	—
492	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
493	C₄×C₆₇	—	2	2	no	—
494	C₄×C₆₇	—	2	2	no	—
495	C₄×C₆₇	—	2	4	no	—
496	C₄×C₆₇	—	2	1	no	—
497	C₄×C₆₇	—	2	2	no	—
498	C₄×C₆₇	—	2	2	no	—
499	C₄×C₆₇	—	4	2	no	—
500	C₄×C₆₇	—	4	2	no	—
501	C₄×C₆₇	—	4	2	no	—
502	C₄×C₆₇	—	4	1	no	—
503	C₄×C₆₇	—	4	1	no	—
504	C₄×C₆₇	—	4	1	no	—
505	C₄×C₆₇	—	4	2	no	—
506	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
507	#61645	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
508	C₂×C₆₇	—	4	2	no	—
509	C₂×C₆₇	—	4	2	no	—
510	C₂×C₆₇	—	4	1	no	—
511	C₂×C₆₇	—	8	2	no	—
512	C₂×C₆₇	—	8	1	no	—
513	C₂×C₆₇	#3484	1	1	yes	characteristic
514	C₂×C₆₇	#3586	1	2	yes	—
515	#3539	C₂×C₆₇	1	1	yes	characteristic, complemented
516	#3486	C₂×C₆₇	1	1	yes	characteristic, complemented
517	#3327	C₂×C₆₇	1	2	yes	complemented
518	#3326	C₂×C₆₇	1	2	yes	complemented
519	#3320	C₂×C₆₇	1	2	yes	complemented
520	#3312	C₂×C₆₇	1	2	yes	complemented
521	#3278	C₂×C₆₇	1	2	yes	complemented
522	#3276	C₂×C₆₇	1	2	yes	complemented
523	#3271	C₂×C₆₇	1	2	yes	complemented
524	#3269	C₂×C₆₇	1	2	yes	complemented
525	#3223	C₂×C₆₇	1	1	yes	characteristic, complemented
526	#3221	C₂×C₆₇	1	1	yes	characteristic, complemented
527	#3201	C₂×C₆₇	1	2	yes	complemented
528	#3197	C₂×C₆₇	1	2	yes	complemented
529	#3127	C₂×C₆₇	1	1	yes	characteristic, complemented
530	#3126	C₂×C₆₇	1	1	yes	characteristic, complemented
531	#3013	C₂×C₆₇	1	2	yes	complemented
532	#3004	C₂×C₆₇	1	2	yes	complemented
533	#2978	C₂×C₆₇	1	1	yes	characteristic, complemented
534	C₆₇	#61645	1	1	yes	characteristic, direct product factor, Sylow
535	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
536	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
537	C₂×#137	C₂²×C₆₇	1	2	yes	—
538	C₂×#137	C₂²×C₆₇	1	2	yes	—
539	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
540	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
541	#560	—	2	2	no	—
542	#553	—	2	2	no	—
543	#553	C₂²×C₆₇	1	2	yes	—
544	#552	C₂²×C₆₇	1	2	yes	—
545	#550	C₂²×C₆₇	1	2	yes	—
546	D₄×Q₈	—	2	2	no	—
547	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
548	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
549	#548	—	2	2	no	—
550	#548	C₂²×C₆₇	1	2	yes	—
551	#548	C₂²×C₆₇	1	2	yes	—
552	#547	C₂²×C₆₇	1	2	yes	—
553	#541	C₂²×C₆₇	1	1	yes	characteristic
554	#540	—	2	2	no	—
555	#540	C₂²×C₆₇	1	1	yes	characteristic
556	#539	—	2	2	no	—
557	#537	C₂²×C₆₇	1	2	yes	—
558	#536	—	2	2	no	—
559	#536	C₂²×C₆₇	1	1	yes	characteristic
560	#536	C₂²×C₆₇	1	1	yes	characteristic
561	#525	—	2	2	no	—
562	#525	C₂²×C₆₇	1	1	yes	characteristic
563	#525	C₂²×C₆₇	1	2	yes	—
564	#525	C₂²×C₆₇	1	1	yes	characteristic
565	#519	C₂²×C₆₇	1	1	yes	characteristic
566	#497	C₂²×C₆₇	1	1	yes	characteristic, complemented
567	#496	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	#494	C₂²×C₆₇	1	1	yes	characteristic, complemented
569	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
570	#491	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	#491	C₂²×C₆₇	1	1	yes	characteristic, complemented
