Subgroups — C₆₇×#59550 #30738801

Order 17152.

2456 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2693	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2691	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2558	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2553	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2489	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2473	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2471	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2464	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2454	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2429	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2407	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2407	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2352	C₂	1	2	yes	maximal, complemented
20	C₆₇×#2341	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
26	#552×C₆₇	—	2	8	no	—
27	#547×C₆₇	—	2	8	no	—
28	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#126×C₆₇	C₂²	1	2	yes	—
30	C₂×#125×C₆₇	C₂²	1	2	yes	—
31	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#123×C₆₇	C₂²	1	2	yes	—
33	C₂×#123×C₆₇	C₂²	1	2	yes	—
34	C₂×#123×C₆₇	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#121×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×#117×C₆₇	C₂²	1	2	yes	—
51	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
52	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
54	#400×C₆₇	C₂²	1	2	yes	—
55	#400×C₆₇	C₂²	1	2	yes	—
56	#399×C₆₇	C₂²	1	2	yes	—
57	#398×C₆₇	C₂²	1	2	yes	—
58	#398×C₆₇	C₂²	1	2	yes	—
59	#398×C₆₇	C₂²	1	2	yes	—
60	#397×C₆₇	C₂²	1	2	yes	—
61	#397×C₆₇	C₂²	1	2	yes	—
62	#396×C₆₇	C₂²	1	2	yes	—
63	#396×C₆₇	C₂²	1	2	yes	—
64	#396×C₆₇	C₂²	1	2	yes	—
65	#394×C₆₇	C₂²	1	2	yes	—
66	#394×C₆₇	C₂²	1	2	yes	—
67	#394×C₆₇	C₂²	1	2	yes	—
68	#392×C₆₇	C₂²	1	2	yes	—
69	#392×C₆₇	C₂²	1	2	yes	—
70	#391×C₆₇	C₂²	1	1	yes	characteristic
71	#391×C₆₇	C₂²	1	1	yes	characteristic
72	#391×C₆₇	C₂²	1	1	yes	characteristic
73	#391×C₆₇	C₂²	1	1	yes	characteristic
74	#390×C₆₇	C₂²	1	1	yes	characteristic
75	#390×C₆₇	C₂²	1	1	yes	characteristic
76	#390×C₆₇	C₂²	1	1	yes	characteristic
77	#390×C₆₇	C₂²	1	2	yes	—
78	#390×C₆₇	C₂²	1	1	yes	characteristic
79	#390×C₆₇	C₂²	1	2	yes	—
80	#389×C₆₇	C₂²	1	2	yes	—
81	#389×C₆₇	C₂²	1	1	yes	characteristic
82	#389×C₆₇	C₂²	1	1	yes	characteristic
83	#389×C₆₇	C₂²	1	1	yes	characteristic
84	#389×C₆₇	C₂²	1	1	yes	characteristic
85	#388×C₆₇	C₂²	1	2	yes	—
86	#388×C₆₇	C₂²	1	1	yes	characteristic
87	#388×C₆₇	C₂²	1	1	yes	characteristic
88	#388×C₆₇	C₂²	1	2	yes	—
89	#388×C₆₇	C₂²	1	2	yes	—
90	#388×C₆₇	C₂²	1	2	yes	—
91	#387×C₆₇	C₂²	1	2	yes	—
92	#387×C₆₇	C₂²	1	2	yes	—
93	#387×C₆₇	C₂²	1	2	yes	—
94	#387×C₆₇	C₂²	1	2	yes	—
95	#386×C₆₇	C₂²	1	2	yes	—
96	#386×C₆₇	C₂²	1	2	yes	—
97	#386×C₆₇	C₂²	1	1	yes	characteristic
98	#386×C₆₇	C₂²	1	1	yes	characteristic
99	#386×C₆₇	C₂²	1	2	yes	—
100	#386×C₆₇	C₂²	1	2	yes	—
101	#386×C₆₇	C₂²	1	2	yes	—
102	#386×C₆₇	C₂²	1	2	yes	—
103	#385×C₆₇	C₂²	1	2	yes	—
104	#385×C₆₇	C₂²	1	2	yes	—
105	#385×C₆₇	C₂²	1	2	yes	—
106	#385×C₆₇	C₂²	1	2	yes	—
107	#385×C₆₇	C₂²	1	2	yes	—
108	#382×C₆₇	C₂²	1	2	yes	—
109	#380×C₆₇	C₂²	1	1	yes	characteristic
110	#380×C₆₇	C₂²	1	1	yes	characteristic
111	#380×C₆₇	C₂²	1	1	yes	characteristic
112	#380×C₆₇	C₂²	1	2	yes	—
113	#380×C₆₇	C₂²	1	2	yes	—
114	#380×C₆₇	C₂²	1	2	yes	—
115	#380×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
123	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
124	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
125	C₂×#41×C₆₇	—	2	4	no	—
126	C₂×#41×C₆₇	—	2	4	no	—
127	C₂×#41×C₆₇	—	2	4	no	—
128	C₂×#41×C₆₇	—	2	4	no	—