572	#488	C₂²×C₆₇	1	1	yes	characteristic, complemented
573	#488	C₂²×C₆₇	1	1	yes	characteristic, complemented
574	#485	C₂²×C₆₇	1	2	yes	—
575	#485	C₂²×C₆₇	1	2	yes	—
576	#484	C₂²×C₆₇	1	2	yes	complemented
577	#483	C₂²×C₆₇	1	2	yes	complemented
578	#482	C₂²×C₆₇	1	2	yes	—
579	#482	C₂²×C₆₇	1	2	yes	—
580	#479	C₂²×C₆₇	1	2	yes	complemented
581	#479	C₂²×C₆₇	1	2	yes	complemented
582	#470	C₂²×C₆₇	1	2	yes	—
583	#470	C₂²×C₆₇	1	2	yes	complemented
584	#469	C₂²×C₆₇	1	2	yes	—
585	#468	C₂²×C₆₇	1	2	yes	—
586	#468	C₂²×C₆₇	1	2	yes	—
587	#468	C₂²×C₆₇	1	2	yes	complemented
588	#467	C₂²×C₆₇	1	2	yes	complemented
589	#465	C₂²×C₆₇	1	2	yes	complemented
590	#464	C₂²×C₆₇	1	2	yes	complemented
591	#463	C₂²×C₆₇	1	2	yes	complemented
592	#462	C₂²×C₆₇	1	2	yes	complemented
593	#462	C₂²×C₆₇	1	2	yes	complemented
594	#461	C₂²×C₆₇	1	2	yes	complemented
595	#460	C₂²×C₆₇	1	2	yes	complemented
596	#452	C₂²×C₆₇	1	2	yes	—
597	#452	C₂²×C₆₇	1	2	yes	—
598	#452	C₂²×C₆₇	1	2	yes	complemented
599	#452	C₂²×C₆₇	1	2	yes	complemented
600	#452	C₂²×C₆₇	1	2	yes	complemented
601	#451	C₂²×C₆₇	1	2	yes	—
602	#451	C₂²×C₆₇	1	2	yes	—
603	#451	C₂²×C₆₇	1	2	yes	—
604	#451	C₂²×C₆₇	1	2	yes	—
605	#451	C₂²×C₆₇	1	2	yes	complemented
606	#449	C₂²×C₆₇	1	2	yes	—
607	#449	C₂²×C₆₇	1	2	yes	—
608	#449	C₂²×C₆₇	1	2	yes	complemented
609	#448	C₂²×C₆₇	1	2	yes	—
610	#448	C₂²×C₆₇	1	2	yes	—
611	#448	C₂²×C₆₇	1	2	yes	—
612	#448	C₂²×C₆₇	1	2	yes	—
613	#448	C₂²×C₆₇	1	2	yes	complemented
614	#441	C₂²×C₆₇	1	2	yes	complemented
615	#440	C₂²×C₆₇	1	2	yes	complemented
616	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
617	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
618	#436	C₂²×C₆₇	1	2	yes	—
619	#436	C₂²×C₆₇	1	2	yes	—
620	#435	C₂²×C₆₇	1	2	yes	—
621	#435	C₂²×C₆₇	1	2	yes	—
622	#433	C₂²×C₆₇	1	1	yes	characteristic
623	#433	C₂²×C₆₇	1	1	yes	characteristic
624	#419	C₂²×C₆₇	1	2	yes	—
625	#419	C₂²×C₆₇	1	2	yes	—
626	#417	C₂²×C₆₇	1	2	yes	complemented
627	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
628	#408	C₂²×C₆₇	1	2	yes	—
629	#407	C₂²×C₆₇	1	2	yes	—
630	2₋¹⁺⁴	—	4	4	no	—
631	C₂×#41	—	2	2	no	—
632	C₂×#41	—	2	1	no	—
633	C₂×#41	C₂³×C₆₇	1	2	yes	—
634	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
635	C₂×#41	C₂³×C₆₇	1	2	yes	—
636	C₂×#41	C₂³×C₆₇	1	2	yes	—
637	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
638	C₂²×Q₈	—	2	1	no	—
639	C₂²×Q₈	—	2	1	no	—
640	C₂²×Q₈	—	2	2	no	—
641	C₂²×Q₈	—	4	4	no	—
642	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
643	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
644	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
645	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
646	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
647	C₂³×C₄	—	2	1	no	—
648	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
649	#137	—	4	4	no	—
650	#137	—	4	4	no	—
651	#137	—	4	4	no	—
652	#135	—	4	4	no	—
653	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
654	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
655	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
656	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
657	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
658	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
659	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
660	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
661	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
662	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
663	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
664	C₂×D₈	C₂³×C₆₇	1	2	yes	—
665	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
666	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
667	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
668	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
669	C₄⋊Q₈	—	2	1	no	—
670	C₄⋊Q₈	—	2	2	no	—
671	C₄⋊Q₈	—	2	2	no	—
672	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
673	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
674	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
675	#127	—	2	2	no	—
676	#127	C₂³×C₆₇	1	1	yes	characteristic
677	#126	—	2	2	no	—
678	#126	—	2	2	no	—
679	#126	—	2	2	no	—
680	#125	—	2	2	no	—
681	#125	—	2	2	no	—
682	#125	C₂³×C₆₇	1	1	yes	characteristic
683	#125	C₂³×C₆₇	1	1	yes	characteristic
684	#124	—	2	1	no	—
685	#124	—	2	2	no	—
686	#124	—	2	2	no	—
687	#124	C₂³×C₆₇	1	1	yes	characteristic
688	#124	C₂³×C₆₇	1	1	yes	characteristic
689	#123	—	2	2	no	—
690	#123	—	2	2	no	—
691	#123	—	2	1	no	—
692	#123	—	2	2	no	—
693	#123	—	2	2	no	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	—	2	2	no	—
698	#123	D₄×C₆₇	1	2	yes	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
708	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
709	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
710	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
711	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
712	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
713	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	—	2	2	no	—
721	#121	—	2	2	no	—
722	#121	—	2	2	no	—
723	#121	—	2	2	no	—
724	#121	D₄×C₆₇	1	2	yes	—
725	#121	C₂³×C₆₇	1	2	yes	—
726	#121	C₂³×C₆₇	1	2	yes	—
727	#121	C₂³×C₆₇	1	2	yes	—
728	#121	C₂³×C₆₇	1	2	yes	—
729	#120	—	2	1	no	—
730	#120	—	2	2	no	—
731	#120	D₄×C₆₇	1	2	yes	—
732	C₄×Q₈	—	2	2	no	—
733	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
734	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
735	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	2	no	—
739	C₄×D₄	—	2	2	no	—
740	C₄×D₄	—	2	2	no	—
741	C₄×D₄	—	2	2	no	—
742	C₄×D₄	—	2	2	no	—
743	C₄×D₄	—	2	2	no	—
744	C₄×D₄	—	2	2	no	—
745	C₄×D₄	C₂³×C₆₇	1	2	yes	—
746	C₄×D₄	C₂³×C₆₇	1	2	yes	—
747	C₄×D₄	C₂³×C₆₇	1	2	yes	—
748	#117	—	2	2	no	—
749	#117	—	2	2	no	—
750	#117	C₂³×C₆₇	1	1	yes	characteristic
751	#117	C₂³×C₆₇	1	2	yes	—
752	#117	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×C₄⋊C₄	—	2	2	no	—
754	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
755	#107	C₂³×C₆₇	1	2	yes	—
756	#107	C₂³×C₆₇	1	2	yes	—
757	#106	C₂³×C₆₇	1	2	yes	—
758	#106	C₂³×C₆₇	1	2	yes	—
759	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