129	C₂×#41×C₆₇	—	4	2	no	—
130	C₂×#41×C₆₇	—	4	2	no	—
131	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
136	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
138	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
144	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
145	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
147	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₄⋊Q₈×C₆₇	—	2	4	no	—
150	#126×C₆₇	—	2	8	no	—
151	#125×C₆₇	—	2	8	no	—
152	#125×C₆₇	—	2	4	no	—
153	#123×C₆₇	—	2	8	no	—
154	#123×C₆₇	—	2	8	no	—
155	#123×C₆₇	—	2	8	no	—
156	C₂²⋊Q₈×C₆₇	—	2	4	no	—
157	C₂²⋊Q₈×C₆₇	—	2	4	no	—
158	C₂²⋊Q₈×C₆₇	—	4	2	no	—
159	C₂²⋊Q₈×C₆₇	D₄	1	8	yes	complemented
160	#121×C₆₇	—	2	4	no	—
161	#121×C₆₇	—	2	8	no	—
162	#121×C₆₇	—	2	4	no	—
163	C₄×Q₈×C₆₇	—	2	4	no	—
164	C₄×Q₈×C₆₇	—	4	2	no	—
165	C₄×D₄×C₆₇	—	2	4	no	—
166	C₄×D₄×C₆₇	—	2	4	no	—
167	C₄×D₄×C₆₇	—	2	4	no	—
168	C₄×D₄×C₆₇	—	2	8	no	—
169	C₄×D₄×C₆₇	—	4	2	no	—
170	#117×C₆₇	—	2	4	no	—
171	#117×C₆₇	—	2	8	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
173	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₆₇	—	4	2	no	—
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
228	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
229	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	2	yes	—
237	#95×C₆₇	C₂³	1	1	yes	characteristic
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	1	yes	characteristic
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	1	yes	characteristic
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	2	yes	—
245	#95×C₆₇	C₂³	1	2	yes	—
246	#95×C₆₇	C₂³	1	1	yes	characteristic
247	#95×C₆₇	C₂³	1	2	yes	—
248	#95×C₆₇	C₂³	1	2	yes	—
249	#95×C₆₇	C₂³	1	2	yes	—
250	#95×C₆₇	C₂³	1	1	yes	characteristic
251	#95×C₆₇	C₂³	1	2	yes	—
252	#95×C₆₇	C₂³	1	2	yes	—
253	#95×C₆₇	C₂³	1	2	yes	—
254	#95×C₆₇	C₂³	1	2	yes	—
255	#95×C₆₇	C₂³	1	2	yes	—
256	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
258	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
259	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
260	#41×C₆₇	—	4	16	no	—
261	#41×C₆₇	—	4	16	no	—
262	C₂×Q₈×C₆₇	—	2	2	no	—
263	C₂×Q₈×C₆₇	—	2	2	no	—
264	C₂×Q₈×C₆₇	—	2	2	no	—
265	C₂×Q₈×C₆₇	—	2	2	no	—
266	C₂×Q₈×C₆₇	—	2	2	no	—
267	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
268	C₂×D₄×C₆₇	—	2	2	no	—
269	C₂×D₄×C₆₇	—	2	2	no	—
270	C₂×D₄×C₆₇	—	2	4	no	—
271	C₂×D₄×C₆₇	—	2	4	no	—
272	C₂×D₄×C₆₇	—	2	2	no	—
273	C₂×D₄×C₆₇	—	2	4	no	—
274	C₂×D₄×C₆₇	—	2	2	no	—
275	C₂×D₄×C₆₇	—	2	4	no	—
276	C₂×D₄×C₆₇	—	2	4	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	—	2	4	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	2	no	—
281	C₂×D₄×C₆₇	—	2	2	no	—
282	C₂×D₄×C₆₇	—	4	1	no	—
283	C₂×D₄×C₆₇	—	4	1	no	—
284	C₂×D₄×C₆₇	—	4	2	no	—
285	C₂×D₄×C₆₇	—	4	1	no	—
286	C₂×D₄×C₆₇	—	4	2	no	—
287	C₂×D₄×C₆₇	—	4	2	no	—
288	C₂×D₄×C₆₇	#41	1	4	yes	—
289	C₂²×C₄×C₆₇	—	2	2	no	—
290	C₂²×C₄×C₆₇	—	2	2	no	—
291	C₂²×C₄×C₆₇	—	2	4	no	—
292	C₂²×C₄×C₆₇	—	2	4	no	—
293	C₂²×C₄×C₆₇	—	2	4	no	—
294	C₂²×C₄×C₆₇	—	2	4	no	—
295	C₂²×C₄×C₆₇	—	2	4	no	—
296	C₂²×C₄×C₆₇	—	2	2	no	—
297	C₂²×C₄×C₆₇	—	2	4	no	—
298	C₂²×C₄×C₆₇	—	2	4	no	—
299	C₂²×C₄×C₆₇	—	2	2	no	—
300	C₂²×C₄×C₆₇	—	2	4	no	—
301	C₂²×C₄×C₆₇	—	2	2	no	—
302	C₂²×C₄×C₆₇	—	2	2	no	—
303	C₂²×C₄×C₆₇	—	2	2	no	—
304	C₂²×C₄×C₆₇	—	2	2	no	—
305	C₂²×C₄×C₆₇	—	2	2	no	—
306	C₂²×C₄×C₆₇	—	2	2	no	—
307	C₂²×C₄×C₆₇	—	4	1	no	—
308	C₂²×C₄×C₆₇	—	4	1	no	—
309	C₂²×C₄×C₆₇	—	4	2	no	—
310	C₂²×C₄×C₆₇	—	4	2	no	—
311	C₂²×C₄×C₆₇	—	4	1	no	—
312	C₂²×C₄×C₆₇	—	4	1	no	—
313	C₂²×C₄×C₆₇	—	4	2	no	—
314	C₂²×C₄×C₆₇	—	4	2	no	—
315	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
331	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₆₇	—	2	2	no	—
336	C₄⋊C₄×C₆₇	—	2	2	no	—
337	C₄⋊C₄×C₆₇	—	2	4	no	—
338	C₄⋊C₄×C₆₇	—	2	4	no	—
339	C₄⋊C₄×C₆₇	—	2	4	no	—
340	C₄⋊C₄×C₆₇	—	2	2	no	—
341	C₄⋊C₄×C₆₇	—	2	4	no	—
342	C₄⋊C₄×C₆₇	—	2	2	no	—
343	C₄⋊C₄×C₆₇	—	2	4	no	—
344	C₄⋊C₄×C₆₇	—	2	4	no	—
345	C₄⋊C₄×C₆₇	—	2	4	no	—
346	C₄⋊C₄×C₆₇	—	2	4	no	—
347	C₄⋊C₄×C₆₇	—	2	4	no	—
348	C₄⋊C₄×C₆₇	—	2	2	no	—
349	C₄⋊C₄×C₆₇	—	2	2	no	—
350	C₄⋊C₄×C₆₇	—	2	2	no	—
351	C₄⋊C₄×C₆₇	—	2	2	no	—
352	C₄⋊C₄×C₆₇	—	4	2	no	—
353	C₄⋊C₄×C₆₇	—	4	2	no	—
354	C₄⋊C₄×C₆₇	—	4	1	no	—
355	C₄⋊C₄×C₆₇	—	4	2	no	—
356	C₄⋊C₄×C₆₇	—	4	2	no	—
357	C₄⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
358	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
359	C₂²⋊C₄×C₆₇	—	2	4	no	—
360	C₂²⋊C₄×C₆₇	—	2	2	no	—
361	C₂²⋊C₄×C₆₇	—	2	2	no	—
362	C₂²⋊C₄×C₆₇	—	2	4	no	—
363	C₂²⋊C₄×C₆₇	—	2	2	no	—
364	C₂²⋊C₄×C₆₇	—	2	4	no	—
365	C₂²⋊C₄×C₆₇	—	2	2	no	—
366	C₂²⋊C₄×C₆₇	—	2	4	no	—
367	C₂²⋊C₄×C₆₇	—	2	4	no	—
368	C₂²⋊C₄×C₆₇	—	2	4	no	—
369	C₂²⋊C₄×C₆₇	—	2	2	no	—
370	C₂²⋊C₄×C₆₇	—	2	4	no	—
371	C₂²⋊C₄×C₆₇	—	4	2	no	—
372	C₂²⋊C₄×C₆₇	—	4	1	no	—
373	C₂²⋊C₄×C₆₇	—	4	2	no	—
374	C₂²⋊C₄×C₆₇	—	4	2	no	—
375	C₂²⋊C₄×C₆₇	—	4	2	no	—
376	C₂²⋊C₄×C₆₇	—	4	2	no	—
377	C₂²⋊C₄×C₆₇	—	4	2	no	—
378	C₂²⋊C₄×C₆₇	—	4	2	no	—
379	C₂²⋊C₄×C₆₇	—	4	1	no	—
380	C₂²⋊C₄×C₆₇	—	4	1	no	—
381	C₂²⋊C₄×C₆₇	—	4	1	no	—
382	C₂²⋊C₄×C₆₇	—	4	2	no	—
383	C₂²⋊C₄×C₆₇	C₂×D₄	1	8	yes	—
384	C₂²⋊C₄×C₆₇	#41	1	4	yes	complemented
385	C₄²×C₆₇	—	2	4	no	—
386	C₄²×C₆₇	—	2	4	no	—
387	C₄²×C₆₇	—	2	2	no	—
388	C₄²×C₆₇	—	2	2	no	—
389	C₄²×C₆₇	—	2	4	no	—
390	C₄²×C₆₇	—	2	2	no	—
391	C₄²×C₆₇	—	2	2	no	—
392	C₄²×C₆₇	—	4	1	no	—
393	C₄²×C₆₇	—	4	1	no	—
394	C₄²×C₆₇	—	4	2	no	—
395	C₂³×C₆₇	—	2	1	no	—
396	C₂³×C₆₇	—	2	2	no	—
397	C₂³×C₆₇	—	2	2	no	—
398	C₂³×C₆₇	—	2	1	no	—
399	C₂³×C₆₇	—	2	1	no	—
400	C₂³×C₆₇	—	2	1	no	—
401	C₂³×C₆₇	—	2	1	no	—
402	C₂³×C₆₇	—	2	1	no	—
403	C₂³×C₆₇	—	2	2	no	—
404	C₂³×C₆₇	—	2	2	no	—
405	C₂³×C₆₇	—	2	1	no	—
406	C₂³×C₆₇	—	2	1	no	—
407	C₂³×C₆₇	—	2	1	no	—
408	C₂³×C₆₇	—	2	2	no	—
409	C₂³×C₆₇	—	2	2	no	—
410	C₂³×C₆₇	—	2	1	no	—
411	C₂³×C₆₇	—	2	1	no	—
412	C₂³×C₆₇	—	2	1	no	—
413	C₂³×C₆₇	—	2	1	no	—
414	C₂³×C₆₇	—	2	1	no	—
415	C₂³×C₆₇	—	2	1	no	—
416	C₂³×C₆₇	—	2	1	no	—
417	C₂³×C₆₇	—	2	1	no	—
418	C₂³×C₆₇	—	2	1	no	—
419	C₂³×C₆₇	—	2	1	no	—
420	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
421	C₂³×C₆₇	C₂×#41	1	4	yes	—
422	C₂³×C₆₇	C₂×#41	1	2	yes	—
423	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
424	Q₈×C₆₇	—	2	8	no	—
425	Q₈×C₆₇	—	4	4	no	—
426	D₄×C₆₇	—	2	8	no	—
427	D₄×C₆₇	—	4	4	no	—
428	D₄×C₆₇	—	4	4	no	—
429	D₄×C₆₇	—	4	8	no	—
430	D₄×C₆₇	—	4	4	no	—
431	D₄×C₆₇	—	4	8	no	—
432	D₄×C₆₇	—	4	8	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	1	no	—
445	C₂×C₄×C₆₇	—	2	8	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	1	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	2	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	1	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	1	no	—
462	C₂×C₄×C₆₇	—	2	1	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	1	no	—
465	C₂×C₄×C₆₇	—	2	1	no	—
466	C₂×C₄×C₆₇	—	2	2	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	2	no	—
472	C₂×C₄×C₆₇	—	2	2	no	—
473	C₂×C₄×C₆₇	—	2	2	no	—
474	C₂×C₄×C₆₇	—	2	2	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	1	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	4	8	no	—
483	C₂×C₄×C₆₇	—	4	4	no	—
484	C₂×C₄×C₆₇	—	4	8	no	—
485	C₂×C₄×C₆₇	—	4	8	no	—
486	C₂×C₄×C₆₇	—	4	8	no	—
487	C₂×C₄×C₆₇	—	4	4	no	—
488	C₂×C₄×C₆₇	—	4	4	no	—
489	C₂×C₄×C₆₇	—	4	4	no	—
490	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
492	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