760	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
761	#103	C₂³×C₆₇	1	2	yes	—
762	#103	C₂³×C₆₇	1	2	yes	—
763	#103	C₂³×C₆₇	1	2	yes	—
764	#103	C₂³×C₆₇	1	2	yes	—
765	#103	C₂³×C₆₇	1	2	yes	—
766	#103	C₂³×C₆₇	1	2	yes	—
767	#103	C₂³×C₆₇	1	2	yes	—
768	#103	C₂³×C₆₇	1	2	yes	—
769	#103	C₂³×C₆₇	1	2	yes	—
770	#103	C₂³×C₆₇	1	2	yes	—
771	#103	C₂³×C₆₇	1	2	yes	—
772	#103	C₂³×C₆₇	1	2	yes	—
773	#102	C₂³×C₆₇	1	2	yes	—
774	#102	C₂³×C₆₇	1	2	yes	—
775	#102	C₂³×C₆₇	1	2	yes	—
776	#102	C₂³×C₆₇	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
783	#97	C₂³×C₆₇	1	1	yes	characteristic
784	#97	C₂³×C₆₇	1	1	yes	characteristic
785	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
786	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
787	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
788	#41	—	2	4	no	—
789	#41	—	4	2	no	—
790	#41	—	4	2	no	—
791	#41	—	4	2	no	—
792	#41	—	4	8	no	—
793	#41	—	4	2	no	—
794	#41	—	4	2	no	—
795	#41	—	4	2	no	—
796	#41	—	4	2	no	—
797	#41	—	4	4	no	—
798	C₂×Q₈	—	2	4	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	2	2	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	4	no	—
805	C₂×Q₈	—	2	4	no	—
806	C₂×Q₈	—	2	4	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	—	4	2	no	—
809	C₂×Q₈	—	4	2	no	—
810	C₂×Q₈	—	4	2	no	—
811	C₂×Q₈	—	4	4	no	—
812	C₂×Q₈	—	4	8	no	—
813	C₂×Q₈	—	4	4	no	—
814	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
815	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
816	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
817	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
818	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
819	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
830	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
831	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
832	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
833	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
834	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	4	no	—
848	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
849	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
853	Q₁₆	—	2	4	no	—
854	Q₁₆	—	2	4	no	—
855	Q₁₆	—	4	2	no	—
856	Q₁₆	—	4	2	no	—
857	Q₁₆	—	4	2	no	—
858	SD₁₆	—	2	4	no	—
859	SD₁₆	—	2	4	no	—
860	SD₁₆	—	4	2	no	—
861	SD₁₆	—	4	2	no	—
862	SD₁₆	—	4	2	no	—
863	SD₁₆	—	4	2	no	—
864	D₈	—	4	2	no	—
865	M₁₆	—	4	2	no	—
866	M₁₆	—	4	2	no	—
867	M₁₆	—	4	2	no	—
868	C₂×C₈	—	4	2	no	—
869	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
870	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
871	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
872	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
889	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
890	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
891	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
892	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
893	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
894	C₂²⋊C₄	—	2	1	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