493	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
495	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
496	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
497	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
498	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
499	C₂²×C₆₇	—	2	2	no	—
500	C₂²×C₆₇	—	2	4	no	—
501	C₂²×C₆₇	—	2	2	no	—
502	C₂²×C₆₇	—	2	2	no	—
503	C₂²×C₆₇	—	2	2	no	—
504	C₂²×C₆₇	—	2	4	no	—
505	C₂²×C₆₇	—	2	2	no	—
506	C₂²×C₆₇	—	2	4	no	—
507	C₂²×C₆₇	—	2	2	no	—
508	C₂²×C₆₇	—	4	1	no	—
509	C₂²×C₆₇	—	4	2	no	—
510	C₂²×C₆₇	—	4	1	no	—
511	C₂²×C₆₇	—	4	1	no	—
512	C₂²×C₆₇	—	4	2	no	—
513	C₂²×C₆₇	—	4	1	no	—
514	C₂²×C₆₇	—	4	1	no	—
515	C₂²×C₆₇	—	4	1	no	—
516	C₂²×C₆₇	—	4	2	no	—
517	C₂²×C₆₇	—	4	1	no	—
518	C₂²×C₆₇	—	4	1	no	—
519	C₂²×C₆₇	—	4	2	no	—
520	C₂²×C₆₇	—	4	1	no	—
521	C₂²×C₆₇	—	4	1	no	—
522	C₂²×C₆₇	—	4	1	no	—
523	C₂²×C₆₇	—	4	1	no	—
524	C₂²×C₆₇	—	4	1	no	—
525	C₂²×C₆₇	—	4	1	no	—
526	C₂²×C₆₇	—	4	1	no	—
527	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
528	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
529	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
530	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
532	C₂²×C₆₇	#585	1	1	yes	characteristic
533	C₂²×C₆₇	#585	1	1	yes	characteristic
534	C₄×C₆₇	—	2	2	no	—
535	C₄×C₆₇	—	2	4	no	—
536	C₄×C₆₇	—	2	4	no	—
537	C₄×C₆₇	—	2	2	no	—
538	C₄×C₆₇	—	2	2	no	—
539	C₄×C₆₇	—	2	2	no	—
540	C₄×C₆₇	—	4	1	no	—
541	C₄×C₆₇	—	4	1	no	—
542	C₄×C₆₇	—	4	2	no	—
543	C₄×C₆₇	—	4	2	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	—	4	2	no	—
546	C₄×C₆₇	—	4	1	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	2	no	—
549	C₄×C₆₇	—	4	2	no	—
550	C₄×C₆₇	—	4	1	no	—
551	C₄×C₆₇	—	4	1	no	—
552	C₄×C₆₇	#546	1	4	yes	—
553	#59550	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
554	C₂×C₆₇	—	4	2	no	—
555	C₂×C₆₇	—	4	4	no	—
556	C₂×C₆₇	—	4	2	no	—
557	C₂×C₆₇	—	8	1	no	—
558	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
559	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
560	C₂×C₆₇	#3475	1	1	yes	characteristic
561	C₂×C₆₇	#3497	1	1	yes	characteristic
562	C₂×C₆₇	#3515	1	1	yes	characteristic
563	C₂×C₆₇	#3520	1	1	yes	characteristic
564	C₂×C₆₇	#3539	1	1	yes	characteristic
565	C₂×#552	C₂×C₆₇	1	1	yes	characteristic, complemented
566	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
567	#2693	C₂×C₆₇	1	2	yes	complemented
568	#2691	C₂×C₆₇	1	2	yes	complemented
569	#2558	C₂×C₆₇	1	2	yes	complemented
570	#2553	C₂×C₆₇	1	2	yes	complemented
571	#2489	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#2485	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#2473	C₂×C₆₇	1	2	yes	complemented
574	#2471	C₂×C₆₇	1	2	yes	complemented
575	#2464	C₂×C₆₇	1	2	yes	complemented
576	#2454	C₂×C₆₇	1	1	yes	characteristic, complemented
577	#2446	C₂×C₆₇	1	1	yes	characteristic, complemented
578	#2429	C₂×C₆₇	1	1	yes	characteristic, complemented
579	#2417	C₂×C₆₇	1	1	yes	characteristic, complemented
580	#2407	C₂×C₆₇	1	1	yes	characteristic, complemented
581	#2407	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
583	#2352	C₂×C₆₇	1	2	yes	complemented
584	#2341	C₂×C₆₇	1	1	yes	characteristic, complemented
585	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
586	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
587	#2297	C₂×C₆₇	1	1	yes	characteristic, complemented
588	C₆₇	#59550	1	1	yes	characteristic, direct product factor, Sylow
589	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
590	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
591	#552	—	2	8	no	—
592	#547	—	2	8	no	—
593	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
594	C₂×#126	C₂²×C₆₇	1	2	yes	—