910	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
911	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
912	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
913	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	2	no	—
918	C₄²	—	2	1	no	—
919	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
920	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
921	C₂³	—	2	1	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	4	1	no	—
924	C₂³	—	4	2	no	—
925	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
926	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
927	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
928	Q₈	—	2	4	no	—
929	Q₈	—	2	2	no	—
930	Q₈	—	2	2	no	—
931	Q₈	—	2	2	no	—
932	Q₈	—	2	2	no	—
933	Q₈	—	2	2	no	—
934	Q₈	—	2	2	no	—
935	Q₈	—	4	1	no	—
936	Q₈	—	4	4	no	—
937	Q₈	—	4	4	no	—
938	Q₈	—	4	4	no	—
939	Q₈	—	4	2	no	—
940	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
941	D₄	—	2	2	no	—
942	D₄	—	2	2	no	—
943	D₄	—	2	2	no	—
944	D₄	—	4	1	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	2	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	4	no	—
949	D₄	—	4	2	no	—
950	D₄	—	4	4	no	—
951	D₄	—	8	2	no	—
952	D₄	—	8	2	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	2	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	C₂×C₄	—	2	4	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	4	2	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	4	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	4	2	no	—
979	C₂×C₄	—	8	2	no	—
980	C₂×C₄	—	8	2	no	—
981	C₂×C₄	—	8	2	no	—
982	C₂×C₄	—	8	2	no	—
983	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
984	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
985	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
986	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
988	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
989	C₈	—	2	2	no	—
990	C₈	—	2	2	no	—
991	C₈	—	2	2	no	—
992	C₈	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	4	4	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1008	C₄	—	2	2	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	4	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1022	C₂	—	4	2	no	—
1023	C₂	—	4	1	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	8	2	no	—
1026	C₂	—	8	1	no	—
1027	C₂	C₆₇×#3484	1	1	yes	characteristic
1028	C₂	C₆₇×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3539	C₂	semidirect
2. C₆₇×#3486	C₂	semidirect
3. C₆₇×#3327	C₂	semidirect
4. C₆₇×#3326	C₂	semidirect
5. C₆₇×#3320	C₂	semidirect
6. C₆₇×#3312	C₂	semidirect
7. C₆₇×#3278	C₂	semidirect
8. C₆₇×#3276	C₂	semidirect
9. C₆₇×#3271	C₂	semidirect
10. C₆₇×#3269	C₂	semidirect
11. C₆₇×#3223	C₂	semidirect
12. C₆₇×#3221	C₂	semidirect
13. C₆₇×#3201	C₂	semidirect
14. C₆₇×#3197	C₂	semidirect
15. C₆₇×#3127	C₂	semidirect
16. C₆₇×#3126	C₂	semidirect
17. C₆₇×#3013	C₂	semidirect
18. C₆₇×#3004	C₂	semidirect
19. C₆₇×#2978	C₂	semidirect
24. C₂×#137×C₆₇	C₂²	semidirect
25. C₂×#135×C₆₇	C₂²	semidirect
51. #497×C₆₇	C₂²	semidirect