595	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
596	C₂×#125	C₂²×C₆₇	1	2	yes	—
597	C₂×#123	C₂²×C₆₇	1	2	yes	—
598	C₂×#123	C₂²×C₆₇	1	2	yes	—
599	C₂×#123	C₂²×C₆₇	1	2	yes	—
600	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
601	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
602	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
603	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
604	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
605	C₂×#121	C₂²×C₆₇	1	2	yes	—
606	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
607	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
608	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
609	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
610	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
611	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
612	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
613	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
614	C₂×#117	C₂²×C₆₇	1	2	yes	—
615	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
616	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
617	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
618	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
619	#400	C₂²×C₆₇	1	2	yes	—
620	#400	C₂²×C₆₇	1	2	yes	—
621	#399	C₂²×C₆₇	1	2	yes	—
622	#398	C₂²×C₆₇	1	2	yes	—
623	#398	C₂²×C₆₇	1	2	yes	—
624	#398	C₂²×C₆₇	1	2	yes	—
625	#397	C₂²×C₆₇	1	2	yes	—
626	#397	C₂²×C₆₇	1	2	yes	—
627	#396	C₂²×C₆₇	1	2	yes	—
628	#396	C₂²×C₆₇	1	2	yes	—
629	#396	C₂²×C₆₇	1	2	yes	—
630	#394	C₂²×C₆₇	1	2	yes	—
631	#394	C₂²×C₆₇	1	2	yes	—
632	#394	C₂²×C₆₇	1	2	yes	—
633	#392	C₂²×C₆₇	1	2	yes	—
634	#392	C₂²×C₆₇	1	2	yes	—
635	#391	C₂²×C₆₇	1	1	yes	characteristic
636	#391	C₂²×C₆₇	1	1	yes	characteristic
637	#391	C₂²×C₆₇	1	1	yes	characteristic
638	#391	C₂²×C₆₇	1	1	yes	characteristic
639	#390	C₂²×C₆₇	1	1	yes	characteristic
640	#390	C₂²×C₆₇	1	1	yes	characteristic
641	#390	C₂²×C₆₇	1	2	yes	—
642	#390	C₂²×C₆₇	1	2	yes	—
643	#390	C₂²×C₆₇	1	1	yes	characteristic
644	#390	C₂²×C₆₇	1	1	yes	characteristic
645	#389	C₂²×C₆₇	1	1	yes	characteristic
646	#389	C₂²×C₆₇	1	1	yes	characteristic
647	#389	C₂²×C₆₇	1	1	yes	characteristic
648	#389	C₂²×C₆₇	1	2	yes	—
649	#389	C₂²×C₆₇	1	1	yes	characteristic
650	#388	C₂²×C₆₇	1	1	yes	characteristic
651	#388	C₂²×C₆₇	1	2	yes	—
652	#388	C₂²×C₆₇	1	2	yes	—
653	#388	C₂²×C₆₇	1	2	yes	—
654	#388	C₂²×C₆₇	1	2	yes	—
655	#388	C₂²×C₆₇	1	1	yes	characteristic
656	#387	C₂²×C₆₇	1	2	yes	—
657	#387	C₂²×C₆₇	1	2	yes	—
658	#387	C₂²×C₆₇	1	2	yes	—
659	#387	C₂²×C₆₇	1	2	yes	—
660	#386	C₂²×C₆₇	1	2	yes	—
661	#386	C₂²×C₆₇	1	2	yes	—
662	#386	C₂²×C₆₇	1	2	yes	—
663	#386	C₂²×C₆₇	1	2	yes	—
664	#386	C₂²×C₆₇	1	1	yes	characteristic
665	#386	C₂²×C₆₇	1	2	yes	—
666	#386	C₂²×C₆₇	1	1	yes	characteristic
667	#386	C₂²×C₆₇	1	2	yes	—
668	#385	C₂²×C₆₇	1	2	yes	—
669	#385	C₂²×C₆₇	1	2	yes	—
670	#385	C₂²×C₆₇	1	2	yes	—
671	#385	C₂²×C₆₇	1	2	yes	—
672	#385	C₂²×C₆₇	1	2	yes	—
673	#382	C₂²×C₆₇	1	2	yes	—
674	#380	C₂²×C₆₇	1	1	yes	characteristic
675	#380	C₂²×C₆₇	1	2	yes	—
676	#380	C₂²×C₆₇	1	2	yes	—
677	#380	C₂²×C₆₇	1	2	yes	—
678	#380	C₂²×C₆₇	1	1	yes	characteristic
679	#380	C₂²×C₆₇	1	1	yes	characteristic
680	#380	C₂²×C₆₇	1	1	yes	characteristic
681	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
682	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
683	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
684	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
685	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
686	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
687	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
688	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
689	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
690	C₂×#41	—	2	4	no	—
691	C₂×#41	—	2	4	no	—
692	C₂×#41	—	2	4	no	—
693	C₂×#41	—	2	4	no	—
694	C₂×#41	—	4	2	no	—
695	C₂×#41	—	4	2	no	—
696	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
697	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
698	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
699	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
700	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
701	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
702	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
703	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
704	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
705	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
706	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
708	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
709	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
710	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
711	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
712	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
713	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
714	C₄⋊Q₈	—	2	4	no	—
715	#126	—	2	8	no	—
716	#125	—	2	8	no	—
717	#125	—	2	4	no	—
718	#123	—	2	8	no	—
719	#123	—	2	8	no	—
720	#123	—	2	8	no	—
721	C₂²⋊Q₈	—	2	4	no	—
722	C₂²⋊Q₈	—	2	4	no	—
723	C₂²⋊Q₈	—	4	2	no	—
724	C₂²⋊Q₈	D₄×C₆₇	1	8	yes	complemented
725	#121	—	2	4	no	—
726	#121	—	2	8	no	—
727	#121	—	2	4	no	—
728	C₄×Q₈	—	2	4	no	—
729	C₄×Q₈	—	4	2	no	—
730	C₄×D₄	—	2	4	no	—
731	C₄×D₄	—	2	4	no	—
732	C₄×D₄	—	2	4	no	—
733	C₄×D₄	—	2	8	no	—
734	C₄×D₄	—	4	2	no	—
735	#117	—	2	4	no	—
736	#117	—	2	8	no	—
737	C₂×C₄⋊C₄	—	2	8	no	—
738	C₂×C₄⋊C₄	—	2	4	no	—
739	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
742	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
746	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
747	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
754	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
758	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
760	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
762	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
763	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
764	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
769	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
770	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
783	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
789	C₂×C₄²	—	4	2	no	—
790	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
791	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
792	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
795	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
796	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
797	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
798	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
800	#95	C₂³×C₆₇	1	1	yes	characteristic
801	#95	C₂³×C₆₇	1	2	yes	—
802	#95	C₂³×C₆₇	1	1	yes	characteristic
803	#95	C₂³×C₆₇	1	2	yes	—
804	#95	C₂³×C₆₇	1	1	yes	characteristic
805	#95	C₂³×C₆₇	1	2	yes	—
806	#95	C₂³×C₆₇	1	1	yes	characteristic
807	#95	C₂³×C₆₇	1	2	yes	—
808	#95	C₂³×C₆₇	1	2	yes	—
809	#95	C₂³×C₆₇	1	2	yes	—
810	#95	C₂³×C₆₇	1	2	yes	—
811	#95	C₂³×C₆₇	1	1	yes	characteristic
812	#95	C₂³×C₆₇	1	2	yes	—
813	#95	C₂³×C₆₇	1	2	yes	—
814	#95	C₂³×C₆₇	1	2	yes	—
815	#95	C₂³×C₆₇	1	1	yes	characteristic
816	#95	C₂³×C₆₇	1	2	yes	—
817	#95	C₂³×C₆₇	1	2	yes	—
818	#95	C₂³×C₆₇	1	2	yes	—
819	#95	C₂³×C₆₇	1	2	yes	—