52. #496×C₆₇	C₂²	semidirect
53. #494×C₆₇	C₂²	semidirect
54. #492×C₆₇	C₂²	semidirect
55. #491×C₆₇	C₂²	semidirect
56. #491×C₆₇	C₂²	semidirect
57. #488×C₆₇	C₂²	semidirect
58. #488×C₆₇	C₂²	semidirect
61. #484×C₆₇	C₂²	semidirect
62. #483×C₆₇	C₂²	semidirect
65. #479×C₆₇	C₂²	semidirect
66. #479×C₆₇	C₂²	semidirect
68. #470×C₆₇	C₂²	semidirect
72. #468×C₆₇	C₂²	semidirect
73. #467×C₆₇	C₂²	semidirect
74. #465×C₆₇	C₂²	semidirect
75. #464×C₆₇	C₂²	semidirect
76. #463×C₆₇	C₂²	semidirect
77. #462×C₆₇	C₂²	semidirect
78. #462×C₆₇	C₂²	semidirect
79. #461×C₆₇	C₂²	semidirect
80. #460×C₆₇	C₂²	semidirect
83. #452×C₆₇	C₂²	semidirect
84. #452×C₆₇	C₂²	semidirect
85. #452×C₆₇	C₂²	semidirect
90. #451×C₆₇	C₂²	semidirect
93. #449×C₆₇	C₂²	semidirect
98. #448×C₆₇	C₂²	semidirect
99. #441×C₆₇	C₂²	semidirect
100. #440×C₆₇	C₂²	semidirect
101. C₄×Q₁₆×C₆₇	C₂²	semidirect
102. C₄×SD₁₆×C₆₇	C₂²	semidirect
111. #417×C₆₇	C₂²	semidirect
112. C₂×#103×C₆₇	C₂²	semidirect
507. #61645	C₆₇	direct (N × H)
515. #3539	C₂×C₆₇	semidirect
516. #3486	C₂×C₆₇	semidirect
517. #3327	C₂×C₆₇	semidirect
518. #3326	C₂×C₆₇	semidirect
519. #3320	C₂×C₆₇	semidirect
520. #3312	C₂×C₆₇	semidirect
521. #3278	C₂×C₆₇	semidirect
522. #3276	C₂×C₆₇	semidirect
523. #3271	C₂×C₆₇	semidirect
524. #3269	C₂×C₆₇	semidirect
525. #3223	C₂×C₆₇	semidirect
526. #3221	C₂×C₆₇	semidirect
527. #3201	C₂×C₆₇	semidirect
528. #3197	C₂×C₆₇	semidirect
529. #3127	C₂×C₆₇	semidirect
530. #3126	C₂×C₆₇	semidirect
531. #3013	C₂×C₆₇	semidirect
532. #3004	C₂×C₆₇	semidirect
533. #2978	C₂×C₆₇	semidirect
534. C₆₇	#61645	direct (N × H)
539. C₂×#137	C₂²×C₆₇	semidirect
540. C₂×#135	C₂²×C₆₇	semidirect
566. #497	C₂²×C₆₇	semidirect
567. #496	C₂²×C₆₇	semidirect
568. #494	C₂²×C₆₇	semidirect
569. #492	C₂²×C₆₇	semidirect
570. #491	C₂²×C₆₇	semidirect
571. #491	C₂²×C₆₇	semidirect
572. #488	C₂²×C₆₇	semidirect
573. #488	C₂²×C₆₇	semidirect
576. #484	C₂²×C₆₇	semidirect
577. #483	C₂²×C₆₇	semidirect
580. #479	C₂²×C₆₇	semidirect
581. #479	C₂²×C₆₇	semidirect
583. #470	C₂²×C₆₇	semidirect
587. #468	C₂²×C₆₇	semidirect
588. #467	C₂²×C₆₇	semidirect
589. #465	C₂²×C₆₇	semidirect
590. #464	C₂²×C₆₇	semidirect
591. #463	C₂²×C₆₇	semidirect
592. #462	C₂²×C₆₇	semidirect
593. #462	C₂²×C₆₇	semidirect
594. #461	C₂²×C₆₇	semidirect
595. #460	C₂²×C₆₇	semidirect
598. #452	C₂²×C₆₇	semidirect
599. #452	C₂²×C₆₇	semidirect
600. #452	C₂²×C₆₇	semidirect
605. #451	C₂²×C₆₇	semidirect
608. #449	C₂²×C₆₇	semidirect
613. #448	C₂²×C₆₇	semidirect
614. #441	C₂²×C₆₇	semidirect
615. #440	C₂²×C₆₇	semidirect
616. C₄×Q₁₆	C₂²×C₆₇	semidirect
617. C₄×SD₁₆	C₂²×C₆₇	semidirect
626. #417	C₂²×C₆₇	semidirect
627. C₂×#103	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3539	2
C₆₇×#3486	2
C₆₇×#3327	2
C₆₇×#3326	2
C₆₇×#3320	2
C₆₇×#3312	2
C₆₇×#3278	2
C₆₇×#3276	2
C₆₇×#3271	2
C₆₇×#3269	2
C₆₇×#3223	2
C₆₇×#3221	2
C₆₇×#3201	2
C₆₇×#3197	2
C₆₇×#3127	2
C₆₇×#3126	2
C₆₇×#3013	2
C₆₇×#3004	2
C₆₇×#2978	2
#61645	67

Subgroups — C67×#61645 #30740896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61645 #30740896