820	#95	C₂³×C₆₇	1	2	yes	—
821	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
822	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
823	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
824	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
825	#41	—	4	16	no	—
826	#41	—	4	16	no	—
827	C₂×Q₈	—	2	2	no	—
828	C₂×Q₈	—	2	2	no	—
829	C₂×Q₈	—	2	2	no	—
830	C₂×Q₈	—	2	2	no	—
831	C₂×Q₈	—	2	2	no	—
832	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	4	no	—
836	C₂×D₄	—	2	4	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	4	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	4	no	—
841	C₂×D₄	—	2	4	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	4	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	4	1	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	—	4	1	no	—
851	C₂×D₄	—	4	2	no	—
852	C₂×D₄	—	4	1	no	—
853	C₂×D₄	#41×C₆₇	1	4	yes	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	4	no	—
857	C₂²×C₄	—	2	4	no	—
858	C₂²×C₄	—	2	4	no	—
859	C₂²×C₄	—	2	4	no	—
860	C₂²×C₄	—	2	4	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	4	no	—
863	C₂²×C₄	—	2	4	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	4	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	4	1	no	—
873	C₂²×C₄	—	4	1	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	1	no	—
879	C₂²×C₄	—	4	1	no	—
880	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
881	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
884	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
886	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
888	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
890	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
891	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
899	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	4	no	—
903	C₄⋊C₄	—	2	4	no	—
904	C₄⋊C₄	—	2	4	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	4	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	4	no	—
909	C₄⋊C₄	—	2	4	no	—
910	C₄⋊C₄	—	2	4	no	—
911	C₄⋊C₄	—	2	4	no	—
912	C₄⋊C₄	—	2	4	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	4	1	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	2	no	—
922	C₄⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
923	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
924	C₂²⋊C₄	—	2	4	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	4	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	4	no	—
932	C₂²⋊C₄	—	2	4	no	—
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	4	no	—
936	C₂²⋊C₄	—	4	1	no	—
937	C₂²⋊C₄	—	4	1	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	4	1	no	—
941	C₂²⋊C₄	—	4	2	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	1	no	—
948	C₂²⋊C₄	C₂×D₄×C₆₇	1	8	yes	—
949	C₂²⋊C₄	#41×C₆₇	1	4	yes	complemented
950	C₄²	—	2	4	no	—
951	C₄²	—	2	4	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	4	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	4	1	no	—
958	C₄²	—	4	1	no	—
959	C₄²	—	4	2	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	1	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	1	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
986	C₂³	C₂×#41×C₆₇	1	4	yes	—
987	C₂³	C₂×#41×C₆₇	1	2	yes	—
988	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
989	Q₈	—	2	8	no	—
990	Q₈	—	4	4	no	—
991	D₄	—	2	8	no	—
992	D₄	—	4	8	no	—
993	D₄	—	4	4	no	—
994	D₄	—	4	4	no	—
995	D₄	—	4	8	no	—
996	D₄	—	4	4	no	—
997	D₄	—	4	8	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	8	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	4	8	no	—
1048	C₂×C₄	—	4	4	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	—	4	8	no	—
1051	C₂×C₄	—	4	8	no	—
1052	C₂×C₄	—	4	4	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	4	4	no	—
1055	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1056	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1057	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1058	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1059	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1060	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1061	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1062	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1063	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	4	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	2	2	no	—
1071	C₂²	—	2	4	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1093	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1094	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1095	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1096	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1097	C₂²	#585×C₆₇	1	1	yes	characteristic
1098	C₂²	#585×C₆₇	1	1	yes	characteristic
1099	C₄	—	2	2	no	—
1100	C₄	—	2	4	no	—
1101	C₄	—	2	4	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	2	no	—
1117	C₄	#546×C₆₇	1	4	yes	—
1118	C₂	—	4	2	no	—
1119	C₂	—	4	4	no	—
1120	C₂	—	4	2	no	—
1121	C₂	—	8	1	no	—
1122	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1123	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1124	C₂	C₆₇×#3475	1	1	yes	characteristic
1125	C₂	C₆₇×#3497	1	1	yes	characteristic
1126	C₂	C₆₇×#3515	1	1	yes	characteristic
1127	C₂	C₆₇×#3520	1	1	yes	characteristic
1128	C₂	C₆₇×#3539	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#552×C₆₇	C₂	semidirect
2. C₂×#547×C₆₇	C₂	semidirect
3. C₆₇×#2693	C₂	semidirect
4. C₆₇×#2691	C₂	semidirect
5. C₆₇×#2558	C₂	semidirect
6. C₆₇×#2553	C₂	semidirect
7. C₆₇×#2489	C₂	semidirect
8. C₆₇×#2485	C₂	semidirect
9. C₆₇×#2473	C₂	semidirect
10. C₆₇×#2471	C₂	semidirect
11. C₆₇×#2464	C₂	semidirect
12. C₆₇×#2454	C₂	semidirect
13. C₆₇×#2446	C₂	semidirect
14. C₆₇×#2429	C₂	semidirect
15. C₆₇×#2417	C₂	semidirect
16. C₆₇×#2407	C₂	semidirect
17. C₆₇×#2407	C₂	semidirect
18. C₆₇×#2361	C₂	semidirect
19. C₆₇×#2352	C₂	semidirect
20. C₆₇×#2341	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₆₇×#2297	C₂	semidirect
159. C₂²⋊Q₈×C₆₇	D₄	semidirect
384. C₂²⋊C₄×C₆₇	#41	semidirect
553. #59550	C₆₇	direct (N × H)
565. C₂×#552	C₂×C₆₇	semidirect
566. C₂×#547	C₂×C₆₇	semidirect
567. #2693	C₂×C₆₇	semidirect
568. #2691	C₂×C₆₇	semidirect
569. #2558	C₂×C₆₇	semidirect
570. #2553	C₂×C₆₇	semidirect
571. #2489	C₂×C₆₇	semidirect
572. #2485	C₂×C₆₇	semidirect
573. #2473	C₂×C₆₇	semidirect
574. #2471	C₂×C₆₇	semidirect
575. #2464	C₂×C₆₇	semidirect
576. #2454	C₂×C₆₇	semidirect
577. #2446	C₂×C₆₇	semidirect
578. #2429	C₂×C₆₇	semidirect
579. #2417	C₂×C₆₇	semidirect
580. #2407	C₂×C₆₇	semidirect
581. #2407	C₂×C₆₇	semidirect
582. #2361	C₂×C₆₇	semidirect
583. #2352	C₂×C₆₇	semidirect
584. #2341	C₂×C₆₇	semidirect
585. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
586. C₄×#121	C₂×C₆₇	semidirect
587. #2297	C₂×C₆₇	semidirect
588. C₆₇	#59550	direct (N × H)
724. C₂²⋊Q₈	D₄×C₆₇	semidirect
949. C₂²⋊C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₆₇	2
C₂×#547×C₆₇	2
C₆₇×#2693	2
C₆₇×#2691	2
C₆₇×#2558	2
C₆₇×#2553	2
C₆₇×#2489	2
C₆₇×#2485	2
C₆₇×#2473	2
C₆₇×#2471	2
C₆₇×#2464	2
C₆₇×#2454	2
C₆₇×#2446	2
C₆₇×#2429	2
C₆₇×#2417	2
C₆₇×#2407	2
C₆₇×#2361	2
C₆₇×#2352	2
C₆₇×#2341	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₆₇×#2297	2
#59550	67

Subgroups — C67×#59550 #30738801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59550 #30738801